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Doctoral Thesis

Photodissociation and excited states dynamics of the allyl radical

Author(s): Castiglioni, Luca

Publication Date: 2007

Permanent Link: https://doi.org/10.3929/ethz-a-005479225

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DISS. ETH No. 17338

Photodissociation and Excited States Dynamics

of the

Allyl Radical

A dissertation

submitted to the

SWISS FEDERAL INSTITUTE OF TECHNOLOGY

ETH ZURICH

for the degree of

Doctor of Sciencesin the subject of

Physical Chemistry

presented by

Luca CastiglioniDipl. Chem. ETH

born January 25, 1979

citizen of Menzingen ZG

accepted on the recommendation of

Prof. Dr. Peter Chen, examiner

Prof. Dr. Martin Quack, co-examiner

Zurich, 2007

Habe nun, ach! Philosophie,Juristerei und Medizin,Und leider auch TheologieDurchaus studiert, mit heißem Bemuhn.Da steh ich nun, ich armer Tor!Und bin so klug als wie zuvor;

Johann Wolfgang von Goethe“Faust, der Tragodie erster Teil”

AcknowledgementsI am very grateful to Prof. Dr. Peter Chen for supervising my Ph.D. Throughoutmy graduate studies he gave me the necessary scientific freedom to accomplish myprojects. He always supported my thesis and the knowledge he shared so readily wasa great source of inspiration.

I am indebted to my co-examiner, Prof. Dr. Martin Quack, for the interest in thisthesis and some valuable comments. I appreciate helpful discussions about statisticaland non-statistical molecular dynamics.

I was a great pleasure for me to work in the small laser spectroscopy team, lead bymy mentor, Dr. Andreas Bach. He introduced me to the world of laser spectroscopyand taught me all the experimental techniques. He assisted my project in the early daysof my graduate studies and did the major part of the proofreading of this manuscript.Without his continuous efforts to keep our computer cluster running, not many calcu-lations presented in this work could have been performed.

I will miss the endless discussions about chemistry and the meaning of life withJonas Hostettler, who had the fate to share the notorious G201 office with me. MichaelGasser was never at a loss for a good joke and introduced us into the odd nightlife ofGrindelwald. I wish good luck to him as my successor in the allyl project, which nowturned into the methylallyl project.

The graduate lectures about numerical quantum chemistry were the key to the the-oretical part of this thesis. I acknowledge interesting discussions about the electronicstructure of the allyl radical with PD Dr. Tae-Kyu Ha.

Didier Zurwerra and Daniel Meier were working with me during the course of theirdiploma thesis and ‘Semesterarbeit’. I would like to thank for their assistance in theexperimental work and wish good luck to them with their own career.

The experiments could never have been performed without the precise mechanicaland electronic parts made by Rene Dreier and Heinz Benz.

Special thanks go to Yvonne Ogg and Annette Ryter for all the administrative work,which ensured my regular income.

I would like to acknowledge the friendly and sociable atmosphere in the wholegroup. Eva Zocher was always kind enough to carefully proofread a lot of mymanuscripts including large parts of this thesis. Our austrian ‘skiing-tiger’ Sebas-tian Torker proved to be a capable organizer of various skiing outings. Together with

vi

Marc-Etienne Moret they always joined for a bit of sport in form of a table soccermatch after the lunch. Alexey Fedorov provided an interesting insight into russian cul-ture on an exciting trip to St. Petersburg and Moscow. When it came to computerissues, Luca Cereghetti always readily offered his help. For the good time and a lot ofinteresting discussions I would like to thank to all the current members of the group,Dr. Esther Quintanilla, Dr. Fereshteh Rouholahnejad, Dr. Xiangyang Zhang, SanjaNarancic, Deborah Mathis, Fabio Di Lena and Lai Yu-Ying.

I enjoyed many long runs in the Honggerberg forrest with Dr. Marc Bornand whoalso motivated me to participate in various competitions. I will remember nice af-ternoons discussions in the ‘Bistro’ and the explorations of Zurich’s nightlife withDr. Christian Defieber. His expertise in synthetic organic chemistry was very helpfulin numerous situations. Patrick Krecl was a competent advisor for graphical design,challenged me in the Zurich marathon and joined me on a lot of unforgettable hikes toalpine peaks.

Last but not least I want to express my gratitude to my family. I appreciated uncon-ditional support from my parents from the first moment I came in touch with chemistryand throughout my undergraduate and graduate studies.

Published Parts of this Thesis

Reviewed Articles• “Spectroscopy and Dynamics of A [2B1] Allyl Radical”

Luca Castiglioni, Andreas Bach and Peter ChenPhys. Chem. Chem. Phys. 8, 2591 (2006)

• “Probing Centrifugal Barriers in Unimolecular Dissociationof the Allyl Radical”Luca Castiglioni, Andreas Bach and Peter ChenJ. Phys. Chem. A, 109, 962 (2005)

Poster and Oral Presentations• “Photodissociaton Dynamics of Small Hydrocarbon Radicals”

Presented at the International Symposium on Reactive Intermediates and Un-usual Molecules (ISRIUM)Ascona, August 19-24, 2007

• “Photodissociation and Excited States Dynamics of A [2B1] and C [2B1] AllylRadical”Presented at the 42nd Symposium on Theoretical ChemistryBerlin, September 3-6, 2006

• “Spectroscopy and Dynamics of Small Hydrocarbon Radicals”Oral presentation at the optETH / MPQ Joint SymposiumGarching (Munich), July 12-14, 2006

• “Photodissociation Dynamics of the Allyl Radical after Electronic Excitation tothe A [2B1] and C [2B1] States”Presented at the 28th International Symposium on Free RadicalsLeysin, September 4-9, 2005

Contents

Abstract xv

Zusammenfassung xvii

1 Introduction 1

I Theory and Methodology 5

2 Photodissociation Dynamics 72.1 Types of Photodissociation . . . . . . . . . . . . . . . . . . . . . . . 72.2 Unimolecular Kinetics . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.2.1 Statistical Rate Theories . . . . . . . . . . . . . . . . . . . . 12

3 Fundamentals of Photofragment Spectroscopy 153.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153.2 Molecular Beam Methods . . . . . . . . . . . . . . . . . . . . . . . . 163.3 Multiphoton Ionization . . . . . . . . . . . . . . . . . . . . . . . . . 183.4 Photofragment Spectroscopy . . . . . . . . . . . . . . . . . . . . . . 19

3.4.1 Action and Transient Spectoscopy . . . . . . . . . . . . . . . 203.4.2 Photofragment Doppler Spectroscopy . . . . . . . . . . . . . 20

4 Experimental Setup 234.1 Molecular Beam Machine . . . . . . . . . . . . . . . . . . . . . . . . 23

4.1.1 Generation of Radicals . . . . . . . . . . . . . . . . . . . . . 244.1.2 Ion Optics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274.1.3 Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

4.2 Lasers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 344.2.1 Pump Laser . . . . . . . . . . . . . . . . . . . . . . . . . . . 344.2.2 Probe Laser . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

4.3 Controlling and Timing . . . . . . . . . . . . . . . . . . . . . . . . . 384.4 Data Acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

x CONTENTS

II Photodissociation Dynamics of the Allyl Radical 41

5 The Allyl Radical 435.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 435.2 Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 445.3 Excited Electronic States . . . . . . . . . . . . . . . . . . . . . . . . 45

5.3.1 Primary Photophysical Processes . . . . . . . . . . . . . . . 485.4 Photochemistry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

6 Spectroscopy and Dynamics of A [2B1] Allyl Radical 516.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 516.2 Multiphoton Ionization (REMPI) . . . . . . . . . . . . . . . . . . . . 526.3 Photofragment Action Spectroscopy . . . . . . . . . . . . . . . . . . 53

6.3.1 Rotational Contour Analysis . . . . . . . . . . . . . . . . . . 556.3.2 Vibronic Band System . . . . . . . . . . . . . . . . . . . . . 56

6.4 Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 606.4.1 H-Atom Transient Spectroscopy . . . . . . . . . . . . . . . . 606.4.2 Doppler Spectroscopy and Kinetic Energy Release . . . . . . 62

6.5 Results from Isotopically Labeled Allyl Radicals . . . . . . . . . . . 636.5.1 Kinetic Isotope Effect . . . . . . . . . . . . . . . . . . . . . 646.5.2 Site Selectivity of Hydrogen Loss and Reaction Channels . . 65

6.6 The Direct Hydrogen-Loss Channel . . . . . . . . . . . . . . . . . . 696.6.1 Product Translational Energy . . . . . . . . . . . . . . . . . . 69

6.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

7 C [2B1] Allyl Radical Photodissociation Dynamics 757.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 757.2 Photofragment Action Spectroscopy . . . . . . . . . . . . . . . . . . 767.3 Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

7.3.1 H-Atom transient spectroscopy . . . . . . . . . . . . . . . . . 787.3.2 Doppler Spectroscopy and Kinetic Energy Release . . . . . . 80

7.4 Centrifugal Effects in Allyl Radical Unimolecular Dissociation . . . . 827.4.1 Rotational Effects in Unimolecular Dissociation . . . . . . . 837.4.2 Unusual Stability of Highly Rotationally Excited Allyl Radi-

cals Towards Dissociation . . . . . . . . . . . . . . . . . . . 877.4.3 J-Dependent Dynamics in Allyl Radical Unimolecular Disso-

ciation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 887.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94

8 Statistical Interpretation of the Dissociation Dynamics and ab initio Cal-culations 978.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 978.2 C3H5 Ground State Potential Energy Surface . . . . . . . . . . . . . 99

CONTENTS xi

8.2.1 Ab initio Calculations . . . . . . . . . . . . . . . . . . . . . . 998.2.2 Coupled Cluster Calculations . . . . . . . . . . . . . . . . . 1048.2.3 Anharmonic ab initio frequencies . . . . . . . . . . . . . . . 1078.2.4 Reaction Pathways . . . . . . . . . . . . . . . . . . . . . . . 108

8.3 RRKM Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . 1118.3.1 Vibrational Frequencies of the Transition States . . . . . . . . 1128.3.2 The Different Reaction Paths . . . . . . . . . . . . . . . . . . 112

8.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

9 Outlook - Photodissociation Dynamics of Methylallyl Isomers 1199.1 Non-statistical effects in hydrocarbon radicals . . . . . . . . . . . . . 1199.2 Methylallyl radical photodissociation . . . . . . . . . . . . . . . . . . 121

III Excited States Dynamics 125

10 Excited Electronic States of the Allyl Radical 12710.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12710.2 Electronic Structure of the Allyl Radical . . . . . . . . . . . . . . . . 12810.3 Ab initio Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . 130

10.3.1 Configuration Interaction (CI) . . . . . . . . . . . . . . . . . 13010.3.2 Multi-Reference Methods . . . . . . . . . . . . . . . . . . . 13110.3.3 Choice of the Active Space . . . . . . . . . . . . . . . . . . . 133

10.4 Results of the Calculations . . . . . . . . . . . . . . . . . . . . . . . 13410.4.1 Geometry of the A 2B1 State . . . . . . . . . . . . . . . . . . 13410.4.2 Vibrational Frequencies in the A 2B1 State . . . . . . . . . . . 13510.4.3 Adiabatic Excitation Energy of the A 2B1 State . . . . . . . . 13510.4.4 Vertical Excitation Energies of Higher Excited States . . . . . 136

10.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136

11 Electrocyclic Reactions 13911.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13911.2 Allyl-Cyclopropyl Interconversion . . . . . . . . . . . . . . . . . . . 140

11.2.1 Experimental Evidence . . . . . . . . . . . . . . . . . . . . . 14011.2.2 State Correlation . . . . . . . . . . . . . . . . . . . . . . . . 142

11.3 Ab initio Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . 14411.3.1 Conrotatory Ring-Closing of the A-state Allyl Radical . . . . 14411.3.2 2A2-2B1 Conical Intersections . . . . . . . . . . . . . . . . . 14611.3.3 Photochemical Deactivation Pathways . . . . . . . . . . . . . 147

11.4 Conclusions and Outlook . . . . . . . . . . . . . . . . . . . . . . . . 14711.4.1 Primary Photophysical and Photochemical Processes in the

Allyl Radical . . . . . . . . . . . . . . . . . . . . . . . . . . 14711.4.2 Excited State Direct Dynamics and Surface Hopping . . . . . 148

xii CONTENTS

IV Appendix 149

A Synthesis of Deuterated Precursors 151A.1 General Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151A.2 2-D-Allyl alcohol . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152A.3 2-D-Allyl iodide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152

B Curve Fitting of Transients and Doppler Profiles 153B.1 Hydrogen Atom Transients . . . . . . . . . . . . . . . . . . . . . . . 153B.2 Doppler Profiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155

C Power Normalization of Action Spectra 157

D Parameters for RRKM Calculations 159

E Results of ab initio Calculations 161E.1 C3H5 PES Ground State Calculations . . . . . . . . . . . . . . . . . 161

E.1.1 Energies and Geometries . . . . . . . . . . . . . . . . . . . . 162E.1.2 Anharmonic Frequencies of Stationary Points on the C3H5 PES 170

E.2 Allyl Radical Excited States Calculations . . . . . . . . . . . . . . . 172E.2.1 Energies and Geometries of Selected Points . . . . . . . . . . 172E.2.2 Vibrational Frequencies of the A-state . . . . . . . . . . . . . 174

Bibliography 175

List of Figures 187

List of Schemes 189

List of Abbreviations and Acronyms 191

Curriculum Vitae 195

xiv CONTENTS

Abstract

Small hydrocarbon radicals play a key role in the chemistry of high energy environ-

ments such as combustion processes, higher regions of the atmosphere and interstellar

space. Furthermore, they are important intermediates in hydrocarbon cracking, the

possibly largest industrial chemical process. In many cases, the chemistry in these

systems is governed by the dynamics of a few key radical species. That is why de-

tailed information on the reaction dynamics of such radicals is of great interest.

