46601 - ourspace.uregina.ca
TRANSCRIPT
46601
••
riitv National Library thhliollitquo national o • Y of Canada du Canada
CANADIAN THESES Tiltsa CANA011 NNE'S
ON MICROFICHE SUR AfICROriClif
NAME OF AUTHOR/NOM DE L'AUTEUR Christian Gerard SimOn
TITLE OF THESIS/TTTITEDEAAJBESE_ The Conformations of Alkyl-Substi tuted Ethylenes. A
----C- mb-ines ear Magnetic Resonance and Force Field of
Study
UNIVTRSITY/UNWERS/TE
DEGREE FOR WHICH THESIS WAS PRESENTED/, GRADE POUR LEDua CETTE THESE FUT PRESENTEE
University of Regina
Doctor of Phi losophy in Chemistry
YEAR THIS DEGREE CONFEFIRED/ANNEE D'OBTENTION DE CE DEGO 1980.
NAME OF SUPERVISOR/NOM DU DIRECTEUR DE THESE F. H. A. Rumens
Permission is hereby granted to the NATIONAL LIBRARY OF
CANADA to microfi lm this thesis and to lend or sell copies
of the film.
The author reserves other publication rights, and neither the
thesis net extensive extracts from it may be printed or other-
wise reproduced without the author's written permission.
DATED/DA leJune 20, 1980
SIGNED/S/GNE
Cautorisation est, par la prdsente, accorae 6 la 'OSUMI%
DUE NATIONAL( DU CANADA de microfilmr cette these et
de prEter pu de vendre des ekemplaires du film.
L'auteur se reserve les autres droits k publication; ni la
theseni de longs extraits de celle-ci ne doivent etre- imprimds
of/ autrement reproduits sans l'autorisation eCrIte de I:auteur.
PERMANENT ADDRESS/ADDRESS/RESIDENCE Flil Rue du 8 Ma i 1945
Aigurande, France 361/0
a
FIL•111 111011
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
I + National Library of Canada Collections Development Branch
Bibliotheque nationale du Canada Direction du developpement des collections
Canadian Theses on Microfiche Service •
NOTICE
Service des theses canadiennes sur microfiche
The quality of this microfiche is heavily dependent upon the quality of the original thesis submitted for microfilming. Every effort has been made to ensure the highest quality of reproduction possible.
If pages are missing, contact the university which granted the degree.
AVIS
La qualite de cette microfiche depend grandement de la qualite de la these soumise au microfitmage. Nous awns'. tout fait pour assurer une qualite superieure
• de reproduction.
—S-anc—pages--may--14avri indistinct print especially if the original pages were typed with a poor tyoeWriter — -ribbon or if the university sent us a poor photocopy.
Previously copyrighted materials (journal articles, published tests, etc.) are not filmed.
Reproduction in full or in part of this film is gov-erned by the Canadian Copyright Act, R.S.C. 1970, c. C-30. Please read the authorization forms which accompany this thesis.
THIS DISSERTATION HAS BEEN MICROFILMED EXACTLY AS RECEIVED
Ottawa, Canada KlA ON4
S'il manque des pages, veuillez communiquer avec l'universite qui'a confere le grade.
La qualite d'impression de certaines pages peut hisser a desirer_surtogt si les pages originales ont ete dactylographiees a l'aide d'un ruban use-ou si site nous a fait parvenir une photocopie de mauvaise qualite.
Les documents qui font 6'0 I'objet d'un droit d'auteur (articles de revue, examens publies, etc.) ne sont pas microfilmes.
La reproduction, meme partielle, de ce microfilm est sournise a la Loi canadienne sur le droit d'auteur, SRC 1970, c. C-30. Veuillez prendre connaissance des formules d'autorisation qui accompagnent cette these.
LA THESE A ETE MICROFILMEE TELLE QUE
NOUS L'AVONS RECUE
Ni 339 (Rev OAT
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
' THE CONFORMATIONS OF ALKYL-SUBSTITUTED ETHYLENES.
A COMBINED NUCLEAR MAGNETIC RESONANCE AND FORCE FIELD STUDY
A Thesis
--------------Submitted to the Faculty of GribuateS_tudies and Research
In Partial Fulfilment.of the Requirements
for the degree of
,Doctor of Philosophy
in Chemistry
Faculty of .Science
# University of Regina
by
Christian Gerard Simon
Regiha, Saskatchewan
May, 1980
Copyright 1980. C.G. Simon
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
UNIVERSITY OF REGINA
Faculty of Graduate Studies and Research 1/4
SUMMARY OF THE THESIS
Submitted in Partial Fulfillment
of the Requirements fo'r the
DEGREE OF DOCTOR OF PHILOSOPHY
in
CHEMISTRY
by
CHRISTIAN GERARD SIMON
Doctorat 3eme Cycle
(Universite d'Orleans, France)
June, 1980
Committee in Charge:
W D. Chandler (Department Head) F.H.A. Rummens (Supervisor)
D.G. Lee S. Levine
B.D. Kybett . B.E. Robertson C. W. Blachford (Dean of Graduate Studies and Research)
External Examiner:
M. St•Jaeques. Professor of Chemistry University of Montreal
Montreal, Quebec
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
THESIS.
THE CONFORMATIONS OF ALKYL-SUBSTITUTED ETHYLENES. '
A COMBINED NUCLEAR MAGNETIC RESONANCE AND FORCE FIELD STUDY
Variable temperature proton NMR parameters (aPmical shifts and coupling constants) have been obtained for cis- and trans-2,2,5-trimethy1-3-hexene and for czs-2,5-dimetliy1-3-hexene using high precision experimental techniques, coupled with a powerful spectral technique (NUMARIT).
Detailed structural and energetic information for the above-mentioned molecules was obtained employing a Force Field procedure.
The general approach for the interpretation of the experimental results involved the combined use of the (AJ/A0) data calculated earlier by Rummens and Kaslander, the structural geometry calculated using the Force Field method and the theorem of Boltzmann population statistics. In many cases the technique was proven to be reliable.
No such generally useful structure-parameter stratagem was found frir the interpretation of chemical shifts. Differential solvent effects are suspected to be the cause of this failure. For the same reasons, the carbon-la spectra, obtainW for cis- and trans-2,2,5-trimethyl-:3-hexene were not useful for the interpretation of the totameric changes.
The temperature dependence .of coupling constants for trans-2,2,5-trimethyl-3-hexene is explained in terms of an anti-gauche equilibrium. The difference, in Gibbs free energy between the anti and gauche forms could be determined as AG" = 531+59J.mol (127+14cal.mol l); the Force Field method overestimates this
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
.01
difference by about 4KJ.mol ' (IKcal.mol l). No evidence of interaction between the isopropyl and tert-butyl rotors could be found.
In ci -2,2,5-trimethy1-3-hexene, it was concluded that the two substituents (isopropyl and ieri-butyl groups) are in anti position in the ground state. It seems clear from the experimental data that there exists a second low-lying minimum (AG" 2.1KJ.mol ' or 0.5Kcal,mol 1), not in concordance with the Force Field calculation.
The results on cis-2,5•dimethyl•3-hexene indicated a ground state with an anti-anti conformation. There exists a low energy
second conformer (AG" 1.13KJ.mo1- ' or 0.27Kcal.mol 1 ), but its
structure could not be determined. The anti•syn structure obtained from the Force Field as the second conformation was disproved by the NMR results. The latter point tb a skew-skew
structure as a likely form.
BIOGRAPHICAL
1969
CHRISTIAN GERARD SIMON
Diplorcy Universitaire d'Etudes Scientifiques, Universit6 d'Orleans (Prance).
1972 Maitrise de Physique, Universito d'Orleans.
197:3 Diplome d'Etudes Approfondies, Universite d'Orleans.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1974 Doctorat de 3 .me Cycle (specialty: solid state physics), Universite d'Orleans.
1976, 1977 Gerhard ferzberg Fellowship, Universit of Regina.
1978 Samps J. Goodfellow Scholarship, Univ rsity of Regina.
1978, 1979 Province of Saskatchewan University Graduate Scholarship, University of Regina. Province of Saskatchewan University Gradtiate Summer Scholarship, University of Regina.
1979 Teaching Assistantship, University of Regina.
1980 Research Technician, University of Regina.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
ABSTRACT
Variable temperature proton NMR parameters (chemical shifts and
coupling constants) have been obtained for cis- and trans-2,2,5-trimethyl-,
3-hexene and for cis-2,5-dimethy1-3-hexene using high precision experimen-
tal techniques, coupled with a powerful spectral analysis technique
(NUMARIT).
Detailed structural and energetic information f95 the above-
mentioned molecules was obtained employing a Force Field procedure.
The general approach for the interpretation of the experimental
results involved the combined use of the (a(A0) data calculated by
Rummens and Kaslander, the structural geometry calculated using the Force
Field method and the theorem of Boltzmann population statistics. In many
cases the technique is proven to be reliable.
No such generally useful structure-parameter stratagem is found
for the interpretation of chemical shifts. Differential solvent effects
are suspected to be the cause of this failure. For the same reasons, the
carbon-13 spectra, obtained for cis- and trans-2,2,5-trimethy1-3-hexene
were not useful for the interpretation of the rotameric changes.
The'teniperature dependence of coupling constants for trans-2,2,5-
trimethyl-3-hexene is explained in terms of an anti-gauche equilibrium.
The difference in Gibbs free energy between the anti and gauche forms
could be determined as AGo 531±59J.mol-1 (127±14cal.mol-1); the'Force
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Field method overestimates this difference by about 4KJ.mol (1Kcal.mol-1 ).
No evidence of interaction between the isopropyl and tert-butyl rotors
could be found,
-In cis-2,2,5-trimethyl-3-hexene, it is concluded that the two
substituents (isopropyl and tert-butyl groups) are in anti position in
the ground state. It seems clear that there exists a second low-lying
J ai-rrlinum (AG° = 2.1KJ.mo1-1 or 0.5Kcal.mo1-1) not in concordance with the
Force Field calculation.
The results on cis-2;5-dimethy1-3-hexene give definitely a
ground state with an anti-anti conformation. There exists a low energy
second conformer (Ae = 1.13KJ.mol -1 or 0.27Kcal.mo1-1), but its struc-
ture could not be determined. The anti-syn structure obtained from the
Force Field as second conformation is disproved by the NMR results. The
latter point to a skew-skew structure as a likely form.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
UNIVERSITY OF REGINA
FACULTY OF GRADUATE STUDIES AND RESEARCH
CERTIFICATION OF THESIS WORK
We, the undersigned, certify that Christian Gerard Simon
candidate for the Degree of Doctor of Phi losophy in Chemistry
has presented a thesis on the subject
Alkyl-Substituted Ethylenes. A Combined Nuclear Magnetic Resonance
The Conformations of
and Force Field of Study
that the thesis 1% acceptable in form and content, and that the student
demonstrated a satisfactory knowledge of the field covered by the thesis
in an oral examination held on June 20, 1980
External Examiner citt,LA.(1)), .... Dr. Maurice 2I-Jacq s, rofessor of Oemjstry..Uoiversi y.o Montreal._
Internal Examiners
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
UNIVERSITY OF REGINA
PERMISSION TO USE POSTGRADUATE THESES •
Title of Thesis The Conformations of Alkyl-Substituted
Ethylenes. A Combined Nuclear Magnetic Resonance and Force
r Field of Study
Name of Author Christian Gerard Simon
Faculty of Science Faculty
Doctor of Phi losophy in Chemistry Degree.
In presenting this thesis in partial fulfi lment of the requirements for a postgraduate degree from the University of Regina, I agree that the Libraries of this University shal l make it freely avai lable forinspection. I further agree that permission fbr extensive copying of this thesis for scholarly purposes may be granted by the professor or professors who supervised my thesis work, or in their absence, by the Associate Dean of the Division, the Chairman of the Department or the Dean of the Faculty in which my thesis work was done. It is understood that any copying or publ ication or.use of this thesis or parts thereof for financial gain shal l not be al lowed without my written permission. It is also understood that due recognition shal l be given to me and to the University of Regina in any scholarly use which may be made of any material in my thesis.
Signature...
Date June 20, 1980
'100 cc. /am 1/2/80
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
ACKNOWLEDGEMENTS
It is my pleasure to.thank Dr. F.H.A. Rummens for his guidance
and supervision throughout this work.
Sincere appreciation is also expressed to Dr. J.S. Martin and
Dt. T. Nakashima for the use of their spectrometer.
I wish to thank Dr. 0. Ermer for providing a version of his
valence Force Field program.
Grateful acknowledgement is made to the University of Regina
for providing continuing financial assistance in the form of a Gerhard
Herzberg Fellowship, a University Graduate Scholarship, a Sampson J.
Goodfellow Scholarship, a Summer Scholarship and a Teaching Assistantship
in Chemistry. The National Science and Engineering Research Council
is also acknowledged for providing financial aid through temporary
employment as a technician to assist Dr. F.H.A. Rummens in his
work.
iii
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
TABLE OF CONTENTS
page
ABSTRACT i
ACKNOWLEDGEMENTS iii
LIST OF TABLES ix
LIST OF FIGURES xiii
PREFACE xvii
CHAPTER I FORCE FIELDS 1
1.1 INTRODUCTION 1
1.2 DESCRIPTIONi9F THE MECHANICAL MODEL 4
1.3 FORCE FIELD CONSTANTS USED 9
1.4 ENERGY MINIMIZATION 14
1.5 DESCRIPTION OF THE "CFF" PROGRAM 22
1.6 CALCULATION OF NORMAL MODES OF VIBRATION 24
1.7 CALCULATION OF CONFORMATIONAL INTER-CONVERSION , 26
1.8 CALCULATION OF THERMODYNAMIC PROPERTIES WITH FORCE FIELDS 27
1.8.1 Enthalpy 28
1.8.2 Entropy 29
1.8.3 Gibbs free energy function G 32
CHAPTER II THEORY OF HIGH RESOLUTION NUCLEAR MAGNETIC RESONANCE 35
iv
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
TABLE OF CONTENTS (continued)
'2.1 INTRODUCTION
page
35
2.1.1 ' Chemical shifts ' 35
2.1.2 Coupling constants 37
2.2 THEORY OF THE ANALYSIS OF NMR SPECTRA. . 38
N __Hamiltonian operator 38
2.2.2 Subspectral analysis csing the composite particle method Q 42
Subspectral analysis using the X approximation 45
2..2.4. General procedure to analyze'NMR spectra 46
2.3 CHEMICAL' SHIFTS AND STRUCTURE " 47
2.3.1 Classification of shielding effects 47
2.3.2 Interpretation of proton cifemical shifts 49
2.3.3 Interpretation of carbon-13 chemical shifts 57
2.4 COUPLING CONSTANTS AND STRUCTURE 65
2.4.1 Description of coupling •65
2.4.2 Nature of the coupling 67
2.4.3 Empirical and semi-empirical correlations, between coupling constants and structure. 69
2.4.4 Coupling constants and electronegativity effects 76
\2.51 NMR STUDIES ON ROTAMERS 79
2.5.1 Description of phenomenon 79
2.5.2 Completely averaged spectra and their temperature dependence studies ' 81
2.5.3 Dynamic equilibria and line shape analysis 86
2.6 NUMERICAL ANALYSIS USING THE PROGRAM "NUMARIT" 39
1",
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
TABLE OF CONTENTS (continued)
•
page
2.6'.1 Introduction 89
2.6.2' Method of iteration 39
2.6.3 Error analysis 94
'CHAPTER III CONFORMATIONAL AND THERMODYNAMIC PROPERTIES OBTAINED FROM FORCE FIELD CALCULATIONS: RESULTS AND PRELIMINARY DISCUSSION 98
3.1 INTRODUCTION 98
3.2 RELEASE OF STRAIN AND CONFORMATION 98
3.2.1 Release of strain through widening of.the C=C-R valence angles 99
3.2.2 Other types of release 109
3.2.3 Repartition of steric energy 109
3.3, ENERGY IN CIS/TRANS TRANSFORMATION 111
3.3.1 Cis/trans enthalpy differences 111
3.3.2 Entropy and Gibbs energy reliability 115
3..4 STRAIN ENERGY DIFFERENCES BETWEEN ROTAMERS 117
3.4.1 - 3-Methyl-l-butene 117
3.4.2 trans-2,5-Dimethy1-3-hexene 119
3.5 INTERCONVERSION PATH AND THERMODYNAMIC PROPERTIES 121
3.5.1 cis-2,5-Dimethy1-3-hexene 121
3.5.2 trans-2,2,5-Trimethyl-3-hexene 128
3.5.3 cis-2,2,5-Trimethy1-3-hexene 134
3.5.4 4,4-Dimethyl-3-tert-butyl-1-pentene 140
APPENDIX 145
vi
No.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
TABLE OF CONTENTS (continued)
page
,CHAPTER IV NMR EXPERIMENTAL RESULTS 160
4.1 EXPERIMENTAL CONDITIONS 16Q
4.2 SPECTRAL ANALYSIS OF THE PROTON SPECTRA. . 164
4.2.1 cis- and trans-2,2,5-Trimethy1-3-hexene 164
4.2.2 cis-2,5-Dimethyl-3-hexene 173
4.2.3 cis- 4,4-,Di methyl -2- pen tene 177
CHAPTER V INTERPRETATION OF THE NMR DATA 189
5.1 INTRODUCTION 189
5.2 TRANS-2,2,5-TRIMETHYL-3-HEXENE 191
5.2.1 Analysis of the temperature dependence of the coupling constants
5.2.2 Coupling constants and conformational structure
5.2.3 Proton chemical shifts and conformations
5.2.4 Carbon-13 chemical shifts and structure
5.2.5 Conclusion
5.3 CIS-2,2,5-TRIMETHYL-3-HEXENE
5.3.1 Introduction
5.3.2 Analysis of the temperature dependence of several coupling constants
5.3.3 /Coupling constants and conformations
5.3.4 Proton chemical shifts and structure
5.3.5 Carbon-13 chemical shifts and structure
5.3.6 Rotational barriers and line intensities
5.3.7 Conclusion
vii
191
197
202
209
214
216
216
218
222
231
242
249
253
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
ti
TABLE OF irENTS (continued)
page
5.4 CIS-2,5-0IMETHYL-3-HEXENE 255
5.4.1 Temperature dependence of coupling. constants 255
5.4.2 Coupling constants and structure 260
5.4.3 Proton chemical shifts and structure 264
5.4.4 Conclusion 269
CHAPTER VI , EPILOGUE 271
TABLE OF REFERENCES 282
Viii
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
LIST OF TABLES
Table ' page
1.3-1 Valence Force Field constants for olefins as given by Ermer and Lifson [3]. 10
3.2-1 Effect of a fir't alkyl substitution on the valence angles of ethylene, as found experimentally. 101
3.2-2 Force Field-derived variations of valence angles with monosubstitution of one hydrogen atom by an alkyl group in an ethylene molecule, when the molecule is in its minimum of lowest energy. 102
3.2-3 Calculated effects of alkyl monosubstitution on valence angles for ethylene molecules. 104
•
3.2-4 Effect of second substitution in cis or trans position on valence angles for monoalkyl ethylenes, as calculated for the minimu'" energy conformation.
Difference between Force Field-derived and experi-mentally obtained Valence angles for various ethylene molecules.
105
106
3.2-6 Calculated steric energies (KJ.mo1-1) in various conformations of lowest energy of olefins as calculated by the "CFF" method. 110
3.3-1 Difference in steric energy (C) and in enthalpy (M) between cis and trans isomers of various molecules as calculated with the Ermer and Lifson Force Field; comparison with the experimental enthalpy di-fferences. 112
3.3-2 Comparison .of cis/trans enthalpy differences as calculated using three Force Field methods and as obtained experimentally.
3.3-3 Comparison between calculated entropy difference .is/ Trans (for conformation of lowest energy) as obtained from Force Field technique and as deduced from experimental data.
114
116
ix
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
LIST OF TABLES (continued)
Table
3.5-1 Contributions to calculated steric energies for various conformations of cis-2,5-dimethyl-3-hexene.
3.5-2 Calculated thermodynamic properties of cis-2,5-dimethy1-3-hexene conformations.
3.5-3 Calculated thermodynamic properties of crans-2,2,5-trimethy1-3-hexene conformations.
3.5-4 • Calculated thermodynamic properties of cis-2,2,5-trimethy1-3-hexene conformations.
3.5-5 Cal culated thermodynamic properties of 4,4-dimethyl-3-tert-butyl-l-pentene conformations.
page
126
127
133
139
143
4 2-1 Comparison between parameters as obtained from the NUMARIT program (a) iterating all the coupling constants, (b) iterating only the coupling constants of sizeable magnitude. The example is given for the trans-2,2,5-trimethyl-3-hexene at 345.5K. . 167
4.2-2 List of proton chemical shifts (in ppm from TMS) and of H-H coupling constants (in Hz) which give the best fit with the experimental spectra for the trans-2,2,5-trimethy1-3-hexene at each investigated temperature. 171
4.2-3 '.ist of proton chemical shifts (in ppm from TMS) and of H-H coupling constants (in Hz) which give the best fit with the experimental spectra for the cis-2,2,5-trimethyl-3-hexene at each investigated temperature. 173
4.2-4 List of proton chemical shifts (in ppm from TMS) and of H-H coupling constants (in Hz) which give the best fit with the experimental spectra for the cis-2,5-dimethyl-3-hexene at each investigated temperature. 177
4.2-5 Proton chemical shifts and H-H coupling constants for cis-4,4-dimethyl-2-pentene at various temperatures. 178
4.3-1 Carbon-13 chemical shifts (in ppm from internal TMS) of trans-2,2,5-trimethy1-3-hexene as a function of temperature. 187
4.3-2 Carbon-13 chemical shifts (in ppm from TMS) of2,2,5-trimethyl-3-hexene as a function of temperature. ' 188
x
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
LIST OF TABLES (continued)._
Table page
5.2-1 Sets of coupling constants and Gibbs energy differences as obtained by the GBM method applied to the experi-mental data of trans-2,2,5-trimethyl-3-hexene. 196
5.2-2 Sets of coupling constants and energy separations between rotamers by the GBM method applied to the experimental data of trans-2,2,5-trimethy1-3-hexene.
5.2-3 Carbon-13 chemical shifts of some trans disubstituted ethylenes for which one substituent is a tert-butyl group, in ppm upfrequency from TMS.
5.2-4 Carbon-13 chemical shifts of some trans disubstituted ethylenes for which one substituent is an ;sopropyl group, in ppm from TMS.
5.3-1 Sets of coupling constants and energy separations between rotamers obtained by the GBM method for the three considered transformations (see Figure (5.3-1)) of the cis-2,2,5-trimethyl-3-hexene.
5.3-2 Sets of 4taJ coupling constants as obtained by the GBM method for the three considered transformations (see Figure (5.3-1)) ofthe cis-2,2,5-trime hy1-3-hexene, with energy separations as taken from the 3CJ and 3vj results.
5.3-3 Sets of proton chemical shifts and energy separations between rotamers as obtained from the GBM method for the three considered transformations (see Figure (5.3-1)) of the cis-2,2,5-trimethy1-3-hexene. The GBM method is applied to uncorrected chemical shifts in ppm from TMS.
5.3-4 Sets of proton chemical shifts and energy separations between rotamers as obtained from the GBM method applied to shifts corrected for unwanted contributions for the three considered transformations (see Figure (5.3-1)) of cis-2,2,5-trimethy1-3-hexene.
5.3-5 Sets of proton chemical shifts and :heir differenck' as obtained by the GBM method applied to shifts corrected for unwanted contributions;'the enthalpy separations for the three considered transformations (see Figure (5.3-1)) are as given in Table 5.3-1.
xi
198
210
213
221
230
236
237
239
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
LIST OF TABLES (continued)
Table page
5.3-6 .Carbon-13 chemical shift (pom) dependence on temperature for the cis-2,2,5-trimethyl-3-hexene referenced to the methyl tert-butyl carbon C5. 243
5.3-7 Sets of carbon-13 shifts and energy separations obtained from the GBM method for the three transformations considered (see Figure (5.3-1)) of the cis-2,2,5-tri-methyl-3-hexene. The shifts are referenced to C5.
5.3-8 Sets of carbon-13 chemical shifts and their difference as obtained from the GBM method with the enthalpy separations as given in Table 5.3-1 for the three considered transformations (see Figure (5.3-1)) of cis-2,2,5-trimethy1-3-hexene.
5.3-9 Carbon-13 chemical shifts of sdme cis disubstituted ethylenes for which one substituent is a tert-butyl group, in ppm from TMS.
5 3-10 Temperature dependence of the intensity of tert-butyl and isopropyl groups in cis-2,2,5-trimethyl-3-hexene (proton NMR).
5.3-11 Temperature dependence of the intensity of tert-butyl and isopropyl groups in cis-2,2,5-trimethyl-3-hexene for carbon-13 NMR.
5.4-1 Sets of coupling constants and energy separations between rotamers as obtained by the GBM method applied to the experimental data of cis-2,5-dimethy1-3-hexene up to a temperature of 300K.
5.4-2 Sets of proton chemical shifts and energy separations as obtained by the GBM method applied to experimental data of cis-2,5-dimethyl-3-hexene up to a temperature of 300K.
"s. •
xii
244
245
247
251
252
259
266
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
LIST OF FIGURES
Figure _page
1.4-1 A comparison of best-step Newton descent- and standard steepest descent. 17
1.5-1 General scheme of the Lifson-Ermer Force Field calculation. 23
2.3-1(a) Definition of the coordinate system (Oxyz). (b) Shielding and deshielding regions due to magnetic aniso-
tropy of the C=C bond; model A according to Pople [32], model B according to ApSimon et al. [28].
(c) Definition of R and 4) in Vogler's model. 52
2.4-1 Molecular fragments used for the definition of: (a) allylic coupling constants (b) homoallylic coupling constants. 73
2.5-1 Free energy profile for two stable conformations. 82
2.5-2 Temperature dependence of the NMR spectrum as a result of chemical exchange (uncoupled AB case). 88
3.2-1 Schematic description of valence angle variation with increasing size of the alkyl group substituent for monsubstituted ethylenes. 100
3.2-2 Schematic description of valence angle variation with increasing size of the alkyl group R2 for cis- and trans-disubstituted ethylenes with an isopropyl group as first substituent. 108
3.4-1 Calculated molecular geometries of the anti and gauche conformations of 3-methyl-l-butene. 118
3.4-2 Steric energy increases with successive anti-gauche transformations of the isopropyl group in 3-methyl-l-butene and in naans-2,5-dimethy1-3-hexene as obtained from Force Field calculation. 120
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
-Lrg OF FIGURES (continued)
Figure
3.4-3 Calculated molecular geometries for the various conformations of minimum energy of trans-2,5-dimethyl-3-hexene.
3.5-1 Calculated steric energy profile for the interconver-Sion of (aa) and (as) conformers of cis-2,5-dimethy1-3-hexene.
,3.5-2 Calculated molecular geometries of the three conforma-tions of lowest minimum energy of cis-2,5-dimethyl-3-hexene.
page
122
123
125
3.5-3 Calculated steric energy profile for the rotation of the isopropyl group of trans-2,2,5-trimethy1-3-hexene. 129
3.5-4 Calculated steric energy profile for the rotation of the tert-butyl group of trans-2,2,5-trimephy1-3-hekene. 130-
3.5-5 Calculated molecular geometries of the conformationsof minimum energy for trans-2,2,5-trimethyl-3-hexene. 131
3.5-6 Calculated steric energy profile for the rotation of the tart-butyl group of cis-2,2,5-trimethyl-3-hexene. 135
3.5-7 Calculated steric energy profile for the rotation of the isopropyl group of cis-2,2,5-trimethyl-3-hexene. 136
3.5-8 Calculated molecular geometries of conformations of minimum energy for cis-2,2,5-trimethyl-3-hexene.
_3.5-9 Calculated steric energy profile for 4,4-dimethyl-3-tert-butyl-l-pentene as obtained by driving the HC sp 2-C sp3H dihedral angle.
3.5-10 Calculated molecular geometries of the two conformations of lowest minimum energy for 4,4-dimethy1-3-tert-butyl-1-pentene.
4.2-1 Numbering system and nomenclature used for (H,H) coupling con,tants of cis- and trans-2,2,5-trimethyl-3-hexene.
4.2-2 Methine region of observed (upper spectrum) and computer simulated (lower spectrum) 90MHz proton spectra of trans-2,2,5-trimethy1-3-hexene.
xiv
138
141
142
165
168
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
LIST OF FIGURES (continued)
Figure
4.2-3 Temperature dependence of the methine region of the 90MHz proton spectrum for trans-2,2,5-trimethyl-3-hexene. The upper spectrum was recorded at 330K, the lower one at 270K.
page
169
4.2-4 Methine region of computer simulated (lower spectrum) and observed (upper spectrum) 90MHz proton spectra of cis-2,2,5-trimethyl-3-hexene. 172
4.2-5 Numbering system and nomenclature for (H,H) coupling constants of cis-2,5-dimethyl-3-hexene. 174
4.2-6 Methine region of the observed 90MHz proton spectrum of cis-2,5-dimethy1-3-hexene recorded at 354K under the conditions given in Section 4.2. 176
4.3-1 Numbering system of the carbon-13 atoms for cis- and trans-2,2,5-trimethyl-3-hexene. 180
4.3-2 Natural abundance 22.63MHz proton noise-decoupled carbon-13 spectrum of trans-2,2,5-trimethyl-3-hexene. 181
4.3-3 Natural abundance 22.63MHz proton noise-decoupled carbon-13 spectrum of cis-2,2,5-trimethy1-3-hexene. 182
4.374 Non-olefinic region of a natural abundance proton noise-decouplied carbon-13 spectrum of trans-2,2,5-trimethyl-3-hexene. 183
4.3-5 Non-olefinic region of a natural abundance proton noise-decoupled carbon-13 spectrum of cis-2,2,5-trimethyl-3-hexene. 184
4.3-6 Temperature dependence of the olefinic carbons C1 and C2 chemical shifts for cis-2,2,5-trimethy1-3-hexene. 185
5.2-1 Temperature dependence of the vicinal coupling constant (J23) for trans-2,2,5-trimethy1-3-hexene. 193
5.3-1 Schematic reoresentation of the transformations considered in the discussion of the NMR results for r:s-2,2,5-tri-methy1-3-hexene. 217
5.3-2 \Temperature dependence of the vicinal coupling constant (J23) for the Ji3-2,2,5-trimethy1-3-hexene. 220
xv
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
LIST OF FIGURES (continued)
Figure
5.3-3 Olefinic proton (H1) chemical shift dependence on temperature for: A - cis-4,4-dimethyl-2-pentene referenced to TMS 3 - cis-2,2,5-trimethy1-3-hexpne referenced to TMS C - cis-2,2,5-trimethy1-3-hexene referenced to TMS,
but corrected for temperature dependence of intrinsic contribution.
5.3-4 Olefinic proton (H2) chemical shift dependence on temperature for: A - cis-4,4-dimethyl-2-pentene referenced to TMS B - cis-2,2,5-trimethy1-3-hexene referenced to TMS C - cis-2,2,5-trimethyl-3-hexene referenced to TMS,
but corrected for temperature dependence of intrinsic contribution.
5.3-5 Proton chemical shift dependence on temperature for: A -.methyl proton of cis-4,4-dimethy1-2-pentene
referenced to TMS B - methine proton of cis-2,2,5-trimethy1-3-hexene
referenced to TMO C - methine proton of cis-2,2,5-trimethy1-3-hexene
referenced. to TMS, corrected for temperature dependence of intrinsic contribution.
5.4-1 Temperature dependence of vicinal coupling constant (J12) for cis-2,5-dimethyl-3-hexene.
5.4-2 Temperature dependence of the methine proton (H2) chemical shift for cis-2,5-dimethyl,-3-hexene.
5.4-3 Temperature dependence of the olefinic protons, chemical shift for cis-2,5-dimethyl-3-hexene.
xvi
page
233
234
235
258
265
268
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
PREFACE
Interest in high resolution NMR spectra of olefins originates
from various sources. Besides the aspect of basic structure determina-
tion that certainly ranges among the most important applications, the
conformational analysis of olefins has been tremendously advanced through
'the information obtained from chemical shifts and spin-spin coupling
constants. In addition, these parameters are dependent on the electronic
structure of the individual systems and valuable details about chemical
bonding become available.
On the other hand, the NMR spectra of olefins with known
stereochemistry have served as a source of experimental data that paved
the way for a better understanding of the mechanisms which determine
chemical shifts and coupling constants in organic molkules. NMR/
chemical structure correlations can thus be established while theoretical
investigations are stimulated.
Besides these static parameters related to molecular geometry
and bonding, the sensitivity of the NMR method to intramolecular rate
processes has led to a wealth of information related to the dynamic
'properties of molecules, including conformational equilibria. The
temperature dependence of the spectrum has thus to be studied.
The successful use of NMR spectroscopy as an analytical tool
depends on the extraction of the fundamental parameters from the spectrum.
xvii
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
In many cases, and particularly in this thesis, a full mathematical .
analysis using one of the computer programs available is required for
complete interpretation of the spectrum. The availability of such
sophisticated programs and of a new generation of NMR spectrometers at
the beginning of the seventies has made possible the interpretation of
more and more complex spectra. Also, up to the mid-sixties, virtually
all conformational studies carried out by NMR were based on proton
resonances, but that situation changed radically in the subsequent period
and presently a large number of studies involving carbon-13 nuclei are
reported in the literature. In this thesis, both proton and carbon-13
NMR are employed.
Studies on methyl substituted ethylenes by electron diffraction
and rotational spectroscopy have shown that in all these molecules the
preferred conformation is such that one CaH eclipses the C=C bond and is
therefore anti relative to the C-H at tire neighbouring olefinic carbon.
NMR studies on mono- and trans-dialkyl ethylenes have indicated that the same
conformational situation prevails in these molecules, although the
population of the different forms varies with the nature of the substi-
tuent(s). In these latter studies, it was proposed that the coupling
between rotors proceeds through valence electrons of the C=C moiety. The •
consequent valence angle changes would then be transmitted to the coupling
constants of the second rotor.
It was thought that variable temperature NMR studies of the two
isomers of 2;2,5-trimethyl-3-hexene and of _,1:0-2,5-dimethy1-3-hexene
would provide decisive information with regard to the above proposal.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
A
The study of such cis/trans pairs of isomers would also, hopefully, shed
new light 'cm the nature of cisoid alkyl interaction. In this respect it
should, be remembered that the strueture of cis-2-butene (as obtained from
rotational spectroscopy) was the only accurate piece of inforMation
hitherto available on such cisoid interaction.
In order to succeed in this approach, additional information is
needui. The introduction of molecular Force Field calculations has as
the main purpose the provision of an estimation of energy differences
between various rotameric structures. A second objective of using Force
Field calculations was to obtain the basic structural information corres-
ponding to the minima in steric energy. This Force Field method allows
one to extend the knowledge of conformational geometries beyond the
simple molecules for which electron diffraction, rotational spectroscopy
?nd X-ray cristallography provide accurate geometries. With the help of
Force Field calculations as an auxiliary technique, structure-parameter
relations.can be investigated. Indeed, since the beginning of the
seventies, the Force Field procedure has been extensively developed and
presently, the various Force Fields contribute to obtain information on
structure and energy'of molecular conformations.
The theoretical material in this thesis is arranged in two main
sections; the first section describes the Force Field employed, while the
second one gives an extensive review of NMR/chemical structure correla-
tions as well as the methodology used in spectral analysis. The results
obtained from Force Field calculations for various substituted ethylenes
are detailed in Chapter III; this is followed in Chapter IV by a summary
xix
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
of the experimental data obtained by proton and carbon-13 NMR spectro-
scopy. Interpretation of the results for each molecule investigated using
a structure-parameter relationship approach is given in Chapter V, while
the epilogue of the study is given in Chapter VI.
Throughout this thesis, the energy has been expressed in J.mo1-1
except in some specific cases. These values are followed by their equiva-
lent in cal.mol-I placed between parentheses. The cis-trans system for
naming configurational isomers, being unambiguous for the molecules
studied, has been used preferentially co the Z-E system.
xx
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
CHAPTER I
FORCE FIELDS
1.1 INTRODUCTION
The Force Field method considers only the positions of the
nuclei in the molecule; the electronic system is not considered
explicitly as it is in ab initio energy calculations.
In this method (Force Field method) a classical approach of the
problem is employed; a set of equations in the form of the classical
equations of motion is assumed to exist for each molecule. The problem
from this point of view is one of establishing just which equations are
necessary, and of determining the numerical values for the force
constants which appear in the equations.
A great deal of experimental information regarding small mole-
cules (e.g., equilibrium bond lengths, bond angles, heats of formation)
is available. For small molecules the force constants are usually also
available from normal coordinate analysis and the Raman and infrared
spectra. A large molecule consists of the same features, but they are
combined and strung together in different ways. The problem is to
formulate the structure of a large molecule in terms of the elementary
features of these small molecules. This is both the aim and the basic
tenet of the Force Field method, to develop a universal Force Field,
1
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
employing force constant pertaining to small structural elements,
allowing the calculation of structures of entire molecules, both small
and large.
The Force Field method discussed here is a useful method for
determining the structure and energy of a moledUl But there are many
other properties of a particular molecule that can be found after the
structure and energy are known. These include vibrational frequencies
and thermodynamic functions such as free energy and free enthalpy of
activation for rotation.
The Force Field method has also its shortcomings; it is a semi-
empirical method, in that its force constants are found by data fitting
on a large volume of experimental data. These data must exist for a
given class of compounds before the method can be developed and applied
to any particular compound in this class.
Real molecules at roam temperature occupy a series of vibra-.
tional states, and the atoms are not at rest but are vibrating. The
energy of the total assembly varies with temperature because the mole-
cules occupy the vibrational levels according to a Boltzmann distribution.
The calculation carried out by the semi-empirical'Force Field method
gives a potential function and the molecule is regarded as being a rigid
structure at rest at an energy minimum. This type of structure is
usually adequate for many purposes; in cases where the dynamic nature of
a structure is important, one can use the vibrational levels calculated
by standard methods of statistical mechanics, using the force constants
as used for the "rigid" structure calculation.
2
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
There is another way to determine the structure of a molecule
by calculation: the so-called ab initio method. Regardless of other
shortcomings (truncation of wave function, neglect of correlation between
electrons) the ab initio calculation is considerably slower (factor of
103 for small molecules that increases with the size--see for example a
review by Allinger [2]). At present the accuracy of ab initio structure
calculation is not as good as with Force Field methods.
The development of a Force Field begins by imagining a mechani-
cal model of a molecule as a series of masses (atoms) attached by springs
(bonds). This general idea can be traced back to Andrew [2]. Deforma:
tion of the structure results in an energy change which can be calculated
if the forcelaws and force constants involved are known. The complete
set of force constants is referred to as the Force Field. The latter is
developed by deciding what kinds of forces and constants are needed to
reproduce the known structures of small molecules. A model is then
constructed; it may reproduce the experimental facts, but this does not
mean that the model is in every respect a faithful reproduction of the
molecule under study. It means on1S, that the information used to develop
the model is reproduced by it. If one wants to calculate properties of a
molecule, one prefers the particular Force Field that is developed from
the properties of interest. In the present study the Consistent Force
Field calculation developed by Ermer and Lifson [3] has been chosen. As
far as this study is concerned (calculation of energy conformation and
thermodynamical properties of substituted ethylenes) it is the most
accurate one available. Experimental data used for the optimization of
3
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
energy parameters comprised: 259 experimental vibrational frequencies of
ethylene, trans- and cis-2-butene, isobutylene, cyclohexene, 1, 4-cyclo-
hexadiene l nd trans, trans, trans-1, 5, 9-cyclododecatriene, 44 conforma-
tional data on ethylene, propene, cis- and skew-l-butene, isobutylene,
cyclopentene, cyclohexane, trans-cyclooctene, cis, cis-1, 6-cyclohexane;
ten cis/trans differences and excess values (over cyclohexene) of the
heat of hydrogenation involving the 2-butenes, the 1, 2-di-tert-butylethy-
lenes, the 1, 2-methyl-tert-butylethylenes and the five- to ten-membered
cyclic mono-olefins.
- In the next section the potential function used by Ermer and
Lifson [3] will be described.
1.2 DESCRIPTION OF THE MECHANICAL MODEL
To develop a classical valence Force Field, the molecule will
be represented as though it were a serif; of masses joined together by
springs, with Hooke's law applying within the Newtonian laws of motion.
The mechanical model thus becomes a description of the various types of
deformation, as detailed below.
(i) Bond stretching and valence angle bending
Bonds tend to have a certain "normal" length. If a bond is stretched
it is assumed that Hooke's laws apply as it would for a spring. A
similar relationship applies for bending angles. Thus a stretching
energy (Eb) and a bending energy (E0) can be defined for a molecule by
equations (1.2-1) and (1.2-2) in which the summations are over all the
4
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
bond lengths and valence angles in the molecule (respectively b and e).
Eb = E Kb (b-b0)2
Ee
h E He (0-8
o)2
(1.2-1)
(1.2-2)
bo and eo
are parameters representing the corresponding reference
values. It is known from vibrational spectroscopy that valence angle
deformations require much less energy than bond length deformations.
The respective force constahts differ by about one order of magnitude:
bond angles display a greater variability than bond lengths and are
more relevant for conformational calculation.
Equations (1.2-1) and (1.2-2) are strict* speaking only valid
for relatively small deformations. For larger deformations higher
order polynomial terms could be added or a Morse potential could be
employed instead. By making use,only of quadratic terms, one is thus
faced with a general limitation. in terms of molecular geometry para-
meters, Ermer [4] estimates roughly 0.1A and 15° as upper limits for
deviations of bond lengths and valence angles from their respective
reference values, as validity range for equations (1.2-1) and (1.2-2).
(ii) Torsional terms
Ti account for the energy difference between eclipsed and staggered
ethane one has to introduce a torsional term in the potential. For
ethane this term is described by equation (1.2-3):
5
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
E4) = li H4) (1-cos34)) (1.2-3)
where 4) is the H-C-C-H dihedral angle, 114) the force constant.
Ermer and Lifson [3] have generalized this formula to include
all torsional motions in alkanes and alkenes:
E4) = 1/2 E H 9 (1 + s cos n4)) ;1.2-4)
s and n depend on the type of the bond around which rotation occurs:
the energetical description of rotations around bonds with high tor-
sional barriers (double bonds) demands the evaluation of the influence
of higher cosine terms.
(iii) Non-bonded interactions
In addition to the terms already defined, Van der Waals interactions
exist between all pairs of atoms which are not bonded to one another,
nor to a common atom (these cases are excluded because if the atoms
are bonded together the Van der Waals interaction is taken into
account by the bond stretching, and if they are bonded to a common
atom it is at least partly allowed for in the bond bending).
The attractive part of the Van der Waals curve is a result of
electron correlation and is inversely proportional to the sixth power
of the di.,tance separating the atoms. The repulsive part of the
potential is more steeply dependent upon distance in the Lifson-Ermer
Force Field; an inverse power of 9 is used to express this behaviour.
6
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Enb
= E e (2(r*/r)9-3(r*/r)6) (1.2-5)
where r* is an equilibrium "radius" and e measures the softness or
hardness of the potential. A thorough discussion of alternative non-
bonded potentials has been given by Williams et al. [5].
All the terms described up until this point are common to all
Force Fields; the remaining terms to be discussed are specific to some
workers.
(iv) Out of plane bending
For pyramidal distortion without twisting (out-of-plane bending) a
potential developed by Warshel et al. [6] has been applied. This out
of plane bending is different from torsion as it involves the inter-
actions between the three orbitals of the same atom, while the other
involves those between two neighbouring atoms.
Ex = H
xx2
(v) Cross terms
(1.2-6)
In cyclobutane, if an angle is opened bond the tetrahedral value the
repulsion between adjacent bonds is reduced and the bond lengths can
contract. Clearly, bond length and bond angle are correlated and not
as independent as equations (1.2-1) and (1.2-2) would indicate. The
apparent solution to the problem Cs to add a stretch-bend interaction
7
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
term into the energy expression. Thus an energy of the form repre-
sented by equation (1.2-7) is introduced,
Ebe . z E Fbe (b-bo) (0-0o) (1.2-7)
Fb6
is the force constant used to express the strength of coupling ..."--
between the bond length b and the adjacent angles 6. Similarly, a
cross term is.added for two adjacent bonds (b) and two adjacent angles
(e), and two adjacent out of plane bendings (x); this leads to energy
terms as given by equations (1.2-8), (1.2-9) and (1.2-10).
Ebb'
= E E Fbb' (b-bo) (b'-boi) (1.2-8)
Eee,= z z F66' (6-60 0 ) (A-6') (14.2-9)
EXX
1 = E E FXX'XX'
(1.2-10)
Finally the complete potential expression used can be written
in the following form:
Or:
V = Eb + EA + Enb + Ex + Ebe + Ebb' + E56 1 4. E(x 1 (1.2-11)
8
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
• V = 1/2 E Kb (b-bo)2 + 1/2 E He (e-eo)2 h E K (1 + s cos 0)
+ E E(2(r*/r)9 - 3 (r*/r)6) + E E F
be (b-b
o) (0-e
o)
+ E E Fbb (b-bo) (b 1-bc;) + E E Fee (e-e0) (e'-e(;)
+ 1/2 E HX
x2 + E E FXX
XX'
1.3 FORCE FIELD CONSTANTS USED
(1 .2-12)
As previously indicated, the constants have been determined
using a reasonably large set of experimental data, representing a large
variety of properties and structural features. A total of 313 observed
quantities were used by Ermer and Lifson [33, and incorporated. into the
least-squares fitting process: 259 vibrational frequencies, 44 conforma-
tional data and 10 thermodynfical quantities. •
The results are listed in Table 1 .3-1. The average absolute
differences between the 44 observed and calculated bond lengths, bond
angles and torsion angles used in the optimization of parameters, were 0
0.003 A, 0.5° and 1 .0° respectively.
9
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
TABLE 1.3-1 Valence Force Field constants for olefins as given 'by Ermer and Lifson [3]i
I Diagonal terms
KD'
boD
KR'
boR
KT' boT
KL' b02.
K b S' oS
Kd' bod
Kr' b or
HE, C 0
bond stretch
C —C
C (0 3 ) C (0 3 )
C ( 0 j ) '-C(?)---
H 4H C C
b C " C
'C NH
C C
11/ti C H
C C A/ C / \\
H H
1-I-i
I-I
angle bend
C r e /C
C C C.
iC
N H ,,
C 4...\ C C
if 1309.9 , 1.333
645.3 , 1.526
645.3 , 1.501
723.0 , 1.089
660.0 , 1.105
654.0 , 1.105
681.5 , 1.105105i
72.4 , 122.3
104.3 , 115.4
93.2 , 110.5
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
TABLE 1.3-1 (continued)
HA, Ao
H r ' '0
H 40 o
q'o
H , v o
Hy, yo
HS' 60
H , n n o
H6'
do
Ha, a0
HE
C C
C C C H
C C
C—Ce.
H C C,
C
ec
C c
C c
H
H
A—r1H
C C
_AH H
H
93.2 , 109.47
93.2 , 110.0
67.5 , 121.2
75.0 , 116.5
88.8 , 108.9
88.8 , 109.2
88.8 , 112.4
66.7 , 117.6
79.0 , 109.6
79.0 , 106.4
torsions
Fk H H /C.-.E.--C\/
\ C÷ ,C\ 37.9
H H H/ C
1'
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
0
I TABLE 1 .3-1 (continued)
-CNH
H 121
HT
HER
HX C
FRR 28 . 5 C
Frr
H C
H—C
c (
(
CC 32.7 N.
C
I) ( -2) 2.532
-5) ( 2.845
22.9
II Cross terms -4
, FRw = 60.2 C----e -(E= 38.4 C. )
-7.9 H
-7.9
H ,C F Ry ' = 0 C----.0 F' = 0 F4 7
YY k....NC C
fYw = -10.5 1
( 4C 4116 f rr = -10.0 ((a l FXX = 3.31
III Non bonded interactions
-7.9
H H 1/2 rAw = 1.816 H CI 1/2r*HC = 1.787
1/2 = = 0.1615 6 HH 0.0641 HC
C C 1/2 r*cc = 1.759
e1/2cc = 0.4072
The potential constants are defined in graphical form. The units are Lased on the following units for energies, lengths and angles: Kcal).mo1 -1, A and rad respectively. Reference lengths and angles are given in A and degrees. The parameters for the non bonded potential hold for expression (1.2-5).
12
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
In the absence of strain the local symmetries of methylene and
methyl ,groups are assumed to be C2v and C3v respectively; in addition the
sp2
carbons are supposed to be coplanar with their ligands. These
assumptions lead to a reduction in the number of adjustable parameters.
The following relations have to be fulfilled (see Table 1.3-1 for
notation):
cos yo
- cos ho cos h wo (a)
cos 60 = - ((1 + 2 cos ao)/3)1/2 (b)
no = 2Tr - 240
tpo = 2Tr - 24 - e
0 o
ao = 2Tr - e
o
(c)
(d)
(e)
(1.3-1)
Ermer andlifson [3] evaluated the torsional energy individually
for each n the torsion angles X-C-C-Y around the C-C bonds, making
altogether nine torsional angles for the sp3-ep3 bond and six for the
3 2 sr -sp bond. Then the torsional energy parameters are 1/9 and 1/6 of
13
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
the values for H and H07
listed in table 1.3-1 . 0
In relation (1.2-4) the values for s are -1 for C = C-C-C and
C = C-C-H rotations, and 1 for all other rotations around single bonds.
For pure twisting around the double bond a twofold cosine potential was
applied, with s = -1 and 4 15(0 0 term of = 2145 4'3140' In the cos
relation (1.2-4), n = 3 for all C-C single bonds and n = 2 for double
bonds.
doe
1.4 ENERGY MINIMIZATION
The structure of the molecule will correspond to that geometry
where the energy is at a minimum. Therefore if the energy of the mole-
cule is written as in equation (1.2-12) all one needs to do to find the
structure is to take the derivative of this equation with respect to each
of the degrees of freedom of the molecule, and find the position(s) where
each of those derivatives is simultaneously equal to zero.
There is a variety of mathematical techniques which can be used
to do this; different methods have different advantages and different
drawbacks.
Here the three minimization procedures used in the Ermer-Lifson
program are discussed: the steepest descent iteration, the Fletcher-
Powell method and the Newton-Rahson minimization procedure. A combina-
tion of these ':chniques gives satisfactory results in almost all cases
of practical interest.'
The program uses Cartesian atomic coordinates which is better
14
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
than the alternative of internal coordinates: it is easier to derive all
independent and dependent internal coordinates from a set of independent
easiboqbtainable Cartesian coordinates, than to evaluate the dependent
inter41 coordinates from a set of independent ones. The disadvantage
(that the potential energy.is related to Cartesian coordinates in a more
complex fashion than to internal coordinates) is 'a less serious problem.
One has then to find the minimum of a function of n variables
such as (1.4-1):
V = V(xl, x2 . . . , xn) = V(x)t (1-.4-1)
It is obvious from inspection of equation (1.2-12) that in its
domain of validity, the function used is differentiab16 which allows one
to use the three previously mentioned minimization procedures.
(1) Steepest descent minimization [7]
This method can be used when the function to be minimized has first
derivatives. Given a function V(x), it is known (if the first partial
derivatives exist) that the gradient of the function Vv(x) is a vector
pointing in the direction of t6 greatest rate of increase of V(x).
At any given point (x0) the vector vv(x0) is normal to the contour
that passes through the point (X0). The negative gradient points in
the opposite direction, which is the direction of the greatest rate of
Throughout this thesis vector quantities are italicized.
15
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
decrease of V(X) at this point. The procedure used in this minimiza-
tion method is as follows:
- Start at some initial point (X0).
- The general iteration step begins then; for the ith iteration one
calculates Vv(Xi).
- Move in the direction -VV(xi). To do that one has to determine a
step size hi; in the present program h i depends on the step length
(E (Ax.)2)h, x. being the jth coordinate. J . J
- Calculate the next point: (Xi+1) = (Xi) - hiVv(Xi).
- The calculation stops when relation (1.4-2) is satisfied:
V(Xi) - V(Xi4.1) < e (1.4-2)
where e is some pm-established tolerance. Figure (1.4-1) shows a
graphic representation of the possible succession of points that one
would obtain in the application of this method. In the illustration
the function to be minimized is a two-variable function f(x1, x2).
If one starts at 0 (x x02) and moves in the direction of the nega-
tive gradient, one moves in a direction perpendicular to a tangent to
a contour of f(x1, x2) and in the direction of decreasing f. This
takes to 1 (x11, x.12). Any further movement along the line 01 (in figure
(1.4-1) will increase f. Now the negative gradient at 1 is deter-
mined, and the previous procedure is repeated. In this fashion, one
proceeds to 2, 3, 4 until one reaches the minimum to whatever
tolerance is desirable. The successive steps or directions in which
• 16
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Reproduced w
ith permission o
f the copyright owner. F
urther reproduction prohibited without perm
ission.
)
4
FIGURE 1.4-1 A comparison of best-step Newton descent ( ) and standard steepest descent ( ).
Reproduced w
ith permission of the copyright ow
ner. Further reproduction prohibited w
ithout permission.
to move are orthogonal to each other. One of the implications of this
fact is that if the contours of the function to be optimized are
hyperspheres in n-dimensions, the optimum would be found in one step.
The more the contours of the function depart from sphericity, the
greater is the number of computational steps required to approach the
minimum value.
If the starting point is far from the energy minimum, energy
minimization proceeds fast with this method, but it slows down as one
comes close to it. Then one switches to a different procedure which
is more powerful at small gradients.
(ii) Newton-Raphson method [8]
In the Newton-Raphson method th. function V is replaced by its Taylor
series expansion to the second term:
V = V(xo )4. E 3 V/axi(X0) (xi-x0j)
a2V/3x.ax.(Xo ) (x.-x co .) (x.-x oj.)
i,j j j (1.4-3)
The value of V, its vector of first derivatives and its matrix
(usually called Hessian matrix) of second derivatives must be known at
the location (X0). Setting 3V/3xi = 0 for all i yields the location
of the stationary point of V. From equation (1.4-3) one obtains:
18
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
N 2V/ax.(x ) z a vtax.ax. (x.-x .) = o
o j=1 J j oj (1.4-4)
These N linear equations must be solved simultaneously for the N
unknowns; in vector notation one can write:
X =X0 - ^-1 v17
where V v = [aV/3x]
at the starting point
A = [32v/axiaxj]
(1.4-5)
The Newton-Raphson method has two undesirable features: firstly, it
requires one to calculate the Hessian matrix of partial derivatives
and s4.condly, it cannot be used too far from the minimum, because the
Taylor-series expansion is truncated after the. second term (this means
that the actual function is assumed to be a quaJr'atic function). But
as one approaches the minimum, this approximation becomes more
accurate and the method converges faster than the steepest descent,
the procedure of which is totally dependent on the vanishing first
derivatives. A comparison of the two methods is given in Figure (1.4-1).
The Fletcher-Powell minimization to be discussed next combines the
advantages of both the steepest descent and the Newton-Raphson
methods.
19
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
(iii) The Fletcher-Powell method (also known as the Davidon-Fl4tcher-
Powell method) [9]
This method is devised in such a way that, if the function to be
optimized is quadratic in n variables, the iteration scheme converges
in n iterations. The main difference with the steepest descent is
that it makes use of second order information taken from the function
to be minimized. The scalar hi of the steepest descent method is
multiplied by the Hessian matrix H. The direction of minimization is
no longer the gradient vector (except if the A matrix is the unity
matrix i). Use is made of the infor; .tion contained in the differences
of first derivatives (the array of which is also called a Hessian
matrix) to determine the best direction of minimization. The basic
?"" kiprocedure involves three general steps:
- Computation of the gradient VV(Xi) at some point (Xi).
- Determination of a direction ri along which to make the desired
move; r. = Ai vv(xi).
- Motion along this direction to some new point (X14.1), using Xi4.1
Xi + hr. (where h is the step size in the direction of search)
This general procedure is repeated until the gradient at some particu-
lar point becomes sufficiently small. To use this method, the
explicit calculation of second derivatives is not needed: one has a
second order representation which contains only first-order direct
information by using the gradient at two different points and by
calculating their difference. This method is now known to be a great
improvement over simple steepest descent procedures and is less
20
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
computer time consuming than Newton-Raphson procedures which need
calculation of second derivatives.
Some caution has to be exercised in the energy minimization
process so as not to lose symmetry elements as has been discussed by
Ermer [20]. The molecular symmetry is reflected in the first and second
(and higher) partial derivatives of the energy function V. Hence in all
minimization techniques with simultaneous calculation of the 6xi no
symmetry elements can disappear. This holds as well for the three pro-
cedures described previously. Additional symmetry elements can, however,
'be generated by these methods, if the starting geometry happened to have
a lower symmetry than the geometry at minimum. If one wants to determine
moleculir symmetries by Force Field calculations, one should always start
the minimization with trial structures of sufficiently low symmetry, and
the initial asymmetric distortion should 'not be too small.
The various minimization procedures are different in their
efficiency. By repeating steepest descent procedures, the first deriva-t
tives, the potential energy will be reduced to around 10-1 Kcal.mo1-1.A-1 ,
whilethe reduction in energy from the previous cycle can be of the order
of 5.10-3 Kcal.mol-1. At this stage, reduction offirst derivatives can
take hours of computer time and the calculation is judged to have reached
TWhen dedling with the "CFF" program, the energy has been expressed in calorie which is the unit used in that program. For the final results the energy will be transformed from calorie into Joule (using 1 cal = 4.184 J).
21
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
convergence. However, three to four cycles of the quadratically conver-
gent Newton-Raphson procedure starting from the last point may not reduce
the energy overmuch (about 10-2 Kcal. mol-1 ), but the first derivatives
will be around 10-10 Kcal.mol-1 1 .A and there may be important adjustments
to the torsion angles (about 10°). The general use of a Newton-Raphson
procedure results in more reliable geometry description of molecules in
additisin to a smaller improvement in energy.
The Fletcher-Powell method can lead to derivatives of about
10-6 Kcal .mol-1 1,.A but requires several starting points to avoid
partial minima.
1.5 DESCRIPTION OF THE "CFF" PROGRAM
To illustrate the procedure used in Ermer and Lifson's CFF
program a general set-up is given in figure (1.5-1). The input consists of
the Cartesian coordinates of the trial model (through a subprogram
called "MOLDAT") plus a set of structural parameters (b0, 80, . . .) and
of constants (Kb, H8, . . .) for the potential function: The trial model
is obtained from guessed internal coordinates which are transformed to
Cartesian by the "COORD" program Eli) (which is not part of the "CFF"
program). From a line code of the molecular structure (for example ZH3
AH AH ZH3 in the case of a 2-butene; A represents an sp2-carbon atom, Z
sp-3carbon atom) the subprogram "MOLDAT" sets up a list of all internal
22
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
INPUT Molecular parameters (see Table 1.3-1)
INPUT Starting cartesian coordinates for the molecule under study
CALCULATION Internal coordinates
CALCULATION Steric energy (V) and its derivatives
, MINIMIZATION a- Steepest descent method b- Fletcher-Powell type procedure c- Newton-Raphson method
OUTPUT Cartesian coordinates Internal coordinates Energy (V) and its first derivatives (dV/dx)
OUTPUT Frequencies and Normal modes of vibration
FIGURE 1.5-1 General scheme of the Lifson-Ermer Force Field calculation.
23
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
coordinates (lengths, angles, torsion angles, non-bonded distances) that
contribute to V. Their contributions to V and to the derivatives of V
are subsequently evaluated for the individual internal coordinates and
summed appropriately through the subprogram "MOLECU". The minimization
processes performed on the Cartesian coordinates are chosen in the
routine "CALCDT", which al lows the utilization of the three previously
mentioned procedures (through subprograms called "STEEPD","NEWTON-
RANSON", "DAVIDO").
The output of the "CFF" program consists (besides a list of
energies--bond, theta, . . .--, geometry, vibrational frequencies) of the
Cartesian coordinates of the "refined" model which can be used to restart
the procedure.
1.6 CALCULATION OF NORMAL MODES OF VIBRATIONS
The "CFF" program provides also the ' equencies of the normal
modes of vibrations. These are needed in this study because they enter
in the partition functions which form the basis for the
calculation of thermodynamic properties.
The Taylor expansion of the potential energy function V(r)
around the equilibrium coordinates r0, can be written as in relation
(1.6-1):
V(r) = V(ro) Z(aV/3r.)6r.÷ 1/2 2
2Vrar.3r.)6r.6r. (1.6-1)
i j
24
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
The third term of (1.6-1) represents the potential energy of
molecular vibrations around the equilibrium coordinates r0. It depends
on ro and takes the form:
V(ro; 6r) = V(ro + Sr) - V(ro) (1.6-2)
or V(ro; Sr) = Sr' H(ro) 6r (1.6-3)
where H(ro) is the Hessian matrix of second derivatives. In case the
Newton-Raphson process is used for energy minimization, the evaluation of
the molecular vibrational frequencies is a fairly simple matter since the
H-matrix is available.
For small atomic.displacements, Sr, the kinetic energy of a
vibrating molecule is given in matrix notation by:
6T = 1/2 61,1 M 61, (1.6-4)
where M is a diagonal matrix of the atomic masses.
The secular equation for the normal modes of vibrations as
derived.from the Lagrangian equations of motion takes the following form:
F 6q = A Sq (1.6-5)
where Sq = m 6r, and F = M M
Solving this eigenvalue problem yields the vibrational
25
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
frequencies (square roots of the eigenvalues Ai) and the normal coordina-
tes (eigenvectors with relative mass-weighted CarteMan displacement
O
I
amplitudes as components). The matrix F is sixfold singular as a conse-
quence of the six vanishing eigenvalues for translation and rotation.
In the "CFF" program the problem is solved using the House-
holder-Givens/bisectioh diagonalization procedure [14. These
performed using subprograms called "FREQ" and calculations are
"NMODES". The output gives all the frequencies with their assignments,
and displays also the normal modes of vibrations when required.
1.7 CALCULATION, OF CONFORMATIONAL INTERCONVERSips
Potential energy profiles for conformational interconversions
may be evaluated relatively easily in a point by point fashion.' Conforma-
tional changes are characterized by large changes, of torsion angles which SO
may serve as a model for the reaction coordinate. The calculation is done
by choosing a torsion angle which changes substantially during the inter-
conversion, and by performing a series of constrained energy minimiza-
tions for different fixed values of the chosen torsional angle. This
angle will be called a mapping parameter, following Ermer's notation [4].
It has to be an important part of the reaction coordinate (which is.a
many-dimensional vector describing the d\splacement of all he atoms
during a rate process The torsion angl\chosen as mapping parameter
must not take the same value for two or mote different conformations
through which the interconversion proceeds., the torsional constraint
26
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
required for the mapping is introduced by adding a fictitious potential
to the rorce Field; following calculations done by Ermer [/0], a poten-
tial of the form Kc (4)m -4 )2 is added to the general expression (1.2-12). mo
For Kc a value very much larger than a normal torsional constant is
chosen. The mapping parameter (1)m approaches, the fixed
(Dmo' under minimi-
zation of the energy with respect to all degrees of freedom. By
performing a series of constrained minimizations for different values of
(1)mo the energy profile may then be mapped point by point. This is the
only way to obtaintransition states when they don't contain additional or
different symmetry elements relative to the neighbouring minima.
To find the.exact transition state after mapping, one has to
start with the Raximum:in the mapping curve and then apply the Newton-
Raphsoh method,: which can lead to a maximum as well as to a
minimum. Transition states are characterized by one negative eigenvalue
for the matrix of second derivatives: and this will appear in the
frequency calculation in the form of an imaginary frequency.
1 .8 CALCULATION OF THERMODYNAMIC PROPERTIES WITH FORCE FILLDS
•
From calculations based on equations (1.2-11) and (1.2-12), the
geometry of a single minimum energy conformation of a molecule and the
a4Sociated steric,energy can be obtained. Such steric energies may be
used directly to obtain energy differences between stereoisomers; energy
differences between conformations are examples where steric energies are
directly applicable; heats of formation are required for other types of
27
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
energy comparisons.
The energies calculated with the use of equations (1.2-11) and
(1.2-12) are appropriate for molecules in a hypothetical motionless state
at 0 K [1a]. Corrections for the thermal energy of translation, rotation
and vibration have to be made to convert steric energies into measurable
properties.
1.8.1 Enthalpy
With the knowledge of the frequencies (see equation (1 .6-5)),
vibrational enthalpy contributions Hvib may readily be obtained using the
statistical-mechanical relationship:
3 N-6 i 1 1 Hvib = RT E1 1
X. [-1_5 + exp X1 . - 11 =
(,1.8-1)
where Xi = hvi/kbT; kb is the Boltzmann constant (kb = 1.38066 10-23 J.K-1),
h the Planck constant (h = 6.6262 10-34 J.$); vi represents the frequency
of the ith vibrational state in s-1. The summation extends over all the
real non-zero frequencies calculated. To that enthalpy of vibration one
has to add the enthalpy of rotation and of translation leading to a term
of 3RT where R is the gas constant (R = 8.314 J.K-1 mol -1). The total
enthalpy is then given by relation (1.8-2):
HT = strain + Hvib + 3RT
28
(1.8-2)
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1 .8.2 Entropy
Like the enthalpy, the total absolute entropy (ST) can be
calculated by an appropriate summation over all the partition functions
which depend on the various normal modes of the molecules.
The total entropy is made up of the translational entropy (Str),
the over-all rotational entropy (Sor), the internal rotational entropy
(Sir), and the vibrational entropy (Seib)'
ST = Str + Sor + Sir +Svib (1.8-3)
These different contributions to the entropy will be described
in turn.
(1) Entropy of tranaation
Str = 3/2 R ln(M),+ 3/2 R ln(T) + R ln(V) + 5/2 R
(211- k)3/2+ R In
h3 NA5/2
(1.8-4)
M is the molecular weight, T the temperature in K, V is the
molar volume. k is the ideal gas constant per molecule, h is Planck's
constant, and NA is Avogadro's number. For an ideal gas at 298.15 K
and 1 atmosphere this equation can be written as:
29
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
O
Str = 28.719 log(M) + 108.023
(Str is expressed in J.K-1.mo1-1).
(1.8-5)
(ii) Entropy of over-all rotation
To obtain this thermodynamic quantity it is necessary to evaluate the
moment of inertia about the centre of mass of the molecule.' This can
be done using a program called COORD made available by the "Chemistry
Department of Indiana University" [ii]. Another needed factor is the
symmetry number of the molecule 's'. This factor has been separated
into two portions, the symmetry number of, the molecule as a whole sw
and the symmetry number of the rotating portion sr. The total sym-
metry number s is the product of all the symmetry numbers of the
molecule:
S = S iT S w r (1.8-6)
sw may be defined as the number of different positions into which a
polyatomic molecule can be rotated and still appears unchanged. For a
non-linear gaseous molecule the entropy contribution for overall
rotation is given by (1.8-7)
r711 8ir2kT 3/2 11/2
Sor 1.5 R + R in ---2-- (Ix I y Iz ) h
30
(1 .8-7)
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
where Ix, Iy, Iz are the three components of the moment of inertia of
the molecule. The other constants have the same meaning as above.
(iii) Entropy of internal rotation
Besides over-all rotation, many molecules exhibit internal rotation
between two or more parts of the molecule. For free internal rotation
the entropy of a Single rotating group is given by:
Sir = R + R In (8Tr3kIrT) (1.8-8)
Q Ir represents the moment of the
rotating fragment about its axis.
(iv) Entropy of vibration
The molecule can be considered as composed of several harmonic oscil-
lators. The vibrational entropy is the sum of the contribution from
each of the normal modes. The total contribution is given by equation
(1.8-9):
X.
S = R z
;xp(Xi)-1 ln(1-exp(-Xd 1 vib [
(1.8-9)
where all the constants have the same meaning as in equation (1.8-1).
To these four expressions for the entropy, an entropy of mixing
has to be added each time there exists a mixture of two (or more)
indistinguishable conformations; one adds Smix = 5.761 J.K-1 .mol -1. For
a comparison of conformations of one particular molecule only Sorb Svib and
31
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Smix would be relevant; for comparisons between different molecules all
entropy terms would be relevant.
1.8.3 Gibbs free energy function G
For each -compound one can calculate the Gibbs free energy
function, given by the relation:
G = H - TS (1.8-10)
where H is the enthalpy, S the entropy and T the temperature. For two
conformations with different enthalpies and entropies, we have at the
temperature T:
AG = AH - TAS (1.8-11)
where the AH and AS would be calculated from the equations in sections
1.8.1 and 1.8.2, which are valid only for gases. Under a pressure of one
atmosphere the AG defined above is called the standard Gibbs free energy
and is noted AG°. The thermodynamical property that one can
compare directly with the results given by NMR experiments are the rota-
tional barrier or activation energy Ae'0, and the standard Gibbs free
energy difference AG° between conformations.
CM-
32
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1.9 A NUMERICAL EXAMPLE
To illustrate the preceding sections, calculation of energy
differences between conformers and of structure of molecules have been
performed. Betdeen cis- and trans-2-butene the energy difference calcu-
lated with the "CFF" program is in good concordance with the experimental
data (AV is 10% higher than the experimental difference, while AG is 5%
lower); this is not surprising: these two conformations were part of the
input to :ind the best parameters for the Force Field.
The geometry of the molecule in its minimum energy is well
reproduced by the calculation: differences of less than 1° are found for
all the valence angles of the two butene isomers (the largest difference
being for the valence angle C-C=C of the cis isomer (0.9° from microwave
results obtained by Kondo et al. [24])).
The performance of the program is better tested with the
barrier of rotation for each isomer: reasonable experimental data are
available and they were not included in the input data. Each isomer will
be considered in turn:
(i) Cis-2-butene
The barrier height in cis-2-butene has been determined to be 1.9
Kd.mol-1 (450 cal .mol-1) from heat capacity data [15], 3.06 and 3.13
KJ.mol-1 (respectively 731 and 747 cal.mol-1) from torsional split-
tings in the microwave spectrum [24] [26]. Making allowance for top-
top splitting in the far infrared spectrum, Durig et aZ. [1?] found a
33
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
value of 2.03 KJ.mol-1 (486 cal.mol-1 ). The strain energy (0)
obtained with the "CFF" program is, by far, too large (at least twice
the experimental result). The best concordance comes from the
enthalpy barrier calculated: a value of 3.01 KJ.mo1-1 (720 cal .mo1-1)
is found at room temperature. The free energy of activation is as
large as that of the strain energy and does not give a close fit with
the experimental data. (AG° = 6.3 KJ.mo1-1 or 1.5 Kcal.mo1-1)
(ii) Trans-2-butene
The barrier in this isomer has been reported by Kilpatrick and Pitzer
[15] to be 8.16 KJ.mol,-1 (1950 cal.mo1-1) from heat capacity data. By
the technique of far infrared spectroscopy the gas phase periodic
barrier was calculated to be 6.28 KJ.mol-1 (1500 cal.mol-1) by Durig
et al. [17].
Once again the "CFF" program seems to overestimate the barrier,
but this time the difference is less important (of the order of 1
KJ.mo1-1). Both the enthalpy of rotaticn and the free energy are in
the bracket of the experimental results; a A1-1 of 6.7 KJ.mol-1 (1600
cal.mo1-1) is obtained at room temperature. Under the same conditions
the free energy barrier is of 8.33 KJ.mo1-1 (1990 cal.mo1-1).
34
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
CHAPTER II
THEORY OF HIGH RESOLUTION NUCLEAR MAGNETIC RESONANCE
2.1 INTRODUCTION
Nuclear Magnetic Resonance has been used for a long time as a
tool to determine the structure of molecules, and also to find the -inter-
actions between molecules of solute and molecules of solvent; the spectra
obtained can be expressed by three phenomenological parameters: the
chemical shift of the nucleus, the coupling constant between any two
nuclei and the spin relaxation times. For the kind of flexible molecules
of this study, coupling constants are likely to be the most useful para-
meters followed by the chemical shifts; the relaxation times are mostly
of very limited use and will not be further considered.
2.1 .1 Chemical shifts
Originally this term was introduced to indicate that a given
nucleus could exhibit different resonance fields (or frequencies), when
contained in different molecules. Nowadays, it also expresses the
difference for nuclei of the same isotope inside the same molecule.
Chemical shifts arise from a field-induced magnetic shielding of the
nuclei by the molecular electrons and are quantitatively described by an
appropriate shielding constant ui for each nucleus. Thus, the field in
35
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
the immediate vicinity of a particular nucleus when an external field Ho
is applied, is given by:
H.1 = (1 - ai) HO (2.1-1)
The shielding ai is really a tensor, but in the isotropiemedia
used in this study only the average will be observed. More commonly, the
chemical shift is taken from the spectrum as the frequency separation in
Hz, from a selected reference signal. However, it is more convenient to
express the chemical shift in terms of a dimensionless scalar 6, defined
by:
..-F 6 =
v-v,= ---1 -1-- x106vref
1", ..,...,
In this thesis the following approximation will be used:
6 = v- vref x106 v
o
(2.1-2)
(2.1-3)
where vo
is the fixed frequency of the probe at a field of 21.14 T (i.e.,
90.00 and 22.63 MHz for proton and carbon-13 respectively). For all the
spectra described in this thesis TMS (tetramethylsilane) was added (about
5% v/v) to each sample. Such internal referencing leaves the intramole-
cular aspects of 6 intact, but compensates part of the intermolecular
aspect of 6.
Proton chemical shifts of a molecule are sensitive to the
36
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
spatial orientation of neighbouring and distant moieties. A number of
factors are involved, and in many cases it is difficult to recognize
general trends. The various mechanisms responsible for Ighielding effects
will be discussed in detail in section 2.3.
2.1.2 Coupling constants
High resolution spectra frequently exhibit an abundance of
hyperfine structure. Such fide structure arises from an indirect
coupling between the nuclear moments pi transmitted from nucleus to
nucleus through the paired electrons comprising the valence bonds. Such a
interaction between two spins i and j can be expressed as follows:
E = -Kijpi • uj
or E = /i • /j
(2.1-4)
(2.1-5)
pi and are the magnetic moments of spins i and j, whereas /i and /j
are the spin vectors. The scalar Jij is called the coupling constant and
is usually expressed in Hz. From equation (2.1-5) it is clear that J is
field independent in contrast to, the chemical shift (v-vref) which is
linearly proportional to Ho.
The interaction between the el'ectrons and nuclei arises through
the interaction of the nuclear moments, either with the orbital motion of
the electrons or with the electron spin. It is important to :tote the
37
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
conditions under which coupling between two nuclei can occur. Firstly,
since the interaction is transmitted via a perturbation of the electron
wave function, the nuclei must be in the we molecule..\ Secondly, the
nuclei must experience a constant interaction over a time interval which
is long compared to the reciprocal of the coupling constant expressed in
frequency units. A chemical exchange process which separates a given
pair of nuclei in a time shorter than this will effectively remove the
spin coupling; furthermore, the relaxation times of both nuclei must be
sufficiently long.
Both chemical shift and coupling constants are subject to time
averaging: rapid intramolecular motion between conformers in which a
particular nucleus has different chemical shifts or coupling constants
will produce a spectrum appropriate to the time average only of these
parameters. Slow interconversion produces a superposition of the con-
former spectra.
2.2 'THEORY OF THE ANALYSIS OF NMR SPECTRA
2.2.1 Hamiltonian operator
We consider a molecule containing n nuclei with magnetic
moments pj in.a magnetic field Ho. The actual field at a given nucleus
is altered owing to intramolecular magnetic effects and intermolecular
interactions. Assuming that all these shielding eff6cts are described
by a scalar shielding constant, the field at nucleus j is expressed by
equation (2.1-1).
38
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Meinteraction energy of nucleus j with th e field Hj • is
obtained through relation (2.2-1)
E = -0.J-H. = J w..I. (2.2-1)
where w.J = Tj (1 - a.)-H 0.
If nucleus j is indirectly coupled to the remaining nuclei,
there is, in addition to (2.2-1), the spin-spin energy given by equatiqn
(2.2-2).
E = - E Kjk j u .uk = = n E /./
jk j k (2.2-2)
The total energy for nucleus j is the sum of equations (2.2-1)
and (2.2-2):
E = - n NJ . 1J . E ) k Jk k
(2.2-3)
The Hamiltonian operator, H, for the system is obtained by
summing over j, and is described by relation (2.2-4):
- Ti (E w../i j E
k E
31( 3 I..'1( ) i J
(2.2-4)
It is convenient to write H in angular units; by choosing 71 for
the unit of angular momentum we can express H by equation (2.2-5):
39
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
•
H = - (E v. j
Izj . + E k E Jjk j k ) (2.2-5)
(If Ho is taken to lie along the z axis; vj is then the value of vj along
z, with 2rv.J = (0. and Jjk Jjk .) 27
The problem is then the classical one of finding the stationary
states of a given spin system, i.e., of finding a set of N spin functions
which are eigenfunctions of H: 1,3
Htp.J = A. 4). J J
with j = 1, 2, . . . , N (2.2-6)
ujLetusconsider .(j = 1, . . . , N), a set of zero-order
initial spin functions: they need to be an orthonormal set of eigen-
functions of I . These u form a basis and all the tyj can be expressed
as linear combinations of these functions:
tyj = E akj uk (2.2-7)
Equation (2.2-6) will be written as:
Eakj (H-Xj) uk = 0 (2.2-8)
The result of the application of H on uk can be developed as a
linear combination of basis functions uz:
H uk = E k u
1.4 40
(2.2-9)
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
where H2.1( = <u 1H1uk>.
Finally we get a set of N equations for the akj:
vEaki (Hzk - Xj6k2) = 0 (k = 1, . . . , N) (2.2-10)
' This set has a non-trivial solution if and only if the deter-
minant of the coefficients vanishes:
,f 1 - 1 = 0Hu Xj dzk (2.2-11)
Equation (2.2-11) is an algebraic equation of the Nth degree
for the N characteristic roots Ai. Substituting any one of these, for
example Xj, into equation (2.2-10) leads to a set of equations for the
akj. Only (N-1) equations are independent, but a normalization require-
ment is imposed on the tpj. a Nth independent relation is obtained:
Ea` I k kj
(2.2-12)
The general procedure to solve the, problem is first to find the
set of initial functions uj, which need to be orthonormal eigenfunctions
of Iz' and second to find the components of H as defined by Oiation
(2,2-9).
To reduce the labour involved in the determination of the
components of the Hamiltonian, use of Pasic symmetry functions rather
than of simple,products (aa, as . . .) is made. As a result the basic
41
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
functions can be divided into classes according to their values of Fz
(Fz = E Iz (i)) and their symmetries (there is no mixing between functions . 1
with different values of Fz, and between functions of different symmetry).
The Hamiltonian can be further factorized when the system is
composed of magnetically equivalent nuclei (this is sometimes called the
composite particle method which is described in the following paragraph).
To facilitate maximum factorization of the secular determinant
the X approximation car' be used in some particular cases. The method
and the'necessary condition for application will be outlined in a later
paragraph.
2.2.2 Subspectral analysis using the composite particle method [18]
A set of nuclei is said to be chemically equivalent if each
nucleus of the set has the same electronic environment: all nuclei of a
chemically equivalent set have the same shielding constant o. This
definition has been extended to include sets of .nuclei having the same
environment when averaged over a suitably long period of time; the latter
kind of equivalence is important in molecules where internal rotation
about single bonds may occur. In many molecules ccupling constants from
nuclei within a chemically equivalent group to any particular nucleus
outside the group are equal: the group is then said to be magnetically
equivalent.
To the previously mentioned simplifications, the properties of
a magnetically equivalent group of nuclei allow a further factorization
of the Hamiltonian.
42
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
(i) Coupling between spins within the group does not contri-
bute to the spectrum and can be omitted.
(ii) There is no mixing between wave functions having a
different eigenvalue for the square of the total spin moment
of the group, F2.
It is worthwhile then to define the total spin for the magneti-
cally equivalent group
F(G) = E r(i) (2.2-13) i in G
Each group can be considered as a "composite" particle of
moment F(i) (the numbering is now done by magnetically equivalent group).
Defining a new basis from linear combinations of the simple basis (for
example a6, (la) the Hamiltonian can be reduced into the form:
H = E v, Fz(i) + E ji4 F(i)•F(j) (2.2-14) ' i<j J
where the summation is over the different magnetically equivalent groups.
For a group of n equivalent spin h nuclei, the maximum value for F (spin
of one group) is n/2. Allowed values of F are n/2, n/2-1, . . . , 1/2 if
n is odd; if n is even F can go from n/2 to 0. In the first case (n + 1)/2
spin states are present and (n/2) + 1 in the second. For a spin state of
total spin quantum number F, there are (2F 1) possible eigenvalues for
the Fz of the considered group. This eigenvalue ranges from F to -F
(with aFz = 1). To describe each possible spin state the notation first
43
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
introduced by Whitman et al. [19] will be used: S, D, T, Q, Qt, Sx, . . .
for states with eigenvalues 1/2, 1, 3/2, 2,'3 (S stands for singlet, D
for doublet, T for triplet, Q for quartet, Qt for quintet, Sx for sextet,
etc.). Each spin state has an associated statistical weight g--degene-
racy of the representation in the group--given by equation (2.2-15):
_ (2F+1) n! 9 (n/2-F)! (n/2+F+1)!
(2.2-15)
This equation applies for a state with quantum number F of a
group of n nuclei.
As suggested previously, additional factoring is present when
the Hamiltonian has a further symmetry Quirt and Martin [20] have
developed this Hamiltonian in the case of a twofold symmetry. In NMR
studies such symmetry is usually the result of a plane or twofold axis of
symmetry in the molecule, taking the conformation as an average over an
NMR time scale. By rearranging the expression (2.2-14), the Hamiltonian
can be rewritten as follows:
z vi FZ(i) + z Jij F(i)•F(j) i<j
k J44 [F(i)•F(k) F(i)*F(ki)]
+ kCF (k) + fp')] + k Jkk , F(k).F(k')
44
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
E [Ja[F(k),'F(2) F(k 1)*F(2')] k<2,
+ Jkk [F(k).F(V) F(k 1)•F(Q)1] (2.2-16)
The labeling follows the one used by Quirt and Martin [20]: magnetically
equivalent groups which are transformed into themselves by the twofold
symmetry operation are labeled i, j . . All other groups must appear
in pairs, labeled k, 2, . . ., such that the symmetry operation inter-
changes the primed and unprimed members of each pair. The two different
coupling constants (usually cis and trans) which connect pairs k and 2.
are written Jkz and Jzk.
2.2.3 Subspectral analysis using the X approximation
The X approximation can be defined as a neglect of off-diagonal
elements connecting diagonal elements of widely different numerical
values, i.e., Hmn « IHnn-Hmml . The familiar "first-order" treatment is
the extreme case in which all the off-diagonal elements are neglected.
More often, only some of the coupling interactions are weak; this states
that a coupling constant Jii is small relative to a difference in Larmor
frequencies v.1-v. (a less qualitative definition is that J.1 ./(v.1-v.J) is
equal to, or smaller than, the experimental linewidtii). The term Jij /2
may then be neglected wherever it occurs as an off-diagonal element,
since the difference between the connected diagonal elements includes the
quantity v . -vJ This produces valuable additional factorization of the
45
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
secular equation.
2.2.4 General procedure to analyze NMR spectra
The calculation of NMR spectra may be divided up into several
steps:
(i) Use is made of a complete set of basic symmetry functions
as appropriate linear combinations of basic product functions
(aa, as . . .).
(ii) The matrix elements of the Hamiltonian can be deduced
following simple rules. The diagonal elements are found using
relation (2.2-17):
N E = z v. ((i ).) + 1/4 ZEJ.. T.. jmn i zim . . ij ij 1 1 l<J
with ((Iz)i)m = + h if nucleus i has a spina in um
- 1/2 if nucleus i has a spin 8 in um
and Tij = q 1 if i and j are parallel in um
- 1 if i and j are anti-parallel in um
The non-diagonal elements follow relation (2.2-18)
Hmn
= 11 U Jij
(2.2-17)
(2.2-18)
with U = 1 when um differs from un by an interchange of spins
i and j.
0 otherwise.
46
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
The matrix elements between linear combinations of basic products
are evaluated through expansion.
*The energy levels are solutions of the secular equation
(2.2-11).
*Frequencies are obtained by taking the difference between
energy levels using the selection rules for Iz, Fz(G) d the occurring
symmetries.
2.3 CHEMICAL SHIFT AND STRUCTURE
2.3.1 Classification of shielding effects
It has been pointed out earlier (see 2.1) that the field
experienced by a nucleus in an atom or a molecule differs from the
applied field Ho: a free atom experiences a field which is slightly
less than Ho
due to the motion of the electron(s) around the nucleus.
Extension of the treatment of shielding in free atoms to that
of atoms in molecules is complicated by several factors. An under-
standing of these factors is important as they are related to the way'in
which molecular structure affects the chemical shift. When a hydrogen
is chemically bound, the circulation of electrons is modified in two ways.
Firstly, the electron density at the proton will not be the same as in
the hydrogen atom. Secondly, the distribution of electrons around the
proton is no longer spherically symmetric. Chemical bonding can also
restrict the circulation of electrons, the degree of restriction being a
function of the orientation of the bond with respect to the applied field.
47
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
In the theoretical treatment of shielding in molecules, the
shielding is separated into two terms: the first term is a function of
electron density at the nucleus, the second term takes into account the
restriction imposed on circulation of electrons by chemical bonding.
They are referred to respectively as local diamagnetic and paramagnetic
shieldings.
In addition to the local shielding effects, significant contri-
butions to the shielding may arise from the circulation of electrons
associated with other atoms or•groups in the molecule. A shielding of
this type is called "long-range shielding." This type of shielding
arises only if the magnetic suspectibility of the electrons is aniso-
tropic (i.e., if the circulation induced by the applied field is different
for some orientations of the molecule in the applied field from others).
These effects are referred to as "remote effects" or as "neighbour aniso-
tropy contributions."
For organic compounds chemical shifts are measured, most of the
time, in the liquid phase. In this case, intermolecular effects must be
included in any discussion of chemical shifts. A solvent can contribute
to the shielding of an atom in a molecule by its influence on the
electronic structure of the molecule and by direct magnetic field contri-
butions in case of a magnetically anisotropic solvent. Choosing a non-
reactive internal standard such as TMS minimizes some of the unwanted
solvent effects.
Many effects thus contribute to the value of 6, and most of the
time these 3's are not direct indications of the electron density around
48
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
the nucleus being investigated. Quantitative quantum mechanical evalua-
tion of shielding in various molecules appears formidable, if not hope-
less at the present time. For many systems this shift can be evaluated
by empirical correlations; when these correlations fail, contributions
such as from neighbour anisotropy are often qualitatively invoked. Only'
when deviations are encountered, the molecule is examined to see what
property it possesses that could account for the observed discrepancies.
In the present thesis the analysis of chemical shift variation
with respect to the temperature as representative of variation in
structure will follow the aboye described qualitative approach. Chemical
shifts of many olefins have already been investigated and several trends
in their variations have been suggested (see for example Martin and
Martin [22]).
2.3.2 Interpretation of proton chemical shifts
Despite the disparity of the different effects involved, some
semi-empirical relations have been put forward as an interpretation of
proton chemical shifts in alkenes. In this section, contributions due to
magnetic anisotropy of C=C, C-C and C-H bonds and to electric effects of
the C-H dipoles, also due to non-bonded H....H interactions, are reviewed.
These effects are particularly useful for the interpretation of the methine
proton of an isopropyl group.
(i) Magnetic bond anisotropy
The existence of field-induced moments at atoms in the molecule other
49
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
than the one undergoing the NMR transition, can be felt at the nucleus
being investigated (neighbour anisotropy contributions). This effect
can be best explained in an acetylene molecule HC-CH. The field at
the proton will be strongly dependent upon the orientation of the mole-
cule with respect to the direction of the applied field. When the
applied field is parallel to the internuclear axis, the magnetic field
generated from diamagnetic electron circulations along the CEC bond
will shield the proton, while in a perpendicular orientation, this
same effect around CEC will result in deshielding at the proton. The
magnitude of the induced moment at the CEC bond (and hence the field
at the proton from this neighbour effect) for the parallel and perpen-
dicular orientations will depend upon the susceptibility ofkthe CEC
bond for parallel and perpendicular orientations, xi/ and x1 respec-
tively. This effect can be paramagnetic as well as diamagnetic: both
paramagnetic and diamagnetic neighbour effects must be qualitatively
considered when interpreting proton shifts. With axial symmetry
(along z for example) in solution (averaging factor) the effect (for a
three dimensional molecule) is expressed by the McConnel equation [22].
1 A a= T
R-3 'x (1-3 cos20z) (2.3-1)
where 6x stands for (X71-x)and ez is the angle between the z-axis and
the vector joining the source of the effect and the atom under investi-
gation, R is the length pf this vector. In the absence of special
substituent effects, the anisotropy of the double bond in alkenes will
t 50
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
be the dominating factor that influences the resonance frequencies.
It is generally agreed today (see Gunther and Jikeli [23]) that pro-
tons above or below the plane of the double bond and near the z-axis
(see figure (2.3-1))are shielded, whereas deshielding exists in the (x, y)
plane. The early calculations, made by Till.* [24] and Pople et aZ.
[25] disagree with respect to the sign of the effect near the x-axis,
where shielding [25] as well as deshielding [24] has been predicted.
Only the second alternative seems supporteu by the majority of experi-
mental findings; for example, in s trans-1, 3-butadiene the protons
near the x-axis of the second double bond are deshielded [28].
Similar results are found for the inner protons of the diene systems
of 1, 3-cyclopentadiene and 1, 3-cyclohexadiene [21.
In another calculation ApSimon et al. [28] found that shielding
might also occur in the (x, ',y) plane of the double bond. Then, to
substitute the older picture for the shielding cone of the C=C bond
represented by model A on 'figure 0-1) a new model (B on the same
figure) was proposed. however, in view of the experimental data used, •
Rummens [29] as well as Gunther and Jikeli [23] believe that it is
premature to discard model A in favour of model B. The latter authors .
estimate that model A is supported by more experimental evidence (for
example in 1, 3-butadiene the central protons that come close to the
y-axis of the second double bond are the most strongly deshielded).
However, it should be noted that in model A the shielding cone
is obtained by using the McConnell equation (2.3-1) which is applicable
only to bonds with axial symmetry; furthermore, the results emerging
51
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
z
(a)
/2
A
(c) C
(b)
FIGURE 2.3-1 a) Definition of the coordinate system (Oxyz) b) Shielding and deshielding regions due to magnetic aniso-
tropy of the C=C bond; model A according t.,) Pople [32], model B according to ApSimon et al. [28].
c) Definition of R and m in Vogler's model [.32].
52
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
from any point dipole approximation must be used with circumspection
in unsaturated hydrocarbons; this approximation is valid only for pro-
tons which are remote from the anisotropic centre'of the magnetic
dipole (here the double bond). It has also been noted by Kondo et
[30] and confirmed by Vogler [32] that an R-2 dependence is present to
account for the total effect. The modification on equation (2.3-1)
performed by ApSimon et al. [28] is more appropriate for a double bond
anisotropy, which would make model B more suitable.
To find the proton shieldings in conjugated hydrocarbons,
Vogler [31] calculates the local anisotropy contributions in the frame-
work of an extended theory using the coupled Hartree-Fock perturbation
theory. He finds an anisotropic shift Ad depending on both R and 0
(as these are defined in figure (2.3-1)). Only for small R (< 2 A) and 0
small 0 (< 15°) the theory gives a shielding. With R > 3 A, only
deshielding can occur independent of angle 0; furthermore, the
difference between minimum and maximum anisotropic effects is much
smaller with the Vogler theory than with the ApSimon procedure. For a 0
distance of 2A this difference goes.from 0.5ppm (Vogler) to 1 .5ppm
(ApSimon). In the case of ethylene the difference between experimental
data and Vogler's value is 0.02ppm; a value of 0.29ppm represents the
contribution from the local anisotropy to the shielding.
Not only the anisotropy of a C=C double bond exists, but also
the anisotropy of a C-C or a C-H is not negligible. It has ben
indicated by several workers (see for example references [32], [28])
that the anisotropy of a C-C bond is of the same order of magnitude as
53
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
that of a C-H bond. However, in a recent study, ApSimon et al. [33]
have concluded that it is impossible to calculate reliable magnetic
susceptibilities and susceptibility anisotropies of C-C and C-H bonds
from the collection of chemical shifts reported by Pretsch et al. [34],
while reasonably reliable values for the magnetic anisotropies of C=C
double bonds can be obtained.
Raynes [35] has developed an expression for the calculation of
the contributions of magnetically anisotropic X-Y bonds of freely
rotating -XY3 groups to the shielding of protons of a freely rotating
methyl group elsewhere in the molecule (both groups must have coplanar
axis of symmetry). With slight modification the expression can be
simplified to calculate the contribution of the same group to the
shielding of a fixed proton, or the contribution of a fixed C-H bond
to a freely rotating methyl group, These expressions are applicable,
only for remote moieties.
(ii) Non-bonded interactions
In crowded molecules the local anisotropy effect cannot account for
all of the chemical shift variation of the protons. several causes
have been suggested for these discrepancies. The original idea by
Reid [36] that a shift to lower field could be due to Van der Waals
interactions between a pair of crowded hydrogen atoms, has been
favoured by Jonathan et al. [37] and Memory et a:. [38], though Pople
et 2Z. [39] have been critical of some of Reid's assumptions. Bartle
and Smith [40], however, have preferred to attribute the entire
54
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
discrepancy in phenanthrene to sigma-bond anisotropy effects, con-
cluding that thgre is little, if any, Van der Waals contribution to
the chemical shift of the overcrowded proton in this molecule.
Finally, Cheney [41] has proposed a bond-polarization mechanism where-
by non-bonded electron repulsions between overcrowded hydrogens are
alleviated through charge transfer on to the attached carbon atom;' by
this method he has obtained the empirical expression (2.3-2) relating
the magnitude of the steric shift 6H to the component of the inter-st •
hydrogen repulsion force directed along the H-C axis.
< st . - 105 E cos ei exp(-2.671 r.) O .
(2.3-2)
(where ri is the H....H distance, ei the angle between the C-H bond
and the H....H connection).