The subject of this thesis is the investigation of the photochemistry and photodis-

sociation dynamics of the allyl radical, C3H5, following electronic excitation. The

spectroscopy and dynamics of hydrocarbon radicals have been one of the central re-

search topics in our group for more than a decade. In particular the spectroscopy of

the UV states of the allyl radical was studied in detail.

We present a comprehensive investigation of the spectroscopy and the dynamics

of the first excited state in the allyl radical, the A-state, which has only been poorly

characterized so far. Furthermore, the photodissociation dynamics upon excitation to

the C-state could be studied in much more detail thanks to significant improvements

in the sensitivity and resolution of the experiment.

A cold and clean molecular beam of allyl radicals was generated by supersonic jet

flash pyrolysis of allyl iodide, C3H5I, seeded in helium. Direct characterization of the

A-state via REMPI was not feasible, however, due to the low absorption cross section

of the A [2B1]← X [2A2] transition and the short lifetime of the A-state. Calculated

reactions barriers for unimolecular reactions of the allyl radical suggest that the loss

of hydrogen is possible at the energy of the A-state (∼ 70 kcal·mol−1). Thus we mon-

itored the appearance of hydrogen atoms as a function of excitation laser wavelength

and obtained a spectrum similar to earlier diffuse absorption spectra. Calculated vibra-

tional frequencies of the excited state enabled the assignment of all vibronic bands in

xvi Abstract

the action spectrum.

Time- and frequency-resolved photoionization of the hydrogen atom photoprod-

uct provided information on the unimolecular dissociation dynamics. Measured uni-

molecular dissociation rate constants of ∼ 2 × 107 s−1 are roughly two orders of

magnitude slower than those for C-state dissociation. A kinetic energy release of

6.2 ± 0.5 kcal·mol−1 was derived from the FWHM of the measured Doppler profiles,

corresponding to 43% of the energy available to products. In the experiments on allyl

C-state photodissociation, only 23% of the excess energy was released in translation.

The high kinetic energy release can be rationalized by a calculated reverse activation

barrier of 4.3 kcal·mol−1. The energy of this barrier will be preferentially released as

translational energy.

Extensive calculation of important stationary points on the C3H5 ground state PES

facilitated the identification of reaction channels. Furthermore, microcanonical rate

constants for all unimolecular reactions were calculated using the RRKM theory and

the results obtained for direct loss of the central hydrogen atom correspond best to

the measured dissociation rates. Experiments with partially deuterated allyl radicals

support these findings.

The photodissociation dynamics following excitation to the C-state were reinves-

tigated in more detail in light of recent reports about unusually stable allyl radicals

toward dissociation. Since the increased stability was attributed to centrifugal effects,

the rotationally partially resolved C-state proved to be an ideal starting point for the

investigation of J-dependent dynamics. No discernible difference between the photo-

dissociation dynamics of high and low-J allyl radicals was found however.

Finally, the dynamics of the A-state were examined in an ab initio study. It was

found that the first excited state in the allyl radical correlates to the ground state of the

cyclopropyl radical, confirming earlier qualitative predictions. No significant barrier

was calculated for a conrotatory electrocyclization of A-state allyl radical to cyclo-

propyl radical, explaining the short lifetime of the excited state.

The spectroscopy and dynamics of the first electronically excited state have been

comprehensively investigated and are well understood. Following excitation to the A-

state and fast internal conversion, the allyl radical dissociates statistically on the ground

state surface, leading to allene and a hydrogen atom as the major reaction products.

Zusammenfassung

Kleine Kohlenwasserstoffradikale spielen eine Schlusselrolle in der Chemie von Hoch-

energieumgebungen wie Verbrennungsprozessen, hoheren Schichten der Atmosphare

und im Weltraum. Desweiteren sind sie wichtige Zwischenstufen beim ”Cracken” von

Kohlenwasserstoffen, wohl einem der wichtigsten industriellen Prozesse uberhaupt.

In vielen Fallen wird die Chemie derartiger Systeme massgeblich von der Dynamik

weniger Radikale bestimmt. Aus diesem Grund besteht grosses Interesse an detail-

lierten Informationen uber die Reaktionsdynamik solcher Radikale.

Diese Dissertation befasst sich hauptsachlich mit der Untersuchung der Photo-

chemie und Photodissoziationsdynamik des Allylradikals nach elektronischer Anre-

gung. Spektroskopie und Dynamik von Kohlenwasserstoffradikalen bilden seit mehr

als einem Jahrzehnt ein zentrales Forschungsgebiet in unserer Gruppe. Insbesondere

die Spektroskopie der UV Zustande des Allylradikals wurde bereits im Detail studiert.

Hauptteil dieser Arbeit bildet ein umfassendes Studium der Spektroskopie und Dy-

namik des ersten angeregten Zustands des Allylradikals, des A-Zustands, welcher

bisher nur unzureichend untersucht wurde. Zudem konnte die Photodissoziations-

dynamik nach Anregung in den C-Zustand dank signifikanten Verbesserungen der

Empfindlichkeit und Auflosung des Experiments viel detaillierter betrachtet werden.

Das freie Radikal konnte mittels ultrakurzer Pyrolyse von Allyliodid, C3H5I, in

Helium, gefolgt von einer Uberschallexpansion, in einem kalten Molekularstrahl se-

lektiv dargestellt werden. Eine direkte Beobachtung des A-Zustands durch REMPI

Spektroskopie war aufgrund des niedrigen Absorptionsquerschnitts des A [2B1] ←X [2A2] Ubergangs, sowie der kurzen Lebenszeit des angeregent Zustands, nicht

moglich. Berechnungen der Aktivierungsbarrieren fur unimolekulare Reaktionen

des Allylradikals ergaben jedoch, dass die Abspaltung eines Wasserstoffatoms bei

Energien ahnlich jener des A-Zustands (70 kcal·mol−1) moglich ware. Deshalb

xviii Zusammenfassung

wurde die Konzentration der Wasserstoffatome als Funktion der Wellenlange des

Anregungslasers aufgezeichnet. Das erhaltene ”Action”-Spektrum weist dieselben

Charakteristika auf, wie die alteren, diffusen Absorptionsspektren des Allylradikals.

Samtliche vibronischen Banden im erhaltenen Spektrum konnten mit Hilfe von berech-

neten Schwingungsfrequenzen zugeordnet werden.

Daten zur unimolekularen Dissoziationsdynamik wurden aus der frequenz- und

zeitaufgelosten Photoionisation des Wasserstoffatoms gewonnen. Die gemessene uni-

molekulare Geschwindigkeitskonstante der Dissoziation von∼ 2×107 s−1 ist ungefahr

zwei Grossenordnungen langsamer als jene fur die Dissoziation nach Anregung in

den C-Zustand. Ein Erwartungswert fur die Freisetzung der kinetischen Energie von

6.2 ± 0.5 kcal·mol−1 wurde aus der Halbwertsbreite der gemessenen Dopplerprofile

ermittelt. Dieser Wert entspricht 43% der Uberschussenergie, welche den Produkten

zur Verfugung steht. In den Experimenten nach Anregung in den C-Zustand wurde

allerdings nur 23% der Uberschussenergie in die Translation freigesetzt. Der hohe

Anteil an kinetischer Energie kann durch eine signifikante Barriere fur die Rekombi-

nation (4.3 kcal·mol−1) erklart werden, deren Energie primar als Translationsenergie

freigesetzt wird.

Umfangreiche Berechnungen von stationaren Punkten der C3H5 Grundzustands-

hyperflache erleichterten die Zuordnung der Reaktionskanale. Mikrokanonische

Geschwindigkeitskonstanten fur samtliche denkbaren unimolekularen Reaktionen

wurden mittels RRKM Theorie berechnet. Die berechneten Geschwindigkeitskon-

stanten fur die direkte Abspaltung des zentralen Wasserstoffatoms stimmt am besten

mit den gemessenen Reaktionsraten uberein. Weitere Experimente mit selektiv deu-

terierten Allylradikalen bestatigten diesen Befund.

Kurzlich wurde von Allylradikalen berichtet, welche trotz interner Energie weit

uber der Dissoziationsbarriere nicht dissozierten. Die ungewohnliche Stabilitat dieser

Radikale wurde Zentrifugaleffekten zugeschrieben. Dies motivierte uns, die Dissozia-

tionsdynamik nach Anregung in den teilweise rotationsaufgelostenC-Zustand genauer

zu untersuchen. Wir konnten allerdings keinen Unterschied in der Dissoziationsdy-

namik von Radikalen mit hohem J und niedrigem J feststellen.

Zu guter letzt wurde die Dynamik des A-Zustands mittels ab initio Rechnungen

genauer untersucht. Die Berechnungen zeigen, dass der erste angeregte Zustand des

Allylradikals mit dem Grundzustand des Cyclopropylradikals korreliert. Damit wer-

xix

den fruhere qualitative Vorhersagen bestatigt. Fur einen konrotatorischen elektrozyk-

lischen Ringschluss des Allylradikals zum Cyclopropylradikal ergaben die Berech-

nungen keine signifikante Reaktionsbarriere, was die kurze Lebenszeit des ersten an-

geregten Zustands des Allylradikals erklart.

Die Spektroskopie und Dynamik des ersten angeregten Zustands im Allylradikal

wurden ausfuhrlich untersucht und sind nun gut verstanden. Nach Anregung in den A-

Zustand und schneller interner Umwandlung dissoziert das Allylradikal statistisch auf

der Grundzustandshyperflache. Als Reaktionsprodukte entstehen hauptsachlich Allen

und ein Wasserstoffatom.

Chapter 1

Introduction

Reactive Intermediates and Transient Species

Reactive intermediates are in many aspects the possibly most interesting and exciting

species in chemistry. On their way from reactant to product, chemical reactions pass

through one or more transient stages. It is these reactive intermediates, located at

the key position of the reaction pathway, which determine the course of a chemical

reaction.

For a long time, chemistry was only concerned with the characterization of reac-

tants and products and mechanisms were postulated on the basis of these empirical

observations. The interesting phase of the reaction, however, the transformation of

the reactant to the product, remained clouded. A better theoretical understanding of

the reaction dynamics and the emergence of new experimental methodology made the

investigation of reactive intermediates an important field in physical chemistry. Par-

ticularly new developments in laser spectroscopy and gas phase chemistry enabled a

systematic survey of the characteristics of these species in the past 40 years.

Efficient methods for the generation of these intermediates were created and the

combination with molecular beam methods proved to be useful. The tremendous

progress in theoretical and computational chemistry has accounted for the understand-

ing of the underlying processes. In the meantime, the dynamics of stable molecules are

well understood, whereas reactive intermediates still represent an ongoing challenge.

Generally speaking, highly reactive molecules such as free radicals, ions and car-

benes are termed reactive intermediates. More theoretically, all these species have

2 Introduction

an open shell electronic structure, i. e. they possess one or more unpaired electrons.

While the transient character of these compounds complicates experimental studies,

the open-shell configuration still poses many unresolved problems for theoretical treat-

ment.

This thesis is devoted to the detailed understanding of the reaction dynamics of small

hydrocarbon radicals, and in particular the allyl radical, by means of spectroscopic and

theoretical investigations. It is a continuation of earlier studies on the spectroscopy

and dynamics of the allyl and other hydrocarbons radicals such as ethyl and propargyl

accomplished in this group.[1–3]

Hydrocarbon Radicals

Hydrocarbon radicals are abundant in high energy environments like combustion, hy-

drocarbon cracking, certain regions of the atmosphere and interstellar space. They play

an important role in the chemistry of these environments. In fact, a large part of the

chemistry in these systems is governed by the dynamics of a few key radical species.

That is why great attention has been paid to the understanding of radical chemistry in

the gas phase.

Hydrocarbon radicals with a framework of three carbon atoms are assumed to be

precursors in the formation of polycyclic aromatic hydrocarbons and soot.[4, 5] As soot

is damaging the engine and carcinogenic, understanding its formation is a major chal-

lenge in combustion chemistry. Allyl and propargyl are important intermediates in

propane-, butane- and acetylene-rich flames[4, 6, 7] and were also detected in the com-

bustion of gasoline.[8] Due to their high stability, these radicals can even accumulate to

high concentrations in flames. It has turned out that kinetic modeling of combustion

processes is very sensitive to reactions that produce or consume hydrogen atoms.[9]

Thus, data on the unimolecular dissociation, e. g. photodissociation, of these radicals

is important.