On the purely theoretical side, Marshall and Popll [42] and
Yonemito [43] have provided, respectively, variation and 'perturbation
methods for estimating the downfield shifts due to Van der Waals
interaction in simple systems. In both cases the shielding constant
varies as R-6. For a distance or four Bohr radii (1 Bohr radius
= 5.29 10-1 °m) Yonemoto [43] find.. a deshielding by 0.3ppm, which is
three times larger than the result reached using Marshall and Pople's
[42] expression. According to C.W. Haigh et al. [44] Yonemoto's
method gives predicted down-fi ld shifts due to Van der Weals inter-
actions in aromatic Moletules 'n excellent agreement with the observed
discrepancies. However,. it has been noted by C.W. Haigh et al. [44]
55 p
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
that the relationship of Yonemoto which describes a system of two isolated
hydrogens interacting at long range, cannot strictly be applied when
the separation of the nuclei is less than about 7 or 8 Bohr radii, as
electron exchange effects then become non-negligible; in the range
(< 5-Bohr radii) at which intramolecular steric deshielding of protons
becomes important, it is the repulsive exchange forces and not the
attractive dispersion 'forces which dominate the interactions between
the hydrogen atoms.. •
(iii) Electric field contribution
Even in those systems where the local diamagnetic term dominates the
observed proton shift, there are alternative interpretations for the .
trends. In addition to the trends in the population of the hydrogen
(78) orbital as a consequence of the electronegativity of the attached
group, Buckingham has proposed [45] an electric field model to account
for changes in the electron density of a bound hydrogen atom: the
bonding electron density will be distorted in an attempt to avoid the
negative region of the space. If the electric field arises from
within the molecule (polar group, polarized bonds this effect will
not be averaged to zero: a distortion of the bonding electron density
can result. The contribwoon, calculated by Buckingham [45], to the
proton shielding from this effect, AGE, is given by equation (2.3-3):
AGE = A Ez + B E
2
56
(2.3-3)
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
where A and B take the respective values A = - 2x10-12 and B=-1x10-18esu
for protons. If we take pcH = 0.33D, with the positive end at the
hydrogen, only the linear term is of appreciable value (0.08ppm) for
the cis-2-butene (the two methyl hydrogens being in anti-position with
respect to the olefinic proton). The majority of applications of
equation (2.3-3) have been to the interpretatioh of the observed
,shielding brought about by polar substituents, protonation, and inter-
molecular interaction. Day and Buckingham [46] advise caution in such '
applications. They calculated the changes in the 19F shielding of HF
due to a negative point charge and compared the results with those
predicted assuming that the HF molecule was in a uniform electric
field equal to the field produced by the point charge at the fluorine
nucleus. Poor agreement was obtained eves when the point charge was 0
as far as 8A from the fluorine nucleus. This result suggests the need
to allow for field gradients. Attention to this question has been
given specially in the case of carbon-13 shielding and will be dis-
cussed in the next section.
2.3.3 Interpretation of carbon-13 chemical shifts
TheWidespread interest in carbon-13 NMR has ensured that the
shielding of this nucleus has received a great deal of attention at both
the semi-empirical and ab initio levels of approach. The relative
complexity of quantum chemistry has led to consider the chemical shift in
terms of constitutive or substituent representative parameters. The type
of molecules studied in this work made the theoretical approach virtually
57
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
impossible. Only correlations between carbon-13 chemical shifts and
structural and physicochemical parameters can be attempted.
(i) Influence of the steric effect
The carbon chemical .shifts are usually much more sensitive to steric
interactions than are proton chemical shifts, and non-additive carbon-
13 substituent effects have been discussed in terms of steric crowding.
The a and $ substituent parameters (substitution on the closest and
next to closest atom) which are usually low field, are influenced by
steric factors, but the most noticeable contribution occurs for sub-
stituent groups separated by three bonds froM the carbon of interest
(y-effect), as observed by Buchanan and Stothers [47] and Grant and
Paul [48], for example. It was noted by Grant and Cheney [49] that,
in this case, the substituent increments reflect the angular and
distance dependence of interacting groups. The mechanisms of the
steric effect on carbon-13 chemical shift has been explained by Grant
and Cheney [49]. A model has been proposed by Cheney and Grant [50]
to explain the observed shielding of the carbon t. ler the steric
influence of a remote substituent (y-effect). This wdel involves an
electronic charge polarization in the C-H bond as a result of the non-
bonded hydrow-hydrogen repulsive forces. The increase of ,negative
charge is associated with an electron expansion causing a decrease of
<1/r3> and of the paramagnetic term (upfield shift). Similar to
proton shifts a semi-empirical expression has been derived by Grant
and Cheney [49] for the steric contribution to carbon-13 chemical
58
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
0 shift of a C-H bond:
(5ste
13c = 1680 E cos ei exp(-2.671 ri) ppm
i
(2.3-4)
where the various parameters have the same meaning as in expression
(2.3-2). This formula is reasonably successful in predicting the
chemical shifts of cyclohexane and derivatives (as demonstrated by
Dalling and Grant [5/]), but it fails quantitatively in other cases as
for tricyclene derivatives as shown by Lippmaa et al. [52]. It is now
pointed out that the C-H polarization theory is insufficient, since
diamagnetic y-effects are caused by interactions of many other groups
than hydrogens.
Schneider and Weigand [53] applied the steric perturbation to
shielding as well as deshielding situations, to interactions with
heteroatoms and to carbons not in y-position. For that they proposed
to define the shielding force vector on the Ci-H bond by equation
(2.3-5), which is derived from the Warshel and Lifson [54] potential
for non-bonded interactions:
F = 0.6952x10 (18e/r*) [(r*/r04 -(r*/r07] cos 8. (2.3-5)
This,equation applies to hydrogen-hydrogen interactions,
(eh= 4.109 10-3, r* = 3.632) as well as to carbon-hydrogen interactions
(e = 26.10x10-3, r* = 3.575); ri and ei have the same meaning as in
equation ;(2.3-2). Arguing that repulsive non-bonded interactions are
59
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
extremely sensitive to sma I change in r, they have applied equation
(2.3-5) only to fully relax d molecular structures as obtained by
Force Field energy minimization. They found an adequate linear
correlation between resonance shift and the force previously defined
(despite its dependency upon the Force Field used to find the molecu-
lar structures).
Seidmaniand Maciel [55] have attempted to explore the geometri- .
cal dependence of .methyl-group shielding in systems such as alkenes by
making ab initio calculations using the modified-INDO'finite perturba-
tion theory (FPT/INDO). The conformational dependences of the methyl-
group carbon-13 •shieldings in the n-butenes were qualitatively as
predicted by y-effect trends; nevertheless they,find that this effect
cannot be explained alone by the steric mechanism proposed by Grant
and Cheney [49]. For Seidman and Maciel [55] carbon-13 shielding
appears to depend, in part, on the precise details of the electron,
distribution at a carbon atom rather than on the total electron
density. Calculations for various alkanes [55] point to the conclusion
that the y-effect is related to the details of the conformation of the
CH3-C-C-CH
3 system. Similarly, Gorenstein [56] argues against the
attribution of y-carbon carbon-13 chemical shifts in hydrocarbons to
electron polarization and increased carbon electron density arising
from steric interactions. He proposes that it arises from a
generalized gauche-effect attributed to valence bond-angle and
torsional angle changes. Advantages claimed by Gorenstein for this
interpretation include explanations of upfield carbon-13 shifts in
60
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
cyclohexanes (between gauche and trans) and of the 1, 5-interaction.
In contrast to the well established upfield steric effect of
y-substituents, downfield shifts are observed for groups separated by
four bonds (1, 5-interaction) in a syn-axial orientation as found by
Grover et al. [57]. This alternation in sign between 1, 4- and 1, 5-
interactions cannot be understood by the bond polarization model.
(ii) Correlations between carbon-13 shift and electronegativity
Even if the downfield shift of a carbon atom substituted by an electro-
negative group has been known since the early days of carbon-13 NMR, a
quantitative relation between carbon-13 shift and electronegativity
has only been derived recently. In their study of the dependence of
6C-X in methyl, ethyl and phenyl derivatives on the electronegativity
of the X substituent, Spiesecke and Schneider [58] have observed the
expected increase of the chemica\shift with the electronegativity of
X. Several correlations have been proposed for.certain classes of
compounds. A more general representation of the dependence of carbon-
13 shifts on electronegativity results from a study made by Phillips
and Wray [59]. The screening of a carbon atom, substituted by four
ligands, is expressed in terms of effective electronegativities,
considered as being simple perturbations of the Higgins electronegati-
vity of a group by other substituents.
(iii) InfZuence of bond polarization electric field effect's
Like for proton shifts, an electric field effect has been invoked to
rc
61
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
explain the discrepancies between the theoretical and observed values
of the chemical shifts. Equation (2.3-3) is still valid and the
shielding of a nucleus is expressed as the sum of square electric
field effects, E2, and linear field effects E. Parameter A of equation
(2.3-3) is now positive and takes a value of 30.x10-12 according to
Horsley and Sternlich [60]. This means that if the shielding of a
carbon atom of a C-H bond increases when an electric field acts on the
molecule, the proton of the same C-H bond is deshielded. The
deshielding. symmetry distortion of a Ci atom electron cloud by a
fluctuating C-X dipole is given by equation (2.3-6) where ri is the
distance from the middle of the C-X bond to Ci, Ix is the first
ionization potential of X, and Pcx the polarizability of the C-X bond.
‹E2
3 Ix Pcx r.-6 (2.3-6)
The polarization of electrons at a Ci-Y bond by an intramolecular point
charge? has been approximated by Schneider and Freitag [61], by
equation (2.3-7):
AQ = P Z-1 7r
-2 cos
c.y c.y c.y (2.3-7)
where AQc is the charge separation induced by a static electric 1y
field, P the polarizability of the C.-Y bond, Z its length, r Pc •y ciy
its distance from 8 its angle with the acting electric field vector.
Neglecting higher order terms, equation (2.3-7) represents E and is
62
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
expected to be observable over large intramolecular distances, whereas,
owing to the r-6 term, the Van der Waals effect,<E2 , falls off
sharply. In view of some inadequacies of equation (2.3-3) (see the
electric field effect on the proton shift) it has been suggested to
take into account the effect of the field gradient. Batchelor [62]
has demonstrated that an improved description of linear field shifts
is achieved by the addition of an extra linear term arising from the
field gradient at the nucleus of interest. Batchelor divided the
shielding into contributions from uniform-field linear electric field
(i.e., quadratic field-dependent contributions are ignored) and from
field-gradient electric field shifts. His method of distinguishing
between the two contributions is to determine first the shielding
change for quaternary carbon atoms for which the uniform-field contri-
bution is ignored and the total of the observed shift is attributable
to the field-gradient contribution. Raynes [63] expresses some doubts
about the validity of such a procedure, in particular because of the
omission of long-range factors affecting the local site symmetry.
This may be of relevance since Batchelor data fitted the parameters
required to describe the uniform electric field shift and the field-
gradient shift. He showed also that these parameters depend upon the
site symmetry of the carbon-13 nucleus. These ideas were later applied
by Batchelor et al. [64] to conformational effects. Most of the
information in organic molecules comes from the orientation of the
electric field in the molecule; the field gradient is much less
orientation-dependent (20% frbm Batchelor's estimation), The authors
63
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
introduced a plane of zero shift; if the carbon possesses a z-axis of
symmetry, this plane is the (x, y) plane. A charge placed in this
plane would not affect the chemical shift of this atom if the first
order of the electric field is the only term considered. The direc-
tion of any uniform field shift induced at this atom will depend on
whether the field source lies above or below this plane: an upfield
shift is caused by a positive charge placed on the negative side of
the (x, y) plane. The positive side of this plane is defined as the
one containing the most polarizable bond(s) attached to the carbon
under study. Conformational information should be uncovered by the
knowledge of the position of this plane and of the charges creating
the uniform field.
Interested by the same effect, Seidman and Maciel [65] used a
modification of the'finite perturbation 'theory of the INDO theory to
calculate the effects of point chargeymonopoles with a proton
charge) and dipoles on‘carbon-13 shielding in ethane, ethylene, ace-
tylene, when these charges are about 4 tc 5 bonds from the different
carbon-carbon bonds (5 to 7A). One of the more important findings of
Seidman and Maciel is the much greater effect of the monopole or point
dipole when located on the x-axis (see figure (2.3-1) for the definition
of this axis) as compared with location on y- or z-axis. For example
in ethylene, the closest carbon to the charge displays a shielding of
2.62 ppm with the charge on the x-axis compared 'to -0.03ppm and 0.08ppm
when the charge is on the z- and y-axis respectively. They also
related_the polari-zation-of-o- and-m-electrons -for-ethylene-and
64
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
acetylene to the changes of shieldings. The polarization of C-H bonds
is suspected to play an important role.
2.4 COUPLING CONSTANTS AND STRUCTURE
2.4.1 Description of coupling
In an unsymmetrical molecule of the type X-CHa = CHb-Y
(assuming that X and Y have no influence) the Ha and Hb resonances appear
as doublets. The phenomenon has its origin in the magnetic field
associated with each individual spinning proton. The magnetic field
associated with the spin of the nearby proton, Hb, contributes to the net
field experienced by Ha. If Hb.has a spin, its magnetic moment is
aligned with the applied field and the total magnetic field. at Ha is
slightly stronger than that provided by the applied field of the NMR
instrument alone. Consequently, less applied field is required to
. achieve resonance,thap in the absence of Hb, and tie finds a slight down-
field shift (corresponding to a upfrequency shift). But only half of the
Hb nuclei have a spin; the rest haves spin in which the magnetic moments
are aligned against the field. For these molecules, the net magnetic
field at Ha
is slightly weaker than that given by the applied field
alone. The NMR spectrometer m at th'n provide slightly more magnetic
field in order to achieve r
downfrequency shift).
The nature of the spectra will depend upon the number of bonds
through which spin spin coupling can be transmitted. For proton-proton
onance condition with Ha (resulting in a
65
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
coupling in saturated molecules of the light elements, the magnitude of
the coupling constants falls off rapidly as the number of bonds,between
the two nuclei increases and is usually negligible for coupling of nuclei
separated by more than three bonds. Long-range coupltpg (coupling over
more than three bonds) is often observed in unsaturated molecules. The
relevant mechanism for the r-electron contribution to the coupling
between non-bonded protons (in situation as in X-CHa = CHb-Y) is the
exchange coupling of the a and 7 electron spins. Once the /s orbital
around proton Ha has been magnetically polarized, via "contact inter-
action" (this mechanism is described in the next section), by the nuclear
spin of Ha, it in turn polarizes the spin of the carbon electron in the
sp2-a orbital of the CH bond. The second electron is affected by the
electron to which it is bonded because their spin must be antiparallel,
so that the spin polarization is transmitted from one to the other with a
change of sign. Then, as postulated by McConnell [66], a a-7 exchange
polarization effect between the sp2-a electron on the carbon and the 7
electron on the same atom transmits the spin polarization to the 7 cloUd.
Because of the extensive delocalization of the it system, this r electron
spin polarization is easily spread over the whole molecule. The spin
polarization at an atom can be coupled back to another CH bond, where it
magnetically interacts with the proton (here Hb), thus ensuing the spin-
spin coupling of distant protons. In contrast to this, for protons separated
by carbon-carbon single bonds, the magnetic polarization is entirely
transmitted through the a bonds.
66
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
2.4.2 Nature of the coupling [67]
There are various contributions to the magnitude of the spin-
spin coupling constants; they are transmitted via the electron density in
the molecule and consequently are not averaged to zero as the molecule
tumbles (in the liquid state). Major contributions come from three
effects: the spin-orbital effect, the magnetic dipolar effect (indirect
or through-space coupling) and the Fermi-contact coupling which accounts
for most of the effect.
(i) spin-orbital effect
It involves the perturbation that the nuclear spin moment makes on the
orbital magnetic moments of the electrons around the nucleus. For a
nuclear spin quantum number of 1/2, the orbital magnetic moments of the
electrons will depend upon the nuclear magnetic quantum number IN
(= ill); the field at the nucleus being split will depend on the
moment of the other nucleus. The Hamiltonian for the interaction on
the first atom that is felt at the nucleus being split is:
H = n-2 1N .% 3r
(2.4-1)
where yN and ye are the gyromagnetic ratio for the proton and the
electron respectively. L is the electron orbital angular momentum, I
the nuclear spin moment, and r is the distance between the inter-
acting atoms.
67
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
(ii) dipolar effect
This mechanism corresponds to a polarizatiOn of paired electron
density in a molecule by the nuclear moment. The polarization of this
electron density depends on whether I = ;5 or I = -11, and the modified
electron moment is felt through space by the second nucleus. The
di polar interaction Hami 1 tonian between the (el ectron magnetic moment
S) and the- riuole'ar magnetic moment 71Y) can be written:
8 - 30.zq(S.r))Ye YN k r3 ' r (2.4-2)
The interaction between the electron spin moment and the nuclear
moment polarizes the spin in the parts.of the molecule near the
splitting nucleus. This spin polarization spreads over the entire
wave function, and modified the field ,at the splitting nucleus, which
acts directly through space on the nucleus being split. The direc-
tion of, the effect depends on the I value of the splitting nucleus.
(iii) Fermi-contact term
This term involves a direct interaction of the nuclear spin toment•
with the electron spin moment such that there is increased probability
that the electron near the nucleus will have spin kt.i!t is antiparallel 4'
to the nuclear spin. Thus, if the splitting Amcleus has an a spin,
the spin of the electron in its vicinity will most frequently be 8.
For a directly bonded nucleus the effect on the nucleus being split
will be the opposite: the spin in its vicinity will be a, and thus.
68
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
the nuclear spin has a greater probability to be in the 0 state. In
this way the nucleus being split receives information from the
splitting nucleus. In the theory of spin-spin coupling constants,
the "contact term" is represented by the interaction operator: .
7r , H = $3 yN ye n-2 dkrkN I St • /N (2.4-3)
--where sk is the spin of electron k'_t ip the spin of nucleus N and rkN
the distadve of electron k---to nucleus N. The expectation value of
o(rkN) vanishes tiniest the electron is right at the nucleus tthus in
an 8 orbital).
2.4.3 Empirical and semi-empirical correlations between coupling
constants and structure
The coupling constants are sensitive'tomany aspects of mole- .
cular structure. Nonetheless, coupling constant data are now available
,for such a large number of nuclear species that it is possible to look
for general trends and periodicities.
Semi-empirical methods for the calculation of spir-spin
coupling constants based on the Hartree-Fock theory have been develOped
in the last ten years. The most widely used is the finite perturbation
theory (FPT) of Pople et al. t68]. These methods have permitted to
perform quantitative calculations and to find relations between
structural and electronic properties and coupling constants. It is well
known that proton-proton coupling constants depend on the number and the
69
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
nature of the intervening atoms, the hybridization state of the latter,
the conformation of the bonds forming the H....H coupling path and the
nature of the substituents, their electronegativity in particular.
Extending earlier work done by Karplus [00], on the effect of
.valence angle changes on vicinal coupling constants, Rummens and
Kaslander [70] have performed extensive INDO FPT calculations on
dependence of proton-proton coupling constants with these angles in
ethylene, propylene, cis- and trans-2-butene. A comprehensive list of
(db/d8)--where a are valence angles--parameters has been compiled and the
changes are found to be additive. For coupling' constants involving
------tmethy4-groups„only the conformationally averaged data were given.
Individual data referring to anti and gauche conformation§ were- later
calculated by Rummens et al. [71]. The results indicate that in-path
angle changes have smaller effects on vicinal couplings than exo-path
angles (which have one bond in the coupling path). Twisting the C=C
double bond in cis-2-butene by angle up to 20° leads only to minor
changes in ,the couplings.
(i) Vicinal coupling constants and dihedral angles.
Relations between vicinal coupling constants and dihedral angles have
been thoroughly' studied. All the methods invariably predict a strong
conformational dependence of the vicinal proton-proton coupling
constants on this angle. The prediction of this conformational
dependence is one of the relatively successful applications of the
early theoretical methods. Using the valence bond theory (0) for a
• 70
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
six-electron fragment, Karplus [72] derived the following relations
between the vicinal coupling constant in ethane and the dihedral
HCCH' angle 0:
.•
8.5 cos20 - 0.28 0 < < 90
3, UHH =
9.5 cos2 - 0.28 90 < < 180
(2.4-4)
Later, Karplus [69] modified relation (2.4-4) and obtained:
3JHH' = A + B cos0 + C cos 20 (2.4-5)
For a C-C bond length of 1.543A, sp3 hybridized carbons and an average
excitation energy equal tot_9eV, Karplus [69] gave the following values
for the constants: A = 4.42,1z, B = -0.5Hz, C = 4.5Hz. INDO FPT work
has been done by Maciel et aZ. [73] on this conformational effect.
For the dihedral angle dependence in the ethane molecule, the authors
obtained a curve similar to that given by equation (2.4-5), but with
the minima displaced somewhat from the 90° and 270° values of
suggested by Karplus [69]. They have also investigated the dihedral
angle dependence of the vicinal proton coupling constant in propene
and acetaldehyde. The variations of, 3JHH, versus for the three
molecules resemble each other closely, with lower maxima and higher
minima for the two latter molecules. Theoretical plots of JHH , in
ethane as a function of the dihedral angle have also been given by
71
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Pachler [74] who used the extended HUckel theory (EHT), by Govil [75]
who compared different sum over states (SOS) treatments (and found
the EHT to perform best) and by Gopinathan and Narasimhan [76] who
applied the INDO FPT and the SOS EHT techniques.
(ii) steric contributions to long-range coupling constants
The four-bond couplings in the fragment of figure (2.4-1a) are called
allylic. 4Ju is denoted as cisoid, 4Ju w as transoid. The .1.3 .2.3
orientation of H3 relative to the carbon skeleton is characterized by
the dihedral angle H3C3C2C1 denoted (180° different from defined
for the vicinal coupling constant). KarplUs [77] and Barfield [78]
studied allylic couplings using the 7-electron theories. Barfield
used the valence bond sum over triplet method, and suggested an
identical cos20' dihedral angle dependence of the Tr-electron contribu-
tion to both, the cisoid and the transoid, coupling constants. , The
average value of the n-electron contribution predicted by Barfield
[78] was -1.65Hz,and by Karphs [77] -1 .7Hz. Later ,Barfield et at.
[79] studied the dependence of the transoid and cisoid couplings in
propene on the angle 01, using the INDO FPT method as well as a •combina-
tion of the VBSOT and SOS EHT treatments. The calculated values for
cisoid coupling turned, out to be negative for the whole range of 0'.
A comparison with experimental data by the same authors [79] indicated
that the INDO FPT method overestimates the magnitude of the cisoid
coupling constant, whereas the "combined" (SOS EHT) curve appears to
agree better with experiment. Analogous curves have been drawn by
72
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
a
\
/ H2 C1
\ H
.• ,
\ /t
i H2 C C'3
H 1\ /
/ 2 N
.•` . ., b
I
a
FIGURE 2.4-1 Molecular fragments used for the definition of a) allylic coupling constantsb) homoallylic coupling constants.
73
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
'Barfield et, al. [79] for transoid coupling, ,and in this case, both
treatments appear to reproduce the experiMental data approximately
equally well. For this coupling the zig-zag path (W3C3C2C1H1
figure (2.4-1)) for 4' = 180°, corresponds to the most positive value
of the coupling constant. The INDO VT-Calculated average valu.s of
the transoid coupling constant (4taJ) was -1.19HZ and of the cisoid
(4caJ) -2.05Hz. These may be compared with the experimental values,of
-1.42Hz and -1.78Hz obtained by Rumniens et ai. [71]. Barfield and
Sternhell [80] have studied the conformational dependence of homo-
allylic coupling (the five-bond coupling in the fragment !depicted in
figure (2.4-1b)). The model system chosen by these authors is the 2-
butene. Here the conformational dependence of the homoallylic
coupling constant may be'discussed in terms of the two dihedral
'angles H1C1 C2C3(4)) and C2C3C4H2 (01), both mevured'in a Clockwise
direction from the plane defined by the carbon skeleton. Barfield and
Sternhell [80] applied both the INDO FPT and the VBSOT methods. This
latter was designed to yield the 7r-electron contribution only. This.
contribution was equal for the cis- and trans-2-butene and could be
adequately represented by the expression.:
5JHH2
= 4.99 sin24 sin24 1
(2.4-6)
The INDO FPT' results corresponded to somewhat more'complicated curves
and were similar for the cis- and trans-conformations of 2-butene.
For the orientation corresponding to the closest proximity of the
74
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
coupled protons in cis-2-butend, the calculated coupling constant
; becomes negative, whidh the authors interpreted-as evidence of,a
direct mechanism. Deduction of the Tr-contribution led Barfield and
Sternhel.l [80] to anticipate a small:a-contribvtion even in the highly
favourable arrangements.
( i i,i) Coupling constants and bond lengths
Several approaches have resulted in a semi-empirical correlation
between the values of 3JHH
and the C-C bond engths. Karplus [69]
derived the following relation on the basis of the VB ippfoximation
with a six-electron fragment H-C-C-H:
•
3JHH
3Jst (1-2.9 (rCC - 1.35)) (2.4-7)
where 3Jst is the standard value of the coupling constant
3JHH in
ethylene (rcc in ethylene being taken equal to 1.35A°). Coope'r and Manatt
[81] found the next relationship (Equation (2.4-8)) during a systema- .
tic analys'is of the experimdntal data on the coupling constants in the
conjugated carbocycles:
3JHFt, ' = -36 4 rCC + 58.46 (2.4-8)
*Ammon and Wheeler [82] have proposed Equation (2.4-9) based on the
data for fulvenes and suitable for both double and conjugated bonds:
75
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
a
3JHH
= -28.6 rCC + 43.5 (2.4-9)
Finally Solkan and Sergeyev [83] performed a series of calculations of
in ethylene, while varying the carbon-cal-bon bond disfance in the 0
range from 1.3 to 1.4A. The linear approximation of this dependence
results in the following relationship for the cisoid coupling:
30"/HH = -28.5 rCC + K (2.4-10)
where K stands for the part of the coupling constant not directly
depending upon the bond length. Solkan and Sergeyev [83] noted that
all the relationships are quite cloge to one another, with an increase
of 3JHH by about 0.6 to 0.7Hz with a decrease in the C-C bond length
0 by 0.02A.
2.4-4 Coupling constants and electronegativity effects
The nature of the substituents, in particular their electro-
negativity, can change the value of the various coupling constants quite
considerably. These changes are certainly correlated with inductive
effects controlled by electron densities on the carbon atoms of the
coupling pathway.
A simple linear relationship between vicinal coupling constants
and Pauling electronegativities has been proposed by Karplus [69]:
3cJ = 3cJu (1 - 0.604)'
76
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
(2.4-11)
3tJ = ZtJU (1 - 0.254x) .
in which Ax is the difference in Padling electronegativities between the
attached group and an hydrogen atom; 3tJu and 3cJu a're the values taken
by the coupling constants in the ethylene molecule. Several other
authors have studied the influence of electronegativity of the substituent
on H-C-C-H coupling. In particular, using the Huggins [84] electronega-
tivity, Banwell and Sheppard [85] proposed the following relationship:
3vJ = 7,9 - 0.74x U2.4-12)
where Ax is the difference between the Huggins electronegativity of the
atom attached to the alkyl group and that of hydrogen. Later, Abraham
and Pachle [88] applied a least-squares treatment to 103 vicinal coupling
constants from various sources and desc4Obed the electronegativity effect
Kith equation (2.4-13):
3vJ = 9.4x1 - 0.804x
where 4x has the same meaning as for equation (2.4-12).
(2.4-13)
Rumens and Kaslander [70] estimated the inddctive effect in
arguing that hybridizational effect and electronegative effect are
separable on .the basis that hybridizational changes do not affect the
electron' density on the rehybridizing carbon atoms. After accounting for
77
•
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
steric hindrance contributions (see previous section), they postulate
that,the remaining non-explained quantities were the result of electro,
negative effects. Methyl substitution effects were deduced from
ethylene, propylene and 2-butene molecules. Results appear Consistent
and amounting to -2.22Hz per methyl group for the vicinal olefinic
coupling, 3cJ. Similarly, values of -3.17Hz (comparing ethylene to
.propylene) and of -2.91Hz (comparing ethylene to trans-2-butene) for 3tJ
appear compatible enough to conclude in the correctness of the hypothe-
sis. For the cisoid allylic coupling, 4caJ, the inductive effect has
been found to be virtually nil, and Rumens and Kaslander [70] did anti-
cipate that.the same should be true..for the transoid allylic coupling,
4 taJ .
The difficulty in finding reliable quantitative relations between
coupling constants and the electronegativity of groups lies partially in
the difficulty to find reliable electronegativities for alkyl groups.
Hinze et al. [87], followed by Huheey [88] have made real progress
toward the deriqtion of an electronegativity for groups and radicals,
based on an extension of the definition of electronegativity for atomic
orbitals originally given by Pritchard and Summer [89]. While Hinze
et al. [01 linearly related electronegativity with the occupation of one
orbital, Huheey [88] used the charge in that orbital for the relation.
This led Huheey,[88] to suggest the dependence of/the charge transfer
ability of the substituent group upon the electronegativity (thus its
electron donating or withdrawing ability) of the substituted fragment.
Hinze et al. [87] also -noted the dependence of the electronegativity (as
78
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
defined by Pritchard and Summer [89]) upon hybridization of the atom and
particularly upon the amount of s-character of its bonding orbital. Then
the two effects--hybridization by steric effect and nuclear charge
exchange--are not entirely separable. Changes in hybridization will have
a twofold consequence:
(i) increase in 8-character will increase the coupling directly
(ii) increase in the a-character in the'bonding.orbital will result
in a decrease of the a-character and of the electronegativity
of the substituent groUp. •
2.5 NMR STUDIES ON ROTAMERS
2.5.1 Description of the phenomenon
If a molecule can exist as rotational isomers (rotamers), the
stable forms may possess confOrmations in which the various nuclei find
themselves in different magnetic environments, giving rise to different
chemical shifts, and where the spin-spin coupling Constants also differ A
as. a result of changes in bond angles and bond lengths.
Whether these isomers can be detected experimentally by the
observation of their separate NMR spectra depends first of all on their
abundances at a particular temperature and secondly on the lifetime of
each species. The first factor is merely an instrumental limitation, but
the second is immutable in that it is connected with the inherent time-
scale of the spectroscopic technique. The fact that radiofrequencies are
employed ensures that only those species which have lifetime of the order
79
4.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
of 0,1s. or longer can be observed. This corresponds to activation
energies of 20-25KJ:mo1-1 (5-6Kcil.mo1-1), indicating that the rotation
.must be highly hindered. Most generally one observes a spectrum in which
both the chemical shifts and. the spin-spin coupling constants are
statistically weighted averages of these parameters for the possible
rotamers. Nevertheless, if the rotamer populations can be varied by
changes in temperature (or in the permittivity of the solvent),, then, in
principle, it is possible to obtain values for the free energy
differences AG° of the rotamers as well as for their individual chemical
shifts and coupling constants.
Apart from these two extreme situations, there is. the inter-
mediate region where the transition from a single averaged spectrum to
the superimposed separate spectra of the individual rotamers occurs, and
it is here that NMR is the most valuable, particularly in cases where
rotamers are of equal energy and where their populations ratio is there-
fore fixed. In the latter situation'even though the chemical conforma-
ti ns are identical, a particular nucleus can exchange its position with
another in a dynamic equilibrium. The uncertainty in establishing its
magnetic surrounding' on the NMR scales results in a broadening of. ts., 4P
resonance signals and studies of the line-shapes in this situation can
provide information concerning, the rate processes involved and hence the
free energy of activation AGE of the process.
Over the last decade refinements of both the classical and
quantum-mechanical theory have, been rapid, and have now reached the stage
where the line-shapes of quite complex systems can be analyzed. New
80
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
experimental techniques involving nuclear relaxation time measurements
have also become available.
2.5.2 Completely averaged spectra and their temperature dependence
studies
A simple case of rotational 'isomerism which occurs\ bout a
single' bond' with only two stable conformations can be considered; the
free energy profile of such a transforiatioh 4s schematically Shown in
figure (2.5-1). If the interconversion of the isomers-is very fast, then
the NMR spectrum at ambient temperature yields only the statistically
averaged vicinal coupling constant <J> which 'is related to the mole
fraction qi and the characteristic spin-spin coupling Constants qi of the 0
individual r9tamers by equation0(2.5-1):
<J>* = E q, • Jii
.A similar equation could be written for the statistically
averaged chemical shift <d>, but the sensitivity of chemical shifts to
macroscopic environmental changes (see reference [90]) usually precludes
their Use in the type of analysis to be described here.
Assuming that the two energy forms of the molecule have
degeneracies nl and n2 (subscript 1 refers to the high energy form)‘, then
.the equilibrium constant is given by equation (2.5-2):
K 21. 2.1..exp eq q2 n2
81
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
•uopsp.wacl lnotam pamgaid uoRonpoidai Jaqpnd •JaLIMO 1q6pAcloo ay} uopsp.wed tam peonpoidelj
38
GIBBS FREE ENERGY—'---0-
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
or (2.5-2)
•
eq = nnl exp ( exp (-AH) 2
RT
AS and AH are respectively .the entropy and enthalpy variations;
R has its usual meaning of perfect gases constant.
In this case bne has q1 + q2 = 1; combining equations (2.5-1)
,and (2.5-2) yields to equation (2.5-3):
(J1 Keg + J2) <
= ql jl q2 J2
- (1 + Keg) (2.5-3)
- The determination of the values of the spin-spin coupling
constants J. and of the free energy difference AG from the temperature
dependence of <J> was first advocated by Gutowsky, Belford and MacMahon
[91]. It is this method (often called GBM method) which will be used
here. To apply such a method one has to assume that changes in coupling
constants with temperature variation are only the result of changes in the
relative populations of the various rotamers. This implies that the
potential minima must be sharp enough to make contributions to the
coupling constants from torsional oscillations insignificant.
The other assumption underlyin such treatment is that AG is not
temperature dependent (then AG is equal to AG°): very commonly AS is
assumed to be zero and AH to be.temperature independent. With two
different conformations the problem is reduced to the finding of three
parameters instead of four. This problem is solved by calculating the
83
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
best least-squares fit of equation (2.5-3).
In relation (2.5-3) the unknowns are AG (equivalent to AG°'and
AH° under the assumptions made), Jl and J2. In practice, the procedure
of the least-squares analysis is as follows:
(i) A value of AG° or AH° is fed in, which allows the calculation of
q1 and q2 (using q1 + q2 = 1) from equation (2.5-2),
(ii) for each temperature, these values, when combined with the
experimental measurements of <J> and equation (2.5-3) allow the best-
fit values of J1 and J2 to be obtained,
(iii) these J1 and J2 values lead to a value- for the function
defined by equation (2.5-4):
0 = (<3>Toleas. - <J>
T,calc.)2 (2.5-4)
This procedure is repeated with systematic variations of AG°
(or AH°) until a'minimum value is obtained for 0 which yields the
most probable values for the NMR and thermodynamic parameters.
The method is composed of 2 least-squares analysis; fitting of
the <J> measured at n different temperatures and then, minimization of
the error by choosing the best third parameter AG° (which gives a minimum
value for 0).
If there are m non-identical rotamers, equation (2.5-3)
involves (2m-1) unknowns. Measurement of <J> at (2m-1) different tempera-
tures should be sufficient. However, the accuracy in the measurements
of this coupling constant in the examined temperature range asks for an
84
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
overdetermination, therefore the fitting procedure to find J assuming a
value for AG°.
To find the uncertainty of such a liethod, GutowskY, Belford and
MacMahon [91] supposed a parabolic 0 function near the minimum for all
variables. Defining an uncertainty (d <J>) in the measurements, they
obtained:
- 0 C (ArY)24xpl min min ' (2.5-5)
where a is the consider0 variable, Cmin the coefficient of the parabolic
expansion. exp is defined by (2.5-6):
0exp
=E (a <J>T)2 (2.5-6)
A solution fOr Aa is then straightforward (a can be a J value
or.a AG value). Such an estimate gives only an order of magnitude of the
error (it is normally an overestimation).
The basic assumptions in the method are that AS = 0 and that
the temperature dependence of the measured quantity, <J>, is not signifi-
cantly affected by the temperature variation of 6H, J/ and J2. There is
also the question of the accuracy of the 'best-fit' parameters so
obtained.
Govil and Bernstein [92] were able to check these assumptions
in the case of CHBr2CFBr2 by measuring the average NMR parameters at high
temperature, using the above treatment to obtain the three unknowns, and
85
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
I
then by comparing these values with those obtained by direct measurement
of the spectrumpat such low temperatuYes that the individual spectra of
the rotamers were obtained. The two methods gave very different results,
and in this particular case the authors [92] were able to show that the
a_sumptions of AS ! 0 and of the temperature independence of J1, J2 and
'AH were not the maor cause of the discrepancy. The real reason was that
the observed temperature dependence of the coupling at high temperatures
was not sufficient to allow a precise evaluation of the unknowns. In
conclusion, the erroneous results obtained, and the controversy
, surrounding the application of thiS method, are due entirely to the
neglect of the basic assumptions involved, rather than to any inherent
defect in the method.
To obtain the best results in any applicatiOn of this technique,
it is essential
(i) to pr•uvide some estimate of the intrinsic temperature dependence
of the parameters involved
(ii) to obtain a sufficient variation in the measured quantity with
temperature to provide well-defined values of the three unknown
parameters, or, if not possible,.to determine by another method one
of the three unknowns.
2.5.3 Dynamic equilibria and line shape analysis
If a magnetic nucleus can undergo exchange between two
different positions in a molecule as a result of internal rotation, it
often experiences a different effective magnetic field in the two sites
86
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
and thus exhibits different chemical shifts. This means that, in an
assembly of molecules where the exchange rate is slow, the residence
time of nuclei at each site is long compared to the reciprocal chemical
shift difference, and two different NMR signals Will)e observed. If the
rate of exchange is increased by raising the temperature, eventually a
single resonance signal will be observed, whose position will be inter-
mediate between those of the previously separate signals. In this limit,
the exchanging nuclei experience an effective field which is a weighted
average of the fields at the different sites. At intermediate rates, an
analysis of the change in sine-shape as the signals coalesce can there-
fore yield the rate constants and activation energy of the process
(figure (2.5-2) shows such variations).
In order to arrive at a quantitative measure of the activation
energy of these processes, it is necessary.to study the change in,
appearance of the spectrum as a function of temperature and the complete
line-shape analysis must be performed. Gutowsky et al. [93] we're the
pioneel in this field, and they showed how the phenomenological equa-
tions of Bloch [94] could be modffied to account for the exchange of
magnetism from one site to another during the interconversion of the
isomers. Such a classical approach is valid when the exchanging groups
are not involved in spin-spin coupling, but a quantum-mechanical basis
is required if coupling is involved. The complexity of the solution in
the latter case makes the use of a computer program a necessity. Such
sophisticated programs have been developed, in particular by G. Binsch
et al. [95].
87
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Fast exchange
Near fast
exchange
Coalescence
Intermediate exchange
Slow exchange
Stopped exchange
FIGURE 2.5-2 Temperature dependence of the NMR spectrum as'a result of . chemical exchange (uncoupled AB case). "
88
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
2.6 - NUMERICAL ANALYSIS USING THE PROGRAM "NUMAR1T"
2.6.1 Introduction
To analyse the complex proton NMR spectra, the program to 0.6
used must fulfill certain requirements. One of the molecules studied
represents an ABCD6X9 system and only' few programs can handle such big
systems. The X approximation must be available, because an ABCD6E9 would
be too large and would demand a lot more computer time. The program also
has to include the composite particle method in order to save space and
time during the calculation. I)
The "NUMARIT" program developed by A.S. Quirt, J.S. Martin,
K. Worvill [96] seems, at the moment, the best suited for the analysis of
the spectra obtained with the molecules under present study. It includes
the preceding features, and in addition it makes full use of factorihg
resulting from bgofold frame symmetry.
The output consists of energy levels, keys connecting energy
levels and transitions, transition lists with associated quantum numbers
useful in subspectral analysis, bar plots on the line printer, spectral
simulations on a Calcomp plotter. The shifts and couplings may be
iterated to fit an observed spectrum using the method first developed by
Castellano and P,*hner-By in their program "LAOCN3" [97] (sometimes
cal'l'ed' the BBC thod).
2.6.2 Method of iteration
The method developed by Castellano and Bothner-By is one of the
89
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
two methods most often used for NMR analysis. The other one uses
Reilly and Swalen's approach [98] Recently Castellano and Bothner-By's
method has been even more widely employed. Three reasons for this trend
have been put forward by C.W. Haigh [99):
(i) this method is less likely to run into convergence- difficulties,
(ii) the statistics employed is matheillticalt% impeccable, ,_,.---
(iii) in the Reilly-Swalen me needs to determine all the
energy levels. The,castglano ..ands Bothner-By approach merely requires
to initially-sOecifY a sufficient number of transitions to make the
problem overdetermined.
In the BBC method, when it is desired to calculate a spectrum from a
guessed-at set of shifts and coupling constants, the Hamiltonian of the
system under consideration is determined following the procedure
described in section (2.2). The eigenvalues of determinant (2.2-11) are
the stationary state energies of the system, Xm, and the frequencies of
transitions vi are just the differences. of these eigenvalues:
v. = X -X 1 k m(2.6-1)
Comparison of a calculated spectrum with an observed spectrum
may suggest adjustments in the values of the input parameters (chemical
shifts and coupling constants) which will improve the agreement 'etween
the two spectra. However, al experimental spectrum, consisting of a set
of measured transition frecitiencies and approximate intensities is
unlikely to be exactly interpretable. The best values for' the parameters
90
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
(chemical shifts and coupling constants) are those which make the sum of
the squared residuals of the observables (in this case transition
frequencies only) a minimum. For each parmeter pj the coindition is
described by relation (2.6-2)
( ) E (vobs -vcalc ). = 0 N:ij
vobs is a constant, and only (vcaic)i = f(pi):
Dvcal
1=E1 (vobs-‘'calc)i (a p. )i 0
(2.6-2)
(2.6-3)
where st, is the number of transition frequencies observed and (vobs-vcalc)i
is the difference between the observed and calculated frequencies for the
th i transition.
In the procedure, only transition frequencies are considered;
the weight of each frequency is 1 or 0, depending on whether the observed
frequency is used or not (some programs include a weighing factor).
In the presence of molecular symmetry, parameters occurring in
sets may have equal Values. In such'a case equation (2.6-3) must be
modified and take the form:
+ . . .) z (v -v 2 ap. ap . obs calc) i
= 0 j k
(2.6-4)
where the parameters p are grouped according to their symmetry as
indicated by indices j, k, . . . . It is assumed that if the variations
91
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
of the parameters are small a linear relationship with Avi is "applicable:
Av. 3v. 3v.
rj
_ rj
4 rjor Avi = Api an. (2.6-5)
The coincidence between calculated and observed lines occurs if:
ay.
J E (°Pi) APj = (nobs vcalc)i
Or ip matrix notation: '
DA=N
(2.6-6)
(2.6-7)
where 5 is the matrix of partial differentials, A is the vector of
corrections to the parameters, N is the vector of residuals in the
frequencies. The number of available independent transition frequencies
must exceed the number of 'unknown parameters (overdetermination of the
problem) for the method of least-squares analysis to be applicable.
Standard least-squares procedure is to form the system of normal
equations:
DAt At DA = D.
92
(2.6-8)
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
D t-D is a real symmetric matrix with a non-vanishing determinant. The
normal equations will thus have the solution A = 0 only when bt N = 0,
that is when equations (2.6-3) and (2.6-4) are satisfied for all the
paraMeters. The convergence is thus to the desired leas -squares fit.
When A t 0, a correction will'be made to the paramet ))-squares
give
the least-squares solution If the transition frequencies were linearly
dependent on the parameters.
After solving the eigenequation (2.2-11) using initial values
as parameters, frequencies of transitions are calculated applying
relation (2.6-1). There remains the problem of finding the appropriate
partial differentials-, (av/apj). These differentials are just the
differences:
av1 , DA aI, t m n apj . api %Am A p, ap. ap.
. J J (2.6-9)
As demonstrated. by Bothner-By and Castellano [/00], the
differentials of the eigenvalues are identical to the diagonal elements
ofri .(g1/apj). S, where S and are the eigenvector matrix and its
transpose (equation (2.2-8) i$ equivalent to A = S • H S). The
differentiation of H in the basis repreientation is straightforward, so
the evaluation of (axopj) requires only the knowledge of the eigen-
vectors; thus one has to solve equation (2.2-8).
The general procedure to find the best parameters to fit the
• 93
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
experimental spectrum can then be decomposed as follows:
(i) Using the non iterative capability of "NUMARIT" an approximate
Hamiltonian H is Calculated following the rules described in section
2.2 and using trial parameters.
Eigenvalues and eigetvectors are found by solving equations
(2.2-11) and (2.2-10).
(iii) After calculation of frequencies of transitions (see relation
(2.6-1)) an output is given. Line transition numbers are matched with
line frequencies.
(iv) Assignment of observed frequencies to these line numbers is per-
formed (the number of frequencies assigned must.be.larger than the
number of unknown parameters).
(v) An iterative run of "NUMARIT" is performed. The first two steps
are the same as for a non-iterative calculation.
(TWAfterdeterathlationofv. all the elements of matrix 6 are
calculated (avinpj).
(vii) The least-squares analysis is then performed; if A t 0 each
parameter is varied and put back into a new Hamiltonian to go once
more through the cycle. The iteration ends when A = 0; the final
parameters are obtained with a certain precision.
2.6.3 Error analysis
The determination of errors of optimum parameters p, obtained
by a least-squares method applied to a large number of experimental data
(the measured frequencies of the lines of the spectrum) involves normally
94
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
a two-step procedure: first, the error of the experimental data must be
properly characterized; second, a law of propagation of errors from the
experimental data to the optimum parameters .has to be applied. In the
"NUMARIT" program, error in parameter analysis is given by the variance-
covariance matrix Z. The error for a set of variables is completely
characterized by this matrix: its diagonal elements are the variances
ai2, and its off-diagonal elements represent the covariance. This matrix
is always symmetrical but diagonal only when the variables are
completely independent. A measure of the interdependence between.two,
variables xi and xk is given by e coefficient r defined by relation
(2.6-10):
Ci r = (2.6-10) aiak k
where Cik is the element of the matrix t corresponding to the ith row and
the kth column; ai and ak are the square root of the diagonal element on
the ith and kth rows respectively. The error calculation will give the
matrix E corresponding to the experimental frequencies. This matrix is
supposed to be diagonal in the case of NMR spectra (no correlation
between frequency errors of different lines); each diagonal.eTemeht is
calculated using relation (2.6-11) when all line measurements are of the
same quality:
z . E E2
2 i=1 i a = Z - q
95
(2.6-11)
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Here t is the number of lines assigned (numberof'conditions of the type
of relation (2.6-6)) and q is the number of independent parameters
iterated. e. represents the difference between final computed frequencies •
and experimental frequencies.