Small hydrocarbon radicals exhibit some features, which make them ideal model

systems for probing chemical dynamics. In particular unsaturated π-radicals have low

lying excited electronic states. This means they can be excited at moderate energies,

which are still sufficient to overcome the barriers to unimolecular reactions. Hydrogen

3

abstraction is in many cases the energetically most favorable pathway along with sig-

matropic rearrangements and methyl loss. Often, different reactions channels are close

in energy, giving rise to product branching. In this case, photofragment spectroscopy,

which will be reviewed in detail in the next chapter, is an extremely powerful tool to

examine the different reaction products and the product energy distribution. The exis-

tence of both long-lived, resolved and short-lived, broadened electronic states allows

the determination of microcanonical reaction rates over a wide range of energy.

Furthermore, these radical species exhibit a complex photochemistry, including

radiative and non-radiative deactivation processes such as fluorescence, phosphores-

cence, internal conversion and intersystem crossing. In particular, non-adiabatic pro-

cesses play an important role in the excited states dynamics of these radicals, which is

further discussed in the last part of this work.

Chemical Dynamics and Photodissociation

The fragmentation of a molecule upon absorption of light is called photodissociation.

Photon energy is converted into internal energy of the molecule, and, if the energy

exceeds the binding energy of the weakest bond, the molecule will break apart. A

photodissociation can be considered the second half of a full collision. Whereas in the

full collision, the intermediate complex (AB)∗ is formed by collision of two separate

reactants, (A) and (B), in photodissociation, the excited complex is generated by elec-

tronic excitation of the initially bound parent molecule (AB). The second step of the

reaction, the fragmentation, is equivalent in both processes, therefore, the terminology

half collision.[10] Formally, we define a photodissociation process as

AB +Nphotons × hν −→ (AB)∗ −→ A + B,

where Nphotons is the number of photons of frequency ν. The first step stands for the

absorption of photons by the parent molecule (AB) and the second step indicates the

fragmentation of the excited complex.

The dissociation of an isolated molecule can be considered as the prototype of an

elementary chemical event.[11, 12] Due to the conceptual simplicity, photodissociation

reactions have attracted both theoreticians and experimentalists attempting to under-

stand the chemical dynamics on a microscopic level. In the discussion of photodisso-

ciation dynamics, the following central questions may arise:

4 Introduction

1. What is the quantum state of the intermediate complex?

2. What is the lifetime of the intermediate complex?

3. Which bond is going to be broken and how is it cleaved?

4. What are the primary photofragments?

5. In what quantum states are the product formed?

6. How does the photon energy partition among the various degrees of freedom of

the products?

7. How does the dissociation depend on the initial state or temperature of the parent

molecule?

8. What is the quantum yield of the reaction and how does it depend on the photol-

ysis wavelength?

The aim of this thesis is to answer many of these questions concerning the photodisso-

ciation of the allyl radical. Particular attention is paid to product formation and energy

partitioning in the products. The more theoretical last part of the thesis will primarily

address the characteristics and dynamics of the intermediate complex, i. e. the excited

electronic state of the molecule.

Part I

Theory and Methodology

Chapter 2

Photodissociation Dynamics

2.1 Types of Photodissociation

Photodissociation is the breaking of one or several chemical bonds in a molecule by

absorption of light. Depending on the number of photons required to fragment the

molecule, one can distinguish between single- and multiphoton dissociation.

Dissociation energies1 vary from a few thousandths of an eV for physically bound

Van der Waals clusters to several eV for a chemical bond. The extremely wide range of

possible dissociation energies thus requires the use of different kinds of light sources

to break molecular bonds. Whereas Van der Waals molecules can be fragmented by a

single IR photon, the fission of a chemical bond generally requires a single UV photon

or multiple IR photons.

Scheme 2.1 illustrates the two basic types of photodissociation of a chemically

bound molecule. In case (a), a single UV photon excites the ground state molecule

to a higher electronic state. Given a repulsive potential of the upper electronic state

along the intermolecular coordinate, RAB, the excited complex (AB)∗ immediately

dissociates. Part of the photon energy, hν, is consumed to break the chemical bond

and the excess energy,

Eexcess = hν −D0 = ET + EV + ER (2.1)

1The dissociation energy, D0, is defined as the difference of the zero-point level of the parent

molecule and the zero-point level(s) of the products.

8 Photodissociation Dynamics

hν

E0 E0

RAB

(a) (b)

AB AB

A+B

A+B

P(E)

E=hν+E0

Scheme 2.1: (a) A single UV photon creates a discrete quantum state in the upper, dis-

sociative electronic state. (b) Many IR photons produce an ensemble of

states with energy distribution P (E), above the ground state dissociation

limit.

partitions between the translational energy, ET , and the internal energy, (EV +ER) of

the product atoms or molecules.

UV photodissociation experiments are usually performed with relatively long light

pulses at low intensity and narrow bandwidth. These conditions, in principle, guaran-

tee that the photon creates a single quantum state in the upper manifold with an energy,

E = E0 + hν. The experimental observables, i. e. the absorption spectrum and the

product energy distribution, reflect the molecular wavefunction of the particular quan-

tum state of the parent molecule prior to excitation.

Scheme 2.1 shows a multiphoton dissociation in the electronic ground state. Since

the number of absorbed photons cannot be exactly controlled, the laser creates an

ensemble of quantum states above the dissociation threshold with a distribution of the

energy, P (E). As a consequence, multiphoton dissociation is subject to averaging over

2.1 Types of Photodissociation 9

hν

E0

RAB

(a) (b)

AB

A+B

hν

E0AB

A+B

internal

conversiontunneling

IVR

Scheme 2.2: (a) In an electronic predissociation process (Herzberg type I), the

molecule undergoes a non-radiative transition (IC) from the binding to a

repulsive state and subsequently decays. (b) In the vibrational predisso-

ciation process (Herzberg type II), the photon creates a quasi-bound state

in the potential well, which decays either by tunneling or intramolecular

vibrational energy redistribution (IVR).

many different quantum states.

Photodissociation processes can be classified in four different types, namely the

direct photodissociation as depicted in scheme 2.1(a), electronic and vibrational pre-

dissociation[13] and vibrationally induced dissociation of the hot ground state following

internal conversion of the initially excited electronic state.[10] These indirect types of

photodissociation are illustrated in schemes 2.2 and 2.3.

Whereas the direct dissociation in a repulsive excited electronic state can be treated

to a large extent as a classical mechanical problem, all the other types of dissociation

require a treatment in the framework of quantum mechanics and statistical rate the-

ories. In the case of electronic predissociation (Herzberg type I), the dynamics are


hν

E0

RAB

(a) (b)

AB

A+B

hν

E0AB

A+B

internal

conversion

Scheme 2.3: Unimolecular dissociation induced by electronic excitation. (a) A single

photon creates a bound level in an upper electronic state, which subse-

quently decays via a radiationless transition to a hot ground state above

the dissociation threshold. (b) Overtone pumping directly creates a quan-

tum state above the dissociation threshold in the electronic ground state.

In both cases, the dissociation occurs in the electronic ground state.

governed by the rate of the non-radiative decay process, which depends on the cou-

pling of the two involved electronic states. In the case of vibrational predissociation

(Herzberg type II), the lifetime of the intermediate complex, (AB)∗, depends on the

tunneling rate respectively on the efficiency of the intramolecular vibrational energy

redistribution (IVR).

Two indirect types of photodissociation are illustrated in scheme 2.3. Both types

of excitation eventually lead to a vibrationally excited ground state (hot ground state),

which is subject to dissociation provided the photon energy was higher than the dis-

sociation threshold. Assuming that the formation of the hot ground state either by

internal conversion (a) or overtone pumping (b) is fast compared to the dissociation in

2.2 Unimolecular Kinetics 11

the ground state, the dynamics can be treated within the framework of statistical rate

theories.

The photodissociaton of the allyl radical can be considered as an unimolecular dis-

sociation in the ground state following fast internal conversion of the initial excited

electronic state. The subject of this thesis is the experimental observation of the photo-

dissociation of the allyl radical as well as the rationalization of the experimental results

within the framework of statistical rate theories and quantum chemical calculations. It

will be demonstrated, why the photodissociation of C-state allyl radical can be consid-

ered an indirect dissociation, whereas the dissociation of A-state allyl radical can also

be regarded as an electronic predissociation.

2.2 Unimolecular Kinetics

A gas phase unimolecular reaction is an apparently simple process, where an isolated

molecule undergoes a chemical transformation.[14–16] The whole dynamics therefore

only depend on the inital state of this single molecule. Unimolecular reactions include

isomerization, elimination and dissociation.

Reaching an internal energy sufficient for reaction requires excitation, which can

be by collision with a bath gas at thermal equilibrium,

AB + M −→ (AB)∗ + M,

where A is the reactant and M a bath gas, or by absorption of light,

AB +Nphotons × hν −→ (AB)∗,

where N is the number of photons at frequency ν. The actual reaction event then

occurs in a second step:

(AB)∗ −→ A + B.

An essential characteristic of a unimolecular reaction in the gas phase is that the time

scale of the reaction step is much longer than that of the activation.


2.2.1 Statistical Rate Theories

Transition State Theory

The transition state theory requires no calculations on the dynamics of the reacting

system, since the approximations made in the theory enable one to calculate the rate

coefficient solely in terms of the statistical properties of the system, namely the ther-

modynamics of the activated complex, which is synonymous with the transition state.

A general assumption of the theory is that there exists a critical surface in phase space,

dividing the reactant and product regions, such that only trajectories from the reac-

tant valley cross it, and, having crossed once directly proceed to the products without

recrossing the surface. This a priori exclusion of a recrossing is still a reasonable as-

sumptions, in particular if the barriers are high compared to the available energy and

for irreversible reactions such as gas phase dissociation processes.

The transition state formula for the high pressure rate is given by

k∞uni =kBT

h

Q†

Qe−E0/(kBT ), (2.2)

where Q and Q† are the partition functions of the reactant and the activated complex

respectively.

RRKM Theory

The Rice-Ramsberger-Kassel-Marcus (RRKM) theory is in fact a microcanonical ver-

sion of the transition state theory. There are two important assumptions in the theory,

the first one being the transition state assumption. The second important assumption

is the ergodicity assumption, which states that the coupling between the various vi-

brational degrees of freedom is sufficiently strong for excitation energy to be random-

ized rapidly amongst the active degrees of freedom on the time scale of the reaction.

Such rapid divergence of trajectories means that no matter how a population of excited

molecules is prepared, e. g. by laser or collisional activation, the representative trajec-

tories rapidly become uncorrelated and will be spread in a random fashion over phase

space. Even if the initial distribution is not at equilibrium, it will evolve on a very short

time scale into a random microcanonical equilibrium distribution.

2.2 Unimolecular Kinetics 13

The microcanonical RRKM rate constant can be expressed as

k(E) =W †(E − E0)

hρ(E), (2.3)

where ρ is the density of states of the reactant at total energy, E, and W † is the total

number of states of the transition state having an energy less or equal to E − E0.

For a practical calculation of microcanonical rate constants within the RRKM the-

ory, one only needs to know the vibronic density and sum of states, which can be

computed from the vibrational frequencies.

Whereas the transition state assumption seems very reasonable for irreversible gas

phase dissociation reactions, the ergodicity assumption must be questioned. The pho-

todissociation of the allyl radical can be well described by the RRKM theory, however,

there is a rising number of radicals, where the photodissociation dynamics cannot be

modeled within the framework of statistical rate theories.

Chapter 3

Fundamentals of PhotofragmentSpectroscopy

3.1 Introduction

In an early overview about photofragment spectroscopy, Wilson pointed out that most

excited electronic states, even of relatively small molecules are rather dissociative than

stable.[17] Experimental techniques used to study stable excited states generally provide

little information about, or indeed cannot even be applied to, dissociative excited states.

To provide the sort of detailed information required to describe dissociating states, new

experimental techniques were developed, based on molecular beam methods.

Photofragment spectroscopy is concerned with the characterization of the photo-

products and the dissociation dynamics following the electronic excitation and can

thus be regarded as a combination of spectroscopy and dynamics. The basic principles

were formulated by Herschbach and Zare[18] in 1963 and experimentally implemented

for the first time by Wilson in 1969.[19] Ever since the field has gradually been growing,

in line with the development of laser and molecular beam technology.

This chapter briefly summarizes the theoretical background of experimental

methods used in this thesis, namely molecular beams, multiphoton ionization and

photofragment Doppler spectroscopy.

16 Fundamentals of Photofragment Spectroscopy

3.2 Molecular Beam Methods

A molecular beam is a stream of collimated molecules that has been internally and

translationally cooled relative to its state prior to beam formation. Such cooling was

first observed by Joule and Thomson in their famous experiment. Generally, a molec-

ular beam source consists of a high pressure reservoir, which is separated by a small

orifice from the low pressure region. Gas particles on the high pressure side experience

a pressure gradient when within the orifice and are accelerated into the region of low

pressure, forming a collimated beam of molecules. If the pressure gradient is large, the

beam accelerates to Mach 1 at the exit of the nozzle and then undergoes a supersonic

expansion into the low vacuum region.

The energy of a molecule is equipartitioned among its internal (vibration and rota-

tion) and external (translation) degrees of freedom. Exchange of energy between the

molecule’s degree of freedom can occur upon collision. There is no net transfer of en-

ergy to one degree of freedom though at constant pressure, provided that the ensemble

of molecules is large. When the gas is expanded, such as in a molecular beam, how-

ever, transfer to the translational degrees of freedom is more efficient because once the

molecule obtains kinetic energy, it is free to move into the low pressure region before

another collision can occur. Energy transfer between levels of similar value is most ef-

ficient and thus rotational levels are best cooled, although vibrational and in rare cases

even electronic cooling may occur.

The viscous expansion in the nozzle converts the enthalpy, which is associated

with an undirected movement of the particles, to an unidirectional movement of the

particles, thereby increasing the velocity of the molecular beam. This conversion is

leading to a lower temperature of the molecular beam. The sonic speed, vs, is defined

as

vs =

√γkT

m, (3.1)

where k is the Boltzmann constant, γ is the ratio of the heat capacities, cp/cv and m is

the mass of a particle. Obviously, a decrease in temperature causes a lower sonic speed.

In an ideal molecular beam, the mach number at the most narrow point in the nozzle

is 1. Further expansion is leading to a mach number larger than one and therefore

a supersonic expansion. The expansion and the associated cooling is continued to

the point, where no further collisions occur. After this point, the partition among the

3.2 Molecular Beam Methods 17

degrees of freedom is frozen.

The region in which the beam transverses without collision is called the zone of

silence. This zone forms at the nozzle’s tip and extends out in a parabolic shape, which

is encased by a shock wave. The shock waves that are perpendicular to the axis of the

beam are called mach disk and those along the wings are known as barrel shock.

zone of silence

mach

disk

barrel shock

skimmer

nozzle

Scheme 3.1: Supersonic expansion in a Campargue type molecular beam source.

A conical shaped skimmer is often placed within the zone of silence, which ex-

tracts the cooled beam into a region of high vacuum, where the actual spectroscopy is

performed. A large part of the beam, however, is scattered off of the skimmer, causing

another shock wave, called skimmer shock, which may eventually completely block

the orifice of the skimmer. Campargue attempted to reduce the skimmer shock by test-

ing the effects of a variety of conical shaped skimmers. He converged upon a skimmer

design with an inner angle around 45◦ and an outer angle of 55◦.[20] The skimmer is

very sharp at the tip and gradually increases in width towards the base.

The performance of the molecular beam is often enhanced by heating the molecules

within the nozzle. The higher temperature increases the pressure within the nozzle and

less molecules can pass through the nozzle, keeping the background pressure low. This

extends the length of the zone of silence, adding more flexibility to the skimmer-nozzle

distance. Miller provides a good summery of the thermodynamics and kinetics in a jet

expansion and how they affect the design of a molecular beam apparatus.[21]


3.3 Multiphoton Ionization

Photoionization is the physical process, in which an incident photon ejects one or more

electrons from an atom or molecule. Multiphoton ionization (MPI) is the special case,

where more than one photon is required to cause ionization.

Although the possibility of simultaneous two-photon absorption was pointed out

in 1931 by Goppert-Mayer,[22] experimental observation of two-photon absorption in

the optical region was made possible only after lasers were developped as an intense

incident light source.[23]

Multiphoton processes can be described by time-dependent perturbation theory.[24]

The transition probability for a two-photon absorption process using a first order per-

turbation approximation is given by

W ∝ I2

∣∣∣∣∣∑m

〈Ψf |µmf |Ψm〉〈Ψm|µmi|Ψi〉∆Eim − hνr

∣∣∣∣∣2

, (3.2)

where Ψi and Ψf are the initial and final state wave functions, |Ψm〉 is an (virtual)

intermediate state, µ is the respective dipole moment, ∆Eim is the energy difference

between the initial and intermediate state and m is the number of intermediate states.

Equation 3.2 shows that the transition probability is proportional to the square of the

laser intensity, I , and in more general is proportional to In in an n-photon process.

When the laser frequency, νr, approaches a real intermediate state, a drastic in-

crease in the two-photon signal can be observed, a so-called resonance enhancement.

If a rigorous resonance condition were satisfied, i. e., ∆Eim = hνr, then the magnitude

of the transition probability would go to infinity. Since the energy levels of the inter-

mediate level are not infinitely sharp and higher order radiation-molecule interactions

are neglected in equation 3.2 , the divergence of the transition can be avoided.

It is interesting to note that the vibronic structure appearing in the resonant mul-

tiphoton transition is generally different from that in the non-resonant transition.

Whereas the vibronic structure in the latter case is mainly determined by the Franck-

Condon vibrational overlap integral between the initial and the final state, in case of

resonance, the vibronic structure reflects the potential difference between the initial,

resonant and final states.

In the case of ionization, the transition from the intermediate state to the contin-

uum of states of the cation is only moderately wavelength dependent. If the ionization

3.4 Photofragment Spectroscopy 19

M

M*

M+

(a) (b) (c) (d) (e)

energy

Scheme 3.2: Different types of photoionization: (a) one-photon ionization; (b) (1+1’)

REMPI; (c) (1+1) REMPI; (d) (2+1) REMPI; (e) non-resonant two-

photon ionization, (1+) N2PI.

occurs via a resonant intermediate state, the process is called resonance enhanced mul-

tiphoton ionization (REMPI). Scheme 3.2 summarizes some common types of ioniza-

tion. The fact that charged species can be detected very efficiently makes REMPI an

ideal method for the investigation of excited electronic states.

3.4 Photofragment Spectroscopy

Three different experiments were performed to investigate the dynamics of a photo-

dissociation reaction: (a) action spectroscopy (b) transient spectroscopy (c) photofrag-

ment Doppler spectroscopy. Whereas the first two methods are rather simple and in-

tuitive, the Doppler spectroscopy requires some detailed explanation. All three types

of experiment can be considered pump-probe experiments. One laser generates the

exicted state population and a second laser is used to probe the photoproducts.


3.4.1 Action and Transient Spectoscopy

In an action spectroscopy experiment, the time delay between the excitation and probe

laser is held fixed and the product concentration is detected as a function of excitation

laser wavelength. Thereby, information about the origin of the photoproduct can be

gained.

In a transient experiment, the product concentration is detected as a function of

time-delay between the excitation and probe laser. The wavelength of both lasers is

held fixed. In an ideal case, the microcanonical unimolecular rate constant can directly

be derived from the recorded time-dependent appearance of the photoproduct.

3.4.2 Photofragment Doppler Spectroscopy

Detailed insights into product energy distribution can be gained from photofragment

Doppler spectroscopy. The Doppler shift of a given resonance line is proportional to

the projection of the velocity vector, ~v, of the absorbing molecule onto the axis of the

probe laser, which is defined by the unit vector, ~k. The Doppler shifted absorption

frequency, ν, is related to the unshifted frequency, ν0, by

ν = ν0

(1− ~v · ~k

c

)= ν0

(1− ~v

ccosχ

), (3.3)

where χ is the angle between ~v and ~k and c is the speed of light.[25]

Doppler spectroscopy is particularly useful for the examination of light photofrag-

ments, since they carry away most of the translational energy due to conservation of

linear momentum. The following section describes how the product energy distribu-

tion for a reaction of type RH→R + H can be derived from the Doppler profile of the

hydrogen atom.

Product energy distribution from Doppler profiles

An absorber moving toward a stationary light source with velocity component vz ex-

hibits a shift in absorbtion frequency of vzν0/c, where ν0 is the unshifted frequency of

the absorber at rest. If radiative lifetime and collisional broadening can be neglected

compared to the Doppler broadening, the curve of absorption vs. frequency, P (ν) is

3.4 Photofragment Spectroscopy 21

proportional to the distribution function, fz(vz) in the z-component of the velocity:[26]

P (ν) =c

ν0

fz

{(ν − ν0)

c

ν0

}, (3.4)

where

fz(vz) =

∫f(v)dvxdvy. (3.5)

If the velocity distribution function is isotropic, then one can obtain the velocity

distribution, f(v) as follows:

f(v) =

[−1

2πvz

dfz(vz)

dvz

]vz=v

, (3.6)

where ∫f(v)dv = 1. (3.7)

The translational energy distribution, P (ET ), of the the detected hydrogen atom

photofragment in the molecule coordinate frame is given by

P (ET ) =4πν

mH

(1 +

mH

mR

)f(v), (3.8)

with

ET =1

2mH

(1 +

mH

mR

)v2, (3.9)

being the corresponding translational energy of the hydrogen atom fragment and mH

and mR being the mass of a hydrogen atom and a molecular fragment, respectively.

The expectation value of the translational energy distribution

The Doppler profile of a H-atom reflects its velocity distribution along the detection

axis (vz). For an isotropic velocity distribution, we get

〈ET 〉 =

(3

2

)mH

⟨v2z

⟩, (3.10)

where 〈v2z〉 is the second moment of the velocity distribution in the laboratory coor-

dinate frame. A Gaussian shape Doppler profile indicates a Maxwell-Boltzmann-like

velocity distribution and 〈vz〉 can be derived from the FWHM of the Gaussian fit.[27, 28]

Thus, the translational temperature of the H-atom can be calculated using the expres-

sion

TT =∆ν2

FWHM ·mH

(c

ν0(H)

)8k ln 2

, (3.11)


from which the translational energy, 〈ET 〉 = 32kTT , can be obtained. The expectation

value of the translational energy in the molecular coordinate frame can be calculated

using the momentum conservation law. The calculation of the translational energy of

a deuterium atom can be done in the same fashion.

Chapter 4

Experimental Setup

4.1 Molecular Beam Machine

All experiments described in this thesis were carried out in the molecular beam ma-

chine depicted in figure 4.1. The apparatus mainly consists of an expansion chamber,

an ionization region and a linear time-of-flight mass spectrometer. The whole machine

is built from stainless steel with some extensions made from aluminum and brass. The

original apparatus has been described in detail elsewhere[29–31] and thus only the im-

portant modifications are discussed thoroughly in this chapter.

The expansion chamber (2-4) is evacuated by an EDWARDS (BOC Edwards, Craw-

ley, GB) pump system, consisting of an EH2600 mechanical booster pump backed

by an E2M275 rotary vane pump. The high flow rate of the pump system (530 l/s)

would even enable experiments with continuous molecular beams, a constant pressure

of 2x10−4 mbar can be maintained. The expansion chamber is separated from the ion-

ization region by a skimmer with an orifice of 2 mm diameter. This skimmer cuts out

the cold region of the molecular beam.

The next chamber, the ionization region (5), is pumped by an EDWARDS MK2-

CR250/200M 10 inch oil diffusion pump. A liquid nitrogen-cooled baffle inhibits

back-diffusion of the SANTOVAC 5 propellant (Santovac Fluids, St. Charles, MO,

US) and dissolved substances therein. With a theoretical pumping speed of 3000 l/s,

a pressure of as low as 1x10−6 mbar without gas load and 3x10−6 mbar in operation

can be reached. The ionization region is crossed by two laser beams, perpendicular to

the axes of the molecular beam and the following drift tube of the time-off-flight mass

24 Experimental Setup

roots pump

530 l/s

oil diffusion pump

10 inch

3000 l/s

oil diffusion pump

6 inch

1300 l/s

1

23

4

5

6

78

x

y

z

Figure 4.1: Design of the molecular beam machine: (1) valve mounting, (2) pulsed

valve, (3) pyrolysis nozzle, (4) skimmer, (5) ionization source, (6) ion

optics, (7) drift tube, (8) detector.

spectrometer. This chamber also accommodates the ion optics (6), which accelerate

the generated ions and guide them into the next chamber.

The last chamber, the drift tube (7) is aligned along the y-axis of the system. The

ions are separated during their flight in the field-free region by their m/z ratio. The tube

is pumped by an EDWARDS MK2-CR160/700M 6 inch oil diffusion pump (1300 l/s),

which is constructed in the same way as the preceding 10 inch one. A final pressure of

3x10−7 mbar is reached in operation. The ion detector (8) is placed at the end of the

drift tube.

4.1.1 Generation of Radicals

The generation of radicals for spectroscopy has been an issue for a long time. There

were numerous attempts in the past using photolysis,[32, 33] pyrolysis,[34] electric dis-

charge[35] and chemical reactions.[36] The aim of all methods is the specific generation

4.1 Molecular Beam Machine 25

of radicals in high concentration in the gas phase. Thermodynamic conditions must be

chosen so that unimolecular and bimolecular reactions such as isomerization, recombi-

nation and disproportionation are suppressed. The application of vacuum pyrolysis in

photoelectron spectroscopy was first reported 1971 by Cromford et al.[37] The precur-

sor molecule was directly introduced into the ionization region through a heated fused

silica tube. Using pyrolysis temperatures of 1000 ◦C, the radical was generated in

an effusive beam, together with side products and unreacted precursor. Due to the low

pressure used in the effusive beam, the long contact time in the heated fused silica tube

led to a low concentration of the desired radical and the formation of side products,

which often dominated.