To find the variance-covariance matrix e of the calculated
parameters, the propagation law has to be applied. The relationships between
-frequencies and parameters ai.e generally non-liAlear and the calculation
is carried out by finding the values of their first derivatives. 'If the
matrix 8, previously defined, is known, the transformation from ev to e
can be expressed by the following matrix multiplication:
At 8v (2.6-12) D •
where 5t and D have the same meaning as in equation (2.6-8). The
expression of the errors associated with the parameter pi is:
E s. 2
cr. - mj i
det(Dt •D)(k-(1) (2.6-13)
wherea. isthestanciami deviationoftheParameterj,m. the minor of
-t^ the coefficient (D D)„, the other parameters have the same meaning as in
expression (2.6-11). There are advantages, however, 'to transforming to a
new set of variables before computing the errors. The new set of
variables should be the linear combinations of the parameters which cause
96
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
the matrix I) to be diagonal. The standard deviation is then easier to
compute and takes the form described in relation (2.6-14):
c. 2 i 1 -
b dbb(t-q) (2.6-14)
In this equation, dbb is the bth diagonal element of the diagonalized
matrix, cb is the standard deviation of the bth linear combination of
parameters, obtained from the basis set of parameters and the bth eigen-
vector. These values are printed out as "standard deviation"; the
coefficients of these combinations are called "error vectors" in the
program output (there are as many "standard deviations" as there are
iterated parameters ) .
97
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
CHAPTER III
CONFORMATIONAL AND THERMODYNAMIC PROPERTIES
OBTAINED FROM FORCE FIELD CALCULATIONS;
RESULTS AND PRELIMINARY DISCUSSION
3.1 INTRODUCTION
Conformational and thermodynamic properties of several
substituted ethylene molecules have been investigated using the empirical
"CFF" Force field method described in Chapter I. Steric energies as well
as geometrii'al variations with the substitution are described in the next
section. Mono- and disubstituted ethylenes have been studied. A wti-
cu.for emphasis is put on the rotameric interconversion in cis- and trans-',
2,2,59trimethy1-3-hexene and in cis-2,5-dimethyl-3-hexene. In addition
the different conformations of minimum energy are given for 3-methyl-l-
butene and trans-2,5-dimethy1-3-hexene. To appreciate the behavior of
the Force Field in the case of large strain the rotameric interconversion
path for the 4,4-dimethyl-3-tert-butyl-l-pentene is also reported.
3.2 RELEASE OF STRAIN AND CONFORMATION
When substituting an hydrogen atom by a bulkier alkyl group in
an ethylene molecule, several mechanisms could release the strain
98
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
created; widening of the C=C-C and inner H-C-C valence angles, non-planar
distortions of the C=C double bond and rotation of the.substituent around
a C-C single bond are some of these possibilities.
3.2.1 Release of strain through widening of the C=C-R valence angles
(R = H, C)
When substituting one hydrogen in ethylene by an increasingly
bulky group, the increased steric interaction between the substituent R
and H2 (see figure (3.2-1) for notation) would cause them to move apart.
At the same time, the movement at R would produce a reflex movement of H1,
which suffers little compression. 'Distortion at H2 would propagate to
H3. Mechanisms of these kinds have been investigated by Rummens et al.
[101] and by Cooper et aZ. [102], using IR and NMR spectroscopy; experi-
mental evidence seems to support this picture when replacing a methyl
group by an ethyl group (in going from propene toscis-l-butene--whith is
the conformation of lowest minimum. energy for this molecule) as can be
seen in table 3.2-1. However, the replacement of one hydrogen atom of
the ethylene molecule by a methyl (or an ethyl) group does not lead to
the expected widening of the C=C-H2 valence angle, but to a reverse
effect (even if this effect is small). Meanwhile, the mechanism
described previously is well followed in the geometries obtained using
the "CFF" method, for all the substitutions (see table 3.2-2). The size
of the alkyl substituent is not the only factor affecting the value of
the valence angles; these angles depend also on the type of interaction
between H2 and R. For example, the calculated valence angles are of the
99
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1
ex
A
FIGURE 3.2-1 Schematic description of valence angle variation with 'increasing size of the alkyl group substituent for mono-substituted ethylenes.
100
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
TABLE 3.2-1 Effect of a first alkyl substitution on the valence angles of ethylene, as found experimen,tallyl
81 82 e3 e4 ref.
H 121.7 121.7 121.7 121.7 a
methyl 124.3 120.5 119.0 121.5 b
ethyl(*) 125.4 117.5 c
ethyl(**) 126.7 121.1 119.0 119.8 c
(*)gauche-1-Iptene, one methylene C-H eclipses the double bond. (**).scis-l-butene, in which the C sp 3-Csp 3 bond eclipses the double bond. aData taken from K. Kuchitsu, J. Chem. Phys. 44,906 (1966). bSee reference [121].
cData taken from S. Kondo, E. Horita and Y. Morino, J. Mol. Spectro-scopy, 28, 471 (1968).
tFor notation see Figure (3.2-1).
101
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
I 4.
)
TABLE 3.2-2 ,Force Field-derived variations of valence angles with mono-substitution of one hydrogen atom by an alkyl group in an ethylene molecule, when the molecule is in its minimum of lowest energy.
R . 0.1 02 8-J 04
H 121.4 . 121.4 121.4 121.4
methyl 123.9 122.2 120.5 120.9
isopropyl - 123.8 122.3 t 120.1 120.8
tert-butyl' 127.0 124.1 118.4 119.8
For notation see Figure (3.2-1).
c.
\
102
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
same magnitude for 3-methyl-l-butene and propene (where a C-H bond
eclipses the double'bond), and for 3,3-dimethyl-l-butene and s cis-l-butene
(where a C sp 3-C sp3 eclipses the double bond) as can be seen in table
3.2-3.
A second substitution in trans position in 3-methyl-l-butene
tends to reduce the effect of the first substitution (in the case shown,
the isopropyl group) as can be seen in table 3.2-4. This influence is
understandable in view of the previously proposed mechanism, which leads
to opposite effects on all four (C=C-) angles for the first and second
alkyl subttituents. For both the cis and trans substi,Jtions,both
valence angles H-C=C and C=C-R on the side of the second substituent
(with reference to the double bond) are opened up, while the angles on
the other side are closed down. With•a second substitution in trans
position, the difference between experimental and calculated valence
angles seems reduced compared to the differences for the corresponding
monosubstituted molecule; table 3.2-5 shows such a result for the methyl
substitution (between propene and trans-2-butene). With a second
substitution in cis position, the repulsive forces between the bulky
groups open up the el C=C-H valence angle to a value of 130.2° when the
second substituent is a tert-butyl group. This large value (compared to
120°) is at the limits of validity of the potential used: the deviation
from the reference value is large and quadratic energy terms for wide
angles may not be exact. This direct interaction between the two bulky
groups with a cis substitution leads to a widening of the Al C=C-H
valence angle much more pronounced than the closing of the same angle
103
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
TABLE 3.2-3 Calculated effects of alkyl monosubstitution on valence angles for ethylene moleculesT
R 81 e3 e4
methyl 123.9 122.2 120.4 120.9
A, ethyl, 124.0 122.3 120.1 120.8
:isopropyl(*) 123.8 122.3 120.1 120.8
`ethyl(*) 126.8 123.7 119.0 120.0
B isopropyl 127.1 123.9 118.3 119.8
,t-butyl \ 127.0 124.1 118.4 119.8
A gives the angleS when one (methyl, methine or methylene) C-H bond eclipses the double bond. B gives them for conformations with one C ' 3-C 3 eclipsing the double bond. . sP gP (*) indicates the conformation of lowest Minimum energy(scis-l-butene for ethyl substitution) when several possibilities are given.
tfor notation see Figure (3.2-1).
t
104
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
TABLE 3.2-4 Effect of second substitution in cis on trans position on valgnce angles for monoalkyl ethylenes as calculated for the minimum energy conformation.
R1 R2 R3 1 62 63 64
121.4 121.4 121.4 121.4
isopropyl H H 123.8 122.3 119.9 120.8
isopropyl methyl H 128.1 128.1 117.2 117.9
isopropyl isopropyl H, ' 128.5 128.5 116.8 116.8
isopropyl tert-butyl H 130.2 129.7 115.7 115.5
isopropyl H methyl 123.5 121.4 120.8 123.4
isopropyl H isopropyl 123.4 121.0 121.0 , 123.4
isopropyl H tert-butyl 122.7 119.5 122.7 126.4
105
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
TABLE 3.2-5 Difference between Force Field-derived and experimentally obtained valence angles for various ethylenic molecules. Comparison with errors obtained using an additivity rule (where each 2-butene molecule is considered as the geometri-cal results of the addition of two propene molecules)T
081 A82 083 A84
propene -0.4 1.7 1.4 -0.6
trans-2-butene -0.2 -0.2 -0.3
(*) (-0.3
-1. 3.1 3.1 -1.
cis-2-butene 1.1 1.1 0.9 0.9
(**) [ 1.3 1.3 0.8 0.8
(*)calculated using A01 = Aer(propene). + A04(propene)
AO2 = a 2(propebe) + AO3(propene)
(**)calculated using Ae2 = 681(propene) + A02(propene)
A83 = A03(propene) + AO4(propene)
'AO = 0calc - 0expl
106
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
with a second substitution in trans position relative to R1 (see figure
(3.2-2) and table 3.2-4).
As in the case of a monosubstitution, the effects created by a
second substitution With a methyl or with an isopropyl group are of the
same order; this can be best explained by postulating tat the opening of
the C=C-H valence angle is mainly caused by the repulsion between the
inner hydrogens eclipsing the double bond (in the calculated conformations
of minimum energy for the two molecules one of the methyl hydrogens of 6
the cis-4-methyl-2-penterie and the methine hydrogen of the cis-2,5-dimethyl-
3-hexene are in almost the safe position).
Instead of reducing the difference between experimental and
calculated valence angles, as is the case for a trans second substitution,
a cis second ,substitution lead to an additivity of the errors found for
the corresponding monosubstituted ethylenes (see table 3.2-5 for the
description). Table 3.2-5 shows the difference (experimental to
calculated) for the cis-2-butene. If this effect is general, it can lead
to substantial errors in the case of bulky substitutions; the cis-2,2,5-
trimethy1-3-hexene an example. Estimation of these errors can be made
from the s cis- and jr.,:yhe-l-butene (combining both substitutions lead to the
cis-3-hexene molecule with one methylene C-H for one group, the C-C bond
for the other ethyl group eclipsing the double bond). The -rule of
additivity of errors leads to an overestimation for three out of the four
valence angles. The valence angles 61, e2, 03 are overestimated by 1.2°,
1.9°, 2.8° respectively, while 84 is underestimated by 0.6° 0 1 is
referring to the ethyl group with one C-H methylene eclipsing the double
107
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1
FIGURE 392-2 Schematic description of valence angle variation with increasing size of the alkyl group R2, for cis- and trans-. disubstituted ethylenes with an isopropyl 41.oup as first substituent (R1).
/ 108
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
bond).
3.2.2 Other types of release
Non-planar double bond deformations involve a hard-potential;
for none of the conformations calculated to correspond to the lowest
energy minimum was such a.deformation found to release the strain. Such
a torsion of 4.1° was obtained only for the cis-2,2,5-trimethy]-3-hexene
where it is combined with an out-of-plane methine hydrogen for the
isopropyl group:
Widening of the inner C8/22-C8p3-H angle' is negligible in all
the trans substitutions (the variation is less than 0.4° around the
equilibrium value of 109.4°). For a cia substitution the variation is -
more substantial and takes a value of 2.2° for the cis-2,2,5-trimethy1-3-
hexene.
None of the bond lengths is affected appreciably by an increase
in crowdiness of the molecule; for example •C 3-C 2 bond lengths a're not sp sp varying by more thanj).5 percent around the equilibrium position of
0 1.501A for most of the molecules under study; this variation should not
be a major41i factor in the discussion of the results of NMR spectroscopy
(see Cooper and Manatt [81]).
3.2.3 Repartition of steric energy
Contributions to the total strain energy for various substituted
ethylenes in their conformation of lowest energy are detailed in table
3.2-6. It is remarkable to see, in the case of cis- and trans-hexenes,
109
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Reproduced w
ith permission o
f the copyright owner. F
urther reproduction prohibited without perm
ission.
TABLE 3.2-6 Calculated steric energies (KJ.mol-1) in various conformations of lowest energy of olefins as calculated by the "CFF" method. Between parentheses values in Kcal.mol-,are given.
trans-2,5- cis-2,5- trans-2,2,5--cis-2,2,5- 4,4-dimethyl-3-methyl- dimethyl-
ethylene 1-butene 3-hexene dimethyl- trimethyl- 3-hexene 3-hexene
trimethyl- 3-t-butyl-3-hexene 1-pentene
frond stretching 0.004 0.193 0.423 0.385 1.013 1.280 6.222 - (0.001) (0.046) (0.101) (0.092) (0.242) (0.306) (1.487)
Bond angle bending 0.017 0.594 0.803 7.067 3.117 11.899 20.782 (0.004) (0.142) (0.192) (1.689) (0.745) (2.844) (4.967)
Torsional strain 0.000 0.025 0.050 0.067 0.063 10.791 5.263 o (0.000) (0.006) (0.012) (0,016) (0.015) (2.579) (1.258)
Out of plane bending 0.000 0.000 0.000 0.000 0.000 0.000 0.013 (0.000) (0.000) (0.000) (0.000) (0.000) (0.000) (0.003)
Non-bonded inter- 1.197 8.527 13.949 14.418 21.209 20.635 42.652 action (0.286) (2.038) (3.334) (3.446) (5.069) (4.932) (10.194)
- Cross terms 0.000 0.071 0.222. -1.167 0.255 -1,640 -2.828
(0.000) (0.017) (0.053) (-0.279). (0.061) (-0.392) 4-0.676)
Total steric energy 1.218 9.406 15.443 20.769 25.652 42.965 72.107 (0.291) (2.248) (3.691) (4.964) (6.131) (10.269) (17.234)
Reproduced w
ith permission of the copyright ow
ner. Further reproduction prohibited w
ithout permission.
that the non-bonded energy is about the same within each cis/trans pair
(this kind of energy is even smaller for the cis- than for the trans-
isomer of 2,2,5-trimethyl-3-hexene). At short distance the non-bonded
potential becomes so hard that only the soft bond angle bending and the
torsions can release the strain efficiently. However, the non-bonded
energy increases with the size of the alkyl substituent (for example when
replacing an isopropyl by a tent-butyl group). Among the substituted
ethylenes studied, the cis-2,2,5-trimethyl-3-hexene and the 4,4-dimethyl-
3-tert-butyl-l-pentene are\ the only ones for which angle bending alone
cannot release the strain optimally, so they must resort respectively to
C=C twisting and to C-C torsional deformations.
3.3 ENERGY IN CIS/TRANS TRANSFORMATION
3.3.1 cis/trans enthalpy differences
In the initial discussion of their results, Ermer and Lifson
[3] pointed out that in the least-square process for finding the para-
meters of the Force Field they gave a considerably lower weight to data
obtained from solutions as compared to data obtained from the gas phase;
discrepancies of up to 7.1KJ.mol-1 (1 .7Kcal.mol-1) have been noticed
between gas- and solution phase data. Of 'the molecules given in table
3.3-1, the 2-butene and the 2-pentene enthalpy differences are the only
ones taken from equilibration measurements in the gas p'lase. However, Air
the calculated enthalpy difference (using equations 1 .8-1 and 1.8-2) for
the 2-pentenes is 45 percent larger than the experimental value. Such a
111
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
TABLE 3.3-1 Differences in steric energy (AV) and in enthalpy (iH) between cis and trans isomers of various molecules as calculated with the Ermer and Lifson Force Field; comparison with the experimental enthalpy differences.*
11)
Compound O calc AHcalc
AHexpl P11 P21
2-pentene e(i) 5.19 e(i) 5.36 3.68a e(i) 0.41 e(i) 0.45 (1.24) (1.28) (0.88)
e(ii) 0.63 e(ii) 1.3 (0.15) (0.31)
'OM 4.24 'OM 4.69 e(iii) 0.15 e(iii) 0.27
4-methyl- 5.02 5.65 4.18b
0.20 0.35 2-pentene (1.20) (1.35) (1.00)
2-butene 4.85 5.31 5.23c 0.07 0.02 (1.16) (1.27) (1.25)
4,4-dimethyl- 17.8 17.7 16.14 0.10 0.10 2-pentene (4.25) (4.24) (3.86)
2,2,5,5-tetra-methyl- 47.3 48.4 -38.9b 0.22 0.24 3-hexene (11.3) (11.6) (9.3)
aData taken from D. R. Stull, E. F. Westrum Jr. and G. C. Sinke, The chemical thermodynamics of organic compounds, J. Wiley and Sons, Inc. (1969). bData taken from reference [128].
See reference [106]. dData taken from J. D. Rockenfeller and F. D. Rossini, J. Phys. Chem., 65,267 (1961).
(i) refers to the difference between the two conformers of lowest energy.
(ii) refers to the energy difference between the cis conformer of lowest energy and the tiosconformer of second lowest energy.
(iii) refers to the energy difference between the cis conformer of lowest energy and the equilibrium mixture obtained for the trans conformers when their Gibbt enely separation is 4.05KJ.mo1-1.
e
'Pi 2 1"calc AHexpl l/aexpl P2 = IAHcalc
AHexpl
I/AHexpl *Units: the energies are given in KJ.mo1-1; between parentheses their
values are in Kcal.mo1-1. 112
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
difference is not inside the average absolute difference given by Ermer
and Lifson [3]. For this molecule, the possibility of having two
appreciably populated trans rotamers at room temperature cannot be
rejected. A difference in enthalpy between these two rotamers of
4.1KJ.mol-1
(0.97Kcal.mo1-1) is found using the "CFF" method; thi-S- feads
to 10 percent of the population being in the second conformation. The
difference between calculated and measured enthalpy differences is then
lowered to 1.3KJ.mol-1 (0.30Kcal.mol-1). For the other molecules listed,
part of the disk.repancy between calculated and experimental cis/trans
enthalpy differences has been claimed by Ermer and Lifson [3] to be
caused by the presence of a polar effect in solution. Allinger and
Sprague [103] estimated this effect to account for 4,2KJ.mo1-1 (1Kcal.
mol-1); if such an increase from solution in acetic acid to gas is
present, the discrepancy for the 2,2,5,5-tetramethyl-3-hexene decreased
from 9.5KJ.mol-1 to 5.4 KJ.mol-1 (from 2.3 to 1.3Kcal.mol-1). The
overestimation of the difference then drops to 13 percent.
A comparison of results using various Force Field potentials is
attempted in table 3.3-2. The data displayed show that the potentials
used are equivalent; a slight advantage seems to go to Allinger and
Sprague's results,. A major drawback of these authors' potential lies in
too hard a potential to take account for the non-bonded interactions as
suggested by White and Bovill [104]. This leads to approximate geomet-
ries; for example, in the case of the cis-2-butene, Allinger and Sprague
[/03] found a C2 geometry (one of the methyl group is twisted in order to
release the strain), while'Ermer and Lifson [3] as well as White and
113
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
TABLE 3.3-2 Comparison of cis/trans enthalpy differences as calculated using three Force Field methods* and as obtained experi-mentally.
White and Bovill [/04]
Ermer and Lifson [3]
Allinger and Sprague [/03] Expl
2-pentene 5.23 5.19 3.56 3.68a
(1.25) (1.24) (0.85) (0.88)
4-methyl-2 2.05 5.02 4.18b
pentene (0.49) (1.20) (1.00)
2-butene 5.48 4.85 4.85 5.23c
(1.31). (1.16) (1.16) (1.25)
2,2,5,5- 47.30 43.30 38.9b
tetramethyl- (11.30) (10.35) (9.3) 3-hexene
aData taken from D. R. Stull, E. F. Westrum Jr. and G. C. Sinke, The chemical thermodynamics of organic compounds, J. Wiley and Sons, Inc. (1969). bData taken from reference [128].
cSee reference [1OS]. *For the three methods, the steric energy difference is taken „as representing the enthalpy difference.
114
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Bovill [104] have a minimum energy when the conformation geometry has a A
C2v symmetry with two methyl hydrogens eclipsing the double bond as has
been established by microwave spectroscopy,[14].
3.3.2 Entropy and Gibbs energy reliability
From the frequencies calculated for the conformations of
minimum energy, entropy differences between cis and trans isomers have
been obtained according to equations (1.8-3) to (1.8-10. A comparison
of these values'vith entropy differences obtained from experiments is
given in table 3.3-3. The errors in absolute entropy for the values
given by the American Petroleum.Institute (API) have been estimated by .
Golden et al. [105] to be of the order of f2.9J.mo1-1.K-1 (f0.7e.u.).
Considering the fact that AS values are derived from differences in
absolUte values, they probably have error limits of at least,t2.9J.mol 1.K-1
(f0.7e.u.). Egger and Benson [106] and Golden et al. [105] used the
method of iodine or nitric oxide catalyzed isomerization of olefins to
find the values quoted in table 3.3-3. The calculated entropy differences,
AS ciAltrans, fall within the error limits of the various experimental
data. The standard deviation (from the experimental data) for AS is
about 3.3J.mo1-1.K-1 (0.8e.u.), which would give an uncertainty on AG of
1KJ.mo1-1.K-1 (240cal.mol-1.K-1) at room temperature. The uncertainty in
T AS as compared to the value of T AS itself, leaves one to wonder if the
calculated cis/trans enthalpy difference is not as good a comparison as
is the calculated Gibbs energy difference to the experimental Gibbs
energy difference. In view, however, of the excellent agreement between
115
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
TABLE 3.3-3 Comparison between calculated entropy difference cis/trans (for conformations of lowest energy) as obtained from Force Field technique and as deduced from experimental data.
Compound AS (cis-trans) T = 298K AS-(cis-trans) T = 400K
From "CFF" calc. Expl From "CFF" calc. Expl
(i)-1.1 (-0.26) 5.9 (1.4),a, (i)-1.4 (-0.33) 5.7(1.37)a2-pentene di (ii) 3.6 (0.86) 1.7 (9.4)- d (ii) 3.3 (0.80)
(iii) 0.25 (0.06) * (iii) 0.72 (0.17)
2-butene 3.5 (0.83) 5.23(1.25)a 3.2 (0.77) 5.4(1.3)°4.35(1.04)a ,,2.0(0.5)a
4-methyl- 2.2 (0.53), 5.06(1.21)a 1.92 (0.46) 2.9(0.7)a2-pentene
aFrom D. R. Stull, E. F. Westrum Jr., G. C. Sinke, The chemical thermo-dynamics of organic compounds, J. Wiley and Sons, Inc. ()969); the entropies are deduced from thermal data. •
bSee reference [106]; asee reference [105]. The values taken from references [105] and [106] are obtained from iodine-catalized isomeriza-tion of olefins. d (i) describes the entropy difference between the conformations of lowest energy; (ii) gives the entropy difference when the trans isomer is in its second conformational energy minimum; (iii) gives the expected value when the Gibbs energy difference between the two trans-2-pentene rotamers is taken equal to 4.06KJ.mo1-1 (0:97Kql.m91-1). Units: the values are given in J.mo1-1.0; between parentheses, these quantities are given in cal.mo1-1.K-1.
116
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
experimental and "CFF" calculated vibration of frequencies (see reference
[3]), it is highly likely that the calculated AS values are far more
reliable than the corresponding experimental data.
3.4 STRAIN ENERGY DIFFERENCE BETWEEN ROTAMERS
4'
3.4.1 3-methly1-1-butene
The preferred conformation for the 3-methyl-l-butene is such
that thefflethine C-H fragment of the isopropyl group eclipses the C=C
double bond and therefore anti relative to the olefinic C-H (see
figure (3.4-1)). This result confirms the assumption made by Bothner-By
et al. [207] in their early studies of this molecule by NMR spectroscopy.
zn Rummens et aZ.'s [71] estimation, the population difference between
the anti and'gauche forms is small. These authors estimated (from
variable temperature proton spectra) that AG° = 0.54KJ.mo1-1 (0.13Kcal.
mol-1) between the anti and gauche conformations. "CFF" calculations for
steric energy differepce give a value of AV = 4%7KJ.mo1-1 (1.13Kcal.mo1-1).
Such a value is unacceptable in the opinion of Rumens et al. [71].
According to the "CFF" calculation the strain is mainly
released through an opening of the C=C-C valence angle between the two
rotamers (from 124° in the anti form this angle increases to 127.1° in
the gauche form). This is combined with an opening of the -C-C-C angle
bearing the C-C bond eclipsing the C=C double bond. In the gauche form,
the steric hindrance is further alleviated by a small twisting of the
entire isopropyl group by 6°. The important geometrical features of the
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
I
U rn
I
I
118
•
I
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
two rotamers are given in figure (3.4-1). A more detailed description of
them can be found at the end of this chapter.
3.4.2 trans-2,5-dimethyl-3-hexene
Following a study by Rummens et aZ. [108], four different
rotamers corresponding to energy minimum have been investigated. In
their notation, there is a singlet (aa) state, a 4-fold degenerate (ag)
state [(ag+), (ag-), (g+a), (g-a)], a 2-fold degenerate state consisting
of the (gg) and (g-g-) rotamers and another 2-fold degenerate state of
the (dig-) and (g-g+) rotamers. Energetically the two rotors are almost
independent and the calculated steric energies for the two latter (gg)
states are almost identical (the difference amounts to 0.05KJ.mol or
0.01Kcal.mol-1). The energy increase for each anti-gauche transformation
is not exactly constant and the difference in strain energy between (aa)
and (gg) is not quite twice that of (aa) (-0,g) (10.7KJ:mo1-1 instead of
10.0KJ.mo1-1 for two AVaa g which. is 2.55 instead .of 2.38 in,Kcal.mol-1)
as can be seen from figure (3.4-2). This amount of AV = 5.KJ.mol-1
(1.19Kcal.mol ) is close to the one calculated for the similar transfor-
mation in the 3-methyl-l-butene (which is 4.73KJ.mo1-1 or 1.13Kcal.mo1-1).
However, experimental evidence (seeRummens et al. [71]) suggests much
smaller difference in energy between the rotamers than the calculated value.
Once again the discrepancy between calculated and experimental values is
around 4.2KJ.mol-1 (1.Kcal.mol-1). Such an overestimation seems to be a
general feature of the "CFF" method developed by Ermer and Lifson [3]
when a rotameric C sp 2-C sp3 transformation involving an isopropyl group
119
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Reproduced w
ith permission o
f the copyright owner. F
urther reproduction prohibited without perm
ission.
Iierot. J-2.5 - dimethy1-3-hexerte
20.
AI
0.
5.68 (1.36)
4.97 (1.19)
1
f +, 7,51-11+
14.2 (3.40)
ethylene
3-methyl-1-butene ,40 f reze•nede
4.72 (1.13)
8.19 (1.96)
FIGURE 3.4-2 Steric energy increases with successive anti-gauche transformations of the isopropyl group in 3-methyl-l-butene and in trans-2,5-dimethyl-3-hexene as obtained from Force Field calculation (the figures between parentheses are steric energy differences in Kcal.mo171).
Reproduced w
ith permission of the copyright ow
ner. Further reproduction prohibited w
ithout permission.
occurs. If the value of 550J.mol (130ca1.mol-1) for AG° found for
3-methyl-l-butene is also applicable to both the anti-gauche transforma-
tions of trans-2,5-dimethy1-3-hexene, then all states ((aa), (ag), (gg))
are appreciably populated at room temperature and any NMR experiment at
this temperature would involve the four conformations.
The successive geometrical changes for each anti-gauche trans-
formation are drawn in figure (3.4-3); they are described more thoroughly
in the appendix following the chapter. Each anti-gauche transformation
has the tendency to open up the adjacent C=C-C valence angles while it
closes the opposite C=C-C angles. The two discernable (gg) states have
the same valence angles.
3.5 INTERCONVERSION PATH AND THERMODYNAMIC PROPERTIES
3.5.1 cis-2,5-dimethyl-3-hexene
The path of lc st energy displayed in figure (,3.5-1) has been
obtained by "driving" the torsional angle around one of the Cop 3-C op2
bonds by steps of 10 to 20° to give a smooth conformational change. The
computer calculated %retry of the conformation of lowest energy has a
C2v symmetry; both methine hydrogens are in anti position with respect to
the closest olefinic fragment (this conformation will be referred to as
the (aa) conformation later). The conformation with one of the methine
bonds in ayn position (referred to as (as) conformation) presents only a
Cs symmetry; its steric energy is 12.5KJ.mo1-1 (3.0Kcal.mo1-1) higher
than the energy of the (aa) conformation. In between these o conformations,
ia 0
121
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Reproduced w
ith permission o
f the copyright owner. F
urther reproduction prohibited without perm
ission.
a
II
II
.0
C 4
C
II
1221 C • — C
1;'
H
D IY . /'
C
109 6Se
!.H
C
4, '•.•
X1.334 /s 'C
C 111 31 (7'4. 0H " — • H
6 'I; 12-
II
113 90 C
4.3 34C C
141
H
C
II
C 111111, • • • C
FIGURE 3.4-3 Calculated molecular geometries for the various conformations of minimum energy of trans-2,5-dimethy1-3-hexene as obtained by Force Field calculation.
Reproduced w
ith permission of the copyright ow
ner. Further reproduction prohibited w
ithout permission.
(;;
.06
28S I\J
22.5 (539)
•
H 54\
.,341 133J// 18 \ ri
H 9 129y
[ 7 \
17.3 (4.1.1)
I
I 0 160 270 360
mapping coordinateeN)
FIGURE 3.5-1_ Calculated steric energy profile for the inter-conversion of (aa) and (as) conformers of cis-2,5-dimethy1-3-hexene (the figures between pai-entheses are energies in K.cal.mo1-1).
Reproduced w
ith permission of the copyright ow
ner. Further reproduction prohibited w
ithout permission.
another (shallow) minimum can be seen in the energy path; it corresponds
to a geometry of low symmetry (C1) with one methine hydrogen in gauche
position. The C sp 3-C sp2 single bond bearing the other isopropyl group
is twisted by almost 6°, making the methine C-H stick out of the plane
containing the C=C-C part. The most important geometrical features for
these conformations are given in figure (3.5-2); a more complete picture
of them can be seen in the appendix following this chapter.
Only a few more comments need be made about the calculated
structural and energy parameters of the various conformations and transi-
tion state shown in figure (3.5-2) and table 3.5-1. For the (aa), (as),
(ag) conformers only angle bending and non-bonded energy are of
appreciable magnitude. The (as) conformation has higher bond angle
bending and torsional strain energtei than .t.e (aa) conformation; this is
partly compensated by a smaller non-bonded energy in the (as) state as
can be perceived in table 3.5-1. Much of the strain for the third
conformation (ag) is from the angle bending terms; the repulsive forces
between the two isopropyl groups open the C=C-C valence angles to values
reaching 132.1° and 133.9° (as said previously these values are at the
limits of validity of the method). In this same conformation, release of
the strain is partly obtained through a torsion of 1.8° of the double
bond.
Thermodynamic properties for these various conformations and
for the transition state are given in table 3.5-2. Because of the
extremely low calculated barrier between the (as) and the distorted (ag)
states (5.8KJ.mo1-1 or 1.4Kcal.mo1-1) most of the interest lies in the
124
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
C.
C.
1.333
i/C 11727
0
H
C\\\
03 a 0, t",: . 0.A
, ..-07 ..., C \ 1.331 ( '
C 0.8 At? A -.• - 9 cu-> 4
C 1,„ •••:.
•••
C 111.40
\sO0
.0
\O/
C \ 1.333 / .1
4
(aa)
n2.42 C 00.3 o
CO
tIGURE 3.5.-2 Calculated molecular geometries of the three conformations of lowest minimum energy of cis-2,5-dimethy1-3-hexene.
125
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
TABLE 3.5-1 Contributions to calculated steric energies for various conformations of cis-2,5-dimethy1-3-hexene.*
(aa) (as) (ag)
0.385 0.25 0.561 Bond stretching (0.092) (0.059) (0.134)
Bond angle bending 7.067 (1.689)
11.51 (2.75)
22.55 (5:39)
Torsional 'strain 0.067 10.88 (2.60)
2.50(0.616) (0.597)
Out of plane bending 0.0 0..0 (0.0)
0.0(0.0) (0.0)
Non-bonded energy 14.42 12.5 (2.98)
16.4(3.45) (3.93)
-1.17 -1.74 -3.98 Cross terms (-0.28) (-0.42) (-0.95)
20.77 33.34 38.1 Total steric energy (4.964) (7.97) ' (9.1)
*Units: the energies are given in KJ.mol-1; between parentheses, these quantities are given in Kcal.mol-l.
126 4
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
TABLE 3.5-2 Calculated thermokynpic properties of cis-2,5-dimethy1-3- hexene conformations
(aa) (as) (ag) TS*
° strain
198
• AH
AS
AG
20.8 12.6 17.3 (4.96) (3.00) (4.14)
22.5 (5.38) 1
602 12.0 18.8 21.8 (143.8) (2.88) (4.49) (5(21)
298 615 12.1 18.5 20.8 (147.1) (2.89) (4.43) (4.97)
398 634 12.1 18.3 , 19.9 (151.6) (2.89) (4.38r (4.75)
198 363 -1.55 15.1 -25.1 (86.6) (-0.37) (3.60) (-60)
298 422 , -1.34 14.0 -29.1 (100.7) (-0.32) (3.34) (-6.95)
398 477 -1.17 13.5 -31.8 (114.1) (-0.28) (3.22) (-7.6)
`198 530 12.3 15.8 26.8 (126..6) (2.95) (3.78) (6.40)
298 490 12.5 14.4 15 29.5 (2/7.2) (2.99) (3.43) (7.04) .„..
398 444 12.6 13.0 32.5 (106.1) (3.01) (3.10) (7.77)
The values for the (aa) state are absolute (given in italics); those for the other conformations are relative to (aa). Units: the energies are in KJ.mo1-1, the entropies are in J.mo1-1.K-1. Between Orentheses, these values are given in Kcal.mo1-1 and in cal.mol-I.K-1 respectively. The temperatures are in K. *TS represents the transition state between (aa) and (ag).
127
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
• Alt
(aa) to (as) barrier which is calculated to be 31.8KJ.mo1-1 (7.6Kcal.mo1-1)
at 298K. The large difference between the entropy of the (as) conforma-
7 tion and that of the transition state, and its large variation with
temperature leads to values of enthalpies of rotation (about 21KJ.mol-1
or 5Kcal.mol-1) much lower than the corresponding Gibbs energies. How-
ever, all these values are small enough so that a fast exchange (on the
NMR time scale) beiween these states can be expected at room temperature.
According to the "CFF" calculation, the (aa) conformation is
12.6KJ.Mo1-1 (3.0Kcal.mo1-1) more stable than the (as) conformation.
Their Gibbs energy difference (increasing with temperature) reaches
12.5p.mol-1 (3.0Kcal.mol-1) at room temperature„whereas the enthalpy
difference (almost temperature independent) is 12KJ.mo1-1 (2.9Kcal.mo1-1).
Even with an overestimation of this difference by about 4.2KJ.mol-1
(1Kcal.mol-1) (as suspected for several rotameric energy difference--see
Rummens et aZ. [71]), the (aa) conformation is populated to the extent of
99 percent,at room temperature.
3.5.2 trans-2;2,5-trimethyl-3-hexene
By constraining one torsional angle and "driving" it to
successively increased or decreased values, the pathways of lowest energy
given in figures (3.5-3) and (3.5-4) have been obtained. In both'cases
the two rotors (the isopropyl and tert-butyl groups) are uncoupled. Two
conformations of minimum energy have been found; the more stable shows a
Cs symmetry (called I in figure (3.5-5)), while the other does not
present any plane of symmetry (this is the conformation called II in the
128
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
\ 123/
40.0
<173 \
\ 122.3)
O 12645 \
E
13.31 (3.18)
30.0
6
25.,64L6.13)
20.0 180 • 270
H
<126 3 \
10 9 (2.6)
mapping parameter
H?,
" H
360
FIGURE 3.5-3 Calculated steric energy profile for the rotation of the isopropyl group of trans- , 2,2,5-trimethy1-3-hqxene (the .figures between parentheses are energies in Kcal.mol_ ').
Reproduced w
ith permission of the copyright ow
ner. Further reproduction prohibited w
ithout permission.
Reproduced w
ith permission o
f the copyright owner. F
urther reproduction prohibited without perm
ission.
1 a >-0
33.5
29.3
20.9 I I 180 210
MAPPING COORDINATE ------pr 360
FIGURE 3.5-4 Calculated steric energy profile for the rotation of the tert-butyl group of trans-2,2,5-trimethy1-3-hexene (the figures between parentheses are energies in Kcal.mo1-1).
Reproduced w
ith permission of the copyright ow
ner. Further reproduction prohibited w
ithout permission.
Reproduced w
ith permission o
f the copyright owner. F
urther reproduction prohibited without perm
ission.
X
C
I
114.52 122.
114.07 C 1.334
126.41 122.72
C 113 02
'Ti
112.40
II
FIGURE 3.5-5 Calculated molecular geometries of the conformations of minimun}'energy for trans-2,2,5-trimethy1-3-hexene.
Reproduced w
ith permission of the copyright ow
ner. Further reproduction prohibited w
ithout permission.
figure ). The transition state for transformation I to II has one of the
carbons of the isopropyl group in syn position. During the entire trans-
formation, one of the Csp 3-Csp 3 bOnd of the tert-butyl group is eclipsing
the double bond. The energy barrier which separates these conformations
is small (13.3KJ.mo1-1 or 3.18Kcal.mo1-1), and the rate of exchange would
be too fast to be detected by using the NMR method.
The three-fold symmetry described in figure (3.5-4) has been
obtained by "driving" one of the torsional angles on the tert-butyl side.
Once again the barrier to rotation is small.
Rotational barriers, enthalpy and Gibbs energy differences are
given in table 3.5-3. The Gibbs energy difference at room temperature
between I and II has a value of 4.6KJ.mo1-1 (1.1Kcal.mo1-1). According
to this value, 76 percent of the sample population would be in conforma-
tion I. Following the results obtained by Rummens et al. "7/1 the steric
energy difference between anti and gauche rotamers in isopropyl substi-
tuents is overestimated by 4.2KJ.mo1-1 (1Kcal.mo1-1). If such a correc-
tion would be applied to the present results, it would lower the
difference in steric energy to around 0.4KJ.mol-1 (0.1Kcal.mol-1).
Accepting this value as a correct value 63 percent of the population
should be in conformation II at room temperature.
The geometries outlined in figure (3.5-5) are more thoroughly
described in the appendix at the end of the chapter. The release of
"strain for the gauche isomer (conformation II) is achieved mainly through
valence angle opening; this angle bending energy accounts for 2.6KJ.mol-1
(0,63Kcal.mo1-1). Torsional deformation amounting to 0.2KJ.mo1-1
132
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
TABLE 3.5-3 Calculated thermodynamjc properties of trans-2,2,5-trimethyl-3-hexene conformations
I II TI*
TII*
AVstrain 25.6 5.69 13.3 7.11 (6.13) (1.36) (3.18) (1.70)
T
198 680 5.48 11.0 3.87 (162.5) (1.31) (2.62) (0.93)
AH
AS
AG
298 695 5.19 10.2 3.23 (166.3) (1.24) (2.43) (0.77)
398 717 4.81 9.37 2.56 (171.4) (1.15) (2.24) (0.61)
`198 359 2.38 -8.53 -14.7 (85.9) (0.57) (-2.04) (-3.52)
298 427 1.92 -11.9 -17.4 (102.1) (0.46) (-2.84) (-4.15)
398 491 1.76 -14.1 -19.3 (117.4) (0.42) (-3.38) (-4.62)
`198 607 5.02 12.7 6.81 (145.2) (1.20) (3.04) (1.63)
298 568 4.60 13.7 8.40 (135.8) (1.10) (3.27) (2.01)
398 522 4.10 15.0 10.2 (124.7) (0.98) (3.59) (2.44)
+The values for conformation Dare absolute (given in italics); those for the other conformations are relative to that of (I). Units: the energies are given in KJ.mo1-1, the entropies in J.mo1-1.K-1. Between parentheses, these values are given in Kcal.mo1-1 and in cal.mo1-1.K-1respectively. The tempdratures are in K.
*T represents the transition state for the tert-butyl rotation, while T1 represents that for the isopropyl rotation.
133
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
(0.05Kcal.mo1-1) in addition to the increase of 2.7KJ.mo1-1 (0.64Kcal.mo1-1)
for the non-bonded interaction completes the distribution. Included in
these results is a slight out-of-plane position (6.7°) for the C sp 3-C sp3
bond eclipsing the double bond.
3.5.3 cis-2,2,5-trimethy1-3-hexene
Following the procedure described for the' trans isomer, the
lowest energy profiles given in figures (3.5-6) and (3.5-7) have been
determined. When constraining the H-C sp 2-C sp3-H fragment of the
isopropyl group and "driving0 it, the tart-butyl group is also rotating
due to the through-space coupling with the isopropyl group (see figure
(3.5-7)). But, if the constrained angle is on the tert-butyl side, with
the isopropyl in anti position, the isopropyl group appears uncoupled.
This is the consequence of the *non-reversibility of the process when
"driving" one angle at a time, as already mentioned by Anet and Yavari
[I09]: the computer-driven process follows the lowest energy path for
any given constraint. The calculation leads to three conformations of
minimum energy. The lowest energy is obtained with one of the C sp 3-C sp3
single bonds of the tert-butyl group eclipsing the adjacent C-H olefinic
bond with the methine part of the isopropyl group eclipsing the double
bond; this structure, which has a Cs symmetry is denoted I or (as). In
the second minimum one of the C-C bonds of the tort-butyl group eclipses
the double bond (rotation of 60° from conformation I around the C op 2-C sp3
bond), and this conformation II can be noted (aa). The third minimum
(conformation III) displays a highly strained structure. No symmetry is
134
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Reproduced w
ith permission o
f the copyright owner.
Further reproduction prohibited w
ithout permission.
48.0
7 -3 I 46.0 O E
w z w z
=
7( 44.0
tA
42 0
4.72 (1.13)
2.72 (0.65)
C
\ )
180 270 MAPPING COORDINATE .•
1 360
FIGURE 3.5-6 Calculated steric energy profile for the rotation of the tert-butyl group of cis-2,2,5-trimethy1-3-hexene (the figures between parentheses are energies in Kcal.mol-l).
Reproduced w
ith permission of the copyright ow
ner. Further reproduction prohibited w
ithout permission.
Reproduced w
ith permission o
f the copyright owner.
Further reproduction prohibited w
ithout permission.
95.0
a 70.0 0
0,
0 "
CD g 0
45 0 — 1-
180 270 mapping parameter
.0
‘ss 31.8 113.3
H
37.2 (8.9)
,s;k 41.0 161.7 H
25.5 (6.1)
H 360
FIGURE 3.5-7 Calculated steric energy profile for the rotation of the isopropyl group of cis-2,2,5-trjmethyl-3-hexene (the figures betwqen parentheses are energies in Scal.mor I).
Reproduced w
ith permission of the copyright ow
ner. Further reproduction prohibited w
ithout permission.
its
present in this conformation. Whereas between con rmations I and II the
strain is mainly released through opening of valence angles, tonformation
III has a twisted double bond (4.1°), and none of the bonds of either
alkyl group is eclipsing the double bond; the extra torsional disOace-
ments apparently reduce the strain with the position of\the methine
fragment.18° out of the syn position. Geometries for these conformations
are given in figure (3.5-8); a more detailed description f the structures
,appears in the appendix at the end of this chapter.
The calcUlated rotational barrier between the (as)\and (aa)
conformations is very small as can be seen in table 3.5-4. A fast
exchange between them is occurring at temperatures of usual NMR experi-
ments. The steric energy difference between the (as) and (aa) conforma-
tions is small (2.72KJ.mo1-1 or 0.65Kcal.mo1-1). But the presence of an
extra small vibrational frequency in the (aa) conformation (there is one
frequency with a smaller value than 100cm-1 for the (as) conformation
(35cm-1), while there are two for the (aa) conformation (40 and 23cm-1)
gives a somewhat larger enthalpy difference. The Gibbs energy difference
reaches a sizeable value (about 5.4KJ.mo1-1 or 1.3Kcal..mo1-1 ); this would
lead to a population difference between the (as)"and (aa) states at room
temperature. The presence of a measurable population of rotamer III is
improbable; the Gibbs energy difference between conformatiOns II (also
called (aa)) and is 33KJ.mo1-1 (8.0cal.mo1-1), 28KJ.mo1-1 (6.7Kcal.
mol-1) of which is caused by the strain present. The presence of only
two rotameric conformations at low temperature seems well warranted.
137
141
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
C
H4
114.83 (
'C itt.3
C 107 2 'top
111.83
I 109.87 129.12 130.22 c~ 1.333
C 11408
115.45 115.70
III
\ 134 12 41 135.77
111: 1431 0 1 1,1.75
.7 11291 112.4
H:
II cat.)
iso-propyl
tell°
FIGURE 3.5-8 Calculated molecular geometries of conformations of minimum energy for cis-2,2,5itrimethy1-3-hexene.
•
I •
138
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
TABLE 3.5-4 Calculated thermodynamic properties of cie-2,2,5-trimethy1-3-hexene conformations+
(as) as III TS*
k 43.0 2.72 a strain
. (10.27) (0.651) T
198 ' 695 6.53 31.9 (166. (1.56) .. (7.62)
AH 298 71 5.98 31.5 (1 9.9) (11.43) . (7.52)
398 732 5.48 (175.0) (1.31)
AS
AG
198 366 4.48 (87.6) (1..07)
298 435 • 2.18 004.1 (0.52)
398 500 0.79 (119.4) (0.19)
' 28.2 (6.74)
31.1 (7.43)
-5.69 • (-1.36)
' -7.45 • (-1.78)
4.73 (1.13)
6.42 (1.53)
5.17 (1.24)
3.95 (0.943)
-12.6 (-3.02)
-17.7 (-4.24)
-8.58 -21.3 (-2.05) (-5.09)
198 622 5.65 33.1 8.91 (148.7) (1.35) (7.92) (2.13)
298 581 5.31 33.8 10.5 (138.9) (1.27) (8.09) 2.50
398 533 (127.5)
5.15 34.7 12.4 (1.23) (8.30) (2.97)
The values for the (as) state are absolute (given in italics); those for the other conformations .are relative to that of the (as) state. Units: the energi::: are given in KJ.mol-1, the entropies are in J.mo1-1.0. Betwden parentheses these quantities are given in Kcal.mo1-1 and cal.mo1-1.K-1 respectively. The temperatures are in K.
*TS is the transition state for the tert-butyl rotation.
1 39
e
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
3.5.4 4,4-dimethyl-3-tert-butyl-1-pentene
By driving the H-C sp 2-C sp3-H torsion angle, the energy path
drawn in figure (3.5-9) has been obtained. This profile brings two
conformations of minimum energy. A strain energy barrier of 51KJ.mo1-1
(12.2Kcal.mo1-1) separates both rotamers. Their geometries have a low
symmetry (C1) which is close to be (Cs)
energy; this conformation possesses its
anti position. The other minimum shows
180° around the Csp 2-C sp3 bond from its
lowest energy (i.e., in syn position).
in the case of the lowest minimum
lone methine hydrogen in (almost)
the alkyl group rotated about
poSition in the conformation of
As can be seen in figure (3.5-10),
both rotamers have a highly distorted alkyl group. The strain is
partially released (for the minimum of lowest energy) through a rotation
of one of the tert-butyl group from its staggered position relative to
the methine C-H fragment. This distortion reduces the strain because
this structure avoids the juxtaposition of two pairs of methyl groups of
the tert7butyl groups (which would be present if both tert-butyl groups
were staggered relative to the methine C-H). For these highly strained
conformations, relief is also obtained through stretching of the Ca-CB0
bonds (see figure (3.5-10) for notation); a value of 1.562A is found for 0
these bonds, while the equilibrium length is 1.526A.