Pyrolysis nozzle

To overcome these problems, Chen et al. built a pulsed high-pressure radical source.[38]

The new flash pyrolysis nozzle with very short contact time led to quantitative conver-

sion of the precursor to the corresponding radical, provided the pyrolysis temperature

was sufficiently high and the contact time short enough.[39] In the original version,

an alumina tube is spiral wound with a tantalum wire filament, which was resistively

heated. In a later version, a tube material was used that could be heated directly. In

normal metallic conductors, where electrical resistance decreases with increasing tem-

perature, the maximum temperature occurs halfway between the electrodes. Thus, the

tube exit is much colder than the section upstream, giving rise to radical recombina-

tion in the colder section. Refractory semiconductors however, like silicon carbide, or

solid electrolytes, like zirconium oxide, show a nearly constant temperature from one

electrode to the other. In addition, they can be operated at higher temperatures up to

2000 ◦C and have a significantly longer lifetime.[31] Due to the inverted temperature

coefficient of the resistance of SiC, the tube must be run in series with a current limiter,

e. g. some light bulbs.

The current design, as displayed in figure 4.2, is only a slight modification of the

afore mentioned silicon carbide nozzle. In order to guarantee optimal flow and minimal

lengthening of the gas pulse, the distance between the pulsed valve and the tube exit

was minimized to less than 40 mm. A short design of the nozzle is also important

because there is a pre-expansion within the alumina and SiC tube, but the flow must be

subsonic to allow a supersonic expansion at the exit of the nozzle. HEXOLOYr silicon


Hexoloy SiC tube

reaction-bonded SiC

electrode sleeves

high-temperature

stainless steel clamp

alumina support tube

gold-coated heat shield

General Valve Corp.

Series 9 pulsed valve

gas flow

precursor seeded

in He, ~ 2 bar

poppet valve

12 mm 24 mm

Figure 4.2: Design of the pyrolysis nozzle.

carbide tubes (Saint-Gobain Ceramics, Niagara Falls, NY, US) with an inner diameter

of 2.0 mm and a total length of 24.0 mm were used. The original teflon poppets of

the pulsed solenoid valve (GENERAL VALVE CORP., Series 9, Fairfield, NJ, US) were

replaced by PEEK poppets to prolong their lifetime. An additional gold-coated heat

shield prevents too strong heating-up of the solenoid valve and all the O-ring seals

therein.

Radical precursors

The radical precursors were seeded in an inert carrier gas, normally He, at a stagnation

pressure of 2.0 bar. A seed ratio of 1:100 was found to result in optimal cooling of

the radicals within the supersonic jet expansion. A rotational temperature of the cold

radicals between 30 and 150 K was obtained, depending on the seed ratio and the

distance between the nozzle exit and the skimmer. Typical number densities of the

generated radicals were 1014 cm−3 at the nozzle orifice and around 1010 cm−3 in the

ionization region. The precursors were stored in a new stainless steel sample holder.

The temperature was adjusted, so that the required seed ratio was obtained. A water-

cooled Peltier element controlled the temperature of the sample holder.

Typically, allyl iodide, purchased from ALDRICH and used without further pu-

rification was used for the generation of allyl radicals. Alternatively, allyl bromide,


1,5-hexadiene and 4-butenyl nitrite form allyl radicals as well upon pyrolysis. Highest

conversion and best radical yield was observed for allyl iodide, which was always used

as precursor unless otherwise stated.

4.1.2 Ion Optics

In a time-of-flight mass spectrometer, the ion optics accelerate the ions and guide them

towards the detector. The simplest possible configuration consists of two electrodes

connected to an acceleration voltage. The first electrode, the repeller is under high

voltage and the second electrode, the extractor grounded. Ions are accelerated away

from the repeller towards the extractor and transmitted through a hole therein. In the

following field-free drift tube, the ions are separated by their mass and detected at the

end of the tube.

The resolution of the mass spectrometer is impaired by three factors: (a) different

times of formation or acceleration of ions, (b) different initial localization of ions in

space and (c) different initial velocities of the ions. The time of formation depends

mainly on the laser pulse width in a multiphoton-ionization experiment. Wiley and

McLaren have demonstrated, that an acceleration in two different electric fields may

compensate the spatial distribution and different initial velocities of the ions.[40] This

so-called space focusing narrows the time-frame of arrival at the detector of ions of the

same mass. The original apparatus consisted of two field ion optics including subse-

quent Einzel lens and horizontal and vertical deflectors. One of the key improvements

to increase the resolution and sensitivity of the mass spectrometer was the replacement

of these ion optics.

Space focusing in m-field linear time-of-flight mass spectrometers

Some recent publications conclude that the use of three fields ion optics can signif-

icantly increase the space focusing and thus the resolution of the mass spectrome-

ter.[41, 42] The ion time of flight for the generalized m-field case is given by

Tm =v1 − u0

a1

+m∑i=2

vi − vi−1

ai+Dm+1

vm. (4.1)

Let us now take the different initial localization in space into account. Ions starting

from a general position D1 = D1 + z will have a slightly different time of flight from


D1 D2 D3 D4

u0 v1 v2 v3 velocity

a1 a2 a3 a4 = 0 accelerationsource

E1 E2 E3 E4 = 0 electric field

Scheme 4.1: Schematic diagram of three electric-field TOF configuration along with

the definitions of the lengths, velocities and accelerations used in the

mathematical derivation.

that corresponding to D1. The deviations in time of flight ∆T = T (D1)− T (D1) can

be expressed as a Taylor series in the m-field case:

∆Tm =∞∑n=1

(dnTmdDn

1

)D1

zn

n!. (4.2)

Space focusing requires mechanical and electric-field arrangements that result in as

many of the derivatives of Equation 4.2 as possible being set to zero. The order of

space focusing corresponds to the number of derivatives being set to zero. A second

order space focus is thus achieved by setting both (dT/dD1)D1and (d2T/dD2

1)D1to

zero.

The adoption of certain dimensionless quantities is useful in the evaluation of

the derivatives, as these turn out to be appropriate parameters in space focusing de-

sign. The following substitutions are made in the three-field case: R2 = E2/E1,

R3 = E3/E1, L2 = D2/D1, L3 = D3/D1 and L4 = D4/D1. The ion velocity after

traversing the mth field is given by:

vm =

(u2

0 +m∑i=1

2aiDi

)1/2

, (4.3)

or, applying the previously defined substitutions:(vmv1

)2

= 1 +m∑i=2

RiLiX

= Km, (4.4)


X = 1 +u2

0

2a1D1

= 1 +Mmu2

0

2D1ZeE1

= 1 +U0

D1E1

(4.5)

where X = 1 when u0 = 0.

As shown in equation 4.5, the general space-focusing condition is dependent on

the ion’s initial axial velocity. Within this approximation, the X = 1 condition is

imposed, which is legitimate, if E1 and D1 are set to ensure that u20/(2a1D1) is close

to zero. In an m-field system (m > 2), there exists a general set of n simultaneous

equations, which need to be solved for the nth-order space-focusing condition, i. e.

[(djT/dDj1)D1

= 0]j=1→n. Expressed in appropriate parameters of the TOF system,

the set can be simplified to:{2XKm

[1

Rm

+Kj−1/2m

(1− 1

R2

)+

m−1∑i=2

(Km

Ki

)j−1/2

×(

1

Ri

− 1

Ri+1

)]− (2j − 1)Lm+1 = 0

}j=1→n

. (4.6)

The highest number of equations in the set to be satisfied simultaneously is equal to

the number of parameters. Thus, the highest order of the space-focusing condition that

can be achieved is given by nmax = 2m − 1. It should be noted, however, that the

maximum order of space focus can only be achieved by setting Lm+1 to zero, leading

to unphysical results. The highest useful space-focusing order in practice is 2m − 2

therefore.

Implementation

In our case of a three-field TOF, a space-focusing order of four would be achievable.

Due to initial constraints such as geometrical parameters of the existing beam machine

and the need for a sufficiently strong electric field at the ion source, we decided to

restrict our system to second order space focusing. The electric field at the ion source

(E1) has two duties: the field-ionization of hydrogen atoms in high-lying Rydberg

states and the initial extraction of the ions. A lower order of space focusing also gives

more geometrical flexibility, as certain parameters in the equation system are indepen-

dent and mechanical imprecision can be compensated by an appropriate adjustment of

the electric fields.

For a given set of geometrical parameters as illustrated in figure 4.3, parameters

for the electric field were found that satisfy equation 4.6 to second order. This was


spacer for Einzel lens

spacing sleeves

PEEK rod

tube mounting for Einzel lens

mounting of ion optics

electrodes

rep

elle

r

extr

acto

r 1

extr

acto

r 2

extr

acto

r 3

Ein

ze

l le

nse

gro

un

d

gro

un

d

d1 d2 d3d1 = 5.0 mm

d2 = 5.0 mm

d3 = 10.0 mm

d4 = 1000.0 mm

ion

source

detector

d4

Figure 4.3: Design of the improved three-field ion optics. A thin metal mesh covering

the holes in the three extractor electrodes increases the uniformity of the

electric fields.

done numerically using MATHCAD. Some modes of operation, which result from the

solution of the set of equations are provided in table 4.1.

Mode 3 turned out to be most practical for our type of experiments for several

reasons. The used voltages are in the range of commercial high-voltage power sup-

plies. Furthermore, the fields are strong enough to deflect the ions towards the detector

(y-axis) despite a considerable initial velocity in the x-axis.

The output of conventional high-voltage power supplies often features some tem-

poral drift and is normally perturbed by a considerable ripple, which is due to the

transformer. A new ISEG SHQ 224M (ISEG Spezialelektronik, Radeberg, DE) high

precision power supply was installed to maximize signal stability and reduce electric

noise artifacts. The LOC electronic shop built an adjustable potential divider, so that

all electrodes of the ion optics can be powered from one power supply output chan-

nel, except for the Einzel lens. This was connected to a separate power supply and

normally operated between 0 and 2000 Volt. The field of the Einzel lense results in a


mode V1 / V V2 / V V3 / V E1 / Vcm−1 E2 / Vcm−1 E3 / Vcm−1

1 4342 4097 4000 244.56 195.26 40002 3799 3585 3500 213.99 170.85 35003 3256 3073 3000 183.42 146.45 30004 2172 2048 2000 122.28 97.63 20005 1085 1024 1000 61.14 48.81 1000

Table 4.1: Electric field parameters for various modes of operation that satisfy theequation system for second-order space focusing. Note that V4 = 0 V in allmodes.

SIMION

V1

V2

V3

0.0 V

Einzel lens

drift region

Figure 4.4: Potential energy surface along the electrodes of the 2nd-order space focus-

ing 3-field time-of-flight mass spectrometer.

spatial focus of the ions onto the detector.

Figure 4.4 depicts the potential energy surface and the electric field for mode 3

with the Einzel lens operating at 1400 V. One can clearly see the two weak fields in the

extraction region followed by the strong acceleration field. The two outer rings of the

Einzel lens are both grounded, so that the potential energy of the ions does not change

any more after passing the third electric field.


Mass resolution and calibration

The most important characteristic of a mass spectrometer is the mass resolution, which

is given by

Ms =T

2∆T, (4.7)

where ∆T is equal to the full width at half maximum (FWHM) of the peak measured.

The mass spectrum of a calibration of our system with allyl bromide is depicted in

figure 4.5. We achieved unit mass resolution at about m/z = 1012, which is good for

a linear TOF MS and certainly sufficient for the mass range of our experiments. The

correlation of the peak FHWM and laser pulse FWHM approves the efficiency of the

ion optics. Thus, the main restriction of the mass resolution is the formation time of

the ions, which depends on the laser pulse width.

Mass spectra of known compounds were recorded and the correlation between

time-of-flight and m/z ratio was fitted using the following function:

m/z = A−Bt+ Ct2. (4.8)

Using our setup, we derived the following coefficients, provided the time-of-flight (t)

16.2516.12516.0

ion

sig

nal / arb

. units

time of flight / μs

allyl bromide M+

FWHM = 8 ns

79Br 81Br

13C 13C

Figure 4.5: M+ signal of allyl bromide. The isotope pattern is well resolved and the

FWHM of the peak corresponds to the pulse width of the ionization laser.


was given in µs.

A = 0.57614 B = 0.43592 C = 0.49139

4.1.3 Detector

The ions are detected at the end of the drift tube on a CHEVRON Model 3025 MA

detector assembly (Burle Industries, Sturbridge, MA, US). The detector consists of

two microchannel plates attached to a metal anode readout as depicted in scheme 4.2.

ions

MCP 1

MCP 2

counter anode

teflon spacer

PEEK spacer

5.0 mm

1.0 mm

2.0 mm

2.2 MΩ

5.2 MΩ

HV

1.0 MΩ

1.0 MΩ

50 Ωoutput to

oscilloscope

25.0 mm

(detection diameter)

Scheme 4.2: Design and connection diagram of the ion detector.

Before the ions hit the detector, they are reaccelerated in a strong electric field of

∼ 4000 V/cm, to increase their kinetic energy. Upon impact on the microchannel plate,

they release electrons, which release further electrons on collision with the walls. This

double electron-cascade leads to a signal gain of ∼ 107 at an operation voltage of

−2400 V. The electrons finally arrive at the anode and induce an electric current which

is recorded using a digital storage oscilloscope.

The channel plates are powered by the second output of the ISEG SHQ 224M high

precision power supply. It should be noted, that the detector assembly is operated under

negative voltage. The highest voltage is on the first microchannel plate (MCP 1). This

leads to the strong acceleration field between the MCP and the earthed electrode 5 mm

in front. The generated electrons are accelerated towards MCP 2, which is operated at

a lower negative voltage, and finally towards the counter anode.


4.2 Lasers

In this work, tunable nano-second laser light was generated using commercial Nd:YAG

pumped dye lasers. They were operated at a repetition rate of 20 Hz unless otherwise

stated.

4.2.1 Pump Laser

For the investigated transitions in the allyl radical, laser light in the wavelength ranges

of 240-250 and 370-420 nm was required. A NARROW SCAN dye laser (Radiant Dyes

Lasers GmbH, Wermelskirchen, DE) was pumped by the 355 nm third harmonic output

of a QUANTA-RAY GCR 3 Nd:YAG laser (Spectra-Physics, Mountain View, CA, US).

The dye laser consists of only two cuvettes, one of which is used as oscillator and

pre-amplifier at the same time and the other serves as amplifier. Wavelength selection

within the resonator is provided by a grazing incident grating. A laser band width of

< 0.1 cm−1 can be achieved.

For the 400 nm wavelenght range, the dye laser was operated with various

EXCALITE dyes in dioxane. 250 nm laser light was generated using coumarine dyes in

methanol and subsequent frequency doubling in a BBO-crystal. In the visible range, a

typical output power of 7-9 mJ/pulse was reached and 2-3 mJ/pulse in the UV.

4.2.2 Probe Laser

Generation of tunable coherent vacuum-UV radiation

Generation of vacuum ultraviolet radiation for the soft ionization of organic radicals as

well as atomic hydrogen was performed by frequency tripling of the output of Nd:YAG

and dye lasers in rare gases. The generation of laser third harmonic by four-wave

mixing in rare gases has been discussed in detail and has been applied to numerous

problems.[43–52]

Frequency tripling of the 355 nm third harmonic of a Nd:YAG laser leads to 118

nm VUV-light, which is particularly useful for diagnostic purposes, because at this

energy, hydrogen iodide, an undesired sideproduct in pyrolysis, can be ionized and

detected. Tunable VUV radiation, however, is generated by frequency tripling of the

output of a dye laser. Another NARROW SCAN dye laser was pumped by the 532 nm

4.2 Lasers 35

second harmonic of a QUANTA-RAY G250 Nd:YAG laser. Using pyridine 2 dye in

methanol, 730 nm light was generated and frequency doubled in a BBO-crystal to 365

nm UV light. This output was frequency tripled in a krypton cell and led to tunable

VUV light around the Lyman-α-transition in atomic hydrogen (∼ 121.6 nm).

The efficiency of the nonresonant frequency tripling for output wavelength λ is

given byPoutP 3in

=8.125× 10−2

(3λ)4

[χ(3)(λ)

]2N2F1

(b∆k,

b

L, 0.5, 1

), (4.9)

where χ(3)(λ) is the third order susceptibility, N the number density of the nonlinear

medium and F1 the phase matching condition of L, the length of the medium, b, the

confocal parameter and ∆k, the wavevector mismatch. Within the tight focusing limit

(b� L), the solutions of the phase optimization integral F1(b∆k, b/L, 0.5, 1) have the

form

F1(b∆k, 0, 0.5, 1) = (πb∆k)2eb∆k, for ∆k < 0

0, for ∆k � 0. (4.10)

The confocal parameter b is a measure for the the tightness of the focus and is small, if

the focus is tight. The first requirement on a frequency tripling medium which is used

with a tightly focused laser beam is that it be negatively disperse, meaning that ∆k < 0

and hence η(λ) < η(3λ). As both, the frequency tripling efficiency, (Pin/P 3out), and

the refractive index, η(λ), are a function of the number density, N , the phase matching

conditions and the conversion efficiency can be tuned by adjusting the pressure of the

rare gas. The optimum conditions for frequency tripling in krypton and xenon are

given by Hilbig and Wallenstein[46] and adjusted experimentally to be 50-80 mbar for

xenon generation of 118.3 nm photons and 80-180 mbar for krypton generation of

121.6 nm photons.

The conversion efficiency is low, typically between 10−6 and 10−9 in gaseous me-

dia. A photon flux of the order of 1018 photons/s results from the 365 nm fundamental

laser power of 8 mJ/pulse. Assuming a frequency tripling efficiency of 10−7, a VUV

photon flux of 1011 photons/s can be gained. Due to the high intensity of the remain-

ing UV light, significant photochemistry may occur in the ionization region if both the

fundamental and third harmonic are focused at the same point. This problem though

is avoided applying a technique called differential focusing.


Because the refraction index, η, of some medium is a function of the wavelenght

of the light to be refracted, the UV (365 nm) and VUV (121.5 nm) radiation is focused

at different places. For thin lenses, the ratio f1/f2 at two given wavelengths λ1 and λ2

with corresponding refractive indexes η1 and η2 is given by

f1

f2

=η2 − 1

η1 − 1. (4.11)

For applications in the VUV, lenses are made from alkali and alkaline earth fluorides,

which have a transmission range down to 110 nm. Their refractive indexes have been

measured for the whole range.[53, 54] An MgF2 lens at the exit of the rare gase cell

focuses the VUV light into the ionization region (∼ 5 cm) and the residual fundamental

further away (∼ 10 cm).

Furthermore, the ratio between third harmonic and fundamental light can also be

adjusted slightly by the pressure of the rare gas, as this is absorbing at both wave-

lengths. Finally, it is evident from the function of the conversion efficiency (4.9), that

the third harmonic generation is a third order process and therefore cubically dependent

on the fundamental laser intensity. Thus, a good signal quality is strongly dependent

on the power stability of the fundamental laser beam.

Detection of atomic hydrogen

The detection of atomic hydrogen via resonant two-photon ionization is a well-

elaborated method.[55] Compared to other hydrogen detection methods such as laser-

induced fluorescence (LIF),[56] this method is more sensitive as the detection efficiency

for ions is nearly equal to one.[25]

Ionization of hydrogen and deuterium atoms occurs via the resonant 2P states. The2P1/2 and 2P3/2 states are very close in energy (82258.921 cm−1 and 82259.287 cm−1

in hydrogen and 82281.301 cm−1 and 82281.667 cm−1 in deuterium) with a relative

intensity of 1:2.[57] This is the so-called Lyman-α transition, the first one in the Lyman

series of the hydrogen atom spectrum. Absorption of another UV photon may lead to

ionization. In our case, the residual 365 nm UV light from the frequency tripling will

ionize the 2P3/2 hydrogen atoms, but is not sufficient for ionization of the 2P1/2 state,

leading to high-lying Rydberg states.

Because the ionization occurs in a static electric field (F = 183.4 V/cm), the levels

of the Rydberg states are shifted due to the linear Stark-effect. The presence of an

4.2 Lasers 37

ionization threshold

high-lying Rydberg states

2P3/2

2P1/2

2S1/2

con

tinu

um

VUV

(121.5 nm)

UV

(365 nm)

ene

rgy

Scheme 4.3: Energy level diagram for the detection of atomic hydrogen via 1+1’

REMPI.

electric field leads to a saddle point in the Coulomb potential of the electron. In the

classical limit, the energetic position of the saddle point with respect to the field-free

ionization limit is given by

Es = −6.12√F , (4.12)

where Es is given in cm−1 and F in V/cm.[58] Therefore, the ionization threshold in

the electric field present at the ion source is lowered by 82.3 cm−1. The Rydberg

state generated via the 2P1/2 transition with a total energy of 109678.51 cm−1 lies

only 0.2129 cm−1 below the field-free ionization limit (109678.77 cm−1) and hence is

subject to field-ionization.

In deuterium, the situation is similar. Direct ionizations follows excitation to the2P3/2 state, whereas 2P1/2 deuterium atoms are excited to high-lying Rydberg states,

which are subsequently field-ionized.


4.3 Controlling and Timing

All experiments were controlled using a personal computer (INTEL Pentium IV) and

two STANFORD RESEARCH DG 535 digital delay generators (Stanford Research Sys-

tems, Sunnyvale, CA, US). An overview of the experimental setup, timing and data

acquisition is provided in scheme 4.4.

The master trigger (STANFORD RESEARCH DG 535) supplies TTL signals on mul-

tiple exits, with variable delays from one to another. The output of the master trigger

is sent to the driver of the valve without any delay (A). After a delay of 500− 1600 µs,

the time-of-flight of the gas pulse from the nozzle to the ionization region, the lamps

of the GCR 3 laser are triggered (E), 230 µs later the Q-switch (F). Depending on the

type of experiment, two more delayed signals trigger the lamp (B) and Q-switch (C) of

the G250 laser. The signal of the G250 laser Q-switch (C), with some short additional

delay, triggers the oscilloscope, which starts measuring the time-of-flight of the ions.

For the measurement of time-dependent signals, the delay for the Q-switch of the

GCR 3 laser (E) is varied. This can be done manually or using a LABVIEW-program.

For this purpose, one delay generator was connected to the PC using the GPIB interface

bus. The timing of the excitation (pump) and probe laser is adjusted using a photodiode

and by comparison of the ion signals from REMPI and direct ionization in the MS.

The stepping motors for the grazing incidence gratings of the dye lasers and the

tracking of the BBO-crystals are connected to the PC via a serial interface bus. The

wavelength can be set using the software of the manufacturer and own LABVIEW-

programs. The crystals are tracked with the help of a recorded crystal-tuning curve.

4.4 Data Acquisition

The signal from the detector at the end of the time-of-flight tube is integrated by a

LECROY LT 584 digital storage oscilloscope (1 GHz, 2 GS, LeCroy, Chestnut Ridge,

NY, US).

For calibration and setup, 15 laser shots are typically directly averaged on the os-

cilloscope. For the recording of spectra many more shots are accumulated (200-300

for transient, action and doppler spectra and 500-1000 for mass spectra). The sam-

pling rate of 4 giga samples per second (if operated in one-channel mode) allows a

4.4 Data Acquisition 39

365 nmkrypton cell

121.6 nm

TOF-MS

detector

ionoptics

valvedriver

Q-switch

lamp

delaygenerator

532 nm

Nd:YAG

(GCR 3)

3rdharmonic

dye lasercoumarin

151

BBOfrequencydoubled

Nd:YAG

(G 250)

2ndharmonic

dye laserpyridine 2

BBOfrequencydoubled

355 nm

248 nm

Q-switchlamp

PC

oscilloscope

sample holder

Peltier element

pyrolysis

nozzle

carrier

gas (He)

A B C D E F

Scheme 4.4: Experiment control, laser setup and data acquisition for pump-probe

multiphoton ionization experiments. The delay generator and the os-

cilloscope are connected to the PC by a GPIB interface bus, the lasers by

a serial interface bus.


temporal resolution of 4 data points per ns and leads to oversampling at a bandwidth

of 1 GHz, as the Nyquist-rate is exceeded by a factor of two. In practice, this means

the signal can be recorded at maximum bandwidth without any loss. Typically, a time

windows of 20 µs - suitable for the investigated mass range - was integrated and lead

to 80’000 sample points. The setting of multiple gates enables simultaneous recording

of different mass channels.

Data from the oscilloscope is transferred to the computer using its GPIB interface

bus. Home made LABVIEW-programs were used for recording and processing of the

data.

Part II

Photodissociation Dynamics of theAllyl Radical

Chapter 5

The Allyl Radical

5.1 Introduction

The allyl radical is presently one of the best understood polyatomic radicals. In

fact, much more studies have been devoted to this species than to many closed shell

molecules of comparable size. It is the simplest π-conjugated hydrocarbon radical,

thus serving as the very prototype for the understanding of π-stabilization effects. The

allyl radical is probably the most prominent textbook example of resonance stabiliza-

tion apart from benzene and terms like ”allylic stabilization” or ”allylic rearrangement”

belong to the everyday speech of an organic chemist.

However, the interest in this radical is not only of theoretical nature. The allyl rad-

ical is abundant in many reactive environments reaching from interstellar space[59] and

the atmosphere of Saturn’s larger moon, Titan,[60, 61] to combustion processes.[4–7,62–64]

The modeling of the chemistry of such complex high-energy environments requires a

detailed knowledge of its individual compounds. Information on the reactivity of the

allyl radical, e. g. dissociation dynamics, is of substantial interest.

The allyl radical is stable in the electronic ground state, provided a collision free

environment. In fact, the allyl radical is the minimum-energy conformation of all pos-

sible C3H5 isomers. Upon electronic excitation, e. g. by absorption of an UV photon,

the allyl radical becomes very reactive and various photoproducts have been detected.