The nergy difference separating both minima is calculated to
be 17.1KJ.mo1-1 (4.1Kcal.mol-1 ). This corresponds to enthalpy and Gibbs
energy differences of 17KJ.mo1-1 (4.06Kcal.mo1-1) and 18KJ.mol
(4.3Kcal.mo1-1) respectively as is shown in table 3.5-5'. Due to the
small variation in difference in entropy, these values can be assumed to
140
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Reproduced w
ith permission o
f the copyright owner.
Further reproduction prohibited w
ithout permission.
120.0
2 03 t 95.0
0
0
70 0
H
C \ /23.6/
\ H
50.88 (12.16)
C C
5H 128._5,
\ H
17.15 (4.1).
L 180 270
mapping parameter,
360 0 —11..
FIGURE 3.5-9 Calculated steric energy profile for 4,4-dimethy1-3-tert-butyl-1-pentene as obtained by driving the HCET2-Csp31-1 dihedral angle (the figures'between parentheses are energies in Kcal.mo1-1).
Reproduced w
ith permission of the copyright ow
ner. Further reproduction prohibited w
ithout permission.
Reproduced w
ith permission o
f the copyright owner. F
urther reproduction prohibited without perm
ission.
CV``
3 "Si/ CH:
1:566\‘ \ • CH
3 I \ FI 105.79 C.
r
1.344
c‘; . " eb. - 1"/ Jig 61 CA ) " " • • CH3
0, • . -A1.335 /".'-
Ci7 ---\-- s.0
3
Q. HC2C,H 345.99
LHC2C"Cp .7234.99
L ViC2Ca Cp ,.: 97.24
L H C„ H =784 5 5
kHc2c.„cfr 77. 77
HC2CaC,= 297.37
0,9 CH3 si
••- CH3"
• • Oi.70 ‘ °4
A, H
H H
FIGURE 3.5-10 Calculated molecular geometries of the two conformations of lowest minimum energy for 4,4-dimethy1-3-tert-butyl-1-pentene.
Reproduced w
ith permission of the copyright ow
ner. Further reproduction prohibited w
ithout permission.
TABLE 3.5-5 Calculated thermodynamic properties of 4,4-dimethyl-3-tert-butyl-l-pentene conformationsT
anti syn TS* 0
AV strain
T
72.0 (17.2)
17.2 (4.10)
51.0 (12.2)
198 877 17.0 53.6 (209.7) (4.07) (12.8)
AH 298 897 17.0 52.7 (214.3) (4.07) (12.6)
398 923 17.1 51.5 (220.5) (4.08) (12.3)
198 385 -3.19 -15.7 (91.9) (-0.76) (-3.76)
AS 298 465 -3.09 -20.4 (111.2) (-0.74) (-4.88)
398 543 -3.00 -23.8 (129.7) (-0.72) (-5.68)
198 801 17.7 56.8 (191.5) (4.22) I (13.3)
AG 298 758 17.9 58.7 (181.1) (4.29) (13.6)
398 706 18.2 61.1 (168.8) (4.36) (14.6)
tThe values for the anti form are absolute (given in italics); those for the other conformations are relative to the anti form. Units: the energies are given in KJ.mo1-1, the entropies in J.mo1-1.K7 1 Between parentheses, these quantities are given in Kcal.mo1-1 .1<-1 respectively. The temperatures are in K. TS* is the transition state.
143
\
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
be temperature indepeident. These large quantities, even if somewhat
overestimated, indicate that this molecule should be exclusively in the
anti form at room temperature.
Following the opinions expressed by several authors (see for
example [2.70] and [M]) as well as the results of the above study
7) (particularly sections 3.1 to 3.3' the reliability of the Force Field
approach is acknowledged to be greater in the prediction of structural
observations than in energies. The geometric parameters will therefore be
used with more confidence in the discussion of the experimental NMR data
than will be the various kinds of energies obtained by the Force Field
method for the same molecules.
144
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
APPENDIX
In the following pages, the internal coordinates of the various
molecules studied as obtained from the Force Field calculation are given
in full detail. The numbering system of the atoms is shown for the
conformation of lowest energy of each molecule. An example of how to use
the tables is given below for the propene molecule (the distances are in 0 A, the angles in degrees).
Example: •
8 112.54
6 1153
7;""; 1 9 c.; —' cr cc?) -- ---k?' (Y)
6,e•:,---/
S. c?,t'' Y 11- ( ' e 3 2
/ 'ND 1 eii Sic)..--QT:1 sy—--0
4 5
R12 = 1.090 R23 = 1.334
1 is a hydrogen atom, 2 and 3 are carbon atoms.
TH123
= 122.18
NA NB NC ND atom (D) RCD THBCD ' PHABCD
1 2 3 4 H 1.090 120.47 180.00 4 3 2 5 H 1.090 120.89 0.00 1 2 3 6 C 1.503 123.88 0.00 2 3 6 7 H 1.106 113.53 0.00 2 3 6 8 H 1.105 112.54 239.74 2 3 6 9 H 1.105 112.24 120.26
145
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
3-METHYL-1-BUTENE
10 9
11-°•,„ / 7 13 2--;6 1
)' \ 14 % 15 3===2
/ 1 5 4
(anti) form
R12 = •
1 '090 R23 = 1.334 TH123 = 122.35
NA' NB. NC ND atom (D) A RCD THBCD PHABCD
1 2 3 5 H 1.091 120.10. 180.00
5 3 2 4 H 1.089 12P.78 0.00
1 2 3 6 C 1.508 123.80 0.00
2 3 6 7 H 1.107 109.42 0.00
2 3 6 8 C 1.532 110.10 241.33
2 3 6 12 .
C 1.532 110.10 118.67
3 6 8 9 H 1.106 113.'9 298.74
3 6 8 10 H 1.106 112.49 58.89
3 6 8 11 H 1.106 112.73 178.41
3 6 12 13 H 1.106 112.73 181.59
3 6 12 14 H 1.106 112.49 . 301.11
3 6 12 15 H 1.106 113.19 61.26
146
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
3-METHYL-1-BUTENE
(gauche) form
The numbering of the atoms is the same as for the (anti) form.
R12 = 1.089 R23 =
1.334 TH123 = 123,80„.
1 is a hydrogen atom, 2 and 3 are carbon atoms.
NA NB NC' -ND atom (D) RCD THBCD PHABCD •
1 2 3 5 H 1.091 118.33 179.92
5 3 2 4- H 1.090 119.82 -0.02
1 2 3 6 C 1.505 127.10 359.88
2 3 6 7 H 1.107 107.37 , 235.36
2 3 6 8 C 1.535 109.57 .118.43
2 3 6 12 C 1.530 113.70 354.55
3 6 8 9 H 1.106 112.97. 297.33
3 6 8 10 H 1.106 112.66 51..48
3 6 8 11 H 1.106 112.77 177.04
3 6 12 13 H 1.106 112.17 182.73
3 6 12 % 14 H 1.106 113.00 301.74
3 6 12 15 H 1.106 113,56 62.97
1 147
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
TRANS-2,5-DIMETHYL-3-HEXENE
14 25 (aa) form
13=13 ,7 9, 5 10
111 3==-4 2( 22
4/ \ .21-2324
T20 \
k 18 19
R12 = 1.509
1, 2, 3 exe carbon atoms.
R23 = 1.335 TH123 = 123.38
NA NB NC ND atom (D) RCD THBCD PHABCD
1 2 3 4 H 1.091 120.99 0.00
1 2 3 6 C 1.509 123.38 180.00
4 3 2 5 H 1.091 120.99 180.00
2 3 6 7 H 1.107 109.50 0.00
2 3 6 12 C 1.532 110.01 241.32
2 3 6 8 C 1.532 110.01 118.68
3 6 8 9 H 1.106 113.19 61.21
3 6 8 10 H 1.106 112.47 301.08
3 6 8 11 H 1.106 112.75 181.56
3 6 12 13 H 1.106 112.75 178.44
3 6 12- 14 H 1.106 112.47 58.92
3 6 12 15 H 1.106 113.19 298.79
3 2 1 16 H 1.107 109.50 0.00
3 2 1 17 C 1.532 110.01 241.32
3 2 1 21 C 1.532 110.01 118.68
• 2 1 17 18 H 1.106 112.47 58.92
2 1 17 19 H 1.106 113.19 298.79
2 1 17 20 H 1.106 112.75 178.44
2 1 21 22 H 1.106 112.75 181.56
2 1 21 23 H 1.106 112.47 301.08
2 1 21 24 H 1.106 113.19 61.21
148 •
I Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
TRANS-2,5-DIMETHYL-3-HEXENE
(ag) form
The numbering of the carbon atoms is the same. as for the (aa)
conformer.
R12 = 1.511 R23 = 1.334
N123 = 122.80
NA NB NC ND atom (D) RCD THBCD PHABCD
1 2 3 4 H 1.091 119.55 0.04
1 2 3 6 C 1.507 126.49 179.94
4 3 2 5 H 1.090 122.49 179.82
2 3 6 7 H 1.107 107.30 125,46
2 3 6 12 C 1.539 113.90 6.21
2 3 6 8 C 1.535 109.41 242.28
3 6 8 9 H 1.106 112.95 62.74
3 6 8 10 H 1.106 112.66 302.61
3 6 8 11 H 1.106 112.79 183.03
3 6 12 13 H 1.106 112.13 177.02
3 6 12 14 H 1.106 113.03 58.05
3 6 12 15 H 1.106 113.61 296.72
3 2 1 16 H 1.107 109.65 359.78
3 2 1 17 C 1.532 109.9.4 .241.04
3 2 1 21 C 1.532 109.92 118.50
2 1 17 18 H 1.106 113.20 298.87
2 1 17 19 H 1.106 112.47 59.00
2 1 17 20 H 1.106 112.75 178.52
2 1 21 22 H 1.106 112.75 178.51
2 1 21 23 H 1:106 , 112.47 58.99
2 1 21 24 H 1.106 113.20 298.86
149
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
TRANS -2,5-01METHYL-3 -HEXENE
(gleg+) anct,(g-g-) forms
The numbering of the atoms is the same as for the (aa) conformer.
1.509 R23 = 1.334 THBCD = 126.01 R12 =
1, 2, 3 are carbon atoms.
NA NB NC ND ' atom (D) RCD THBCD
1
1
4
2
2
2
3
3
3
3
3
3
3
3
3
2
2
2
2
2
s, 2
•
2
2
3
3
3
3
6
6
6
6
6
6
2
2
2
1
1
1
1
1
1
3
3
2
6
6
6
8
8
8
12
12
12
1
1
1
17
17
17
21
21
21
4
§
5
7
12
8 •
9
10
11
13
14
15
16
17 21
18
19
20
22
23
24
H
C
H
H
C
C
H
H
H
H
H
H
H
C C
H
H
H
H
H
H
„
1.089
1.509
1.089
1.107
1:629
1.536
1.106
1.106
1.106
1.106
1.106
1.106
1.107
1.536
1.529
1.106
1.106 ,
1.106
1.106
1.106
1.106
121-:06
126.01
121.07
107.20
114.31
109.26
112.94
112.66
112.80
112.07
113.07
113.66
107.20
109.26
114.31
112.94
112.66
112.80
112.07
113.07
113.66
PHABCD
0.10
179.86
179.65
125.90
6.56
242.52
62.88
302.76
183.18
176.84
57.92
296.48
234.10
117.48
353.44
297.12
57.24
176.82
176.84
i 57.92
.r296.48
150
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
TRANS72,5-DIMETHYL-3-1HEXENE
(g+g-) and (g-g+) forms
The numbering of the atoms is the same as for the (aa) conformer,
R12 =•1.509 R23 = 1.334 TH
123 = 126.,02
NA NB NC ND atom (D) RCD THBCD PKAgaD
1
1
4
2.
2
2
3
3
3
3
3
3
3
3
3
2
2
2
2
2
2
2
2
3
3
3
3
6
6,
6
6
6
6
2
2
2
1
1
1
1
1
1
3
3
2
6
,, 6
6
8
8
4, . 8,
12
12
12
1
1
1
17,
17
17
21
21
21
ti
4
6
5
7
12
8
9
10
11
13
14
15
16
17
21
18
19
20
22
23
24
H
C
H
H
C
C
H
H
H
H
H
H
H
C
C
H
H
H
H
H
H
1.089
1.509
1.089
1.107
1.529
1.536
1.106
1.106
1.106
1.106
1.106
1..106
1.107
1.536
1.529
1.106
1.106
1.106
1.106
1.106
1.106
121.07
126.02
121.07
107./19
114.31
109.28
112.95
:112.66
112.79
112.07
113.07 le,113.66
107.19
109.28
114.31
112.66
112.95
112.79
112.07
113.66
113.07
359.96
180.00
180.00
125.87
6.56
242.49,
62.91
302.78
183.20
176.81
57.89
296.46
125.87
242.49
6.56
302.78
62.91
183.20
183.19
63.54
302.11
m
151
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
CIS-2,5-DIMETHYL-3-HEXENE
(aa)' form
9
j
R12 = 1.50?
1, 2, 3 are carbon atoms.
2F 23 16
„p.24 g0 / 17-19
2 18
5
R23 = 1.333 TH123 = 128.51
NA
1
1
4
2
2
2
.3
3
3
3
3
3i
3,
3
3'
2
2 .
2
2
2
2
NB NC ND atom (D) 'RCD BCD PHABCD
2' 3 4 H 1.091 116.82 180.00
12 3 6 C 1.502 128.51 0..00
3 2 5 H 1.091 116.82 0.00
Q 6 7 H 1.104 111.41 0.00
3 6 a 12 C 1.534 109.87 119.04
,3 6 8 C 1.534 109.87 240.96
4,6 8 9 H 1.106 112. 3 59.64
16 8. 10 H 1.106 113.24 299.48
6 8 11 H 1.106 112.71 179.11
6 12 13 H 1.106 112.71 180.89
6 12 14 H '1.106 113.24 60.52
. 6 12 15. H 1.105 112.43 300.36
2 1 16 H 1.534 111.41 0.00
2 1 17 C 1.534 109.87 119.04
2 1 21 C 1.106 109.87 240.96.
1 17 18 H 1.106 112.71 179.11
1, 17 19 H 1.106 112.43 59.64
1 17 , 20. H 1.106 113.24 299.48
1 21 22 H 1.106 112.43 59.64
1 21 23. H 1.106 113.24 299.47
' 1 21 24 ' H 1.106 112.71 179.11
a ., .t • . I 1 1 1 152
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
CIS-2,5-DIMETHYL-3-HEXENE
(as) form
The numbering of the atoms is the same 0 for the (aa) form.
= 1.500 R12
1, 2, 3 are carbon atoms.
R23
1.333 TH123 = 129.98
NA NB NC ND atom (0) RCD THBCD
•
PHABCD
1 2 3 4 H 1.091 116.29 180.00
1 2 3 6 1.500 129.20 0.00
4 3 2 5 H 1.091 116.06 0.00
2 3 6 7 H 1.103 111.40 0.00
2 3 6 12 C 1.534 109.24 119.05
2 3 6 8 C 1.534 109.92 240.95
3 6 8 9 H 1.106 112.48 59.49
3 6 8 10 H 1.106 113.23 299.32'
3 6 8 11 H 1.106 112.69' 178.98
3 6 12 '13 H 1.106 112.69 181.02
3 6 12 14 H 1.106 113.23 60.6e
3 6 12 15 H 1.106 112.48 300.51
3 2 1 16 H 1.108 105.87- 180.00
3 2 1 17 C 1.529 112.43 295.78
3 2 1 21 C 1.529 112.43 64.22
2 1 17 18, H 1.106 112.30 172.45
2 1 '17 19 H 1.106 112.38 ' 53.61
2 1 17 20 H 1.104 114.58 292.78
2 1 21 22 1.106 112.38 53.61
2 1 '21 23 H 1.104 114.58 292.78
2 1 .21 24 H 1.106 112.30 172.45
153
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
CIS-2,5-DIMETHYL-3-HEXENE
(ag) form
The numbering is the same as for the (aa) form.
R12
= 1.497
1, 2, 3 are carbon atoms. .
R23 = 1.331 TH123
= 133.98
NA
1
1
4
2
2
2
3
3
3
3
3
3
34.
3 3
2
2
2
2
2
2
' NB MC ND atom (0) RCD THBCD PHABCD
2 3 4 H 1.091 114.34 178.49
2 3 6 C 1.496 132,.11 358.18
3 2 5 H 1.092 113.97 1.47
3 6 7 H 1.100 112.41 354.57
3 6 12 C 1.534 109 95 114.41
3 6 8 C 1.536 109.77 235.93
6 8 9 H 1.106 112.40 59.74
6 8 10 H 1.106 113.32 299.51
6 8 11 H 1.106 112.64 179.15
6 12 13 H 1.106 112.70 180.46
6 12 14 H 1.106 113.21 60.12
6 12 15 ft 1.106 112.50 299.97
2 1 16 H 1.107 105.63 133.45
2 1 ' 17 C 1.537 109.38 248.51
' 2 1 21 C 1.523 117.27 14.86
1 17 18 H 1.106 112.77 174.96
1 . 17 19 H 1.106 112.66 55.37
1 17 20 H 1.106 112.94 295.26
1 21 . 22 H 1.106 ;3.65 48.79
1 21 23 H 1.105 114.11 285.41
1 21 24 H 1.106 111.31 167.24 r
154
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
TRANS-2,2,5-TRIMETHYL-3-HEXENE
(anti) form 16 15
17,4, / ,18 12..mo..°\ 10 13•1
14 2-- --1t 212 / z is \ -23
11 \ _6%0s 24
R12 = 1.334
1, 2, 3 are carbon atoms.
26' 27 "7 -21
R23 = 1.512 19 zo TH123
= 122.66
NA NB NC ND atom (D) RCD THBCD PHABCD
1 2 3 4 C 1.532 109.91 241.27
1 2 3 5 C 1.532 109.91 118.73
3 2 1 6 C 1.511 126.41 180.00
2 1 6 7 C 1.539 108.30 239.17
2 1 6 8 C 1.539 108.31 120.84
2 1 6 9 C 1.534 113.02 0.00
3 2 1 10 H 1.091 119.52 0.00
6 1 2 11 H 1.089 122.72 0.00
1 2 3 18 H 1.107 109.66 0.00
2 3 5 12 H 1.106 112.76 181.48
2 3 5 13 H 1.106 113.20 61.13
2 3 5 14 H 1.106 112.46 301.01
2 3 4 • 15 H 1.106 112.75 178.52
2 3 4 16 H 1.106 112.46 59.00
2 3 4 17 H 1.106 113.20 298.87
1 6 7 19 H 1.106 113.05 181.36
1 6 7 20 H 1.106 112.70 61.34
1 6 7 21 H 1.106 112.99 301.46
1 6 8 22 H 1.106 113.05 181.37
1 6 8 23 H 1.106 112.70 61.34
1 6 8 24 H 1.106 112.99 301.46
1 6 9 25 H 1.106 112.99 180.00
1 6 9 26 H 1.106 113.36 299.41
1 6 .9 27 H 1.106 113.37 60.59
155
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
TRANS-2,2,5-TRIMETHYL-3-HEXENE
(gauche) form
The numbering of the atoms is the same as for the (anti) conformer.
1.334 R23 = 1.509 MI23 = 125.89 R12 =
1, 2, 3 are carbon atoms.
NA NB
1 2
1 2
3 2
2 1
2 1
2 1
3 2
6 1
1 2
2 3
2 3
2 3
2 3
2 3
2 3
1 6
1 6
1 6
1 6
1 6 1 A 6
1 6
1 6 i
1 6 /
1
NC • ND atom (D). RCD THBCD . PH ABCD
• 3 4 C 1.529 114.34 6.74
3 5 C 1.536 109.24 242.C9
1 6 , C 1.514 126.03 180.07
6 7 C 1.540 108.19 238.98
6 8 C 1.540 108.17 120.83
6 9 C 1.533 113.36 359.92
1 10 H 1.090 120.94 359.93
2 11 H 1.089 121.31 0.03
3 18 H 1.107 107.18 126.08
5 12 H 1.106 112.80 183.19
5 13 H 1.106 112.94 62.90
5 14 H 1.106 112.66 302.78
4 15 H 1.106 112.06 176.76
4 , 16 H 1.106 113.07 57.84
4 1 17 H 1.106 113.67 296.39
7% 19 H 1.106 108.19 181.53
q 20 H 1.106 112.68 61.50
7', 21 H 1.106 113.00 301.62
8 22 H 1.106 113.05 181.50
/ 8 823
24
H
H
1.106
1.106
112.68
113.00
. 61.48
301.60
9 25 H 1.106 112.36 .179.99
9 26 H 1.106 113.41 299.35
9 27 H 1.106 113.41 60.63
156
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
CIS-2,2,5-TRIMETHYL-3-HEXENE
conformation (as)
•
12 r . 2322
11;5. 18 24-8,1 ,19 14 -,3/ 25,90 5 ----k-20 15 .4/ \ 26- / '
*--4 \ 2/ 21 16/ I 2 1
17
R12 = 1.333
1, 2, 3 are carbon atoms
/ \ 11 . 10
R23
=11499 TH123
= 130.22
NA NB • NC • ND atom (D) RCD THBCD g
PHABCD
1 2 . 3 4. C 1.535 109.87 119.16
1 2 .3 5 C 1.535 109.87 240.87
3 2 1 6 C 1.506 .-a..
129.12 0.00
2 1 6 7 C 1.55? 108.09 180.02
2 1 6 8 C 1.534 111.35 62.59
2 1 6 9 C 1.534 111.35, 297.43
3 2 1 10 H 1.091 115.45 181.00
6 1 2 11 H 1.091 115.70 181.00
1 2 3 18 H 1.102 111.83 0.02
2 3 5 12 H 1.106 112.68 179.11
2 3 5 13 H 1.106 112.47 59.63
2 3 5 14 H . 1.106 113:24 299.46
2 3 4 15 H 1.106 112.68 180.89
2 3 4 16 H 1.106 113.24 60.53
2 3 4 17 H 1.106 112.47 300.37
1 6 7 19 H 1.106 112.83 180.00
1 6 7 20 H 1.106 112.92 60.09
1 6 7 21 H 1.106 112.92 299,61
1 6 8 22 H 1.106 112.63 185.27
1 6 8 23 H 1.106 114.56 65.21
1 6 8 24 H 1.106 112.59 304.63
1 6 9 25 H 1.106 112.63 174.72
1 6 9 .26 H 1.106 114.56 294.78
1 6 -9 27 H 1.106 112.59 55.36
157
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
CIS-2,2,5-TRIMETHYL-3-HEXENE
(aa) form, conformation II
The numbering of the atoms is the same as for the (as) form.
R12 = 1.331
1, 2, 3 are carbon atoms.
R23 = 1.496 TH.123 = 133.37
NA NB NC ND atom (0) Rco .TH BCD - pH ABCo '
1 2 3 4 C 1.536 109.75 119.37
1 2 3 5 C 1.536 109.75 4' 1240.63
3 2 1 6 C 1.502 133.97 0.00
2 1 6 7 C 1.545 107.71 121.68
2 1 6 8 C 1.527 116.45 0.00 2 1 6 9 C 1.545 107.71 ` 238.32
3 2 1 10 h 1.092 114.05 180.00
6 1 2 11 H 1.091 113.67 180.06
1 2 3 18 H 1.099 113.16 0.00
2 3 5 12 H 1.106 112.66 179.66
2 3 5 13 H 1.106 112.41 60.22
2 3 5 14 H 1.106 113.29 300.03
2 3 4 15 H - 1.106 , 112.66 180.34
2 3 4 16 H 1.106 113.29 59.97
2 3 4 17 H 1.106 112.41 299.77
1 6 7 19 H 1.106 113.06 177.10
1 6 7 20 H 1.106 113.05 57.01
1 6 7 21 H 1.106 112.61 297.10
1 6 8 22 H 1.106 111.79 180.00
1 6 8 23 H 1.106 113.75 61.65
1 6 8 24 H 1.106 113.75 298.35
1 6 9 25 H 1.106 113.06 177.10
- 1 6 9 26 H 1.106 112.61 297.10
1 6 9 27 H 1.106 113.05 57.01
158
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
CIS-2,2,5-TRIMETHYL-3-HEXENE
Conformation III
The numbering of the atoms is the same as for the (as) conformer.
R12 = 1.331
1, 2, 3 are carbon atoms.
R23 = 1.494 TH123
= 135.77
NA NB NC ND atom (D) RCD TMBCD PHABCD
1 .2 3 4 C 1.524 115.36 47.91
1 2 3 5 C 1.52.8 112.60 275.57
3 2 1 6 C 1.501 134.12 355.66
2 1 6 7 .0 1.556, 107.22 201.96
2 1 6 ' 8 C 1.535 110.50 85.56
2 1 6 , 9 C 1.530 114.28 318.90
3 2 1 10 H 1:092 112.91 175.31
.6 1 2 11 4V H 1.092 112.48 183.56
1 2 3 18 ii 1.108 104.03 161.79
2 . 3-- 5 12 H 1.106 111.67 188.94
2 3 5 13 H 1.106 112.38 68.41
2 3 5 14 H 1.103 114.71 307.73
2 3 4 15 H 1.106 112.30 166.53
2 3 4 16 H 1.106 112.57 48..42
2 3 4' 17 H 1.101 115.63 286.20
1 6 7 19 H 1.106 112.87 180.36
1 6 7 20 H 1.106 112.70 60.41
1 6 7 21 H 1.106 113.14 300.19
1 6 8 22 H 1.106 112.87 184.41
1 6 8 23 H 1.103 113.96 84.13
1 '6 8 24 H 1.106 112.62 304.07
1 6 9 25 H 1.106 112.18 170.62
1 6 9 26 H 1.100 115.12 289.64
1 6 9 27 H 1.106 112.87 51.77
159
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
CHAPTER IV
NMR EXPERIMENTAL RESULTS
4.1 EXPERIMENTAL CONDITIONS
Cis- and trans-2,2,5-trimethylS3-hexene were obtaindd by Van
der Heijden (see reference [112]) by reduction of the corresponding
hexyne. The trans isomer was formed by reduction of the hexyne in liquid
ammonia solution of alkali metal; preparative gas chromatography yielded
the final pure product. The second isomer (cis) resulted from a selec-
tive hydrogenation cif, the hexyne over a deactivated palladium catalyst
(palladium on barium sulfate deactivated by pure synthetic quinoline).
The hexene was then purified using the same gas chromatography technique
as for the trans isomer.
The cis-2,5-dimethy1-3-hexene was obtained from Aldrich
Chemical Co. The purity of this sample has beer tested by Rummens et al.
[108]; a presence of a weak band near 960cm-1 in the infrared spectrum
was an indication of the presence of a small amount of trans isomer in
the sample; this was later confirmed by the NMR signals of the methyl
region of the compound. This small impurity never interfered• with the
analysis of the NMR spectra reported in this work.
The cis-4,4-dimethy1-2-pentene was purchased from Chemical
Procurement Laboratories Inc., and was used without any further purifica-
tion.
160
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
The proton NMR spectra of the three compounds studied (cis- and
trans-2,2,5-trimethyl-3-hexene and cis-2,5-dimethyl-3-hexene) have been
recorded at 90MHz with a Bruker HX90 spectrometer. Additional runs at
100MHz have also been performed using a Varian HA100 spectrometer. As it
turned out, however, the 90MHz spectra show more detail; henceforth only
the results from the 90MHz spectra will be discussed.
The proton spectra were run using a proton lock. The TMS
(tetramethylsilane) single line was used as the internal lock signal. To
the neat sample of cis-2,2,5-trimethy1-3-hexene, 12.5% v/v of TMS were
added; 12% of TMS, 25% of CDC13 and 63% of the trans isomer composed the
other sample. Approximately 5% of the lock compound was mixed with the
cis-2,5-dimethy1-3-hexene and with the cis-4,4-dimethy1-3-pentene. The•
proton spectra were run using the CW mode. A linewidth of 0.1Hz was
achieved with the magnet, as deter Mined from acetaldehyde spectra run as
a reference. Each spectrum is composh of three regions: the olefinic
part at high frequency, the methine part in the medium range and the
methyl part at high field close to the,TMS reference signal. To obtain
the best possible resolution each part was recorded separately. For each
temperature three runs were performed uhder identical conditions:. scan
. rate of 0.03Hz.sec-1 using a display scale of 1Hz.cm-1, the filter was
set in such a way that the signal-to-noise ratio was the best possible-
without distortion of the signals. Each region (olefinic, methine,
methyl) was recorded in small sections--usually 5Hz wide or less. The
calibration was 'made using a HP5216A electronic counter, by determining
the frequency at the beginning and at the end of each section. All line
161
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Positions, by this procedure, had an internal precision of ±0.03Hz or
less (when well defined); the exact display scale was calculated to vary
from 0.998Hz.cm 1 to /.009Hz.cm-1.
The temperature variation was accomplished using a Bruker
BST-100/700 temperature control unit. Following the Bruker procedure the
thermocouple is situated immediately below the sample in the heat exchange
gas. At room temperature and above, air is blown around the sample; at
lower temperature nitrogen is used, as the heat exchange gas. The flow
rate,. for either gas, is 3001,he1 in order to reach equilibrium in a
reasonable time. Monitoring and controlling the temperature is done by
the thermocouple sensor, the comparison circuitry of the BST unit in
conjunction with a small heater resistance put in the path of the heat
exchange gai. The exact temperatures were determined using the ethylene
glycol shift for the high temperature measurements and the methanol shift
fop beloW ambient temperature. Van Geet'S equatiqns for the calibration
bf both compounds were used to provide the exact temperature of the
0
sample [113].
Natural abundance carbon-13 experiments were done on the cis-
and trans-2,2,5-trimethyl-3-hexene, using the Bruker HX90 spectrometer in
its FT mode. A Nicolet 1080 computer provided the computing facilities. DBTFE
(1, 2-dibromotetrafluoroethane) was added to both samples to be Used as
a fluorine lock compound. For each temperature two spectra were recorded:
one to give the whole spectrum (4000Hz wide), the other to expand the
region around the methyl carbons (850Hz). A pulse width of 4us was used
in all cases with a trigger time (time between two pulses) of 6s for an
162 •
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
acquisition time of 2.41s for the 850Hz width spectra; a trigger time of
is we: used when pulsing over 4000Hz. The FID (free induction decay) was
completed after 512 or 1K pulses. Therefore, the data resolution was 4
0.41Hz and 1.95Hz 'for spectral widths of 850 and 4000Hz.respectively.
Fourier transformation was applied to these data points to which 4K
"zeros" were added in order to increase the definition of the spectrum as
stated by Bartholdi and Ernst [114]. In this manner, the accuracy of the
line position was increased to ±0.10Hz and ±0.49Hz respectively for each
spectral width.
All carbon-13 spectra were proton-noise decoupled. As for the
proton spectra, a 5mm probe,was used in every experiment. The temperature
variation was achieved in exactly the same way as for the proton experi-
ment. No correction was applied because of the heating effect caused by
the interaction between molecules and the high radio-frequency fields;' .
the amount of heat developed is supposedly small and the heat transmission
through the sample as well as the cooling capacity of the temperature
regulating 'gas flow are supposedly sigh enough to maintain a temperature,
in the sample, equal to, or slightly higher than the temperature of the
gas flow (the difference should not have exceeded 2K). Such a belief is A
reinforced by a study on the effect of proton-noise decoupling,on the
heat of a sample, made by Led and Petersen [115]. 4
163
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
4.2 SPECTRAL ANALYSIS OF THE PROTON SPECTRA
4.2.1 Cis- and trans-2,2,5-Trimethy1-3-hexene
For both isomers three characteristic regions can be distin-
guished. The olefinic region between 6 = 4.5 - 5.5ppm, the methine
region between 6 = 2.2 - 2.3ppm and the region of the methyl groups of
thetert-butyl and isopropyl groups 6 = 0.8 - 1.0ppm. In Figure (4.2-1)
the nomenclature for the spin-spin coupling constants !IL] is given
(coupling constants between nuclei separated by n bonds are noted 72.3)
together with that for the chemical shifts.
The nine protons of the tert-butyl group are assumed to be
magnetically equivalent, but they are weakly coupled with all the other
protons of the molecule: an X approximation can be used to describe the
system. The isopropyl group is composed of six equivalent methyl protons
and one methine proton. The two remaining protons of--te moleCule are
'the .olefinic protons. Using the conventional notation (first introduced N
by Bernstein et al. [/16]), the spin system can be begt described as an
ABCD6X9.for both isomers. ThiS system consists of two subsystems, the-
ABCD6 system which has been extensively developed by Van der Heijden in
his thesis [1/2] and the X9 system. The inclusion of the X subsystem
increases the number of transitions from 736 (ABCD6 system) to more than
40 000. This makes the use of an iterative computer program imperative.
Ten coupling constants and five Larmor'frequencies (chemical shifts) are
sufficient to fully describe the ABCD6X9 system.
Throughout the iteration process, the chemical shifts of the
164
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
471.,
j I2
j 23traJJ fin tiC0.,C;0-"H rrea
Jm= • ..134---r"J (in HC.04.7C:0-1141
23" J ft (in Hi.4 J•C 7H ) 7r
• ' '113' J- •
j 34= -11J. HC0 .1C0./H)
lhquRE 4.2=1 Numbering system and nomenclature used for, the (11,H) coupling constant§ of cis= and trans-2,2,5-trimettly1-3-hexane:..
AIN
•
Reproduced w
ith permission of the copyright ow
ner. Further reproduction prohibited w
ithout permission.
methyl protons composing the isopropyl group were kept constant at a
value equal to the average between the two isopropyl lines. Initially,
all the coupling constants were iterated. Only four of them were of
sizeable magnitude, and in a second step only these were varied during
the iteration, while'the other six coupling constants were put equal to
zero. An example of the difference between the parameters obtained by
the two above techniques is given in Table 4. 1. All the subsequent
--results will only be given for the second techriique (only four non-zero
coupling constants).
The starting parameters for both isomers were taken from Van
der Heijden's thesis [112]; the procedure to find the best set of these
parameters was exactly as outlined in chapter II. The best experimental
spectrum for the trans isomer shows 26 totally resolved lines in the
methine region, to 'vhich 141 transitions were assigned. The 'differences
between observed and final calculated line frequencies never exceeded•
0.05Hz. Figure (4.2-2) shows the kind of agreement reached between the
experimental spectrum and the final theoretical spectrum for the methine
part of the trans isomer. A decrease in line separations- 'resulting in a
smaller number of assigned lines was observed when lowering the tempera-
ture. This change can be seen in Figure (4.2-3). At the lowest tempera-
ture of measurement, the total number of transitions assigned was down to
100. Of the eight lines compoiing the olefinic region (the AB part of
the spin system), seven were well resolved (in the entire range of 41
temperatures); this made possible the assignment of 53 transitions to the
seven experimental frequencies. Chemical shifts and coupling constants
166 •
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
• TABLE 4.2-1 Comparison between parameters as obtained from the NUMARIT
program,(a) iterating all the coupling constants, (b) itera-ting only the'coupling constants of sizeable magnitude. The examplg is given for the trans-2,2,5-trimethyl-3-hexene at 345.50
a
61 5.38813±7x10-5 5.38817±6x10-5
62 5.27556±5x10-5 5.27557±7x10-5
63 2.20826±3x10_ 5 2.20826±3x10-5
64 0.9545 0.9545
----______A 0.9818±2x10-4 0.9818±2x10-4
J1-2 15.710±0.008 15.710±0.008
J1-3 -1.336±0.01 -1:338±0.02
J1-A 0.005±0.02
J1-5 -0.001±0.004
J2-3 6.787±0.004 6.789±0.004
J2-4 -0.001±0.007
J2-5 0.004±0.007 ---
J3-4 6.744±0.002 6.744±0.002
J3-5 0.000±0.002 ---
J4-5 -0.001±0.02 N ---
RMS* 0.025 0.025
Units: the chemical shifts are in ppm from TMS, the coupling constants in Hz.
The numbering system is given in Figure (4.2-1). *The RMS represents the residual mean-squares of the transitions.
167
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
4. •
I
210 200 190
Hz from TMS 180
FIGURE 4.2-2 Methine region of observed (upper spectrum) and computer simulated (lower spectrum) 90MHz proton spectra of trans-2,2,5-trimethyl-3-hexene. The observed spectrum was recorded at 298K.
168
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
a
v
2.3 34 1.1 ppm from TMS
34
FIGURE 4.2-3 Temperature dependence of the methine region of the 90MHz proton spedtrum for trans-2,2,5-trimethyl-3-hexene. The upper spectrum was recorded at 330K, the lower one at 270K.
169
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
CD
c7i m. o
0
TABLE 4.2-2 List of proton chemical shifts (in ppm from TMS) and of H-H coupling constants (in Hz) which give the best fit with the experimental spectra for the trans-2,2,5-trimethy1-3-hexene at each investi-gated temperaturet
0 0 -0
T (K) 361 356 345.5 340 324 314 298 279 270 257 251, 246 238
61 5.3917 5.3906 5.3881 5.3857 5.3831 5.3810 5.3771 5.3724 5.3697 5.3679 5.3661 5.3650 5:3043
62
5.2819 5.2799 5.2756 5.2727 5.2680 5.2645 5.2578 5.2501 5.2465 5.2438 5.2408 5:2381 5.2304
63
2.2071 2.2089 2.2083 2.2081 2.2073 2.2079 2.2070 2.2070 2.2076 2.2085 2.208 ,
64
0.9544 0.9555 0.9545 0.9542 0.9533 0.9540 0.9534 0'.9528 0.9532 0.9530 0.9531 .0':6529 0.9528
@ -0 8 a c
-4 c) 65
J1-2
0.9823
15.702
0.9829
15.721
0.9818
15.710
0.9812
15.716
0.9804
15.671
0.9800
15.667
0.9808
15.617
0.9701
' 15.00
0.9777.'0.9776
15.663 15-050
0:074
15.637
0.9773
15.618
0.9768
15.615 0.
J1-3
-1.375 -1.359---1.338 -1.394 -1.353 -1.356 -1.320 -1.354 4..315 -1.375 ,-1.350 -1.382 -1.347
0 3 J2-3 6.775 6.777 6.789 6.836 6.816 6.860 6.824 J5.895 6.890 6.946 6.936 6:981 6.970
m 0_ J3-4 6.744 6.745 . 6.744 6.740 6.744 0,734. 6.741 6.735, 6.745 6.738 6.734 6.762 6.754
*' 78-
----- RMS 0.021 0.023 0:025 0.015 0.014 0":020 0.032 0.017 0.029 0.023 0.021 0.028 0.026
0 c -0
5 a . Cl) 5' z
.+the numbering system is given in Figure (4.2-1).
Reproduced w
ith permission of the copyright ow
ner. Further reproduction prohibited w
ithout permission.
I
J I
vU
4)
270 260 Hz from TMS
250 240
0
•
FIGURE 4.2=4 Methine region of computer simulated (lower spectrum) and observed (upper spectrum) 90MHz proton spectra of cis-2,2,5-trimethyl-3-hexene. Tf* observed spectrum was • recorded at 298K.
• 171
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
-0 8
TABLE 4.2-3 List of proton chemical shifts (in ppm from TM) and of H-H coupling constants (in Hz) which . give the best fit with to experimental spectra for the cis-2,2,5-trimethyl-3-hexene at each'
N0 investigated temperature
05-' m - T (K) 354 345.5 335 - 324 314 299 284 271 257 246 229
co
-Ps s< 61 5.1643 5.1648 5.1646 5.1652 5.1662 5.1680 5.1698 5.1726 5.1741 5.1764 5.1804 m. m-
62 4.9215 4.9212 4.9201 4.9196 4.9188 4.5186 4.9183 4.9184 4.9181 4.9182 4,9191 o
63
2.8459 2.8451 2.8432 2.8422 2:8403 2.8385 2.8352 2.8335 2.8324 2.8309 2.8282
64 0.9382- 0.9378 0.9367 0.9362 0.9352 0.9347 0.9339 0.9328 0.9321 0.9317 0.9305 c a-
65
1.1107 1.1100 1.1090 1.1086 1.1074 1.1067 1.1052 1.1046." 1.1041 1.1037 1:1020 @ IN3
,4 -0 J
1-2 11.989 11.984 11.990 11.960 11.940 11.951 11.942 11.913 11.896 11..884- 11.861
J1-3
-0.711 -0.722 -0.708 -0.702 -0.709 -0.677 -0.667 -0.606 -0.715 -0.625 -0.658 o m0 J2-3 10.506 10.507 10.527 10.531 10.545 10.577 10.584 10.611 10.632 10.653 10.693 8 - I 6- 7 J3-4 6.533 6.557 6.549 6.556 6.546 6.562 6.561 6.565 6.568 6.555 6.563
a .
a RMS 0.017 0.024 0.021 0.018 0.023 0.016 0.019 0.018 0.013 0.018 0.034
74 o +the numbering system is given in Figure (4.2-1).
z
Reproduced w
ith permission of the copyright ow
ner. Further reproduction prohibited w
ithout permission.
for this isomer are listed in Table 4.2-2.
For the,cis isomer, at most 20 lines were resolved in the
methine region. Once again the number of assigned transitions, for this
region, went down with the lowering of temperature (from 74 it 366K to 58
at 229K). Figure (4.2-4) gives an idea of the fitting obtained between
experimental and computed patterns. Forty-seven transitions have been
assigned to the six frequencies of the resolved lines in the olefinic
portion of'the spectra for all the temperatures of measurement. The
final parameters are listed in Table 4.2-3.
4.2.2 cis-2,5-Dimethyl-3-hexene
In this case, full use of the symmetry feature present in the
"NUMARIT" program has been made. A weak coupling has been assumed to
exist between the olefinic protons and all other protons in the molecule.
Similar to.the 2,2,5-trimethy1-3-he isomers, the six methyl protons
of each isopropyl group are chemically and netically equivalent. The
spin system is therefore treated as in AA'XX 1Y6 6 system (following the
notation introduced by Diehl and Pople [217]) involving eight coupling
constants and three chemical shifts. Because of.the symmetry involved,
some of the coupling constants are not obtained independently through fhe
iteration process. They are rather the sum and the difference of two
computed parameters. For example, following the notations given in
Figure (4.2-5), 3vJ(sp2-sp
3) is the sum of two iterated parameters, while
4taJ is their difference.
The analysis was started with a set of parameters obtained by
1,73
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1
C
•
j Yelj
• 11
J 12= (7 1 -3'
)
J 21= J
ievi; J22-4 J
y
J23 J (0. -71'')
FIGURE 4.2-5 Numbering system and nomenclature used for 4-11,N) coupling constants of cis-2,5-dimethy1-3-hexene.
s
Reproduced w
ith permission of the copyright ow
ner. Further reproduction prohibited w
ithout permission.
-o 3 a
a
•
CD 0 0
"fi cQ
0
7 CD
,j un
CD
CD -o 3 a C o.
= -E3 3 7
a
FIGURE 4.2-6 Methine region of the observed 9014Hz proton spectrUm of cis-2,5-dimethy1-3-hexene recorded at 354K under the conditions described in Section 4.2.
O
I 250 230 210
Hz from IMS
•
Reproduced w
ith permission of the copyright ow
ner. Further reproduction prohibited w
ithout permission.
4
7J m a -0_C C) m 0_
7'
5 TABLE 4.2-4 List of proton chemical shifts (in ppm from TMS) and of H-H coupling constants (in Hz) which give thg best a.'4*
fit with the experimental spectra for the cis-2,5-dimethyl-3-hexene at each temperature investigated o 0 0
5' m T(K) 354 349 344 333 323.5 .313 297 293 288 280.5 271 260.5 2g0 ' 239 0 0
co 0-o
m
c -n
a-gi0-
0. 0.0
-0 a = a:
a
78-:0 c -0
0--
61 5.0389 5.0387 5.0387 5.0383 5.0381 5.0383 5.0391 5.0393 5.0399 5.0405 5.0418 5.0430 5.0430 5.0480
62 2.6000 2.5999 2.6002 2.6003 2.6007 2.6011 2.6018 2.6023 2.6029 2.6034 2.6047 2.6064 2.6080- 2.6094
63
0.9448 0.9451 0.9437 0.9443' 0.9430 0.9429 0.9409 0.9420 0.9420 0.9418 0.9416 0.9414 0.9426 0.9423
3c J1 _ 1, 10.850 10.843 10.828 10.824 10.824 10.829 10.801 10.787 10.817 10.803 10.805 10.782 10.795 10.769
3ua 1-2 to
9.428 .91445 9.458 9.477 9.498 9.496 9.505 9.539 9.554 9.548 9.575* 9.599 9.619 9.655
---4 Cr4 J2-1 -1.061 -1.061 -1.047 -1.061 -1.058 -1:034 -1.008 -1.036 -1.029 -1.027 -1.007 -1.025 -1.994 -1.021
J1-3
0.186 0.188 0.177 0.203 0.242 0.240 0.269 0.232 0.229 0.240 0.227 0.220 0.210 0.226
J3-1 -0.032 -0.034 -0.033 -0.038 -0.046 -0.046 -0.051 -0.040 -0.041 -0.046 -0.043 -0.042 -0.034 -0.034
5cha j2...2., 0.373 .0.386 0.375 0.392 0.397 0.393 0.408 0.390 0.387 0.403 0.394 0.391 0.358 0.367
J2-3 6.640 6.641 6.640 6.641 6.648 6.646 6.647 6.651 6.643 6.648 6.655 6.650 6.651 6.654
RMS. 0.023 0.020 0.022 0.023 0.018 0.025 0.026 0.021 0.029 0.024 .0.022 0.023 0.024 .
0.027
5 +numbering system: (CH3)2-CH-CH=CH-C1H-(CH,),.
0. 3 2 i 1 2 1 1 i i I,
o
I/
Reproduced w
ith permission of the copyright ow
ner. Further reproduction prohibited w
ithout permission.
Rummens et al. [108]. For the best spectrum recorded at the highest
temperature- achieved (354K), 109 frequencies have been determined with
,248 transitions assigned to these. In a similar fashion as for the
2,2,5-trimethy1-3-hexenes, lines of the methine region are getting closer
together as the temperature is lowered, and the number of frequencies
which can be distinguished drops to 45 at 250K with 191 transitions
assigned. Fifty-nine of these transitions have been assigned to the %ix
frequencies of the olefinic part (the AA' part of the spin system). An.
example of the methine region recorded is displayed/in Figure (4.2-6).
The parameters which give the best fit are reported in Table 4.2-4.
4.2.3 'Cie-4,4-dimethy1-2-pentene
The spectra were analyzed as due to an ABC3 system using the
"NUMAR1T" program, assuming that the coupling between the tert-butyl
group and any other protons is negligible; consequently this coupling has been
dropped from the analysis. The starting parameters were those obtained
by Nicholas et al. [118] (with the 8C coupling positive). A temperature
range of 117K (from 249 to.356K) was investigated. At high temperature
. (where the best spectra are recorded), 22 frequencies were assigned to 22
transitions of the possible 61 transitions. At lower temperatures (below
- 270K) the number of assigned frequencies dropped to 17. The final para-
meters are listed in Table 4.2-5.
177
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
TABLE 4.2-5 Proton chemical shifts and H-H coupling constants for cis-4,4-dimethy1-2-pentene at various temperature.*
T (K) 249' 265 308 323 344 356
5.2943 5.2920. 5.2905 5.2903 5.2911 5.2917
52 5.2248 5.2244 5.2241 5.2242 5.2246 5.2250
.53 , 1.6864 1.6860 1.6864 1.6865
.1.6872 1.6873
J1-2 11.948 11.949 11.952 11.946 11.953 11.950
J1-3 -1.818 -1.810 -1.843 -1.846 -1.837
J2-3
*
7.280 7.281 7.301, 7.298 7.286 7.303
1114St 0.028 0.031 0.024 0.022 0..020 0.018
*A11 coupling constants are in Hz, all chemical shifts in ppm from TMS. Numbering of the atoms: CH,-CH=CH-C-(CH3)3 0
1
178
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
4.3 CARBON-13 DATA
Carbon-13 experiments have been performed for the two isomers
of the 2,2,5-frimethyl-3-hexene. The numbering system (similar to the
one for the, proton) is given in Figure (4.3-1) and will be used through;
out. THe assignment of each spectrum is based in part on relative peak
heights for the methyl carbons of the isopropyl and tert-butyl groups.
The assignments for carbons C3 and C6 have been made in such a way that
°the carbon C6 is downfield compared with carbon C3. Such a relative
shift has been obsertied for the 4,4-dimethyl-2-pentene and the 2,2-
dimethy1-3-hexene [119] (i.e., with successive replacement of the iso-
propyl group by a methyl and an ethyl group). This is furthermore
confirmed by the presence of a nuclear Overhauser effect (NOE) which
enhances the signal for carbon C3 as compared to the signal for carbon C6.
• The room temperature carbon-13 NMR spectra for both isomers are
shown in Figures (4.3-2) and (4.3-3). The expansions of the methyl part
are given in Figures (4.3-4) and (4.3-5). As can be seen, there is only
a single resonance for the two olefinic carbons in the cis isomer spectrum
(where the height of the peak is twice that of a single carbon). The
variable temperature measurements show that the coincidence of the two
olefihic "esonances occurs between .290 and 310K. This leads to an
ambiguous assignment for the cis isomer; a discussion of the different
possibilities will be given in the following chapter. A representation
of the temperature dependence of both olefinic resonance frequencies is
shown in Figure (4.3-6). For the trans isomer, the olefinic carbon
179
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Reproduced w
ith permission o
f the copyright owner. F
urther reproduction prohibited without perm
ission.
8
C
(*)
(s)
FIGURE 4.3-1 Numbering system used for the carbon atoms of cis- and trans-2,2,5-trimethy1-3-hexene.
f
Reproduced w
ith permission of the copyright ow
ner. Further reproduction prohibited w
ithout permission.
I.
i 1 1 I 1 1 1 1
140 120 100 80 60 40 20 0
ppm from TMS
FIGURE 4.3-2 Natural abundance 22:63MHz proton noise-decoupled carbon-13 spectrum of trans-2,2,5-trimethy1-3-hexene recorded at 298K under the conditions described in Section 4.3.
181
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
13C
re
son
an
ce
w tr.. 1--co ra
8 g 0 . 1
• • • • • • • • • • II • m • • • • . 1••• • 1.......
co Z )--
. dwe410641411 4,4ra
I 1 i I 1 I I I 140 120 100 80 60 40 20 0
ppm from TMS
FIGURE 4.3-3 Natural abundance 22.63MHz proton noise-decoupied carbon-13 spectrum of cis-2,2,5-trimethyl-3-hexene recorded at 298K under the conditions described in Section 4.3.
182
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
(CH3 )2 —CH—CH=CH—C—(CH3)3 a b c d
b
C
34 32 30 28
ppm from TMS
26 24 22
FIGURE 4.3-4 Non-olefinic region of a natural abundance proton noise-decoupled carbon-13 spectrucof trans-2,2,5-trimethy1-3-hexene recorded at 298K under the conditions described in Section 4.3.
183
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
8 o. C)o_
a.
0
C)
0
M.
0
7
m
8
8 0_ a
8
74:
o_
0
0 0
d (CH3)2 — CH-- CH=CH—C —( CH3)3
a b c d
I I I I I I I34 32 30 28 26 24-- --- 22
ppm from TMS
FIGURE 4.3-5 Non-olefinic region of a natural abundance proton noise-decoupled carbon-13 spectrum of cis-2,2,5-trimethy1-3-hexene recorded at 298K under the conditions described in Section 4.3.
Reproduced w
ith permission of the copyright ow
ner. Further reproduction prohibited w
ithout permission.
Reproduced w
ith permission o
f the copyright owner. F
urther reproduction prohibited without perm
ission.
137.9
137.4
0
• •
136 9
200 250 300 350
T [K
FIGURE 4.3-6 Temperature dependence of the olefinic carbons C1 and C2 chemical shifts for cis-2,2,5-trimethyl-3-hexene. 0
Reproduced w
ith permission of the copyright ow
ner. Further reproduction prohibited w
ithout permission.
bearing the text-butyl group is assumed downfield with respect to the
other olefinic carbon following assignments already made for various
trans olefins. For example, Nicholas et aZ. 1118] assigned the carbon
bearing the tert-butyl group to the downfield line in the case of the
trans-4,4-dimethyl-2-pentene. Listed in Tables 4.3-1 and 4.3-2 are the
chemical shifts expressed in ppm downfield from internal tetramethylsilane
(TMS). The shifts are estimated to be accurate to within 0.05ppm for the
methyl region.
,ft
186
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
TABLE 4.3-1 Carbon-13 chemical shifts (in ppm-from internal TMS) of ' trans-2,2,5-trimethy1-3-hexene as a function of temperature. The numbering of, the atoms is given in Figure (4.3-1).
T (K) 61 62 3 64 165
200 138.36 131.79 3.1.54 22.99 29.81 32.93
220 138.45 131.88 31.54 --„ -2i.99 ,---
29.81 32.84
240 138.53 132.05 --11.53 23.06 29.91 32.78
260 138.66 --112.18 31.52 23.06 29.97 32.75 ..--
280 138.79 132.31 31.50 23.06 30.02 32.75
300 138.92 132.48 31.50 23.07 30.07 32.71
310 139.03 132.60 31.49 21,06 30.14 32.73
320 139.08 132.66 31.49 23.06 30.14 32.73
340 139.22 132.79 31.50 23.07 30.20 32.75
350 139.27 132.87 31.50 23.07 30.24 32.75
p
187
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
TABLE 4.3-2 Carbon-13 chemical shifts (in ppm from TMS) of cis-2,2,5-trimethyl-3-hexene as a function of temperature. The numbering is given in Figure (4.3-1). The chemical shifts of the olefinic carbons (1 and 2) are given in Figure (4.3-6).
T (K) 63 64 65 66
180 27.89 23.33 31.53 32.78
190 27.88 23.36 31.54 32.80
200 27.88 23.39 31.57 32.86
213 27.86 23.41 31.59 32.91
222 27.86 23.44 31.62 32.96
240 27.83 23.48 31.65 33.07
245 27.84 23.50 31.67 33.10
260 27.83 23.53 31.71 33.18
270 27.84 23.54 31.73 33.22
280 27.83 23.55 31.74 33.25
300 27.85 23.60 31.79 33.37
310 27.87 23.61 31.81 33.40.
320 27.87 23.63 31.84 33.46
`j40 27.88 23.65 31.87 33.55
188
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
CHAPTER V
INTERPRETATION OF THE NMR DATA
5.1. INTRODUCTION
In the last decade, several studies have been done by proton
and carbon-13 NMR on substituted ethylene molecules. In particular,
geometrical and thermodynamical features have been related to NMR para-
meters. As far as the latter are concerned AG for a conformational change.
can be linked to changes in coupling 'constants (and chemical shifts) with
temperature by equations, of the type (2.5-2) and (2.5-3), Some difficul-
ties with this approach are the inherent (i.e., not conformation-related
temperature) dependence of coupling and shifts and the possible tempera-
ture dependence of AG itself. In addition, this method requires observed
temperature dependencies that are quadratic, since in general three para-
meters need to be derived from it through least-squares fitting, If the
observed temperature dependence is (almost) linear then it is itore prudent
to attempt to estimate one of the parameters of the set from analogous
cases and to, then, calculate the other two from equations (2.5-2) and
(2.5-3).
A recent procedure developed by Rummens et al. [71] has been
found to give reasonable results in the case of 3-methyl-l-butene. In
their approach, each temperature dependent coupling constant has been
189
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
corrected for non-conformational temperature effects as obtained from
propene. These authors have also used the results of Rummens and
Kaslander's study on the influence of valence angles on coupling constants
[70], and they have introduced consistent Force Field calculations of
optimized geometries. This technique allows.one to extend the knowledge
of conformationally induced geometry changes beyond the simple molecules
for which exact structures are presently known. All the couplings
belonging to anti conformers were derived by4tummens et al. [72] from the
known coupling constants for 4,4-dimethyl-3-tert-butyl-l-pentene. The
AG0's extracted (531 ± 59 J.mo1-1 or 127± 14 cal.mo1-1) using at the same
time a number of independent parameters were consistent thus lending some
credence to the technique. In this chapter, the above-mentiOned procedure
or variations thereof is employed.
Studies on proton and carbon-13 chemical shifts involving
temperature dependence measurements have not been used as often as
studies on coupling constants, mainly because of problems of referencing
and of intermolecular interactions. However, in this study, an attempt
is made to extract some useful structural information from shifts.
Of the molecules described in this chapter trans- and cie-2,2,5-
trimethy1-3-hexene are discussed in the fullest extent, using variable
temperature information on H-H coupling constants and proton and carbon-
13 chemical shifts. cis-2,5-Dimethyl-3-hexene is discussed almost as
fully, except that no carbon-13 study was done. Finally some data for
cis-4,4-dimethy1-2-pentene are discussed, mostly in relation to cis-2,2,5-
trimethy1-3-hexene.
190
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
5.2 TRANS-2,2,5-TRIMETHYL-3-HEXENE
5.2.1 Analysis of.the temperature dependence of coupling constants
For a single, non-sytmetrical rotor such as an isopropyl
3vj, 3tj, 4ca J couplinggroup, the constants are simple-Boltzmann statis-
tical averages, as has been shown for the 3-methyl-l-butene by Rummens
et al. [71]. If p is the population of a rotamer characterized by the
constant Ja (in the case under study, Ja is the constant when the methine
proton is in anti position), and (1-p) that of the two-fold degenerate
rotamer with J as coupling constant (with methine in gauche position),
one has the relation:
<J> = pJ + (1-p) J9
with
a .g
with -2- = exp (1.-42) 1-p 2 RT
(5.2.1)
where AG is the Gibbs energy difference between both conformations; R and
T have their usual meaning.
Accompanying conformational exchange, several significant geo-
metrical changes'in the "rigid" part (e.i. the part excluding the rotor)
can occur. In this case the coupling constant of this "rigid" part (here
3t0 must also become temperature sensitive, and its variation should be
usable for the determination of the energy separation between the rota-
rners and of the coupling constants belonging to each rotamer.
191
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
In order to solve the problem of having too many unknowns for
the number of available relations, various, approaches have been considered
as mentioned previously.
As can be seen in Figure (5.2-1) and Table 4.2-3, the tempera-
ture dependence for all the coupling constants is virtually linear; only
two unknown' parameters can be deduced from .each of these variations.
Thus, for each set of coupling constants, one of the unknowns must be
found by another method. As the energy difference AG obtained byrForce
Field calculation does not seem to be accurate enough (see Rummens et al.
[72]), one of the other parameters (one of the coupling constants) has to
be calculated. For this purpose, the method already tested by Rummens
et al. [71] can be applied. Geometrical features of the conformation
under study, combined with the (AJ/A6) data found by the previous authors
[71] should give an adequate result. For 4caJ and 3vJ, the starting
values are taken from the 4,4-dimethyl-3-tert-butyl-l-pentene molecule
reported by Bothner-8y,et al. [107] and corrected for valence angle
differences as well as torsional angle differences., To complete the
calculation, diffirences in electronegativity have to be taken into
account. For 3vJ and 4caJ this effect is deduced from the experimental
differences (corrected for steric cohtr:Ibution differences) obtained for
propene by Rummens et aZ. [71] (3vJ = 6.47Hz, 4caJ = -1.78Hz) and for
trans-4,4-dimethy1-2-pentene by Nicholas et al. [118] (3vJ = 6.37Hz,
4caJ = -1.33Hz).' It is assumed that the electronegativity effect of the
substitution is the same for the averaged coupling constant as for each
individual coupling constant. For the vicinal 3vJ coupling constant,
192
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
A 6.97
6.871.-
6 77
230
o. a
•
I280
, •
•
330
T [K] ___4 1,..
0 0
NI.
FIGURE 5.2-1 Temperature dependence of the vicinal coupling constant (J23, for notation see Figure (4.2-1)) for trans-2,2,5-tri methyl - 3- hexene , (.) uncorrected values (a) values corrected for temperature dependence of
intrinsic contribution — best fit as obtained from the G8M method us g
corrected values.
193
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
this effect amounts to 0.07Hz and for the allylic cisoid 4aaj coupling
it amounts to 0.21Hz. These corrections lead to coupling constants for
the.anti conformation equal to 10.07Hz and L0.72Hz for 3°J and 4caJ
respectively.
The third coupling constant, 3tJ, should be more sensitive to
substituent effeEts. Replacement of one olefinic hydrogen by a tert-
butyl group gives a decrease for 3tJ equal to -1.62Hz as can be deduced
from data obtained by Lynden-Bell and N. Sheppard [120] and by Nicholas
et at. [118]. After correcting these values for steric contributions, an
electronegativity effect of -3.28Hz has to be assumed to explain the
total substitution effect. Similarly, for an isopropyl group replacing
an olefinic hydrogen (the data are taken from Rumens et al. [72] for the
3-methyl-l-butene) an electronegativity effect of -3.24Hz is obtained.
Combining these results and correcting for the geometrical changes, 3tJ
for the anti conformation of the trans-2,2,5-trimethyl-3-hexene is calcu-
lated to be equal to 14.91Hz (starting from the ethylene molecule). .
Alternately (and avoiding the estimation of any electronegativity effect),
one may consider that the calculated difference between 3tJ for anti and
for gauche conformations is due entirely to steric effects. The calcula-
tions, following Rummens and Kaslander's [70] procedure, give a difference
3tJ .ft = 1 2Hz an -gauche • •
Rummens et al. [71] have found a temperature effect for
several coupling constants in propene which is not related to population
ratio change between conformations, but rather is the result of intrinsic
effects attributed by these authors to electric reaction field effects as
194
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
well as to Van der Waals effects or to population chan s i vibrational
states. Rummens et aZ. [71] assume that it is reasonable to attribute a
similar non-conformational temperature dependence to hydrocarbons of the
same type. A correction was applied to the present experimental results
approximating the intrinsic effect dependence by a linear-type of varia-
tion as has been done by the above-mentioned authors, using their data
for the propene molecule.
In the Gutowsky, Belford and MacMahon's [91] method (hereafter
called the GBM method), the three parameters (two coupling constants and
the Gibbs energy difference) are allowed to vary. Instead of taking the •
set of values corresponding to a minimum in 4)2, the selected set of para-
meters must contain the previously calculated coupling constant(s) (in
the case of 3tJ, the second technique consists in selecting the set of
parameters where the difference between anti and gauche coupling constants
is 1.2Hz). These techniques give the results as shown in Table 5.2-1,
when a correction for intrinsic temperature dependence is applied. By
this procedure, a value for AG is obtained; this value is equal to tH in
the approximation that no entropy difference exists between the various
rotamers. The statistical-mechanical calculation described in Section
3.3 proves that this assumption is not always correct. The intrinsic
temperature dependence of AH can be assumed to be small in comparison
with that of the T AS term. Then, to account for the entropy differences
and their temperature dependence, the GBM method can be easily changed
(AG is replaced by AH-T AS). Using the three calculated entropies which
can be found in Table 3.5-3, postulating a quadratic variation with
195
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
TABLE 5.2-1 Sets of coupling constants and Gibbs energy differences as obtained by the GBM method applied to the. experimental data of trans-2,2,5-trimethyl-3-hexene under the assumption AS = Ot
3vj J*a = 10.07 Jg = 4.70 AG° = 0.795 ± 0.17 (0.190)
3tj** Ja = 14.97 Jg = 16.18 AG° = 1.000 ± 0.21 (0.240)
4caj J*a = -0.72 Jg = -1.77 AG° = 0.670 ± 0.30 (0.160)
Ta° = 0.842 ± 0.091 (0.200 ± 0.022)
4A11 couplings in Hz; AG° in KJ.mo1-1 (Kcal.mo1-1).
*calculated as mentioned in the text.
**the difference between the anti and the gauche coupling is taken equal to 1.2Hz (3tj9
3tja).
196
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
temperature, values of enthalpy separations between rotamers are obtained
by the application of the GBM method. These values, together with the
corresponding standard Gibbs free energy are listed in Table 5.2-2.
These values, which differ from the previous results by around 300J.mol-1
(70cal.mol-1), can be assumed to be more exact, if one believes that the
entropy calculated through the statistical-mechanical method is reliable.
Using statistical weights proportional to the magnitude of the variation
of each coupling constant, an average value of AG° . 531±89J.mo1-1
(127±21cal.mo1-1) is found.
5.2.2 Coupling constants and conformational structure
A Vicinal coupling constant 3vJ (J23)
The anti coupling constant being the result of the previously
described estimation will not be discussed here. The corresponding
gauche coupling is of the same magnitude as found already by Rummens
et aZ. [71] for the same rotor (the isopropyl group) in the 3-methyl-l-
butene molecule. This coupling increases from 4.32Hz (in the monosub-
stituted ethylene) to 4.89Hz (for the disubstituted ethylene in question).
This increase cannot be entirely explained by valence angle contribution
differences (which account for less than 0.01Hz), but it can be correlated
with a change in torsional angle (124.6° for the 3-methyl-l-butene (see
reference [71]) in gauche position and 126.1° for the studied molecule).
This geometrical change is responsible for an increase of 0.25Hz, which •
is qu'alitatively in concordance with the experimental difference (0.57Hz).
197
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
TABLE 5.2-Z Sets of coupling constants and energy separations between rotamers as obtained by the GBM method applied to ,the
4 experimental data of trans-2,2,5=trimethy1-3-hexenef
A) With intrinsic temperature dependence correction
3vJ
3tJ **
4taJ
B)
3vJ
3tj**
4taJ
J* = 10.07 J = 4.89 Aff = 1.10 ± 0.15 (0.2e) a g AG° r- 0.53 ± 0.15 (0.13)
Ja = 14.94 J = 16.14 AH = 1.30 ± 0.50 AG° = 0.72 ± 0.50
(0.31) (0.17)
J* = -0.72 J = -1.74 AH = 0.92 ± 0.18 (0.22) AG° '= 0.35 ± 0.18 (0.08)
Without intrinsic temperature dependence correction
Ja = 10.07 Jg = 4.82 AH = 1.18 ± 0.17 (0.28) AG° = 0.61 ± 0.17 (0.15)
Ja = 15.05 Jg = 16.24 AH = 2.05 ± 0.67 AG° = 1.48 ± 0.67
(0.49) (0.35)
Ja* = -0.72 Jg = -1.73 AH = 0.52 ± 0.16 (0:12) AG° = -0.10 ±0.16 (-0.25)
couplings are in Hz. AG°, AH are in KJ.mo1-1 (Kcal .mol -1) and AS in cal .mol -1.K-1 as calculated from AS = aT' + bT + c with a = 0.35 x 10-5, b = -0.28 x 10-2, c = 0.99.
*coupling constant calculated as explained in the text. **difference between anti and gauche ( 3tJg - 3tJa) taken equal to 1.2Hz.
198
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
The high temperature limit value ((„1 -anti 2Jgauche)I3)'.for
the 3vJ coupling constant is different from that of the 3-methyl-l-butene
(6. z for the molecule under study instead of 6.28Hz for the 3-methyl-
1-butene as given by Rummens et al. [72]). This difference comes mainly
from different HCsp 2-Csp 3H dihedral angles for the gauche rotamers.
B Olefinic coupling constant 3t
J (J12)
It is interesting to note that the GBM-extracted 3t
Janti =
14.94Hz is almost identical to the value 3tJanti = 14.91Hz estimated (in
Section 5.2-1) from that of ethylene with adjustments for electronegativity
and valence angle (steric) effects. The latter estimation technique
having been found rather reliable in many previous cases, th& above
results lend credence to the modified GBM technique employed and to the
other results (for 3t
Jgauche and -M).
A decrease of 1.31Hz is found for the 3t
Jgauche coupling
constant when going from the 3-methyl-l-butene (3t jgauche = 17:45Hz
[71])
to the trans-2,2,5-trimethyl-3-hexene k Jgauche = 16.14Hz). Combining
the INDO-derived (DJAG) data with the Force Field-based a changes, one
obtains an increase of 2.1Hz due to steric effects when going from
3-methyl-l-butene to trans-2,2;5-trimethy1-3-hexene (in their gauche
conformations). An electronegativity effect of /3.40Hz for the replace-
ment of one olefinic proton by a tert-butyl group would explain the total
substitution effect. This value compares relatively well with the
electronegativity effect amounting to -3.28Hz for the same substitution
in the anti conformers (see Section 5.2-1).
199
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
The high temperature limit value ((Janti 2J )/3) for
3tJ (= 15.74Hz), is 0.75Hz larger than the average value obtained for
trans-2-butene (3.J = 14.99Hz). A valence angle (steric) effect amounting
to an increase of 1.22Hz for the substitution of two methyl groups by a
(tent-butyl, isopropyl) pair is calculated. This would leave an electro-
negativity effect of -0.47Hz for the same substitution.
C Allylic coupling constant 4caJ (J13)
The temperature dependence for this coupling is small (aroLnd
'0.03Hz/100 K). In Section 5.2-1, the analysis was made with an approxi-
mate 4coJa coupling constant. Alternately (and avoiding any assumptions)
the analysis from the GBM method can be made with the enthalpy separation
as the known parameter. This enthalpy separation is taken equal to the
previously determined averaged value (1100J.mo1-1 or 265cal.mo1-1), the
best fit between experimental (corrected for intrinsic contributions) and
anti. calculated temperature dependence is obtained for 4caj -0.90Hz and
= -1.65Hz. An approximate value of 4caJantv . = -0.72Hz is 4caJgauche
obtained starting with the 4caJanti coupling given .by Rummens et aZ. [71]
for the 4,4-dimethyl-3-tert-butyl-1-pentene. The close similarity of
these two results could be taken to mean that the assumptions in the
estimation technique for 4caJanti = - 0.72Hz were close to correct. These
included the assumption of a zero electronegativity effects of the tert-
b.tyl group (confirming a similar conclusion [70]) and the assumption of
a zero electronegativity effect due to the replacement of two methyl
groups by terr-butyl groups on the Ca atom.
200
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
A rotation of 126.1° of the CH methirie was calculated by the
Force Field method for the anti+gauche transformation. Using Barfield
et al. 's [79] results (with the VB-SOT treatment corrected with EHMO),
'this transformation gives a difference anti-vauche of -1.34Hz for the
propene molecule. An approximate value for this difference in the case
under study can be calculated by comparing the known geometry [122] of
propene with the Force Pi el d geometries of the trans-2,2,5-trimethyl-3-
hexene and by combining this with the IND° calculated (AJ/A8) data and
with the variation of J with the CCCH dihedral angle (from Barfield et aZ.
[79]). A decrease of -1.26Hz is obtained for the anti+gauche transforma-
tion. The experimentally deduced result is only -0.75Hz (if AH = 1100J.mo1-1
or 2.65cal.mo1-1 is used as the basis) or -1.02Hz (if 4ca j = -0.72Hz is
used as the taasis); the agreement is in any case reasonable.
The high temperature limit for this coupling Asonstant is -1.40Hz.
The corresponding limit is -1.78Hz for the propene molecule. In this
latter molecule, the replacement of the trans olefinic hydrogen by a
tart-butyl group increases the average value by 0.15Hz (see Nicholas
et al. [118]), while the replacement of the methyl group by an isopropyl
group increases it by 0.24Hz (see Rummens et al. [71]). Under a strict
addi tivity rule, the coupling constant, 4caJ, for the trans-2,2,5-tri- t
methyl-3-hexene would be -1.39Hz, close to the experimentally found -1.40Hz.
D Vicinal coupling constant in the HCsp 3-C sp3H fragment
This coupling represents the average of the six couplings which
exist in the isopropyl group. No significant temperature dependence can
201
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
be discerned (see Table*4.2-3). Thus, either there is not any appreciable
increase in strain, in this group, for the anti+gauche transformation or
there is substantial compensation among the six couplings. Furthermore,
this constant is not considerably affected by the substitution of one
olefinic hydrogen by one isopropyl group (a value of 6.80Hz is found by
Rummens et aZ. [108] for the trans-2,5-dimethyl-3-hexene, while the
constant for the 3-methyl-l-butene is 6.77Hz as given by Rummens et aZ.
[71]) or by one tert-butyl group (the value obtained in this study is
6.74Hz). The same observation can be made when comparing the bond lengths
and bond angles calculated by the Force Field method.
5.2.3 Proton chemical shifts and conformations
Because of the presence of a non-negligible and only approxi-
mately known amount of CDC13 in the sample, the tert-butyl resonance,
rather than the TMS line, was chosen as the reference signal for the
temperature dependence of the various proton chemical shifts. This
technique also eliminates the temperature dependence of the TMS resonance.
Knowing the enthalpy difference between the conformations of minimum
energy (taken from the preceding section), the difference in shifts for
the various protons (between the two conformations of minimum energy) can
be calculated using the GBM method. Instead of performing the GBM
analysis wttk.the enthalpy difference and one of the coupling constants
as the two unknowns, the analysis is done with the two chemical shifts as
the unknowns.
202
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
A Olefinic protons
(i) Relative positions of 112 and R2 resonances in the anti conformer
Application of the OM method assuming AG° = 531J.mo1-1 (127cal.mo1-1)
gives the H1 resonance on the high
frequency side of the H2 resonance
in the anti conformation (with a difference of 0.45ppm), while it is
the reverse in the gauche conformation: H1 resonance is at a lower
frequency than H2 by 0.08ppm.
The contribution from the magnetic anisotropies of the bonds
has been evaluated using the point dipole approximation. Atomic
magnetic anisotropic susceptibilities were taken from Pople [32] for
the C=C double bond (AxC=C = -7.15 x 10-30 cm3.molecule
-1 per atom),
with each sp2 atom assumed to be the'point dipole location. The a-
contributions from the C-C and cr1-1 single bonds were calculated using
ApSimon et al.'s [28] Ax values (respectively 11.2 x 10-30 and 7.5 x
10-30cm3.molecule-1). The centre of each considered bond was taken as
the point dipole location.
For the anti conformation, the magnetic bond anisotropy effect,
qualitatively accounts for the di-ó? difference. A separation of
0.26ppm-is calculated for this effect with the Hi resonance on the
high frequency side. If one includes the steric 1,4-interaction, the
calculated separation incregps to 0.38ppm. The linear electric field
effect is negligible, while the (E2> term (see Equation 2.3-6) brings
the difference to 1 .38ppm.
Another contribution may come from a difference in electron
density at the olefinic carbon atoms. The charge distribution over
203
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
the molecule (and particularly on the C=C fragment) is sensitive.to
the electronegativity of the substituents. The inductive effects of
alkyl groups have long been appreciated. The electron donating or
withdrawing ability of such groups has been studied by Huheey [88],
who has shown the dependency of this property upon differential
effects. In the oversimplified case of complete equalization of
charge, the tert-butyl group is calculated to have a higher electron
withdrawing ability on an HC=CH-CH(CH3)2 fragment than has an b
isopropyl. group on an HC=CH-C(CH3)3 fragment (the net positive charge
induced by the tert-butyl grouptis calculated to be 0.01esu). This
tert-butyl group is driving electrons away from the carbon to which it
is attached, and the net effect is a general redistribution of the
electrons in the olefinic fragment, as has been already suggested by
Pople and Beveridge [222] for a propene molecule. The difference in
charge at the olefinic carbon atoms causes a difference in shielding
between their nearest proton neighbours. This difference can be
calculated using the relation suggested by Rummens [29] (Au = -8.1 Aec,
where,Aec is the differenc.. io charge density at the nearest carbon
atom). The electron density being smaller in C1 than in C2 (see
Figure (4.3-1) for notation), H1 resonance is calculated to be 0.08ppm
higher (on the frequency scale) than the H2 resonance. The charge
difference obtained above between C1 and C2 is corroborated by the
difference in frequency resonance obtained by carbon-13 NMR (see
Table 4.3-1). This difference in shielding has been shown by Seidman
and Maciel [65] to be linearly related to the difference in electron
204.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
density at the carbon atoms (with (S(C1)-6(C2) = -300 (e(C1)-e(C2));
e(C) is the electron density on C). The experimental difference in
carbon-13 shift varies (with temperature) between 6.4 and 6.6ppm (with
C1 resonance in high frequency position relative to C2 resonance).
This would indicate a smaller electron density on C1 than on C2 (with
a difference round 0.02esu); this results in a frequency resonance
for H1 0.16ppm higher than that for H2.
(ii) Temperature dependence of the olefinic proton shifts
The application of the GBM method, assuming tiG° = 531J.mo1-1 (127ca1.
mol-1) gives increases in frequency resonance for both olefinic
protons, H1 (0.7ppm) and H2 (1.2ppm) for the antivauche transforma-
tion.
The contribution from the magnetic bond anisotropy of the
double bond is calculated to decrease the frequency resonance for H1
(-0.16ppm) and to increase it for H2 (by 0.12ppm). For both protons,
the major a-contributions come from the methine C-H and the C sp 3-Csp 3
single bonds of the isopropyl group. The combined contribution of all
bonds leads to a down frequency shift for Hi (-0.12ppm) for the anti-}
gauche transformation (in contradiction with the experimental results),
while H2 would have its resonance at higher frequency in the gauche
conformation (with a 0.02ppm difference).
The shielding mechanism by a steric perturbation as proposed by
Grant and Cheney (49], relating the shift of the proton to the effect
of a force created by a neighbouring H atom on the C-H bond, does not
205
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
0
improve the agreement with the experiment: both olefinic protons are
calculated to have their lower resonahce frequency in the gauche con-
formation. Respective decreases of -0.1ppm and -0.02ppm (thus rather
small)"are obtained for H1 and H2 for the anti-gauche-"transformation.
Electric dipole contributions are expected to,play an important
role in determining the magnitude of the proton chemical shifts. To
evaluate'such contributions, use of Equation (2.3-3) was made, where
Ez is the field component along the bond produced at the proton by a
point dipole placed at the centre of any polar bond in the molecule.
The estimation of the linear electric field contributions (first term
of Equation (2.3-3)) was made using Equation (2.3-7) relating this
field to charge separation at the centre of the bond. The change in
charge gives a shielding variation at the atom, which can be calculated
with the Lamb formula (Aa = -17.8AqH). The acting charges were taken
from Seidman and Vlaciel's [55] calculations for trans-2-butene. Only
small differences in shifts were obtained, for both protons, for the
anti-►gauche transformation. For example, the methine C-H dipole
accounts for an upfrequency shift of 0.012ppm for H1 and of less than
O.Olppm for H2, for the anti-►gauche conversion. Similarly, the contri-
bution to the shielding constant at the olefinic protons from the
quadratic term is negligible (second term of Equation (2.3-3)). It
amounts to less than 0.001ppm. Another contribution to the shielding
constant comes from the effect of time-dependent dipole moments in
neighbouring electron groups, giving rise to a non-zero averaged value
'E2> (thus a contribution to E2). This effect is described by
206
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
0 Equation (2.3-6) for distances larger than 3.5A. Despite its lack of
solid support for short distances, Feeney et aZ. [123] have found a
linear relation between this contribution (where the electron .group is
at the centre of the dipolar bond) and the experimental proton shifts
in a series of alkanes (a B value of -1.02 x 10-18esu is deduced from
the work). Ir the trans-2,2,5-trimethy1-3-hexene, for both olefinic
protons, this effect gives sizeable contributions to the shift for the
anti-vauche transformation. From Equation (2.3-6) it was calculated
that, due to the effect of the isopropyl group, 1 would have a
frequency resonance 0.05ppm higher in the gauche conformation (to be
compared with the experimental 0.-70ppm). The contribution from. the
tert-butyl group was calculated to be 0.17ppm for the anti-gauche
transformation. The <E2> term contributes also to give )12 a higher
frequency resonance in the gauche conformation. For this latter pro-
ton, the calculated shift is 0.87ppm, which has to be compared with
the experimental 1.2ppm. Despite its relative agreement with the
experiment, the <E2> contributions have to be taken with caution;
firstly because Equation (2.3-6) is applied outside its range of vali-
dity, which may give absolute shift of far too large magnitude;
secondly, because small changes in distances correspond to relativel, 0
large variations in shielding constants (for example a change of 0.01A 0 0
in a distance of 1.76A gives a variation of 0.4ppm in the contribution)
which implies the need of a high accuracy in the knowledge of
structural conformations. '
207
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Methine proton
The analysis of the temperature dependence of the chemical
shift of the methine proton by the application of the GBM method
(assuming AGo 531J.mol-1 (127cal.mol-1)) indicates a low frequency
resonance in the gauche conformation (with a shielding difference
of.0.2ppm). Such a shielding change is not a general feature of anti
-►gauche transformation involving an isopropyl group: Rummens et al. [71]
have found a high frequency resonance for the same proton in the gauche
conformation (relative to the anti conformation) of 3-methyl-l-butene.
For the trans-2,2,5-trimethyl-3-hexene, the difference in shielding
between the two positions of the methine (anti and gauche) is qualita-
tively explained by the anisotropic effects of the c and it bonds. A
decrease of 0.75ppm in frequency is calculated for the anti+gauche con-
version, when using the point dipole approximation. Of these -0.75ppm,
-0.5ppm is caused by the C=C double bond.
The charge separation induced by the linear electric field
created by a point charge located at the various atoms (making use of
Equation (2.3-7)) does not contribute significantly to the shift change
of the anti+gauche transformation. A difference of less than 0.01ppm was
calC\ulated. The quadratic electric field effects of the time-dependent
dipoL moments in neighbouring electron groups give rise to substantial
variations however; a further decrease of -0.61ppm in frequency for the
anti-gauche conversion comes from this effect. As for the olefinic
protons, this latter contribution is to be taken with great caution, the
smallest distance involved being 2.11A as compared with the validity limit
208
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
of R > 3.5 A of Equation (2.3-6).
5.2.4 Carbon-13 chemical shifts and structure
A Olefinic carbons
(i) Chemical shifts and electron density
Table 5.2-3 displays a list of carbon-13 shifts for various alkyl
trans substitutions on a tert-butyl ethylene. The largest variation
obtained occurs amongst ethylenic carbon atoms. The C1 carbon
(olefinic carbon that the tert-butyl is attached to) has always its
resonance line on the high frequency side of C2 (see Figure (4.3-1)
for notation) resonance. Both shifts reflect the distribution of
electrons surrounding the observed nucleus; Seidman and Maciel [65]
have obtained a linear relation between the difference in computed carbon-
13 chemical shifts for two olefinic carbons (doubly-bonded together)
and the corresponding difference in the computed total valence-shell
electron densities for those atoms. Applying this result to the
trans-2,45-trimethy1-3-hexene would indicate an electropositive
charge on C1 as compared to C2. The induced charge calculated using
Huheey's method [88] is in concordance with the above property. A
tert-butyl group is calculated to have a larger electron withdrawing
ability on a CHX=CH fragment (X standing for a hydrogen atom, a
methyl, ethyl or isopropyl group) than either'a hydrogen atom or a
methyl, ethyl, isopropyl group would have on a (CH3)3-CH=CH fragment.
Using Huheey's method, the induced charge difference between C1 and C2
209
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
TABLE 5.2-3 Carbon-13 chemical shifts of some trans disubstituted ethylenes for which one substituent is a tert-butyl group, in ppm upfrequency from TMS.
C1 C2 C3 C4 C5 C6 jr,ef.
1 135.6 135.6 (31.7) (29.6) 31.7 29.6 • a
2 138.92 132.50 31.50 23.06 30.07 32.75 b
3 140.90 126.77 26.14 14.38 30.34 33.02
4 142.0 118., 16.97 29.1 32.0 a
5 148.6 108.2 28.4 32.8 a
aData taken from reference [118]; neat samples were used. bbata taken from this thesis. °Data taken from reference [119]; neat samples were used.
C c cs 1; I
1 C— C—C=C— C — c 2 C= C — C— C— C —C I
5 6 1 2 3 4
C C C 5
C C I I
3 C— C— C=C —C— C 4 C— C- C=C— C I
CI
C
5 C—C—C=C--- C
C
210
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
is calculated to gradually decrease from 7.4 x 10-2 to 1.0 x 10-2esu
when going from a hydrogen atom to an isopropyl group; this decrease
correlates approximately linearly with the decrease in shift difference
between the two olefinic carbons for the molecules given in Table
5.2-3. A shift of around 550ppm/e is obtained, twice the value gi'ven
by Seidman and Maciel [65] and three times that suggested by Lauterbur
[124]. This factor difference can be caused by the approximate nature
of the electron density calculated using Huheey's technique. This can
be seen from data on propene, for which CNDO calculation by Pople and
Gordon [125] gives a difference in electron density between the two
olefinic carbons of 7.4 x 10-2esu instead of 3.8 x 10-2esu as calcu-
lated using Huheey's method in the oversimplified assumption of
complete equalization of charge.
(ii) Temperature dependence
As can be seen from their temperature dependences (Table 4.3-1), the
resonance frequencies of both olefinic carbons increase virtually
linearly for the anti+gauche conversion. For both carbons, the steric
1,4-interaction described by Grant and Cheney [49] cannot explain the
trend. Using chemical shifts relative to TMS, the GBM method (under
the assumption AGo = 531J.mol-1 (or 127cal.mol-1)) gives increases of
18.lppm and of 21.4ppm for C1 and C2 respectively for the anti-*gauche
transformation. On the other hand, the calculated steric 1,4-inter-
action contributes to increases of only 2.07ppm (for C1) and 0.30ppm
(for C2) for the same anti-*gauche transformation. The linear field
211
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
.,.
effect is not an important factoi' either; variations of less than
0.01ppm are calculated assuming a 200ppm/e variation. As in the case
of the proton shifts, the carbon-13 shifts are dependent upon the
square of the field created by time-dependent dipole moments in
neighbouring groups. Following experimental findings by Rummens and
Mourits [226] for alkanes, the constant B for carbon-13 of Equation
(2.3-3) varies between -17 x 10-18 and-88 x 10-18esu, depending on the
number of alkyl substituents. For the olefinic carbons in question an
estimate of B = -40 x 10-18esu will be used. This Van der Waals shift
effect accounts to an increase of 3.7ppm for C2 due to the anti-gauche
rotation of the isopropyl group. The same structural change gives an
increase of 2.6ppm for Cl. Addition of all these effects gives the
right direction of variation of the shifts of both carbons, but the
calculated values are too small. .
B Methine carbon
) The lack of sensitivity (which could be caused by two antagonis-
tic effects) of the shielding of this carbon upon 1,4-substitution can be
seen in Table 5.2-4, where a list of carbon-13 shifts for substituted
isopropyl ethylenes is given. All the C3 shifts are within 0.2ppm except i
when there is no substitution (molecule 5).
The shift for this carbon in trans-2,2,5-trimethy1-3-hexene
does not display any temperature dependence (see Table 4.3-1). The
application of Grant and Cheney's technique is not possible because of
the absence of any relevant steric 1,4-interaction between hydrogen
212
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
TABLE 5.2-4 Carbon-13 chemical shifts of some trans disubstituted ethylenes for which one substituent is an isopropyl group, in ppm from TMS.
C1 C2 C3 C4 C5 C6 ref.
1 138.92 132.5 31.49 23.06 30.19 32.75 a
2 134.91 134.91 31.64 23.24 (23.24) (31.64) b
3 129.16 136.96 31.41 22.87 14.14 25.89 c
4 121.61 139.04 31.49 21.70 ,17.59 c
5 111.41 145.94 32.70 22.30 d
aData taken from this thesis. bData taken from L. F. Johnson and W. C. Jankowski, 13C NMR spectra, spectrum n315, Wiley and Sons Inc. (1972); CDC13 was used as solvent.
cData taken from reference [119]; the samples were neat. K dData taken from J. W. de Haan, L. J. M. van de Ven, A. R. N. Wilson, A. E. van der Hout-Lodder, C. Altona and D. H. Faber, Org. Magn. Res. 8, 477 (1976).
C4
C .5 1 • 1 1
1 C5 C -6 C= C-2 C3 C4 2 C — C— C=C— C —C
1
C5
4 C-C=C- 0T-C 3 C— C— C=C — C3— C
C
5 C=C— C3 C
213
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
atoms; however, other steric interaction: (for example 1,5-interactions)
could be not negligible and their change for an anti-gauche conversion
could give shift differences. Whereas linear electric field effects
turned out to be not effective for the conversion, the Vander Weals
shift (<E2> factor) was calculated to be substantially different between
the two conformations. A shift of -1.0ppm (thus toward lower frequencies)
was evaluated using Equation (2.3-7) for the anti+gauche transformation.
If this difference is real (the smallest distance affecting <E2> is 0
2.366A), another unknown cn-ltribution has to account for the balance of
an upfrequency shift of 1.0ppm for the conversion. The intrinsic varier
tion of the TMS line reference with temperature, as indicated by
Sc)neider et al. [127], should not be the cause of this shift. At
temperature below 300K, the shift of the TMS resonance is toward higher
frequency (when increasing the temperature) at a rate of about 0.012ppm/K,
meaning that a line in fixed position relative to the TMS reference
would actually be going toward high frequency.
5.2.5 Conclusion
The approach taken.for this molecule in the coupling constant
study seems most valuable. The consistency found for the Gibbs energy
difference results gives some credence to the technique used; it indicates
also the importance of the entropy variation. It is found that the
Force-Field based AG° is much too high (by 4.07KJ.mo1-1 or 0.973Kcal.mol-1 );
this difference is due to an overestimation of the steric energy
(5.15KJ.mo1-1 or 1.23Kcal.mo1-1). This overestimation was noticed first
214
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
by Rummens et al. [71] for the 3-methyl-l-butene, tey suggested that the
cause of the discrepancy was the overestimation of the non-bonded strain
energy in the 1.8-2.2A region. For the trans-2,2,5-trimethyl-3-hexene,
the difference between calculated and experimentally deduced values is
caused by the angle bending energy (2.64Klmol-1 or 0.63Kcal.mo1-1) as
well as by the non-bonded energy (2.68KJ.mo1-1 or 0.64Kcal.mo1-1).
The experimental value AG° = 531±89J.mo1-1 (127cal.mo1-1) 74=-
happens to be the same number as found for 3-methyl-l-butene (5311:60 Jmol-1
or 127cal.mol-1). In the latter case AS was, assumed zero, meaning that
the result is really a FI° value rather a AG° datun; this distinction is
unimportant, mostly because 3-methyl-l-butene is a small molecule. Of
course it is natural to expect that the AG° data for the two molecules
should be equal: there cannot be any direct steric hindrance by the
tert-butyl group and the electronic effeCt of the tert-butyl group
through the C=C double bond causes only minor electronic changes in the
isopropyl group. That virtually equal AG° values are indeed found forms
a strong support for the methodology employed.
The geometrical features, obtained from the Force Field calcula-
tion, combined with the INDO-derived (AJ/60) data have a relative success
in explaining the variations of each coupling constant for the anti-gauche
conversion. However, Rummens et a/. [71] have noticed that the systematic
errors in the (1J/A6) data and in the valence angles (as calculated ty
the Force Field calculation) have a tendency to cahcel out.
The chemical shift study (for proton and carbon-13) was not as
successful as the coupling constant study. The various effects suggested
215
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
to be involved in the conversion (anti to gauche) failed to explain, in
most cases, the variations (particularly their magnitude) of the chemical
shifts. The absence of an appropriate referencing (for proton as well as
carbon-13 spectra) should be one of the major causes of the failure.
Analysis of the results shows that, of all calculated effects, only the
intramolecular Van der Waals effect gives close to the correct magnitude
and always the correct sign of the various trends, thoth for proton and i
carbon-13 data. Another important contribution/for the proton shifts
involves the magnetic anisotropy of the bonds, while for carbon-13 shifts
the steric 1,4-interaction appears to play a non-negligible role for the
anti+gauche transformation.
5.3 cis-2,2,5-TRIMETHYL-3-HEXENE
5.3.1 Introduction ,
In view of the investigations made with the Force Field method
and of the resulting criticisms in the case of the trans isomer, three
possible transformations were foreseen for the cis isomer in the tempera-
ture range of the experiment. These are shown in Figure (5.3-1). The
Force Field method gives transformation(Das the most likely to occur:
starting from the (as) state (rotamer I) a 60° rotation of the tert-butyl
.group leads to the (aa) state (rotamer II), while the major features of
the isopropyl group remain unchanged. In the study of the trans isomer
(see preceding section) the energy difference calculated using the Force
Field procedure was shown to be overestimated by 4.2KJ.mo1-1 (1Kcal.mo1-1)
216
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
aJ
It ad
/ \ / aJ
f
"I
In
FIGURE 5.3-1 Schematic representation of the transformations considered in the discussion of the NMR results for cis-2,2,5-trimethy1-3-hexene
217
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
for an antivauche conversion. Transformation ®for the cis isomer is
calculated to involve a steric energy separation of 2.7KJ.mol-1
(0.65Kcal.mol-1), an amount which is smaller than the above-mentioned
overestimation, thus making transformation(!)(inverse of transformation
®) a possibility. A 160° rotation of the isopropyl group around the
C sp 2-C sp3 single bond defines transformation ©(it involves also profound
changes in the tert-butyl group). Thistis the closest to the anti-gauche
conversion foreseen by Van der Heijden in his thesis [112]. For trans-
formation®, it is assumed that the (as) and (aa) states are true minima
with negligible energy separation. It is also assumed that the energy
change for the conversion is relatively high (the steric energy difference
calculated by using the Force Field method amounts to 28.2KJ.mo1-1
(6.74Kcal.mol-1) when going from the conformation I to conformation III).
5.3.2 Analysis of the temperature dependence of several coupling
constants
If the temperature dependence of the coupling constants is a
reflection of transformation(Dor®, involving states of equal
degeneracy, Equation (5.2,44) used for the anti4gauche conversion has to'
be replaced by the following expression:
<J>T = p J1 + (1-p)J2
with 1-p -2— = exp RT
218
(5.3-1)
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
where p is the population of the more stable of the two conformations and
AG is the Gibbs energy difference between them; R and T have their usual
meaning.
'To make transformation manageable, one has to assume that the
energy difference between the (as) and (aa) states is exactly zero, and
that the entropy difference is also zero; then relation (5.3-1) can also
be used, p being the population of the (as) and (aa) pair of states.
Each 'of the coupling constants would be the average coupling of both
conformations.