Photochemical reactions include the abstraction of a hydrogen atom, sigmatropic re-

arrangements, rupture of a CC bond and cyclization. Upon irradiation around 400

nm, cyclization to the cyclopropyl radical was observed[65, 66] and the absorption of

44 The Allyl Radical

UV photons around 250 nm lead to formation of a product mixture containing allene,

propyne and lower amounts of acetylene and methane.[67]

Despite numerous experimental and theoretical studies on the spectroscopy and

dynamics of the allyl radicals, there are still some unresolved issues and even con-

tradictory results in the literature. The primary subject of this part of the thesis is a

detailed investigation of the spectroscopy and dynamics of the first excited state in the

allyl radical, which is so far only very poorly characterized and understood.

5.2 Structure

The allyl radical belongs to the C2v symmetry group in the electronic ground state.

The principal axis of the molecule are defined in the way depicted in figure 5.1. The

molecule is oriented in the yz-plane with the z-axis being the C2 axis. The molecule-

fixed axis a, b and c are defined according to an increasing moment of inertia, Ia <

Ib < Ic.

Hcentral

H

H

Hexo

Hendo

αα

θ

z (b)

x (c)

y (a)

Figure 5.1: Orientation of the allyl radical in a cartesian coordinate system inclusive

designation of some internal coordinates.

The geometry of the 2A2 electronic ground state was determined in several high-

resolution experiments by IR spectroscopy.[68–71] The rotational constants were deter-

mined to be A = 1.801890 cm−1, B = 0.346320 cm−1 and C = 0.290219 cm−1.

The allyl radical can thus be treated as a near prolate symmetric top molecule. The

5.3 Excited Electronic States 45

parameter X 2A2 B 2A1 C 2B1 X+ 1A1

d(C-C) / A 1.3869 1.40 1.385 1.37d (C-Hcentral) / A 1.0837 1.080d (C-Hendo) / A 1.0815 1.082d (C-Hexo) / A 1.0792 1.084θ(CCC) / ◦ 123.96 112 116.5 116.0α(CCHendo) / ◦ 120.77 120.8α(CCHexo) / ◦ 121.44 121.7δ(dihedral) / ◦ 0.0 20 0.0

Table 5.1: Geometry parameters of the allyl radical for the ground state and severalexcited states. Values in italics are taken from calculations: ground statecalculated at UCCSD/cc-pVTZ level of theory, cationic ground state takenfrom ref. 74. The dihedral angle is defined by the rotation of the terminalCH2 groups out of the yz-plane.

C2v symmetry of the electronic ground state was confirmed in electron spin resonance

(ESR) experiments[72, 73] and by the intensity variation apparent in the spectra due to

nuclear spin statistics.[68, 71]

Geometric parameters of the electronic ground state, the cationic ground state and

some excited states are listed in table 5.1. The provided internal coordinates in the

table are sufficient to completely describe the geometry of the ground state radical in

C2v symmetry as well as the C2 symmetric excited states.

Vibrational frequencies for some electronic states are listed in table 5.2. Ground

state frequencies were determined in the afore mentioned high resolution IR stud-

ies[68–71] and additionally from resonance Raman spectroscopy[75] and IR spectroscopy

in argon matrices.[76, 77] In the excited states, some vibrational frequencies were ob-

tained from MPI experiments.[78–80]

5.3 Excited Electronic States

The excited electronic states have been the subject of spectroscopical investigations

for more than four decades. The existence of two valence excited states, a strongly ab-

sorbing one in the UV at 5.29 eV, and weak one in the visible at 2.74 eV, was predicted

by Longuett-Higgins and Pople already in 1955 based on early LCAO self-consistent


Mode X 2A2 B 2A1 C 2B1

a1 ν1 as CH2 str (in phase) 3114 3029ν2 CH str 3052ν3 sym CH2 str (in phase) 3027ν4 sym CH2 scis 1478ν5 sym CH2 rock 1242 1145ν6 sym CCC str 1068 1019ν7 CCC bend 443 379 385

a2 ν8 as CH2 oop bend 775 680ν9 as CH2 twist 536 596

b1 ν10 CH oop bend 983 840ν11 sym CH2 oop bend 802 1089ν12 sym CH2 twist 522 572

b2 ν13 as CH2 str 3111ν14 as CH str 3020ν15 as CH2 scis 1463ν16 CH bend 1389ν17 as CCC str 1182 1261ν18 as CH2 rock 912 952

Table 5.2: Vibrational frequencies (cm−1) for several electronic states of the allyl rad-ical. Values in italics are taken from anharmonic ab initio frequencies atthe HCTH147/TZ2P level of theory.

orbitals calculations.[81] . This has been experimentally confirmed and the predicted

electronic states correspond to transitions to the A- and C-exited states, which are

listed together with the other electronic states of the allyl radical in scheme 5.1 on the

facing page. It is noteworthy that many modern methods for the calculation of excited

states including CASPT2[82] do not achieve such a good agreement with spectroscopic

measurements.

Currie and Ramsay reported the first observation of an excited state in 1966 in a

flash photolysis experiment of various allylic precursors.[83] They assigned the weak

and diffuse band system in the spectral range between 370-410 nm to a transition

between the ground state and the first excited state of the allyl radical. The location of

the bands was recently confirmed in two cavity ring-down experiments,[84, 85] as well

as in a time-resolved photoelectron spectroscopy study.[86] Due to the diffuse character

of the band system, the vibronic structure remained unassigned.

5.3 Excited Electronic States 47

H

H H

HH

H

H H

HH

3.04

4.975.005.15

6.46

6.57

7.317.59

IP = 8.153

X 2A2

A 2B1

B 2A1

C 2B1

D 2B2

3d 2A1

4s 2A1

5s 2A1

6s-12s 2A1

X+ 1A1

en

erg

y / e

V

Scheme 5.1: Location of the experimentally observed electronic states of the allyl rad-

ical.

A strongly absorbing UV band system between 210 and 250 nm was discovered

only two years after the A-state in a similar experiment.[87] Despite the calculated[88]

and experimentally confirmed[89] high oscillator strength of these electronic transi-

tions, no fluorescence was observed, indicating a short lifetime. This band system

was further investigated in two (2+2) REMPI experiments and the second exited state,

formally a 3s Rydberg state, was assigned.[90, 91]

The relative location of theB-, C- andD-states was determined in (1+1) and (2+2)

REMPI experiments performed in our group on cold allyl radicals prepared by jet flash

pyrolysis.[78–80] The proximity of the B- and C-state origins (∆E = 249 cm−1) and

the appearance of some formally symmetry-forbidden vibronic bands are the most

remarkable features. The signal rapidly decreases to the blue of 240 nm despite the

increasing absorption cross section, which is probably due to a shortening in lifetime.

The unexpected rotational structure observed in this spectrum enabled the deriva-


tion of some geometrical parameters of the excited states. The bands are partially rota-

tionally resolved in the Ka rotational quantum number. A simulation of the rotational

contour using various geometrical parameters allowed the complete assignment of the

vibronic band system. The simulation was achieved by fitting two geometrical param-

eters, the CCC bond angle and the C-C bond distance, which define the molecule’s

moments of inertia to a large extent. However, the two-parameter fit proved insuffi-

cient for the B-state origin, indicating that this state is non-planar with the terminal

CH2 groups rotated out of plane by a dihedral angle of 20 ◦. The non-planarity with an

associated symmetry reduction to C2 also explains the appearance of the B00 band and

the totally symmetric ν7 mode in the one photon spectrum. Both transitions would have

been strictly forbidden in a one photon process if the B-state were of 2A1 symmetry.

Furthermore, several higher lying states have been identified by resonant (2+1)

MPI in the 6.4-8.0 eV energy range and were assigned to a 3d and a series of ns

(n=4-12) Rydberg states. A progression in the ν7 CCC bending mode was also appar-

ent.[92, 93]

The ionization energy of the allyl radical was determined by electron impact tech-

niques[94, 95] and photoelectron spectroscopy[96] to be between 8.07-8.18 eV. A value of

8.153 eV was obtained in a high resolution pulsed-field ionization (PFI) photoelectron

spectroscopy study performed in our group.[97] A slightly lower value of 8.133 eV was

obtained from the extrapolation of the afore mentioned s-Rydberg series. A recent PFI

photoelectron spectroscopy experiment places the ionizaton potential to 8.131 eV[98]

which is consistent with a value of 8.13 eV obtained in a study of the photoionization

of the allyl radical by Fischer et al..[99] They attributed this discrepancy, however, to a

neglect of the rotational structure and hot bands contribution to the spectrum. A very

accurate calculation of the ionization energy at the CCSD(T)/CBS level of theory re-

sulted in a value of 8.158 eV, in agreement with the PFI-ZEKE experiment by Gilbert

et al.[97]

5.3.1 Primary Photophysical Processes

The absence of fluorescence in all observed excited electronic states and the decrease

of MPI signal to the blue of 240 nm, despite the growing oscillator strength, indicates

the presence of fast nonradiative deactivation pathways. The primary photophysical

5.4 Photochemistry 49

processes following excitation to the UV bands of the allyl radical were investigated by

means of time-resolved photoelectron spectroscopy.[74, 86] A lifetime of the UV states

in the range of 15-22 ps was determined in these picosecond pump-probe experiments.

In the same experiment, a resonant enhancement in the range between 400-410 nm was

found. The observed signal decay, however, was limited by the instrument response

function, thus a lifetime < 5 ps of the A-state may be presumed.

5.4 Photochemistry

The short lifetime of the excited electronic states was explained in several studies by

a possible isomerization to the cyclopropyl radical.[83, 100,101] Holtzauer et al. reported

the detection of IR bands associated with the cyclopropyl radical in an experiment

with allyl radicals in an argon matrix irradiated at 400 nm.[65] These findings are sup-

ported by an ESR study of allyl radicals grafted on a silica surface.[66] One may hence

conclude that electrocyclization is an important deactivation pathway upon irradiation

around 400 nm, corresponding to the A-state.

No evidence for formation of cyclopropyl radical, however, was found in studies of

the UV photochemistry of the allyl radical around 250 nm. Irradiation of allyl radicals

in an argon matrix at 254 nm resulted in a mixture of products consisting of allene,

propyne and minor amounts of acetylene and methane.[67]

Stranges et al. studied the UV photodissociation dynamics of the allyl radical at

254 nm in a photofragment translational spectroscopy experiment and identified loss

of a hydrogen atom (84%) and formation of acetylene and methyl radical (16%) as

primary reaction channels.[102] The H-loss reaction channel was further examined in

our group by time- and frequency resolved photoionization of the hydrogen atom reac-

tion product.[103,104] It was demonstrated by isotopic labeling experiments and RRKM

modeling that direct H-loss leading to allene is the dominant reaction channel in UV

photodissociation of the allyl radical.

This part of the thesis addresses a detailed analysis of this reaction channel by means

of further spectroscopic experiments and theoretical modeling. Furthermore, the pho-

todissociation dynamics following excitation to theA-state, which had previously seen

little investigation, despite being the lowest excited electronic state, are investigated


using a similar approach.

Chapter 6

Spectroscopy and Dynamics of A [2B1]Allyl Radical

6.1 Introduction

Whereas the spectroscopy of the B [2A1], C [2B1] and D [2B2] electronically excited

states was studied in detail earlier in our group using resonance-enhanced multipho-

ton ionization (REMPI),[78–80] relatively little is known about the first electronically

excited A [2B1] state, although this was the first experimentally observed excited elec-

tronic state in the allyl radical.[83] The same diffuse band system was recently rein-

vestigated in a cavity ring-down study by Tonokura et al.[84] and they confirmed the

position of the band system in the original work by Currie and Ramsay.[83]

Both studies, however, were carried out in a cell at room temperature upon photol-

ysis of suitable precursor molecules. The vibronic bands in the diffuse band system

could not be assigned and the question was raised, whether measurements under super-

sonic expansion conditions may clarify the situation. This and the energetic proximity

of the A state and the barrier to unimolecular dissociation motivated us to have a closer

look at the spectroscopy and dynamics of this electronic state.

Due to the inherently small number of radicals in the beam (∼ 1010 cm−3) and

the low absorption cross section of the A [2B1] ← X [2A2] transition (∼ 2 × 10−19

cm2 molecule−1 at 402.9 nm),[84] performing standard absorption spectroscopy did not

seem feasible. The oscillator strength associated with this transition (f osc = 0.0013)

is more than two orders of magnitude lower than that observed for the UV-bands

52 Spectroscopy and Dynamics of A [2B1] Allyl Radical

(f osc = 0.26).[89]

6.2 Multiphoton Ionization (REMPI)

The good results achieved in earlier REMPI experiments in the higher-lying electronic

states of the allyl radical encouraged us to use the same approach. From the two afore

mentioned absorption studies, we already knew that the band origin of the A-state is

around 409 nm. Unfortunately though, the excitation energy of the A state excluded

using the simplest (1+1) REMPI detection scheme, as two 409 nm photons were not

sufficient to ionize the radical. In a first attempt, a (1+1’) REMPI scheme was used.