For this isomer, two coupling constants (3vJ and 3cJ) show an
appreciable temperature dependence. Figure (5.3-2) indicates also a non-
negligible curvature in this dependence, which allows one to directly
extract three parameters. The direct application of the GBM method
should, in this case, give reliable answers, without having to estimate
one of the unknowns through another procedure. As for the trans isomer,
an intrinsic temperature dependence, deduced from the results from
propene given by Rummens et al. [71], has been removed. Given in Table
5.3-1 are the results obtained with AS = 0 as well as with AS = f(T)
(deduced from the data of Table 3.5-4 in a similar fashion as that used
for the trans isomer and described in the preceding section). This table
shows the results for each transformation. First of all these results
indicate the major importance of the entropy factor AS, both for the
Gibbs energy separation and for the coupling constants for each conforma-
tion. If one accepts that the Force Field employed results in reasonably
accurate vibrational frequencies, then, as the results of Table 5.3-1 show,
219
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
f
10.7
1$
10.5
10.5
10.4
e
220 270 320
T[K]
FIGURE 5.3-2 Temperature dependence of tie vici,nal coupling constant (J23, see Figure (4.2-1) fo notation) for the cia-2,2,5-trirnethy1-3-hexene (values .0 corrected for temperature dependence of the intrinsic ntribution). (---) represents the best-fit s obtained from the GBM method.
220 POI
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
TABLE 5.3-1 Sets of coupling constants and energy separations between rotamers obtained by the GBM metnod for the three considered transformations (see Figure (5.3-1)) of the cis-2,2,5-tri-methyl-3-hexenef
transformation C) transformation() transformation @
3vJ
3cJ
11H
TG0
AS
Jl =15.047 Jas=11.270
J2 = 5.266 Jaa = 8.502
AN = 0.418±0.38 AH = 3.347±0.25
AG°. 0.418±0.38 AG°= 2.699±0.25
J1 =11.303
J2 =13.204
AH = 1.67±0.33
( AG°= 1.6710.33
0.902±0.36 (0.216)
0.902±0.36 (0.216)
0.0
Jas=11.339
J aa =13.286
AH = 2.678±0.5
AG°. 2.03±0.5
3.096±0.33 (0.74)
2.448±0.33 (0.585)
Jaa=11.362
Jas= 9.388
AH = 0.377±0.35
1.025±0.35
0.11 10-4 T2
-0.001 1+2.81
J aa=11.550
Jas=12.521
AH = 0.418±C.I
AG°= 1.067±0.4
0.39310.37 (0.094)
1.04210.37 (0.249)
-0.11 10-4 T2
+0.011 T-2.81
J/ =11.757
J2 = 4.803
AH = 1.3810.29
AG°= 3.924±0.29
JI =10.741
J2 =16.765
AH = 0.92±0.67
iG°= 3.464±0.67
1.192±0.42 10.285)
3.73610.42 (0.893)
0.25 10-5 T2
-0.0027 T-1.445
The coupling constants are in Hz, AH and AG° in KJ.mol-1 (Kcal.mol-1); AS in cal.mo1-1.0 as calculated by the relations listed.
221
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
it is not allowed to assume that AS is not a function of temperature, let
alone to assume that its value would be equal to zero. Thus the results
from the AS = 0 assumption will henceforth be eliminated from further
discussion. As before, it will be assumed that AH is temperature
independent. All three possibilities (0,(1q),(D) give results that are
internally consistent within the estimated limits_ of error.
Using statistical weights proportional to the magnitude of the
variation of each coupling constant, average values for each transforma-
tion have been calculated as also shown in Table 5.3-1. None of the
other coupling constants (in particular 4 1J) has large enough variations
in the temperature domain investigated to be useful for the determination
of the energy separation between the rotamers. In view of the magnitude
of the Gibbs energy separation deduced from the experiment for transfor-
mation(70(3.74KJ.mol (0.89Kcal.mol-1 )) as compared to the calculated
(by Force Field) value (33.14KJ.mo1-1 (7.93Kcal.mo1-1)), this transforma-
tion will not be given a prime consideratiOn in the following discussions.
5.3.3 Coupling constants and conformations
A Vicinal coupling constant 3vJ (J23)
An alternate estimate for the values of this coupling constant,
for both rotamers, can be given following the procedure used for the
trans isomer (see Section 5.2.1). The value obtained by ,othner-By et al.
[107] for the 4,4-dimethyl-3-tert-butyl-l-pentene is t::,%en as the
starting quantity. A combination of the geometrical features of each
conformation with the (AJ/Ae) data found by Rummens et al. [71] allows
222
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
.,for the steric effect correction. A value of 11.88Hz is thus obtained
for the (as) state (conformation I)? while the same coupling constant for
the (aa) state (conformation II) is similarly calculated to be 0.75Hz
higher, TninsformationOgives the qualitative trend; however, the
experimentally deduced difference between the two conformations• for this
coupling constant exceeds the calculated difference value (1.97Hz instead
of 0.75Hz). For transformations@and®, the calculated values lead to
an overestimation in all cases: in transformation for example, the
experimentally deduced coupling constant for the (-as) conformation is
9.388Hz while the calculation through geometrical structure gives 11.88Hz.
The discussion on the reliability of the geometrical features
of cis isomers given in Chapter III led to question the accuracy of the
valence angles obt.ined through the Fqrce Field method. Following the
• discussion in Section 3.2.1, an estimate of the errors for the cis-2,2,5-
trimethyl-3-hexene in the (aa) state was given. Correction for these
errors leads to a decrease of 0.65Hz for the 3vJaa coupling constant
(thus equal to 11.90Hz, closer to the experimentally deduced 11.36Hz).
At the present time, the inaccuracy of the valence angles for the (as)
state cannot be estimated, because of a lack of experimentally known
structures of olefinic molecules displaying the studied structure. A
correction of more than 2.Hz would have to come from the inaccuracy of
the valence angles to fit the experimental finding (for a® transforma-
tion), meaning an overestimation of the C=C-C valence angles of about 10°
which appears unlikely. A
According to the values deduced experimentally for transformation
223
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
(D, the vicinal coupling constant 3vJ for conformation III is 4.803Hz.
The use of the propene value calculated by Maciel et al. [73] for a 20°
HCCH dihedral angle (this value is 7.5Hz) and its correction for valence
angle differences between propene and the cis-2,2,5-trimethyl-3-hexene
(using the (AJ/iO) calculated by Rummens et al. [72] one calculates
AJ = 0.7Hz) leads to an estimate of 8.2Hz.
On the basis of the results for 3vJ, it appears that transfonma-
tionOgives the wrong relative magnitude'for 3vJaa and 3vJas. Also, as
for the ©transformation, it appears that one of the coupling (this time
3vJaa) as deduced from the experiment is much too low. Such low values
for an anti 3vJ can only be understood if the HCCH dihedral angle is
considerably different from 180°. Such a possibility exists if a slight
modification of conformation III could be considered. A dihedral angle
of 50°, instead of the calculated 20° of conformation III, would give an
adequate fit for.ihe data Of 3vJ (3vJaa,
= 11.757Hz, 3vJIII = 4' 803Hz). '
B Olefinic coupling constant 3cJ (j12)
This coupling is experimentally found to bt larger for the
second minimum (which is the (aa) state if one considers transformation®
and the (as) state if one considers transformation (E)). The steric effect
through valence angle changes and (AJ/Ae) data gives the largest value
for the coupling belonging to conformation (aa), which would favour
transformationOas the correct interpretation. While the GBM method
gives a difference of 1.9Hz for the two couplings of the@transformation,
the calculated difference due to geometrical structure is 2.55Hz, which
224
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
ti
is a reasonable agreement.
As for the trans isomer, this coupling is sensitive to
electronegativity effects. Replacement of an hydrogen atom in the
ethylene molecule by-a tert-butyl group gives a decrease of 0.91Hz (the
data are obtained from Lynden-Bell and Sheppard [120] for the ethylene
molecule, and from Nicholas et al. [118] for the 3,3-dimethyl-l-butene).
After correcting these values for steric contributions, an electronegati-
vity effect of -3.00Hz is calculated. Using the values obtained by
Rummens et aZ. [72], the same procedure leads to an electronegativity
sect of -2.75Hz whey replacing an hydrogen atom by an isopropyl group
(these numbers could be compared with contributioiis of -3.28 and -3.24Hz
respectively calculated for the electronegativity effect on 3tJ, as
discussed in Section 5.2.2). Combining these effects with the steric
contribution present in the cis-2,2,5-trimethyl-3-hexene, a coupling
constant of 10.04Hz is predicted for the (as)`state (starting with the
propene molecule, instead of the ethylene molecule a value of 10.28Hz is
calculated), while 12.59Hz is the value obtained for the (aa) state. The
suggested errors given in Section 3.2.2 for the valence angles of the (aa)
state would decrease the latter value to 11.88Hz, 1.52Hz lower than the
value deduced through the use of the GBM method assuming an transforma-
tion; for a(Dtransformation this value of 11.88Hz is closer to the GBM
result (difference of 0.33Hz) and well within the uncertainty of the
calculation. But the (as) state would still have a lower 3ctl value. An
arbitrary decrease of 10° in-the C=C-C angle as would be required to fit
3vJ (see preceding paragraph) would worsen the situation ((AJ/66) data
225
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
being positive in this case, an overestimation of e leads to an over-
estimation of J). However, one must remember at the electronegativity
effects have been evaluated without taking account of possible errors in
valence angle calculations.
It is interesting to note that a transformation of the type
(as) 4- (aa) has been obtained through the Force Field method for the cis-
4,4-dimethy)-2-pentene (whee the isopropyl group is replaced by a methyl
group) by Ermer and Lifson [3]. For this molecule,.a temperature
dependence study of the NMR spectra (see Table 4.2-5) shows that 3cJ
(corrected or not for intrinsic temperature dependence) is virtually
constant between 250K and 350K'(the variation is less than 10-2Hz). The
standard Gibbs energy separation, resulting from the Force Field calcu-
lation, is 2.9KJ.mo1-1 (0.7Kcal.mo1-1) with a steric contribution -of
1.76KJ.mol-1 (0.42Kcal.mol-1). The expected difference (calculated'
through the geometrical structure given by Ermer and Lifson [3] and using
the (AJ/A8) data) for 3cJ between the two rotamers is 2.21Hz, a value
which is close to the 2.55Hz calculated for the corresponding difference
for either the(Dor(Dtransformation of cis-2,2,5-trimethyl-3-hexene.
The overall experimental temperature independence combined with the
predicted sizeable difference in the two 3cJ couplings, means that
(i) either the calculated AO values are wildly exaggerated
(ii) or AG° for tert-butyl group transformation is very close to zero
(smaller than 0.1KJ.mo1-1 (0.03Kcal.mo1-1))
(iii) or AG° for tert-butyl group transformation is fairly large
(larger than 6.3KJ.mo1-1 (1.5Kcal.mo1-1)).
226
14
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
In view of the AO data shown in Table 3.2 c, (i)'is not likely
to be correct.
If one assumes transformation QA to be the correct one for the cis-2,2,5-trimethyl-3-hexene, the calculated (using the Force Field
procedure) standard GibtA energy separation is overestimated by 2.8KJ.mo1-1
(0.68Kcal.mo1-1) as can be calculated from Tables 3.5-4 and 5.3-1. This
"correction" is likely to be a good approximation for the cis-4,4-dimethyl-
2-pentene because of the identical cisoid steric interaction in the two
molecules compared. The Force Field derived AG° for cis-4,4-dimethyl-2-
pentene is equal to 2.93KJ.mo1-1 (0.700Kcal.mo1-1). After "correction",
in the case of the latter molecule for the overestimation, the Gibbs
energy separation drops to 0.65KJ.mo1-1 (0.015Kcal.mo1-1) making (ii) the
most likely explanation for the temperature independence of the k J
coupling constant.
If transformation(Dis assumed to be the correct one, the
difference between calculated (with the Force Field method) and experi-
mentally deduced (using the GBM method) Gibbs energy is 6.28KJ.mo1-1
(1.5Kcal.mol-1). Correction for this difference leads to'a Gibbs energy
separation between the two rotamers of the cis-4,4-dimethyl-2-pentene
amounting to 3.35KJ.mol-1 (0.8Kcal.mol-1 ); this value is smaller than the
suggested value (6.28KJ.mol .) for the (iii) condition to apply and is
larger than the required difference for condition (ii) to be true.
Assuming a coupling constant difference of 2.21Hz between the rotamers,
an increase of 0.18Hz between 240K and 350K should be observed for a
Gibbs energy separation of 3.35KJ.mol (0.8Kcal.mol-1 ). This would
227
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
indicate that transformationOis not the correct transformation.
It may be noted that the experimental 3°J couplings at 298K are
almost the same for both molecules. While a value of 11.95Hz is found
for the cis-40-dimethy1-2-pentene, 11.94Hz is the coupling reported for
the cis-2,2,5-trimethyl-3-hexene. If AG° = 0 is assumed for the former,
and if one takes 2.21Hz as the difference in 3°J between the two rotamers
of the cis-4,4-dimethyl-2-pentene, values of 3cjas = 10.84Hz and
13.05Hz are obtained (the high temperature limit for the coupling 3cjaa =
being equal to (jaa Jas(2)) for the two rotamers. Neglecting the
differential electronegativity effect between methyl and isopropyl groups
(as suggested by Rummens and Kaslander [70]), values of 10.99Hz and
13.29Hz are then expected for the 3°J coupling constants in the (as) and
(aa) forms of the cis-2,2,5-trimethyl-3-hexene after correction for
steric effect contributions.
As was shown in the beginning of this section, transformation®
gives the wrong relative magnitude for 3cJas and 3cJaa in the case of
cis-2,2,5-trimethy1-3-hexene. It was also shown that transformation®,
if true, leads to a AG° value for cis-4,4-dimethy1-2-pentene which is
irreconcilable with the observed temperature independence. of.3cJ of the
latter molecule. On the other hand, transformation (A the correct
relative magnitude for 3cJas
and 3cJaa (although both are numerically
smaller than those derived from experiment), while in addition transfor-
mation(Dleads to a prediction o G° = 0 for cis-4,4-dimethy1-2-pentene,
which explains the temperat independence for 3cJ of the latter
molecule.
228
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
As for transformationG, transformation(Dgives the right
relative magnitude for 3aJas,aa
and 3cJIII' The predicted value for
3cJIII obtained through steric and electronegativity contributions from
ethylene is too small; a value of 13.51Hz is calculated instead of the
experimentally deduced value of 16.765Hz. The predicted (11.32Hz) and
the experimentally deduced (10.74Hz) values for 3cJas,aa are in fair
agreement.
C Allylic coupling constant 4taJ (J13)
The temperature dependence for this coupling is small (0.1Hz/
100K) with a scatter of about 0.05Hz/100K; as is to be expected, the
extraction of three parameters from this variation, in this case, does
not lead to any reasonable values. Taking for each transformation the
average Gibbs energy difference obtained from the 3cJ and 3vJ temperature
dependence, one deduces from the experimental data (corrected for
intrinsic temperature dependence), using the GBM method, the values
displayed in Table 5.3-2.
For the (as) form, the difference in steric contribution with
the 3-methyl-l-butene (where 4taJ (anti form) = 0.00Hz, see Rummens et al.
[71]) leads to an expected value of 4taJ = -0.42Hz. Similarly, CIS
4tczt)aa = -0.56Hz was calculated. These estimated 4taJ values are in
total variance however, with the GBM-deduced results as given in Table
5.3-2; the magnitude of the (AJ/M) data for this coupling constant (of
the order of 10-2Hz per degree) excludes the errors in valence angles as
the unique explanation; inaccuracy of the experimental data (the scatter
229
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
TABLE 5.3-2 Sets of 4taJ coupling constants as obtained by the GBM
method for the three considered transformations (see Figure (5.3-1)) of the cis-2,2,5-trimethyl-3-hexene, witenergy separations as taken from the 3v3 and 3cJ resultsT
DH
transformation() transformation® transformation ©
x 3.096 0.393 1.192
(0.74) (0.094) (0.285)
4taj Jas
= -0.231 J.aa = -0.243 Jas,as = -0.46
J aa
= -1.927 Jas = -1.364 JIII = -1.17
#A11 couplings are in Hz, AN are in KJ.mol-1 (Kcal.mol-1 ). AS in cal.mo1-1.K-1 as calculated by the relations given in Table 5.3-1.
230
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
is as large as one half of the variation) is the likely explanation.
Using the coupling dependence on dihedral angles as calculated
by Barfield et a7. [79] for propene, and after correction for steric
contribution differences, a positive coupling constant is predicted for
conformation III (the approximate value is 0.2Hz). This result excludes
transformation ©from the possibilities (the variation of 4taJ with
temperature is small, but the tendency is, nevertheless, toward a more
negative value for the second minimum). However, if a slight variation
of conformation III could be considered, to the extent of having a CCCH
dihedral angle of 130° rathqf than 160°, an exact fit for the data of
4taJ would be possible (4 tajQS, aa
= -0,5Hz and 4taJIII = -1.2Hz).
5.3.4 Proton chemical shifts and structure
A Analysis of the temperature dependence of proton chemical
shifts
The values given in Table 4.2-3 are referenced to the TMS line.
A study of the temperature dependence of the resonance frequencies of the
various protons should be made preferably without the unwanted intrinsic
temperature variation of the TMS line. Jn the discussion of the coupling
constants (see 5.3.3),At was suggested that either the cia-4,4-dimethyl-,,
2-pentene is subject to an equal-population equilibrium of theOtype
(meaning AG° smaller than 100J.mo1-1 or 25cal.mo1-1) in the temperature
range of the investigation for the cis-2,2,5-trimethyl-3-hexene or, in
the same range studied, only one conformation of the cia-4,4,dimethy1-2-
pentene is present (meaning that AG° is larger than 6.27KJ.mo1-1
231
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
(1.5Kcal.mol-1)). In either case the proton chemical shift variation of
the cis-4,4-dimethy1-2-pentene should not be caused by population changes,
but rather by the differential solvent effets. The temperature depen-
dence for the olefinic protons are shown in Figure (5.3-3) and Figure
(5.3-4). Due to the similarity of the surroundings for H1 and H2 in cis-
2,2,5-trimethy1-3.7hexene and in cis-4,4-dimethyl-2-pentene, the tempera-
ture dependence resulting from differential solvent effects should be
almost the same. A correction for these unwanted contributions can thus
be made by simple subtraction as shown in Figures (5.3-3) and (5.3-4)
(where do is the chemical shift of cis-4,4-dimethy1-2-pentene assumed to,
be free of unwanted contributions). Despite the fact that the methine
proton in the cis-2,2,5-trimethy1-3-hexene has no direct equivalent in
the cis-4,4-dimethyl-2-pentene, a similar correction was made by subtrac-
ting the temperature dependence of the methyl group of the latter
molecule (see Figure (5.3-5)).
For the three suggested transformations (G),(Dand(D) the
direct GBM method was applied. The results are shown in Table 5.3-3 for
the uncorrected shifts and in Table 5.3-4 for the results based on the
corrected shifts. The inconsistency of the AG° values for each assumed
transformation, as well as their poor correspondence with the AGo yalues
obtained from.the coupling constants, indicates that the corrections
applied were inadequate. Furthermore, due to these corrections, the
individual chemical shifts found are not the true ones; only the
differeice aa -(5as for(D, 6as-(5as for(D, III-(5as,aa for (D) for each
proton considerea has a quantitrtive meaning. Assuming that the mean
232
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
5.30 -
5.29
.0"
5.18
5.16 5.16
'C
220 270
T [pq ________. 320
FIGURE 5.3-3 Olefinic proton (H1) chemical shift dependence on tempera-ture for: A - cis-4,4-dimethy1-2-pentene referenced to TMS B - cis-2,2,5-trimethyl-3-hexene referenced to TMS C - cis-2,2,5-trimethy1-3-hexene referenced to TMS and
corrected for temperature dependence of intrinsic contribution (using curve A).
233
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
5.226
5.224
4.921
I 4.919
0
4.917 4
220 i „.07' 270
[K]
320
FIGURE 5.3-4 Olefinic proton (H2) chemical shift dependence'on tempera-ture for: A -as-4,4-dimethy1-2-pentene referenced to TMS B - cis-2,2,5-trimethy1-3-hexene referenced to IIMS C cis-2,2,5-trimethyl-3-hexene referenced to TMS and
corrected for the temperature dependence of intrinsic contribution (using curve A).
($) represents values obtained using correction extra-polated from the dash part of curve A.
234
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
2.843
2.835
2.825
co
1.690
• a A
1.685 22C 270 320
[K]
FIGURE 5.3-5 Proton chemical shift dependence on temperate for: A - methyl proton of cis-4,4-dimethy1-2-pentene referenced
to TMS B methine proton of cis-2,12,5-trimethyl-3-hexene
referenced td TMS C methine protbn of cis-22,5-trimethy1-3-hexene
referenced to TMS, corr cted for the temperatLre dependence of the intrinsic contribution (using curve A).
235
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
TABLE 5.3-3 Sets of proton chemical shifts and energy separations between rotamers as obtained from the GBM method for the three considered transformations (see Figure (5.3-1)) of the cis-2,2,5-trimethy1-3-hexene. The GBM method i$$ applied to uncorrected chemical shifts in ppm from TMSf
transformation() transformation® transformation
6as=5.274 6aa=5.2475 , 6aa,as
=5.664
H1
6 aa =4.911
AH =2.84± .50(0.63)
bas =5.052
AH =0.33±0.50(0.08)'
'III tH
.-3.3"
=0.67±0.50(0.16)
AG°=2.20±0.50(0.53) AG°=0.98±0.50(0.23) AG° =3.21±0.50(0.77)
6as=2.745 6 =2.780 as . 6 aa,as
=2.641
6 =3.033 aa H
6as=2.928 6III =3.599
methineAN =2.55±0.30(0.61) Ali =0.54±0.30(0.13) AH =0.84±0.30(0.20)
AG°=1.90±0.30(0.45) AG°=1.19±0.30(0.28) AG° =3.38±0.30(0.81)
4Energies are in KJ.mol-1 (Kcal.mol-1 ); AS in cal .mol-1.K-1 as calculated using the relations given in Table 5.3-1.
236
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
TABLE 5.3-4 Sets of proton chemical shifts and energy separation between rotamers as obtained from the GBM method applied to shifts corrected for unwanted contributions for the three considered transformations (see Figure (5.3-1)) of cites-2,2,5-trimethy1-3- hexeneT
transformation® transformation® transformation°
H1
H2
H3 (methine)
AH =0:544±0.25(0.13) AH =-0.544±0.25(-0.13) AH = 0.460±0.30(0.11)
AG°=-0.1040.25(-0.045) AG°= 0.104±0.25(0.025) AG° = 3.00± 0.30(0.72)
das= 5.0359 6 aa= 5.2939 as,aa= 4.1512
aa= 5.2939 bas= 5.0359 ( III = 8.5845
AN = 1.423±0.50(0.34) AH =-1.423±0.50(-0.34) AH =15.06±0.60(3.60)
AG°= 0.774±0.50(0.185) AG°=-0.774±0.50(-0.78) AG° =17.6±0.60(4.21)
(5as= 5.1425 d
aa= 4.6127 aa,as= 4.9170
6 = 4.6127 aa
as= 5.1425 ISIII
= 6.8027
AH = 1.213±0.65(0.29) AH = 3.93±0.65(0.94) AH = 0.251±0.71(0.06)
AG°= 0.565±0.65(0.135) AG°- 4.58±0.65(1.09) iG° = 2.7919.71(0.67)
6 as = 3.3036 8 aa= 2.8165 daa,as= 3.4589
6aa= 2.2-527 Bas= 2'9741. 6111 = 0.9193
tAH and AG° are in KJ.mo1-1 (Kcal.mo1-1); chemical shifts in ppm from TMS. AS in cal.mo1-1.K is taken from Table 5.3-1.
Reproduced w
ith permission of the copyright ow
ner. Further reproduction prohibited w
ithout permission.
enthalpy obtained by the application of the GBM method on the coupling 0
constants is accurate, the corresponding chemical shifts together with
their differences can be found; these results are given in Table 5.3-5.
These latter results seem to be the only rationale basis for further
discussion of the chemical shifts and their temperature dependence as
will be detailed below.
c B Olefinic proton H1
The H1 resonance is found at higher frequency in the
conforma-
tion of lowest energy. Differences in short range anisotropic,effect
were calculated by application of Equation (2.3-1) using the same Ax
parameters as for the trans isomer (see Section 5.2-3) and result in a
0.03ppm frequency decrease for transformation0(the reverse is true for
transformation(D). The differential contribution from the double bond
(0.11ppm) is countered by that from the three' C-C single bonds of the
tert-butyl group (-0.07ppm). If one introduces the quadratic effect from
the time-dependent electric dipoles, a further increase in frequency of
1.42ppm is obtained for transformation®, which disagrees both, in sign
and magnitude, with the experimental difference of -0.24ppm. For trans-
formation®, the direction agrees (of course), but the magnitude of the
discrepancy is far too large (-0.14ppm vs -1.42ppm). However, as for the
trans isomer, Equation (2.3-6) is applied outside the range of its tested
validity. The invariance of the isopropyl group conformation during the
transformation0(or(D) implies a negligible contribution difference for
that transformatiOn caused by the stevic 1,4-interaction.
238
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
x m -0 8 0. c C) m 0.
74: 7'
"0 m TABLE 5.3-5 Sets of proton chemical shifts and their difference as obtained by thq, GBM method g applied to shifts corrected for unwanted contributions; the enthalpy separations for4a' the three considered transformations (see Figure 5.3-1)) are as given in Table 5.3-1T (4. o m 0
m C) 0
. c0
o
transformation® transformation° transformation°
AH 3.096 (0.74)
oas= 5.2320
0.393 (0.094)
&aa= 5.2246
1.234 (0.295)
daa,as= 5.2906
m H1
&aa= 4.9942 dab= 5.0808 (5/// = 4.6018
-n c a-
6as-6aa=0.2378 6aa-6as=0.1438 oaa,as-6///=0.6888
gi m) ca
6 = 4.8980 as S = 4.8998 aa daa,as
= 4.8785
-08 UD H2 6 6aa= 4.9753 bas= 4.9480 d/// = 5.1048
0_ c das-6aa=-0.0773 daa-das=-0.0482 oaa,as-SIII=-0.2263
0.0
-0 (5 = 2.7465 as daa= 2.7547 6aa,as= 2.6802 8 methine H3 6
aa= 3.0856 Sas= 2.9654 d/// = 3.5660
Ei
a S -d =-0.3391 as as • daa-das=-0.1907 Saa,as-6///=-0.8858
74: tAH in KJ.mo1-1 (Kc41.mo1-1); chemical shifts in ppm from TMS.
°c AS AS in cal.mo1-1.K-1 as calculated by the relations given in Table 5.3-1.
Reproduced w
ith permission of the copyright ow
ner. Further reproduction prohibited w
ithout permission.
For transformation ©the sum of linear electric field effects
(-0.002ppm), of quadratic field effects due to time-dependent electric
dipoles (0.77ppm) and of the magnetic anisotropy effects (0.14ppm) cannot
explain the experimental trend (-0.69ppm for transformation (0).
C Olefinic proton H2
The non-monotonic temperature variation of the chemical shift
of this proton (see Figure (5.3-4)) has at least two possible explanations:
(i) the population ratio variation (between the states of minimum
energy) is not entirely responsible for the temperature dependence.
(ii) two successive transformations take place: for example, transfor-
mation(D(or(D) occurs at low temperature, while at higher temperature,
the population of conformation III starts to increase.
Up to this point, no other parameters (coupling constants or
chemical shifts) have given any indication that hypothesis (ii) may be
correct. Furthermore, after a correction is applied, using the tempera-
ture dependence of the H2 proton chemical shift of the cis-4,4-dimethyl-
2-pentene, the (corrected) temperature dependence becomes monotonic. The
magnetic bond anisotropy, as well as the <E2> term (which is the largest
contribution) gives an increased resonance frequency for transformation()
and for transformation (D; this could explain the experimentally found
minimum, if there are two successive transformations, first. transformation
©and then transformation (D. The largest magnetic anisotropy contribution
difference comes from the double bond, giving a high frequency shift for
transformation ®(amounting to 0.14ppm) as well as for(D(amounting to
240
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
0.18ppm). Similarly, the time-averaged square of the electric field,
<E2>, due to fluctuating dipoles increases the frequency for transforma-
tionG)(0.83ppm) as well as for transformation(D(1.09ppm). Both values
a'•a larger than the experimentally deduced shift increases; one obtains
0.077ppm and 0.23ppm for transformation( )and ©respectively.
D Methine proton
For the three transformations, Table 5.3-5 shows that the
methine proton of the lowest minimum energy has its resonance at low
frequency. While linear electric field effect (accounting for less than
0.001ppm for transformation 0) and steric 1,4-interactions (no such
H....H interaction) are not a factor, magnetic anisotropy of bonds
(accounting for -0.64ppm for transformation 0) and quadratic electric
field effects caused by fluctuating bond dipoles (-0.42ppm for transfor-
mationT) seem to favour transformation(i)(the experimentally deduced
shift for this transformation is 0.19ppm to be compared with the calculated
1.06ppm).
For transformation(Dthe bond magnetic anisotropy differences
(a shift of -1.2ppm is calculated, half coming from the double bond) and
quadratic electric field effects due to fluctuating dipoles (a shift of
-0.28ppm is calculated) would rule out transformation ©from the possi-
bilities (a shift of 0.88ppm is experimentally deduced).
241
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
5.3.5 Carbon-13 chemical shifts and structure
A Temperature dependence
As was the case for the proton shifts, the use of the carbon-13
resonance of TMS as a reference does not guarantee that the remaining
variations are exclusively caused by changes in population ratio of
various conformers. The choice of the C5 (for notation see Figure (4.3-1))
frequency line of the cis-2,2,5-trimethy1-3-hexene as a reference was
made, on the basis that, despite large differences between structures and
between population changes of cis and trans isomers, this carbon, in both
isomers, displays a similar increase in resonance frequency for the
temperature range investigated (variations of 0.33ppm and of 0.43ppm are
•observed for the C28 and trans isomers respectively). Also, because of
the symthetry of the tert-butyl group, any effect of conformational change
on C5 resonance will Itend to be minimized. The chemical shift values as
referenced against t ae tert-butyl methyl carbons are given in Table 5.3-6.
Direct application of the GBM method furnished the results as given in
Table 5.3-7. InconsiStency in the energies as derived from the various
carbon-13 shifts can i)e obsemied, and many of the shifts deduced for each
conformation are implausible. As for the proton shifts, the enthalpy
values obtained from the coupling constant study were then used with the
variable temperature carbon-13 shift data to calculate individual confor-
mational shifts. The results are given in Table 5.3-8.
The C5 resonance being taken as reference, was assumed to be not
varying; C4 displaying the same type of variation as C5 (see Table 4.3-2)
242
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
TABLE 5.3-6 Carbon-13 chemical shift (ppm) dependence on temperature for the cis-2,2,5-trimethyl-3-hexene referenced to the methyl tert-butyl carbon C5.
A)
T (K)
Olefinic carbons
Cl and C2
230 136.95 137.42
245 136.99 137.32
261 137.05 137.34
271 137.10 137.26
281 137.09 137.20
303 137.18 137.18
310 137.18 137.18
320 137.25 137.15
330 137.28 137.13
340 137.38 137.12
B) Saturated carbons
T (K) C3 C4 C6
180 27.89 23.33 32.78
190 27.87 23.35 32.79
200 27.84 23.35 32.82
213 27.80 23.35 32.85
222 27.77 23.35 32.87
240 27.71 23.36 32.95
245 27.70 23.36 32.96
260 27.65 23.35 33.00
270 27.64 23.34 33.02
280 27.62 23.34 33.04
300 27.59 23.34 33.11
310 27.59 23.33 33.12
320 27.56 23.32 33.15
340 27.54 23.31 33.21
243
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
x m -0 8 0. c C) 0 a • * .,,,....,
= TABLE 5.3-7 Sets of carbon-13 shifts and energy separations obtained from the GBt4 method for the -0
1 three transformations considered (see Figure (5.3-1)) of the cis-2,2,5-trimethy1-3- hexene. The shifts are references to C5.
a' m o m o transformation® transformation® transformation (D
AH = 6.40±0.96 (1.53) AH = 3.05±2.47 (0.73) AH = 4.81±2.26 (1.15)
AGO- 5.75±0.96 (1.37) AG°= 3.70±2.47 (0.89) AG° = 7.35±2.26 (1.76) C6 6as- 32.64 6aa= 32.58
6as,aa= 32.61 6 = 37.71 aa 6as= 35.40 6III
= 42.58
.., AH = 1.26±1.05 (0.30) AH = 9.62±3.14 (2.30) AH = 0.293±0.20 (0.07)
C* 1/2
AG°= 0.65±1.05
6 as=151.15
(0.14) AG°= 10.3±3.14
6 =136.90 aa
(2.45) AG° = 2.84±0.20
6 as,
aa=159.36
(6.68)
6aa=119.32 6as=153.77 6III = 67.44
AH = 2.47±1.8 (0.59) AH = +0.5±1.84 (+0.12) AH = 0.795±0.53 (0.19)
C* AGO= 1.82±1.8 (0.43) AG°= 0.15±1.84 (0.04) AG° = 3.34±0.53 (0.80)
2/1 6 =140.00 as - 6as=138.79 6as,aa
=145.76
6aa =131.35 6as=134.67 6111 =104.91
, AH = 3.89±0.90 (0.93) AH = 0.88±0.86 (0.21) AH = 1.80±0.94 (0.43)
AG°= 3.24±0.90 (0.77) AG°= 1.53±0.86 (0.37) AG° = 4.34±0.94 (1.04) a' C
3 m. 5
6as= 28.27 6aa= 28.51
,1 6as,aa= 28.76
m 6 = 25.07 aa 6as= 25.92 6III = 20.99
C4 Negligibly small variation
tAG° and AH are in KJ.mo1-1(Kcal.mol-1); the chemical shifts are in ppm. AS is taken as shown in Table 5.3-1.
Reproduced w
ith permission of the copyright ow
ner. Further reproduction prohibited w
ithout permission.
m 77
a 0_ c 0 00_ P: 7' -0 5 TABLE 5.3-8. Sets of carbon-13 chemical shifts and 'their difference as obtained from the GBM a. method with the enthalpy separations as given in Table 5.3-1 for the three . o considered transformations (see Figure (5.3-1)) of cis-2,2,5-trimethy1-3-hexene+ 0 0
5-' m transformation OA transformation transformation° C) . 0 -0 . AH 3.096 (0.74) 0.393 (0.094) 1.234 (0.295)
c0 0-0 6aa
= 28.56 6aa 6aa,as
= 28.83 = 29.63
C3 6 6as
= 25.74 6,II m = 24.98 aa = 18.43
m 6as-6aa= 3.58 6aa-6as= 3.09 6aa,as-6///= 11.20
a-c
' _/) m-gi 6 6 as as
=138.85 6 =138.91 =140.48 IV aa,as
'0 cri C2 or C1
6aa =134.60 . ofII =121.73 a
=132.75 bas _ c o .
bas-6aa= 6.10 6aa-bas= 4.31 6aa,as-6///= 18.75
0 0
0bas tsaa =135.12 =135.19 =133.68 a - 6aa,as
C1 or C2 6aa =142.76 bas =140.23 s,II. =153.34
it a_ 6aa-6aa= -7.64 6
aa-,6as=.-5.04 6aa,as-6///=-19.7
0c 6as = 31.90 csaa = 31.71 = 30.75
C6 6aa = 36.29 6as = 35.21 :III
aa,as = 43.84
1' 6as-6aa= -4.39 a 6aa-6as= -3.50
u). 6aa,as-6///=-13.09
o -1 0 the chemical shifts are in ppm (referenced to C5); AH are in KJ.mol (Kcal.mol-1).
Reproduced w
ith permission of the copyright ow
ner. Further reproduction prohibited w
ithout permission.
is then, as a consequence, also temperature independent.
B Quaternary tert-butyl carbons (C6)
For C6, the application of the GBM method gives the results
displayed in Table 5.3-7 (direct application of the method) and in Table
5.3-8 (with use of the enthalpy values previously determined). None of
the shifts for the second minimum (6aa
for transformation®, óas
for
transformation ©and 6111 for transformation (D) are reasonable. The
reason for this total failure is probably related to the fact that
carbon-13 solvent effects for quaternary carbons are very much smaller
than that for methyl carbonS (see for'example Rummens and Mourits [126]),
so that the C5 referencing is most inappropriate in this case.
C Olefinic carbons
Examination of Table 5.3-9 shows that an increase in bulkiness
(and therefore also in induced charge on C2) of the second substituent
(the first substituent being a tert-butyl group) correlates with an
increase in resonance frequency for C2 (olefinic carbon atom that the
second substituent is attached to) and with a decrease in resonance
frequency for the'Cl olefinic carbon. The difference in electronic
density at both carbons was invoked to explain the shift separation between
C1 and C2 for the trans molecules (see Table 5.2-1). It can be noted,
however, that this separation is smaller for cis isomers than for the
corresponding trans isomers. From Table 5.3-9, it appears that an
increase in C2 resonance frequency is the main cause of the smaller
246
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
U
TABLE 5.3-9 Carbon-13 chemical shifts of some cis disubstituted ethylenes for which one substituent is a tert-butyl group, in ppm from IMS.
Cl C2 C3 C4 C5 C6 ref.
1 138.7 138.7 32.1 32.0 32.0 32.1
2 137.4 137.4 27.85 23.60 31.79 33.37 b
3 139.48 131.00 22.13 15.02 31.62 33.53
4 141.02 122.47 14.27 31.26. 51.44 a
5 148.6 108.2 • 28.4 32.8 a
aData taken from reference [118]; neat samples were used; bData taken from this thesis.
°Data taken from reference [119]; neat samples were used.
I • I 141 C C — C=C— C C 2 C— C — C=C— C C
5 6 1 2 3 4
C C C5
C C I
3 C — C — C=iC— C — C a C --C --C=C---C
C ' I
C
• 1
5 C— C — C
C
247
•
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
separtion for the cis isomers. The C1 resonance shift for the cie."2,2,5-
trimethyl-3-hexene listed in Table 5.3-9 does not follow the general
trend observed above. This fact probably reflects a conformational
equilibrium with unequal populations.
The assignment of the resonance lines of the olefiniC part,
which cross over at around 300K, is ambiguous. One is tempted to assign
the largest value at high temperature to Cl, in order to maintain the
predominance of the induced charge effect, but large structural differences
could upset this predominance. The results from the application of the
GBM method Are given in Tables 5.3-7 and 5.3-8. For transformation®,
one would have high temperature limit averages ((Sas + daa)/2) of 135.80
and 138.94ppm for the C2/C1 pair. Comparison with the data of Table
5.3-9, particularly with molecules 1 and 4, would then lead to good
agreement, provided the assignment <C1> = 138.94 and <C2> = 135.80ppm i§'
made.
For transformation®, no such satisfactory, assignment can be
made. Transformation(Dappears excluded on the basis of excess1'ely
large (6III-6.0ta,as values.)
For transformation®, the steric 1,4-interaction effect on
(6a:das) (less th40..lppm) and the linear electric field effect (around
0.1ppm) are not important. The second order electric field effect due to
fluctuating electric dipoles gives (6aa-
bas) values of 18.9ppm and
27.4ppm for C1 and C2 olefinic carbons respectively, when using Equation
(2.3-6) (the B value of Equation (2.3-3) was taken as-40. x 10-18). Only
one of these results is consistent with the experimentally liduced
248
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
differences since the latter have opposite sign (7.6ppm for one, -6.lppm
for the other). Transformation®, similarly has experimental (6as-6aa)
values which have different signs for C1 and C2.
Methine carbon
Using thl same C5 reference as for the olefinic carbons,
results as given in Table 5.3-7 were obtained after direct application of
the GBM method. With de help of the enthalpies deduced from coupling
constant study, the differences in shift between conformers were calcu-
lated as shpwn in Table 5.3-8.
ITtre absence of steric 1,4-interaction. between polarizable C-H
bonds, the small difference in linear electric field effects and the
small contribution from quadratic electric field caused by molecular
dipoles (high frequency shift of 0.65ppm for transformati,on0) cannot
explain to difference deduced from the experiment (3.584m for transfor-
mation O, 3.09ppm for transormation(E)). In fact, the 6as
and 6aa
values for.either(Dor(Dappear reasonable. , On the other hand, the
6111 = 18.43ppm for ©i4 implausible.
r
9
5.3,6 Rotational barriers and line intensities
In his thesis, Van der Heiiden [/12] has suggested that the
rotational barrier for the tert-butyl group in the cis-2,2,5-trimethy1-3-
• -1 hexene can be as nigh es 62.8KJ.mol (15Kcal.mol-1). Such a barrier was
estimated following a rapid and clear change, around room temperature, in
the ratio of the tere-butyl line intensity to the isopropyl doublet
249
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
intensity. A careful reproduction of this result was attempted. The
proton spectra were recorded using a scanning rate of 0.03Hz per sec.
for a scale of 1Hz.cm-1 for a temperature range of 120K (between 240 and
360K). One of the olefinic lines of the cis-2,2,5-trimethyl-3-hexene
was taken as the lock signal. By this technique the TMS line could be
used as the intensity reference.
The results are given in Table 5.3-10. Intensity changes were
studied for the tert-butyl signal as well as for the isopropyl signals.
None of the quantities indicates a drastic change in intensity ratio at
any temperature. The fluctuations observed in the data of Table 5.3-10
are also present in the half line width of the reference. Variation of
the experimental conditions (most likely in homogeneity) are thought to
be the cause of these variations.
The carbon-13 spectra (recorded under the conditions described
in Section 4.1) likewise show only one signal for the methyl carbons of
the tert-butyl group at a1,1 temperatures between 180K and 340K. There is
no observable broadening and the peak intensity ratio with the TMS signal
(see Table 5.3-11) shows no systematic ..hanger.
The absence of any evidence of a drastic change in intensity
ratio for the tert-butyl group (both for proton and carbon-13) seems to
indicate that the rotational barrier for transformation(Dor&is small
(smaller than 24.0KJ:mo1-1 or 6Kcal.mo1-1) or that the Gibbs energy
difference between the (as) and (aa) conformers is large (i.e., larger
than 8.0KJ.mol-1 or 2.0Kcal.mol-1 ). The Force Field calculation agrees
with the former (AGT = 10.5KJ.mol or 2.5Kcal.mol-1 ) but not entirely
250
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
TABLE 5.3-10 Temperature dependence of the intensity of tert-butyl and isopropyl groups in cis-2,2,5-trimethyl-3-hexene (protonNMR).
T (K) R*t-butyl Rt isopropyl AvIITMS (Hz)
360 .57 .50 .36
350 .59 .53 .43
34C .575 .52 .42
330 .55 .52 .40.
320 .58 .53 .43
310 .53 .51 .40
300 .55 .50 .30
280 .59 .46 .22
270 .595 .47 .22
260 .61 .46 .28
250 .58 .47 .30
240 .57 .
.46 .35
210 .57 .41 .40
*Ra = E Id(ITmc0
E ); a represents either the tert-butyl group or the .l opropyT grai lines.
251
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
TABLE 5.3-11 Temperature dependence of the intensity of tert-butyl and isopropyl groups in cis-2,2,5-trimethyl-3-hexene for ' carbon-13 NMR.
T(K) R*. • tert-butyl 11*,isopropyl
300 0.82 0.75
280 0.81 0.74
260 0.77 0.69
240 0.78 0.70
220 0.77 0.69
210 0.77 0.69
200 0.75 0.66
180 0.74 , 0.65
*Ra = E Ia/(ITMS+E Ia); a represents either the tert-butyl signal or the a a isopropyl signal.
252
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
with the latter (AG° = 5.31KJ.mo1-1 or 1.27Kcal.mo1-1).
Similarly, the constancy of the intensity ratio for the
______i5opropyl group would suggest that either the rotational barrier for
transformation ©is small or the AG° difference between the rotamers of
lowest minimum energy is large. The Force Field would, in this case,
favour the second hypothesis. A rotational barrier AG1 of 49..2KJ.mo1-1
(11.8Kcal.mo1-1) is obtained between the (as, aa) fOrms and conformation
III, while an average Gibbs energy separation AG° of 36.4KJ.mo1:1
(8.7Kcal.mo1-1) is calculated_ between the same'rotamers.
5.3.7 Conclusion
Contradictory results are obtained from the combined investiga-
tion of NMR measurements and of Force Field calculations for the cis-
2,2,5-trimethy1-3-heene.
While transformation(Dis supported by the 3vJ coupling constant
data, transformatiohOis equally favoured by the 3cJ coupling constant
data. This latter transformation leads to a AG° which has the same sign
as that predicted' by the Force Field calculation; this transformation,
gives also a pradiction of AG° = 0 for cis-4,4-dimethyl-2-pentene, which
explains the temperature independence of 3cJ for this latter molecule.
On the other hand, transformation ©leads, for cis-4,4-dimethyl-2-pentene,
to a 40 inco4atible with the temperature independence of 3cJ. On the
basis of the/allylic coupling constant data 4taJ for the cis-2,2,5-
trimethy1-3-ihexene, both transformations (Oand(i)) appear unlikely.
Transformation(Dis relatively successful in explaining the
253
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
(3vJ and
3cJ) coupling constant data and their temperature dependence,
provided oneintroduces an extra 30° (from a CCCH dihedral angle 4, = 160°
to 130°) rotation of the isopropyl group for conformation III (which
would bring the methine proton virtually to a gauche position). Neverthe-
less, this transformation has to be rejected on the basis of the large
discrepancy between the Gibbs energy separations obtained from the GBM
-method and from the Force Field calculation. An energy separation of
3.74KJ.mo1-1 (0.89Kcal.Mo1-1) seems implausible for an (as)-'-(gs) trans-
formation in the case of cis-,2,2,5-trimethy1-3-hexene. This transforma-
tion can be compared with the cis/trans conversion of 2,2,5,5-tetramethyl-
3-hexene (in the cis conformation of this molecule a strong interaction
exists between the two tert-butyl groups, as should4xist for a (gs)
conformation of cis-2,2,5,trimethy1-3-hexene) which has been found
experimentally by Turner et at. [128] to involve an energy of 38.9KJ.mo1-1
(9.3Kcal.mo1-1).
The information gathered from the (proton and carbon-13)
chemical shift study leads, as much as the coupling constant study, to
irreconcilable results. It can be said, however, that the existence of a
kinetic process, involving rearrangement of the substituent group(s) has
been proven and that this process relates to a Gibbs energy separation in
the order of 2.0 to 4.0KJ.mol-1 (0.5-0.8Kcal.mol-1). Such given AGo
values were used to analyze the temperature dependence of the chemical
shifts. None of the foreseen (from the Force Field calculation) trans-
formations gives satisfactory explanations for all the chemical shift
data. While the olefinic proton Hl and the methine proton H3 favour
254
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
transformation®, the temperature variation of the olefinic proton H2
chemical shift is in concordance with transformation(Dor®.
In view of the above-mentioned results, the calculated geometri-
cal minima for the cis-2,2,5-trimethyl-3-hexene obtained using the Force
Field method are unsatisfactory. A adequate interconversion could
involve a 30° rotation of the isopropyl group from the anti position (thus
the double-degenerate second minimum would be in a skew form). The
correctness of this suggestion would mean that the Force Field method is
not well suited for interconversion of crowded molecules. The study of
'the cis-2,5-dimethy1-3thexene, which will be described in the next
section, was started in the hope of a clear outcome allowing'vne to
further test the Force Field method used.
5.4 C119-2,5-0IMETHYL-3-HEXENE
5.4.1 Temperature dependence of coupling constants
to
A Introduction
Following the results of the Force Field calculations, one of
the isopropyl groups is in anti position for the two minima of lowest
energy. As the other isopropyl group has its methine CH either in anti
((aa) state) or in syn ((as) state) position, the initial equilibrium in
question here will be of the (aa)4--).(as) type. If p is the population of
the (aa) state, the population of the (as) state, which is two-fold
degenerate (as and sa), will be (1-p)/2. The observed,(avvaged) vicinal
255
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
and allylic coupling constants (3'J and4ta J respectively) must follow
Equation (5.4-1):
<J>T = pJ + (1=2-) (Jaas
+ Jas) )
au 2 (5.4-1)
Jaa and Jaas are the coupling constants with the methine CH in anti posi-
tion for the (aa) and (as) states respectively. J8as is 'the coupling
constant when the methine.CH of the isopropyl group, is in en position
(HCsp 2-C sp3H dihedral angle = 0°). Application of the GBM method, using
Equation (5.4-1) will give Jam, (Jas + Jas) and the difference in
enthalpy between the conformers. if one uses the second form of Equation
(2.5-2), with the Calculated entropy differences as given in Table 3.5-2.
To calculate the inctividual coupling constants Jas a
and J8s' an estimate
of Jaa has to be given. An approximate difference between J and Jas
can be calculated using the geometries as per Force Field calculations,
plus the (a/o6) data of Rummens et al, [71], if one assumes that only
the steric contributions are involved. Knowing Jas, eas is then,calcu-
lated from the (Jas Jas
) results obtained from the GBM method.
For the homoallylic and olefinic coupling constants (Schaj and
3cJ respectively) one has to replace Equation (5.4-1) by Equation (5.4-2):
<j> = Jaa
+ (1-p) Jas
(5.4-2)
256
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
where p is the population of the (aa) state; Jaa and Jas are the coupling
constants for the (aa) anti (as) rotamers respectively.
B Vicinal coupling constant 3vJ and olefinic coupling constant 3cii
The temperature dependence for 3vJ is given in Figure (5.4-1).
An inflection point is observed at about 300K. Two successive rate
processes have to be invoked to explain such a change in curvature. To
avoid having to solve too complex a problem, it was assumed that below
the inflection point, 'the temperature dependence of the 3',1 coupling
constant follows Equation (5.4-1). Direct application of the GBM method
was made using Equation (2.5-2); the entropy differences and their
variations with temperature were taken from Table 3.5-2. Three parameters
could be obtained from the 3vJ temperature dependence which displays a
small curvature below 300K. The same procedure, using Equation (5.4-2)
was also applied to the olefinic coupling constant 3'J (as for 3vJ, only
the values below 300K were taken into account). The results for both
coupling constants are given in Table 5,4-1. The consistency of the
enthalpy and Gibbs energy differences is not a certain guarantee of the
correctness of the assumption (that only one transformation occurs below
300K). The weighted average Gibbs energy separation between the two
rotamers is calculated to be equal to 1.13±0.04KJ.mo1-1 (0.27±0.01Kcal
mo1-1), while the enthalpy difference is 0.732±0.04amo1-1 (0.175±0.01
Kcal.mol-1). The difference between Force Field ,calculated and experi-
mentally deduced energy separation is far larger than that found for the
trans- and cis-2,2,5-trimethyl-3-hexene (in the hypothesis of transformation
257
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
d • '
9.6
9.5
6
9.4
;so 260 290 320
T {K}
350
FIGURE 5.4-1 Temperatui.e dependence of the vicinal coupling constant (J12, see Figure (4.2-5).for notation) for r:8-2,5-dimethy1-3-hexene (not corrected for intrinsic contribution).
258
•
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
TABLE 5.4-1 Sets of coupling constants and energy separation between rotamers as obtained by the G8M method applied to the experimental data of cis-2,5-dimethyl-3-hexene up to a temperature of 3000
3uj
3cj
J = 11.807 aa (Jas + Jas)/2 = 5.961 AH . 0.711±0.08 (0170)
AG' = 1.11±0.08 (0.265)
Jaa = 10.482 Jas = 11.330 AN, = 0.837±0.08 (0.200)
AG° = 1.23±0.08 (0.295)
TR = 0.732±0.042 (0.175±0.010) 7° = 1.13±0.042 (0.270±0.010)
4A11 J couplings in Hz; AG', AR in KJ.mo1:1(Kcal.mol-1) and AS in cal.mo1-1.K-1,,as calculated from AS . al-4 + bT + c; a . -0.5 10-6, b = 0.748 10-J, c = -0%498.
t
259
1
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
(A or it would amount to 13.22KJ.mo1-1 (3.16Kcal.mo1-1) if one
assumes an (aa)+-0-(as) equilibrium.
All other coupling, constants showed a variation with tempera-
ture barely different from the random scatter; therefore, these could not
be used to determine AG°.
5.4.2 Coupling constant and structure
A Vicinal coupling constant 3vJ
The combined use of the Force Field derived geometries and of
the (AJ/Ae) data as given by Rummens et al. [71], allows one to evaluate
the anti coupling constant, 3v,.1aa, without relying on the experimental
data. The 3vJa
value given -by Rummens et al. [71] for the 3-methyl-l-
butene is the starting value of the calculation. Neglecting the electr:o-
negativity effect of the second isopropyl group (supposedly small, see
Rummens and Kaslander Pop, the steric contribution (calculated with the
Force Field-based geometry combined with the (AJ/Ae) data given by Rumens
et al. [72]) increases the 3vJa value from 10.21Hz (3-methyl-l-butene) to
11.50Hz. This value is close enough to the experimentally deduced
3vJaa = 11.807Hz, to assume that the major geometrical features of the
(aa) state are well described by the Force Field calculation. The
estimated difference (3v
Jaa 3vs - J
aa) calculated by the same procedure is
s 0.18Hz. From the sum (3v Jaa 3v
s Jas) obtained by the applicatio.; of the
s GBM method, one then deduces a value of -0.07Hz for 3v Jas. This value
seems to rule out the Assumed (aa)+4.(as) transformation. Indeed, in,syn
•
26a
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1
position, an FPT-INDO-derived 39J coupling constant of 8.48Hz has been
calculated by Maciel et al. [73] for propene. Neither the steric, nor
the electronegativity contributions would lower this value to reach a
negative coupling. The smallest ' 79J coupling constant obtained by Maciel
et al. [73] is with an HC sp 3-C sp2H dihedral angle of 80° (while the syn
position corresponds to a zero dihedral angle), which gives 39J z 2.3Hz;
this latter value is still too high and correction for steric contribu-
tion would certainly increase this value; the steric hindrance increases
the C=C-C angles and decreases the C=C-H angles while the corresponding
(AJ/A6) data are positive and negative respectively. One possibility is
that, for the second rotamer, none of the methine CH is in anti position.
With a two-fold degenerate state, the sum of the 39J coupling constants
for this rotamer should be 11.92Hz. Postulating equivalent isopropyl
groups, with identical coupling constants, this value of 11.92Hz can be
obtained for HC sp 2-C sp3H dihedral angles of either 40°:T .e., close to
gauche) or 120° (i.e., skew), if one follows the calculatiOns by Maciel
et al. [73] for propene. Of these two the former is least likely because
in this rotamer the four methyl 'groups would be involved in a strong
cisoid interaction. However, neither conformational structure corres-
ponds to an energy minimum according to the Force Field method. ,
Olefinic coupling constant 3eJ
The (aa)-0.(as) transformation explains the observed increase of
3cJ with temperature (see Table 4.2-4). The calculated change due to
steric contributions (0.69Hz)-for this transformation is in good agreement
261
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
with the experimentally deduced increase (0.85Hz). The 3cJaa coupling
constant can be calculated from the 3-methyl-i-butene value (3cJa =
9.63Hz) obtained by 'Rumens et al. [71]. The change in steric contribd-„
tion 4+3.56Hz) and in the electronegativity effect (-2.75Hz) between the
3-methyl-l-butene and the cis-2,5-dimethY1-3-hpxene gives a calculated
3cJaa' for the -latter molecule, equal to 10.44Hz, in ,guod agreement with
0
the experimentally deduced value of 10.48Hz. The indlusion of anticipated
errors in valence angle calculation by the Fqrce Field method would lower
the theoretically calculated 3cJaa down to 9.87Hz (a 1.4°,overestimation
of the C=C-C valence angles and a 2.6° underestimation of the C=C-H
valence angles,have been estimated for the (aa) state, according -to the
discussion in Section 3.2.1).
On the basis of the fair agreement between the results obtained
by the two above procedures, it can be concluded that the calculated ('by
Force Field) geometry of the "rigid" part,(e.i. not including the rotors)
of the molecule is probably accurate.
C LongLrange H-H coupling constants
Acdording to thrfield et a/. [79], the FPT-INDO-derived 4t2J
coupling constant has its minimum value when the mett,ir.le protein eclipses
the 2p atomic orbital of the olefinic carbon (to which the isopropyl
group is attached). Maximum values are obtained foi/Lanti (0.00Hz'
according to.Barffeld et al. [79]) and for syn positions (a theoretical
value of 1.01Hz was calculated by Barfield et al. [79] for propene).
Wowing fOr the steric contribution differences between propene and
262
;
'
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
cis72,5-dimethy1-3-hexene, a 4taJ:s coupling constant of about 0.64Hz is
estimated. The low experimental value (-1.04Hz) and its temperature
dependence (toward more negative values for increasing temperatbre) would
render an (aa)4-+(as) transformation implausible. For this transformation,
Rummens et al. [71] estimated that (averaged) values of between -0.5Hz
and 2.0Himust be expected.
From the application of the GBM method 'assuming AG° = 1.13KJ.
mol 6r-0--,2.7Xcal.moI-1), one obtains values equal to -0..944Hz and
-1.14Hz for 4taJaa and for the sum taa J4-S a-4-1 s_l_cepectively. If
Q
ore postulates that the 4taJaa and 4taJaas couplings are equal, a ,syn
coupling constant 4t2J:s = -1.34Hz results..
The calculated rehybridization effect, for 4taJ, in going from
3-methyl-l-butene to cis-2,5-dimethy1-3-hexene is equal to -0.20Hz. The
4ta Ja'given by Rummens et al. [71]
the former molecule being equal to.
0.0Hz, the above result leaves-,the remaining -0.74Hz unexplained. This
is to be compared with a similar unexplained -0.52hz for the cis-2-butene?-
which is, according to Rummens and Kaslander [70],, not due to a differen-
tial electronegativity effect. No reason can yet be giV•en for either of
these discrepancies.
The homoallylic coupling constant, 5c haj, is difficult to inter-
pret. According to calculations performed by Barfield and Sternhell
[80], both 5chaJ and 5c Jas are negative (equal to -0.75Hz and -0.40Hz aa
respectively) so that any (aa)-.+(as) equilibrium would have a negative °' 4!
<5chaLl>. Since the experimental 5chaJ couplings are all positive (see
Table 4.2-4), once more the above-mentioned transformation seems to be
263
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
ruled out. From Barfield and Sternhell's work [80], it may be seen that
one obtains a positive (and relatively large) 5c haj, when none of the CH
methines is in anti position (a maximum value of 4.99Hz is'reached when
.the and 0' angles are equal to 90° (see Section 2.423 for notations)).
5.4.3 Proton chemical shifts and structure
A Methine proton
The'results shown in Table 4.2-4 and in Figure (5.4-2) indicate
a dect:ease of the methine proton chemical shift. The variation observed
1-siii*--enaigh-not-to-be-uniquely due_ to intrinsic effects. For the _
i;raw and cis-2,2,5-trimethy1-3-hexene the' corrections due to these
effects were much less than the variation observed for the cis-2,5-
dimethyl-3-hexene. This would indicate that the methine proton resonance
frequency decreases for the (aa)++(as) transformation. The GBM method •
(Equation (5.4-2)) was applied to uncorrected (referenced to the TMS
line) and to corrected (of the intrinsic variation of the methyl'protons .
of the propene molecule as given by Rummens et al.,[71]) chemical shifts
(both- are_displayed in Figure (5.4-2)). In both cases, the application
of-
of the GBM method appl-ied up to a temprature of 300K as for the
coupling constants) gives a free 'Gibbs energy separation between the
rotamers close to that obtained,frdm the coupling constant study (AG° =
1.276KJ.mo1-1 or 305ca1.mo1-1). The deduced frequency resonance shift ,
for the (aa)4.4-(as) transformation is equal to -0.32 or -0.41p;m depending
on the values employed (the results are given in Table 5.4-2).
264
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
• 2.610
2.606
ct.
et) 2. •
e<cs.4. 2.602
2.398 220 .270
k T
[K]
320
FIGURE 5.4-2 Temperature.dependence of the methin 'Pr to (H2) chemical shift for cis-2,5-dimethy1-3-hexene. A - referenced to TMS B - referenced to TMS and corrected for the intrinsic
temperature variation found for th-e methyl protons of propene (obtained from reference [71]).
265
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
TABLE 5.4-2 Sets of proton chemical shifts and energy separations as obtained by the GBM method applied to experimental data of cis-2,5-dimethy1-3-hexene up to a temperature of 3000.
•
B
C
From 6H (olefinic). From 6H (methine)
AH° = 83711004200) AH° = 879±250 (210)
AG° = 1234±300 (295) AG° = 1276±250 (305) A
6aa = 5.1782 bas= 4.8092 6 = 2.7210 bas = 2.4025 :aa..6
= -0.318 6as-6aa = -0.369 as aa
AH° = 837±300 (200)
AG° = 1234±300 (295)
AH° = 879±250 (210)
AG° = 1276±250 (305)
6 = 5.2503 6 = 4.6857 D 6 • = 2.7536 6 = 2.3455 aa as aa as
6 -6 = -0.565 6 -6 -0.408 • 'as aa • as as
•AH° = 1137i300 (200).
AG° = 1234306 (298)
6aa = 5.1107 bas = 4.9248
• 6as-6aa -0.186
energie; in J.mol-1 (cal.mol-1) chemical shifts in ppm relative to TMS.
A the reference is uncorrected B reference corrected by subtracting the temperature dependence
of tfie H3 proton in propene C reference corrected by subtracting the average temperature
dependence of the three olefinic protons of propene D corrected,0 subtracting the temperature dependence of the
methyl signal in propene.
266
• a
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
The sum of the magnetic anisotropy effect (-0.74ppm), the ,
steric 1,4-interaction (-0.12ppm) and the <E2> term (0.68ppm) gives a
total expected shift of -0.18ppm for the transformation, in fair agree-
ment with the above-given experimentally deduced shifts. The agreement
may be fortuitous because of the Oconsistency in the success of the
above-mentioned contributions for the other molecules studied (see
.Sections 5.2 and 5.3).
B Olefinic protons
As can be observed in Table 4.2-4 and in Figure (5.4-3), an
increase in the temperature up to 300K is correlated with a deCrease in
resonance frequency of the olefinic protons. Above 3F IC (the inflection
point for the <3vJ> F(T)) the temperature increase is accompanied with
a shift increase. Despite the absence of adequate referencing, the
experimental variation is large enough so that the GBM procedure is not
necessarily upset by the lack of any good correction. Application of the
GBM method on three different sets of values (each set is the result of
various corrections applied to the experimental values, see,Table 5.4-2)
gives, like for the methine protonoareasonable Gibbs energy separation
between the rotamerg of 1.234KJ.mo1.1 (295ca1.mo1-1), which can
be compared with AG° = 1.13KJ,mo1-1 (270cal.mo1-1) obtained froOhe
coupling constant study. Depending on the correction applied, the ,\
resonance frequency shift obtained for the (aa)+-(as) transformation,
varies between -0.19 and -0'.57ppm (see Table 5.4-2).
The magnetic anisotropy of the bonds gives a shift of -0.30ppm,,
267
• Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
4-
5.047_
E a. a.
C
(r) 5.042
x
5.037
230 230 280
T [K]
330
FIGURE 5.4-3 Temperature dependence of the olefinic protons chemical shift for cis-2,5-dimethyl-3-hexene. A - referenced to TMS B - referenced to TMS and Arrected for the temperature
dependence of the intrinsic contribution found for the H3 proton of Oropene(taken from reference [72])
C referenced to TMS and corrected for the mean tempera-ture dependence of the intrinsic contribution found for the three olefinic protons of propene (from reference [72]).
268
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
for this transformation, mainly coming from the CH methine bond effect.
The steric 1,4-interaction does not Iplay any important role in the shift.
The quadratic electric field contribUtion due to the time-dependent
dipoles is calculated to account to a shift of +0.09ppm for this trans-
formation. The sum of the three contributions (-0.21ppm) is in good
agreement with the experimentally deduced shift (see Table 5.4-2). How-
ever, as for the methine proton, the agreement could be fortuitous.
•
5.4.4 Conclusion
Although the study of this molecule leaves some unexplained
facts, some obvious conclusions can be drawn. As for the cis-2,2,5-
trimethyl-3-hexene, the cis-2,5-dimedly1-3-hexene is subject to a kinetic
process involving relatively small Gibbs energy difference of about AG° =
1.13amol-1 (0.27Kcal.mol-1). While the Force Field calculation
indicates the possibility of such a process for the former molecule, the
calculation for the latter rules out the observation of any transformation
for the temperature range investigated.
The belief that the Force Field calculation simply overestimates
Gibbs energy differences between rotamers is not supported by the
analysis of the 31)J, "aJ and 6aha J coupling constant data. The study
gives credence to the idea that the employed Force Field technique over-
looks a low-lying minimum For cis-2,5-dimethyl-3-hexene. An acceptable
fit between experimental data and the calculated (by Force Field)
structure of the molecule cannot be obtained on the assumption of an
(aa)+(as) (or even an (aa)4.(ag)) conversion. •
269
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
However, the 3vJ and 3cJ coupling constant data are compatible
with the Force Field-derived geometry of ,the minimum of lowest energy
(the (aa) state). As well, the "rigid" HC=CH fragment of the second
minimum is adequately reproduced by the Force Field technique (this frav
ment is -only indirectly perturbed by the increase in crowdiness).
The proton chemical shift study does not provide any further
support to the above-mentioned conclusions. Both the olefinic and
methine proton shift data are well explained by the Force Field calculated
geometry of the two minima of lowest energy. The discussion of the trans-
2,2,5-trimethy1-3-hexene data (fOr which the Force Field calculated
geometry is reasonably v.curate) has, however, shown that one cannot rely
too heavily on chemical shift data.
270
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
CHAPTER VI
EPILOGUE
In this thesis several experimental and calculational techniques
have been employed in various combinations, all in search of new Wnowledge
regarding molecular structure. Because of the conflicting eviden/e that r emerged in several cases, this work also became a testing ground for the
techniques and methodologies employed. This requires• a great Oal of
care in every instance of reasoning, of identifying what the particular
premises are and of keeping track of these premises from one case to the
next. In spite of this interweaving of methodology and results, and
perhaps also because of it, an attempt will be made in this final chapter
to distill some overall conclusions and to indicate what future work is
needea.to resolve the outstanding problems.
•
A Experimental NMR at variable temperature and the extraction of
NMR parameters
This study shows that careful experimental work, coupled with
• powerful spectral analysis techniques, such as the NUMARIT computer
program, can give parameters with a precision at or near ±0.005Hz. Such
low error estimates were found before in the variance-covariance treat-
ment of the data, but they were generally considered suspect. The
scatter of the data around the general trend of temperature dependence of
271
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
coupling constants, as shown in this thesis, is also .often less than
±0.005Hz, thereby giving additional evidence for the basic precision as
quoted above. Some sources of systematic error still remain, but these
cannot be much greater than the observed scatter; it follows that most
parameters have an accuracy of better than 0..01Hz.
In terms of sensitivity of NMR temperature effects,it is
believed that this thesis has set a new standard.
B Conformational equilibria as studied by temperature variation
of NMR parameters
If there exists at leatt one non-zero Gibbs free energy
difference AG°.between two states, and if the molecular parameters
observed are population averages and if, additionally,'the'parameters
belonging to the individual states have different values, then,the
observed parameters will be temperature dependent. In the reverse
application of this phenomenon, the observed temperature dependence must
be at least quadratic, because three parameters need to be extracted viz.
the AG° and the parameter values in the two states. The extraction itself
is done by lept squares fit, utilizing an over-determined set of para-
meter values (i.e., determined at more than three temperatures). Because
of the high precision of the parameter data, small temperature effects,
some as small as 0.1Hz/100K, could be successfuily employed. If a
larger effect is observed, greater accuracy for AG° results.
As the results in this thesis indicate, provided the individual
parameter values-differ by 2 to 5Hz, the detection limit for AG° can be
272
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
set at about 0.12KJ.mol (0.03Kcal.mol-1 ) (there exists an upper limit
too for AG , which is probably around 6.3KJ.mol-1 or 1.5Kcal.mol-1 , but
the present study did not involve any such case).
In a number of cases though, the total observed temperature
variation did not exhibit sufficient quadratic character; this thesis
shows some examples of how to cope with such.a situation. Essentially,
either the AG° or one of the individual parameter values, or the
difference of the two of them, must be obtained fr.= another source, so
that the analysis then reduces either to a linear fit, or, as was mostly
done in this thesis, a quadratic fit with one fixed parameter.
.In view of the smallness of all observed temperature effects,
'no attempt was made--or could be made--tcy.test for three-site possibili-
ties, involving two AG° and three parameter values. The molecular
systems were chosen so that the possibility of a thitd low-lying state •
was considered rather minimal. As an extra safeguard against this and
several other possible systematic errors, every molecule Studied had at
least two parameters with a sufficiently large temperature dependence.
One of the more useful conclusions of this thesis is that consistency of
AG° values obtained for one molecule is not only useful, but virtually a.
must. It through this criterion, that it could be established that
coupling constants are much more reliable parameters than chemical shifts
are and also that certain external data (strain energies, conformational a
structure) could be ruled as being in error. Consistency in AGo is
necessary, but not sufficient. To be completely satisfactory, the
process must yield individual parameters which in themselves must be
273
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
reasonable and at least iii semi-quantitative agreement with the proposed
structure as indicated through additional structure-parameter relation-
ships. As again this study shows, it is possible to obtain consistency
in AG°, together with totally unacceptable individual parameter values.
Such results mean that indeed a kinetic process was observed, with a AG°
as calculated (except when the actual degeneracy is diffdrent from the
assumed one), but these results mean also that at least one of the
individual structures is quite different from the anticipated one.
•
C Structure-parameter relations
The general approach of this thesis has been to start with
certain proposed structures for the rotamers in question and to then see
whether the (two) sets of deduced parameters are in concordance with that
hypothesis. The strong dependence on dihedral angle(s) of vicinal,
allylic and homoallylic couplings has long been known and has been used
extensively in the past (and in this thesis). A new dimension was added
by the realization that, with a rotameric transition, the entire molecule - •
changes, particularly in its valence angles e (bond distance may also .
change, but this effect was found negligibly small for the systems
studied in this thesis): Because of this, parameters belonging to the
so-called rigid part Of the moledule are different in the two rotamers
and their observed 4yerageF are therefore temperature dependent.
A key.role in the discussion of these effects are the (AJ/AB)
data calculated earlier by Rumens and Kaslander. Starting with two
proposed structures and the AA (and,U) differences between them, as
274
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
calculated.by Force Field techniques (vide infra), the differences AJ.'
belonging to a rotameric transition could be calculated, independently
from the experimental tJ (as determined from the temperature dependence).
This technique had been used only once.before, but proved to be reliable
several times over in this thesis. Because of these repeated successes,
failure of(this technique is now concluded to meadthat'the'workihg hypothe-
sis has been wrong.
An extensive effort was made to find a 'similarly useful
structure-parameter stratagem for the interpretation of chemical shifts.
The nearly complete failure of this attempt has two basid reasons.
Firstly, chemical shifts are susceptible to solvent effects. Even though
the molecules in question were almost non-polar (and dissolved in non-
polar solvent) and even though 44MS was added as an internal reference,
the remaining differential Van der Waals solvent effect is not zero and
is different for each observed nucleus; this differential solvent effect
has also a temperature dependence which may well obscure the sought-after
intramolecular effects. Not only is there a site-effect operative both
for protons and carbon-13, but the basic Van der Waals equation
(aw -B E2) has different B values for carbons of different substitution
character. This latter point is brought out in the thesis: whatever
little could be said about the proton shift data, the carbon-13 shift
data proved virtually useless.
The second set of reasons derives from the various mechanisms
that can be invoked to explain (proton) shift differences between related
molecules. One such mechanism is that due to magnetic anisotropies (ax)
275
0
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
of chemical bonds. The present study with its pair of rotamers (each
rt,g,with its set of chemical shifts) is particularly useful in testi g \ this
mechanism. Surprisingly (in view of the many publications extoll and
using this mechanisOlt was found systematically that the Ax effect * . .)
falls short by, close to one.order of magnitude in explaining the shift
differences between rotamers. Linear and quadratic electric field
effects (due to the polarity of C-H bonds mainly) were found to be even
smaller in magnitude. The remaining possibility, an intramolecular Van
' sometimes even quantitatively) explaining rotampric shift differences.
This- result is surprising, as such effect has'rarely been invoked as a
significant factor in intramolecular shifts. Consequently, the theory is
only rudimentary; it would seem worthwhile, however, to further pursue
this in any future studies,
der Waals shift effect, turned out to be capable of qualitatively (and
D Force Field calculation
The introduction of Force Field calculations had, as a main
purpose, to give rough.estimation of energy differences'between various
proposed rotameric structures in order to see that the smallest AG° would
be in the observable range and to ensure that any further AG°'s would,be
high enough so as not to interfere. A second objective was to obtain the
basic structural information (usually a dihedral angle) corresponding to
the'-minima in steric energy. The Ermer-Lifson Force Field was chosen for
several reasons: firstly it was based on spectroscopic, thermodynamic and
structural information; secondly it was available in a fully iterative
276
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
r-, calculation gives 4KJ (1Kcal) more. The error can be traced back to the
input data for-the optimization of the force constants. The only rota-
meric energy irfput relates to (correct) AG° = 0 values for cis- and
trans-2-butene, propene and isobutylene, plus a AG° = 0..63KJ.mo1-1
(0.15Kcal.mol-1) for 1-butene. This sole non-zero AG° input data ts. not
well reproduced by the Force Field calculation. This latter method i1
version (the only one at the time) and lastly, but not least, .it was
the only Force Field that correctly predicted the C=C double bond eclip-
sing stricture for the C-H bonds in cisj-2-butene.
It became clear that this Force Field still has its short-
comings; For example, both for 3-methyl-l-butene and trp/s-2,2,5-tri-
methy1-3-hexene, the experimental NMR based) Gibbs free energy
difference is AG° = 531j:mol-1 (127cal.mo1-1) while the Force Field,
'indicates that the gauche isomer is more stable thanmde s-cis isomer
by 4.9 KJ.mol-1
(1.2 Kcal.mol ). Unfortunately one does nat•know which
force constants got particularly thrown off, but they are likely to
• include the torsional modes and the non-bonded interaction. From
the limited experien.ce available, it appears thatthis error is
almost a constant and therefore not too seriou , in the mono-
alkyl-and trans-dialkyl-substituted ethylene In parti r it is
tentatively concluded that the 0 and (and a d A(1)) d a
pertaining to the calculated structures of minimum energy are
substantially correct for the molecules mentioned. Serious problems were
encountered with the interpretation of the data on cis-2,2,5-trimethy1-3-
hexene and cis-2,5-dimethyl-3-hexene. It was concluded in both cases
• 277
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
that the calculated structure of the-llowest (or one of the two lowest for
the former molecule), energy is basically correct but that the calcUlated.
second (and third) minimum are totally wrong, both in the sense of -
predicting a too high AG° and in the sense of- putting the energy minimum
at the wrong place (i.e., the wrong dihedral e angle) or, even worse,
possibly overlooking an entire minimum.
The conclusion is that the Force Field requires recalibration;
four reasonably reliable AG° values are now available, in two cases
thereof with rather complete knowledge of the structures involved (in the
other two cases only the ground state structure is adequately known).
The Force Field calculations provide two more bits of informa-,Y
tion, which initially were thouyht rather unimportant, but turned
out to be highly interesting. One of these, the'precise a and Ae infor-
mation together with its use for calculation of J and AJ values has
already been detailed. It appears that no longer one has to rely
exclusively on rotational spectroscopy and electron diffraction to obtain
suc structural data, data which are only availa e experimentally for
small olecules.
More or less as a by-product, the calClations also provide a
list of all the vibrational frequencies and their degeneracies. These
data are essential, however, once entropies have to be calculated. In
earlier studies on conformational equilibria in olefins, it was generally
assumed that AS = 0, that therefore AG = AH and that AG = AE, where AE is
the steric energy differerice of the equilibria minima. As is shown in
this study, AS is rather different from zero and strongly temperature
278
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
-' dependent and 'even AG° can be quite different from AE. -This means that
even the "sorting out" of energy minima and maxima is hazardous if based
only on Force Field energy calculations, unless supplemented by entropy
calculations. A second ,consequence is that in the least squares fitting
for AG and two. special parameters (the GBM method), one has to correct at
each temperature for the -T AS term: in essence one then data-fits the
experimental values in search for a AH (assumedly temperature independent).
E s. Molecular conformational structure
Trans-2,2,5ztrimethy1-3-hexene was shown to have a conforma-
tional equilibrium with AG° = 531J.mol ( 27cal.mo171), which could be
assigned to an anti4gaicche transition (fo the methine proton) in the
isopropyl group, in complete agreement wig arlie esults on 3-methyl-
1-butene. One consequence of this result i that, apparently, the trans-,
tert-butyl substituent has little or no eff• t on the AG° of the isopropyl
group'. It may well be though that there is such an effect but that it is
so small (smaller than 120J.mo1-1 or 30cal.mo1-1) as.to be hidden in the
error margins of the AG°'s obtained. For this molecule no indication was
found for any conformational process within the tert-butyl group. It is
believed, however, that the Force Field result of pred4pting the most
stable conformation to be with one methyl CH3 group of the tert-butyl
group eclipsing the double bond is basically correct. The finding that a
trans substituent does not noticeably influence the energetics of the
conformational equilibria of the other substituent is important, particu-
larly in application on trans disubstituted ethylenes where both AG°'s
279
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
I
are non-zero (for example the trans-2,5-dimethy1-3-hexene):
In cis-2,2,5-trimethyl-3-hexene it could be concluded that in
the ground state both substituents have an anti conformation. In addi-
tiori. it seems clear that there exists• ,Inother low-lying minimum (with
AG° = 2.1KJ.mo1-1 or 0.5Kcal.mo1-1), but it has been found impo&siblao
determine the structure:of such a second conformer. It is not even
known whether the conformational change involves primarily the isopropyl
group, the tert-butyl group or both,(concerted rotation). From ,a limited
study of cis-4,4-dimetby1-2-pentene, it appears that there exists no
conformational equilibrium corresponding to a small AG° (i.e., below
6.3KJ.mo1-1 or 1.5Kcal.mo1-1) in this molecule. That would mean that in
cis-2,2,5-trimethyl-3-hexene the possibility of the tert-butyl being
primarily involved in the conformational process can be eliminated.
The results on cis-2,5-dimethyl-3-hexene are similar. There
exists a low energy second conformer, with AG° = 1.13KJ.mo1-1 (0.27Kcal.
mol-1); the ground state is most definitely the anti-anti conformation,
but the structure of the second state could not be determined. The Force
Field prediction of this second conformation being the anti-syn structure
is definitely disproved by the NMR results. The latter are not unequivo-
cal, however, but point as a likely structure to a skew-skew structure as
the second structure.
F Overall conclusion
This study has been an exercise in developing a combination of
variable temperature NMR with Force Field calculation as an independent
280
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
0.
technique for studying conformational equilibria and the rotamer Struc-
tures involved. It is concluded that the potential of this approach has
been established, but that the full fruition can only ,be expected after
apparent errors in the Force Field calcylations have been removed.
•
281
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
vok
LIST OF REFERENCES
1. N. L. Allinger in Adv. Phys. Org. Chem. 13, 1 (1976).
2. D. H. Andrew, Phys. Rev. 36, 544 (1930).
3. O. Ermer and S. Lifson, J. Am. Chem. Soc. 95, 4121 (1973).
4. O. Ermer in Structure and Bonding 27, 161 (1976).
5. J. E., Williams, R. J. Stang and P. Von R. Schleyer in Ann. Rev. Phys. Chem. 19,. 591 (1968).
6. A. Warshel, M. Levitt and•S. Lifson, J. Mol. Spectrosc. 33, 84 (1970).
7.• J. Kowalik and M.,R. Osborne, Methods for unconstrained - optimization problems, edited by R Bellman (1968).
8. G. R. Walsh, Methods of optimization, edited by J. Wiley & Sons (1975).
9. R. Fletcher, M. J. D. Powell, Computer J. 6, 163 (1963.).
• ' 10. O. ,Ermer, Tetrahedron 31, 1849 (1975).
11. M. J. S. Dewar and N. C. Baird, Atomic Cartesian Coordinates . for Mb'Tecules (COORD), Program 136, Quantdm Chemistry
Program Exchange, Indiana University (1974).'•
, 12. R. Zurahl,, Matrizen and ihre' technischen Anwendungen edited by Springer (1964).
• 13. S. Chang, D. McNally, S. Shary-Tehrany, M. J: Hickey and
R. H. Boyd, J. Am. Chem. Soc. 92, 3109 (1970),
14. S. Kondo, Y. Sakurai, E. Hirota and Y. Morino, J. Mol. Spectrosc. 34, 231 (1970).
15. i J. E. Kilpatrick and K. S. Pitzer, J. Res. Nat. Bur. Stand. 37,163 (1946).
16. T. N. Sarachman, J. Chem. Phys. 49, 3146 (1968).
282
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
17. J. R. Durig, C. W. Hawley, J. Bragin, J. Chem. Phys. 57, 1426 (1972). -
18. ' P. Diehl, R. K. Harris and 11:-M.,LJones in Prog. Nucl. Magn. Reson. Spectrosc. 3, 1 (1967). •
19. D. R. Whitman, L. Onsager, M. Saunders and H. T. Dubb, J. Am. Chem. Soc. 82,.67 (1960).
20. A. R. Quirt and J. S. Martin, J. Magn. Reson. 5, 318 (1971).
21. G. J. Martin and M. L. Martin, Prog. Nucl. Magn. Reson. 8, 163 (1972).
22. H. M. McConnell, J. Chem. Phys. 27, 226 (1957).
23. H. Gunther and G. Jikeli,,Chem. Rev. 77, 599 (4977).
24. J. Tillieu, Ann. Phys. 2, 471, 631 (1957).
25. J. ,,„"f ple, J. Chem. Phys. 37, 60-R962).
26. R. T. Hobgoot and J. H. Goldstein, J. Mol. Spectrosc. 12, 76 (1964).
27. M. A. Cooper, D. D. Elleman, C. D. Pearce and S. L. Manatt, J. Chem. Phys. 53, 2343 (1970).
28. J. W. ApSimon, W. G. Craig, P. V. Demarco, D. W. Mathieson, L. Saunders and W. B. Whalley, Tetrahedron 23, 2339 (1967).
0 29. F. H. A. Rummens, J. Magn. Reson. 6, 550 (1972).
30. M. Kondo, I. Ando, R. Chujo and A. Nishioka, Mol. Phys. 33, 463 (1977).
31. - H. Vogler, J. Am. Chem. Soc. 100, 7464 (1978).
32. J. A. Pople, Discuss. Faraday Soc. 34, 7 (1962).
33. J. W. ApS,imon,.J. Elguero and A. --ichier, Can. J. Chem. 52, 2296 (1974).
34. E. Pretsch, H. Immer, C. Pascual Schaffner and W. SiMon, Hely. Chim. Acta 50, 105 (1967).
35. W. T. Raynes, J. Mol. Phys. 20, 321 (1971).
36. C. Reid, J. Mol. Spectrosc. 1, 18 (1957).
283
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
37. N. Jonathan, S. Gordon and Ell P. Dailey, J. Chem. Phys. 36, 2443 (1962).
38. J. D. Memory, G. W. Parker and J. C. Halsey, J. Chem. Phys. 45, 3567 (1966).
i • 39. J. A. Pople, W. G. Schneider and H. J. Bernstein, High-%
resolution NMR, p254, edited by McGraw-Hill (1959).
40. K. D. Bartle and J. A. S. Smith, !rctro-6im. Acta, Part A 23, 1689 (1967),.
„--41. B. V. Cheney, J. Am. Cheim:-Soc. 90, 5386 (1968).
42. T. W. Marshall—and J. A. Pople, Mol. Phys. 3, 339 (1960).
43. T. YoneMoto, Can. J. Chem. 44, 223 (1960.
44. C. W. Haigh, R. B. Mallion and E. A. G. Armour, Mol. Phys. 18, 751 (1970).
45. A. D. Buckingham, Can. J. Chem. 38, 300 (1960).
46. B. Day and A. D.-Buckingham, Mol. Phys. 32, 343 (1976).
47. G. W.'Buchanan and J. B. Stothers, Can. J. Chem. 47, 3605 (1969).
48. D. M. Grant and E. G. Paul, J. Am. Chem. Soc. 86, 2984 (1964).
49. D. M., Grant and B. V. Cheney, J. Am. Chem. Soc. 89, 5315 (1967).
50. B. V: Cheney and D. M. Grant, J. Am. Chem. Soc. 89, 5319 (1967).
51. D. K. Dalling and D. M. Grant, J. Am. Chem. Soc. 89, 6612 (1967).
52. ' E. Lippman, T. Pehk and J. Paasivirta, Org. Magn. Reson. 5, 277 (1973).
53. H. J. Schneider and E. F. Weigand, J. Am. Chem. Soc. 99, 8362 • -(1977).
54. A. Warshel and S. Lifson, J. Chem. Phys. 53, 582 (1970).
55. K. Seidman and G. E. Maciel, J. Am. Chem. Soc. 99, 659 (1977).
56. D. G. Gorenstein, J. Am. Chem. Soc. 99, 2254 (1977).
284
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
57. S. H. Grover, J. P. Guthrie, J. B(Stothers and C. T. Tan, J. Magn. Reson. 10,'227 (1973)2
58. H. Spiesecke and W. G. Schneider, J. hem. Phys. 32, 1227 (1960).
59. L. Phillips and V. Wray J. Chem. Soc. 8, 2068 (1971).
60. W. J. Horsley and H. SternlichL, J. Am. Chem. Soc. 90, 3738 (1968). N
s'N---,-- -' 4-61. H. J. Schneider and W. Freitag, J. Am. Chem. Soc. 99, 8363 (1977).
62. J. G. Batchelor, J. Am. Chem. Soc. 97, 3410 (1975).
63. W. T. Raynes in Spec. Period. Rep.: Nucl. Magn. Reson. 7, 1 (1978).
64. J. Z. Batchelor, 3. Feeney and G. C. K. Roberts, J. Magn. - Reson. 20, 19 (1975).
65. K. Seidman and G. E. Maciel, J. Am. Chem. Soc. 99, 3254 (1977).
66. H. M. McConnell, J. Chem. Phys. 24, 460 (1956); J. Mol. Spectrosc. 1, 11 (1957).
67. (a) N. F. Ramsey, Phys. Rev. 91, 303 (1963); (b) J. A. Pople and D.P. Santry, Mol. Phys. 8, 1 (1964); (c) C. J. Jameson and H. S. Gutowsky, J. Chem. Phys. 51, 2790 (1963).
68. J. A. Pople, J. W. Mc Iver and N. S. Ostlund, J. Chem. Phys. 49, 2960 (1968).
69. .M. Karplus, J. Am. Chem. Soc. 85, 2870 (1963).
70. F. H. A. Rummens and L. Kaslander, Can. J. Chem. 54, 2884 (1916).
71. F. H. A. Rummens, C. Simon, C. Coupry and N. Lumbroso-Bader, Org. Magn. Reson. 13, 33 (1980).
72. M. Karplus, J. Chem. Phys. 30, 11 (1959).
73. G. E. Maciel, J. W. Mc Iver, N. S. Ostlund and J. A. Pople, J. Am. Chem. Soc. 92, 4497 (1970).
74. K. G. R. Pachler, Tetrahedron 27, 187 (1971).
285
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
75. G. Govil, Indian J. Chem. 9,.824 (1971).
76. M. S. Gopinathan and P. T. Narasimhan, Mol. Phys. 2T, 1141 (1971).
77. M. Karplus, J. Chem. Phys. 33, 1842 (1960).
78. M. Barfield, J. Am. Chem. Soc. 93, 1066 (1971).
79. M. Barfield, A. M. Dean, C. J. Fallick, R. J. Spear, S. Stern-hell and -P. W. Westerman, J. Am. Chem. Soc. 97, 1482 (1975).
80. M. Barfield and S. Sternhell, J. Am. Chem. Soc. 94, 1905 (1972).
81. M. AO Cooper and S. L. Manatt, J. Am. Chem. Soc. 91, 6325 (1969).
82. H. L. Ammon and G. L. Wheeler, Chem. Commun., 1032 (1971).
83. W. N. Solkan and N. M. Sergeyev, Org. Magn. Reson. 6, 200 (1974).
84. M. L. Huggins, J. Am. Chem. Soc. 75, 4123 (1953).
85. C. N.: Banwell and N. Sheppard, Discuss. Faraday Soc. 34,_ 115 (1962).
' 86\ R. J. Abraham and K. G. R. Pachler, Mol. Phys. 7, 165 (1963).
87. J. Hinze, M. A. Whitehead and H. H. Jaffe, J. Am. Chem. Soc. 8, 148 (1963).'
88. J. E. Huheey, J. Phys. Chem. 69, 3284 (1965); J. Org. Chem. 36, 204 (1971); J. Org. ChFi. 31, 2365 (1966).
89. H. O. Pritchard, F. H. Summer, Proc. R. Soc. London, ser. A235, 136 (1956).
90. J. W. Emsley, J. Feeney and L. H. Sutcliffe, Hight-resolution Nuclear magnetic resonance spectroscopy vol. 1, edited by Pergamon Press (1965).
91. H. S. Gutowsky, G. G. Belford and P. E. MacMahon, J. Chem. Phys. 36, 3353 (1962).
92. G. Govil and H. J. Bernstein, J. Chem. Phys. 47, 2818 (1967).
93. (a) H. S. Gutowsky, D. W. McCall and C. P. Schlichter, J. Chem. Phys. 21, 279 (1953); (h) H. S. Gutowsky and A. Saika, J. Cheri: Phys. 21, 1688 (1953); (c) H. S. Gutowsky and C. H. Holm, J. Chem. Phys. 25, 1228 (1956).
286
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
94. F. Bloch, Phys. Rev. 70, 460 (1946).
95. G. Binsch, Top. Stereochem. 3, 97 (1968); Mol. Phys. 1.5?-469 (1968); J. Am. Chem. Soc. 91, 1304 (1969).
rte_ --9 . A. S. Quirt, J. S. Martin and K. Worvill, NUMARIT program version 1971.
(7' \
97.\ S. M. Castellano and A. A. Bothner-By J. Chem. Phys. 41, 3863 (1964).
98. C. A. keilTiand J. D. Swalen, J. Chem. Phys. 37, 21 (1962). s.,
99. C. W. Haigh/ A Annu. Rep. NMR Spectrosc. 4, 311 (1971).t '
100. A. A. Bothner-By and S. M. Castellano, Computer programs for Chemistry/De Tar, Edited by W. A. Benjamin, Inc. (1968).
101. (a) F. H. A. Rummens, Rec. Tray. Chim. Pays-Bas 84, 5 (1965); (b) F. H. A. Rummens and J. W. de Haan, Org. Magn. Reson. 2, 351 (1970).
102. M. A. Coqper and S. L. Manatt, Org. Magn, Reson. 2; 511 (1970); J. Am. Chem. Soc. 92, 1605 (1970); J. Am. Chem. Soc. 92, 4646 (1970).
103. N. L. Allinger and J. T. Sprague, J. Am. Chem. Soc., 94, 5734 (1972).
104. D. N. J. White and M. J. Bovill, J. Chem. Soc., Perkin Trans. 2, 1610 (1977).
105. D. M. Golden, K. W. Egger and S. W. Benson, J. Am. Chem. Soc. 86, 5416 (1964).
106. K. W. Egger and S. W. Benson, J. Am. Chem. Soc. 88, 236 (1966).
107. (a) A. A. Bothner-By and C. Naar-Colin, J. Am. Chem. Soc. 83, 231 (1961); (b) A. A. Bothner-By, C. Naar-Colin and , H. Gunther, J. Am. Chem. Soc. 84, 2748 (1962).
108. F. H. A. Rummens, L. Kaslander, A. R. Quirt and J. S.. Martin, Org. Magn. Reson. 23, 16 (1978).
109. F. A. Anet and J. Yavari, J. Am. Chem. Soc. 99, 6986 (1977).
110. K. Mislow, D. A. Dougherty and W. D. Hounshell, Bull. Soc. Chim. Beig. 87, 555 (1978).
287
•
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
J
• 111. J. D. Dunitz and H. B. Burgi in MTP Int. Rev. Sci., Phys. Chem.
Ser: Two 11, 81 (1975).
112. S. P. N. Van der Hejden, M. Sc. thesis, University of Saskat-chewan, Regina Campus (1971).
113. A. L. Van Geet, Anal. Chem. AO, 2227 (1968).
, 114: E. Bartholdi and R. Ernst; J. Magn. Reson. 11, 9 (1973).
115. J. J. Led and S. B. Petersen, J. Magn. Reson. 32, 1 (1978).
116. H. J. Bernstein, J. A. Pople and W. G. Schneider, Can. J. Chem. 35, 65 (1957). .t„
117. P. Dielh and J. A. Pople, Mol. Phys..3, 557 (1960).
118. P. P. Nicholas, C. J. Carman, A. R. Tar ley Jr. and J. H. Gold-stein, J. Phys. Chem. 76, 2877 (1972).
119. J. W. de Haan and L. J. M. van de Vert', Org: Magn. Reson. 5, ' 147 (1973).
120. II. M. Lynden-Bell and N. Sheppard, Proc. R. Soc. London, Ser. A269, 385 (1962). •
121. D. R. Lide and D. Christensen, J. Chem. Phys. 35, 1374 (1961).
122. J. A. Pople and D. L. Beveridge, Approximate Molecular Orbital theory, Ser. in Adv. Chem., Edited by McGraw-Hill (1970).
123. J. Feeney, L. H. Sutcliffe an\S. W. Walker, Mol. Phys. 11, 117 (1966). •
124. P. C. Lauterbur, J. Am. Chem. Soc. 83, 1838 (1961).
125. J. A. Pople and M. S. Gordon, J. Am. Chem. Soc6 98, 478.
126. F. H. A. Rummer1 and F. M. Mourits, J. Can. Chem. 55, 3021 (1977).
127. H. J. Schneider, M. Schommer and W. Freitag, J., Magn. Reson. 18, 393 (1975). •
128. R. B. Turner, D. E. Nettleton Jr. and M. Perelman., J. Am. Chem. Soc. 80, 1430 (1958).
288
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.