The requirement of the second photon was its wavelength to be 6 240 nm, presuming

an adiabatic ionization energy of 8.153 eV.[74, 92,96,97]

Unfortunately, the D [2B2] state is located in this wavelength region. Towards

higher energy, series of higher Rydberg states appear. Apparently though, there are

gaps in the (1+1) REMPI spectrum around 234 and 237 nm. The second laser was

therefore fixed at wavelengths with minimal (1+1) REMPI signal, while the other was

scanned around 409 nm. Due to the constant ion background signal produced by the

UV laser, no wavelength dependent signal could be detected. No wavelength for the

UV laser with a sufficiently low ionization background could be found to detect the

weak A-state band system.

In another attempt, the 409 nm laser beam was focused into the ionization re-

gion using a 300 mm lense. We hoped to find a resonance using a (1+2) ionization

scheme. The high intensity of the focused laser lead to fragmentation. A mass spec-

trum recorded is depicted in figure 6.1. Apart from a weak allyl signal at m/z = 41,

all possible fragments could be detected. The relative intensity of the signals must not

necessarily represent their concentration in the ionization region though, as the ion-

ization cross section may vary for the different species. Even in the (2+1) REMPI, no

wavelength dependence of the allyl signal could be found, most of the signal must be

due to non-resonant processes.

The low number density of radicals in the beam combined with the low absorption

cross section of this transition and the presumably short lifetime of the A-state made

REMPI spectroscopy impossible.

6.3 Photofragment Action Spectroscopy 53sig

na

l in

ten

sity / a

rb. u

nits

0 2 4 6 8 10

time of flight / μs

H+

C+ - CH3

+

C2+ - C2H3

+

C3+ - C3H5

+

Figure 6.1: Mass spectrum detected upon irradiation with focused 409 nm laser light.

Non-resonant ionization and fragmentation leads to any possible carbon

and hydrocarbon species.

6.3 Photofragment Action Spectroscopy

Calculated reaction barriers for unimolecular reactions of the allyl radical estimate the

dissociation threshold to be around 60 kcal/mol. Loss of a hydrogen atom, the energet-

ically most favorable dissociation channel, should therefore be possible at the energy

of the A-state (∼ 70 kcal/mol). We set up an experiment to detect hydrogen atoms

from allyl radical dissociation. The energetics and the detection scheme of the exper-

iment are provided in scheme 6.1. The excitation (pump) laser generates A-state allyl

radicals, which are subject to rapid internal conversion and decay non-radiatively to

form hot ground state radicals. These radicals bear enough internal energy to over-

come the reaction barrier to unimolecular dissociation, namely H-loss. The abstracted

hydrogen atoms are ionized by the second laser, the probe laser, via (1+1’) two photon


IC diss.

pump-probe delay (Δt)

408.5 nm

121.6 nm

365.0 nm

C H + H3 4C H3 5

1 Ss2

2 Pp2

A B2

1

X A2

2

IP

Scheme 6.1: Schematic energy level diagram for the pump-probe experiments. Upon

electronic excitation, the allyl radicals decay non-radiatively to form hot

ground state radicals that dissociate into C3H4 and hydrogen. The hydro-

gen atoms are ionized by 1+1’ REMPI.

ionization. Monitoring the appearance of hydrogen atoms as a function of excitation

laser wavelength resulted in the spectrum provided in figure 6.2.

The A [2B1]← X [2A2] transition

The excited states of the allyl radical have been the subject of numerous quantum

chemical calculations. The vertical excitation energy for the first excited state has been

calculated between 2.7 and 3.5 eV.[81, 82,88,100] For this transition, we calculated a zero-

point energy corrected adiabatic excitation energy of 3.04 eV at the MRCI/cc-pVXZ

(X = D,T,Q, extrapolated to basis set limit) level of theory, which is in quantitative

agreement with the experiment.[105]

The electronic configuration of the A-state can be described as a linear com-

bination of the following two configuration state functions: (1b1)1(1a2)2(2b1)0 and

(1b1)2(1a2)0(2b1)1. This corresponds formally to either a π → n or a n→ π∗ transi-

tion. The theoretical treatment of the excited electronic states is discussed in more

6.3 Photofragment Action Spectroscopy 55

H-a

tom

sig

na

l / a

rb.

un

its

24500 25000 25500 26000

9

9

8

7 16

155

14

12A

1

0

A0

0

A2

0

A1

0

A1

0 A1

0

A1

0A

1

0

A1

0

A1

0

wavenumber / cm-1

Figure 6.2: Power-normalized action spectrum obtained by monitoring the total flux

of hydrogen atoms while scanning the excitation laser. The delay time

between excitation and probe laser was 100 ns.

detail in chapter 10.

The A [2B1]← X [2A2] transition is allowed by electronic selection rules in both

C2v and C2 symmetry. Thus the right symmetry of this state could not be readily

deduced from the electronic selection rules and a detailed analysis of the vibronic

spectrum was undertaken.

6.3.1 Rotational Contour Analysis

If a transition between states with different symmetry is considered, the selection rules

must be applied to the common elements of symmetry, which is C2 in this case. The

dipole transition moment lies along the long axis of the molecule (y) if the transition is


treated inC2v symmetry, leading to an A-type band. WithinC2 symmetry the transition

dipole moment lies in the xy−plane, leading to an A,C-type hybrid band.

The rotational contour in the A-state was simulated using the AsyrotWin pro-

gram.[106] The rotational constants for the ground state were taken from the equilibrium

geometry, which was determined with high accuracy by high-resolution IR laser spec-

troscopy.[68–70] We took the upper state rotational constants from the ab initio A-state

equilibrium geometry, calculated at the CASSCF/6-311+G(3df,3pd) level of theory.

A simulation as an A,C-type hybrid band with a line FWHM of 2 cm−1 gave the

best fit of the A 000 origin peak at 408.5 nm and is depicted in figure 6.3. A rotational

temperature of 100 K was assumed, as we derived this temperature from an analysis

of the partially rotationally resolved REMPI spectrum of the C-state under the same

experimental conditions. The band origin is ∼ 10 cm−1 red-shifted from the peak

maximum. The best correspondence of the simulation as an A,C-type hybrid band with

the experimental spectrum confirms the C2 symmetric non-planar A-state equilibrium

geometry, which was obtained in the ab initio calculations.

The diffuse character of the band system can be explained in terms of life-time

broadening and was earlier attributed to either predissociation[83] or isomerization to

cyclopropyl radical.[65, 107] The used line FWHM of 2 cm−1 corresponds to a lifetime of

∼ 2.5 ps, which is in good agreement with a time-resolved photoelectron spectroscopy

study of allyl A-state that resulted in a presumable lifetime shorter than the instrument

response function of 3.5 ps.[86] 1

6.3.2 Vibronic Band System

Despite the considerable lifetime broadening of the band system, the vibrational struc-

ture is still resolved. The redmost peak can safely be assumed to be the A-state origin.

The lack of bands redshifted from the A 000 origin, i. e. hotbands, indicates that the jet

expansion conditions were cold enough. The intervals between the A 000 band origin

1Achkasova et. al. reported some rotational structure in a band they assigned to the A-state origin

in their cavity ring-down experiment at a rotational temperature of ∼ 40 K (Ref. 85). J−Dependent

lifetime broadening in the A-state, i. e. Coriolis coupling, at the higher rotational temperature in our

experiment would lead to a broadened action spectrum arising from preferential dissociation of high-J

radicals. Test simulations of the rotational band contour at our rotational temperature and omitting the

low-J lines showed no significant deviation from the band depicted in figure 6.3.


245002445024400b

an

do

rigin

simulatedspectrum

experimentalspectrum

wavenumber / cm-1

Figure 6.3: Simulation of the rotational contour in the A state origin region as an A,

C-type hybrid band. The rotational temperature was set to 100 K and a

line FWHM of 2.0 cm−1 was used.

and the vibronic bands are listed in table 6.1 on the next page. To facilitate the assign-

ment of the vibronic bands, the vibrational frequencies of the excited state equilibrium

geometry were calculated.

Ab initio vibrational frequencies

Harmonic frequencies were calculated at the CASSCF level of theory for the C2 sym-

metric A-state equilibrium geometry. The frequency scaling factors were calculated

by linear regression to the experimental frequencies obtained from the tentatively as-

signed vibronic bands. The obtained scaling factors are in the same range as derived

from other calculations with uncorrelated methods using similar basis sets, which is

typically between 0.90 and 0.95. The root-mean-square (rms) error of the scaled har-

monic frequencies is 30.8 cm−1 for the 6-311+G(3df, 3pd) basis set and 33.1 cm−1 for

the cc-pVTZ basis set, which is much lower than the rms errors reported for various

Hartree-Fock (HF) methods by Scott and Radom.[108]


Vibrational frequencies (cm−1) of A-state allylCASSCFa CASSCFb

Mode cc-pVTZ 6-311+G (3df, 3pd) expt.c

a ν1 as CH2 str (in phase) 3055 3029ν2 CH str 3003 2976ν3 sym CH2 str (in phase) 2966 2939ν4 sym CH2 scis 1439 1425ν5 sym CH2 rock 1095 1082 1032ν6 sym CCC str CH2 rock 880 872 (934)ν7 as CH2 wag 511 509 553ν8 CCC bend 403 400 381ν9 sym CH2 twist 160 156 135

b ν10 as CH2 str 3055 3028ν11 sym CH2 str 2966 2939ν12 as CCC str 1593 1572 1501ν13 as CH2 scis 1394 1382ν14 CH rock 1230 1215 1232ν15 as CH2 rock 922 913 934ν16 as CH2 twist CH wag 750 751 752ν17 sym CH2 wag 500 500ν18 CH wag (in phase) 418 415

rms error 33.1 30.8

Table 6.1: Ab initio and experimental vibrational frequencies of A-state allyl. Thecomputed harmonic frequencies were scaled by: (a) 0.910 (b) 0.902.(c) The experimental frequencies were taken from the action spectrum infigure 6.2, the uncertainty of the intervals is 6 ±10 cm.


A-state geometry and vibrational modes

Upon electronic excitation, the allyl radical undergoes significant changes in geometry.

The C2 symmetric A-state geometry has a non-planar equilibrium structure, with the

two terminal CH2 groups rotated out-of-plane by a dihedral angle of ∼ 40◦. The CC-

bonds are substantially lengthened from 1.39 to 1.47 A, while the other coordinates

remain essentially unchanged. Both lengthening of the CC bond as well as the out-of-

plane twisting of the CH2 groups can be explained by the promotion of electrons from

the bonding π orbital to the non-bonding n or anti-bonding π∗ orbital.

A striking feature is the strong peak only 135 cm−1 blueshifted from the origin.

This low frequency mode corresponds to a torsional movement of the terminal CH2

groups. The frequency of this ν9 asymmetric CH2 twist mode is lowered from 547

cm−1 in the ground state to 135 cm−1 in the excited state. As this twist is one of the

major changes in equilibrium geometry upon electronic excitation, the ν9 is prominent

in the spectrum and its first overtone also appears with about half of the intensity of

the fundamental. Nearly all peaks observed in the action spectrum can be assigned to

a vibrational mode of A-state allyl with the help of the ab initio frequencies. These

tentative assignments, together with the calculated frequencies are listed in table 6.1

on the facing page.

The non-planar geometry of the excited state equilibrium geometry results in a

double-well potential for the ν9 mode. Tonokura and Koshi calculated the height of

the inversion barrier to be around 400 cm−1,[84] which is in good agreement with our

own calculations. This leads to an inversion doubling of levels at or below the barrier,

but the splittings are far too small to be observed in the experimental spectrum.

The diffuse character of the bands seems to increase towards higher energy in

the spectrum, possibly indicating a further shortening of the lifetime. Unfortunately

though, the band system was no further investigated at energies higher than 26200

cm−1 because these wavelengths cannot be accessed by our laser-system without ex-

tensive modifications. We observed continuos absorption and hydrogen abstraction

around 365 nm, however, during the setup of the experiment sometimes. Non-optimal

differential focusing conditions lead to a high intensity of the 365 nm fundamental of

the probe laser, causing undesired photochemistry (see chapter 4.2.2 on page 35).


6.4 Dynamics

We could reproduce the earlier absorption spectra of the A [2B1] ← X [2A2] band

system in the H-atom photofragment channel. It is thus demonstrated that allyl loses a

hydrogen atom upon excitation into the A-state. The good agreement of experimental

with calculated frequencies further supports this argumentation.

One question that may immediately arise is whether the dissociation occurs in the

excited state or on the ground state surface. The photodissociation of the B, C and D-

states were investigated in an earlier study and it was found that dissociation occurred

on the ground state surface after fast internal conversion.[103,104]

Time- and frequency-resolved photoionization of the hydrogen atom photoproduct

provides additional information on the unimolecular dissociation dynamics. The re-

sults of these experiments are discussed in the following sections in terms of ground

state vs. exited state dissociation, kinetics, product energy distribution and selectivity

of the hydrogen atom abstraction.

6.4.1 H-Atom Transient Spectroscopy

The kinetics of the unimolecular dissociation were investigated by detection of the

reaction products. We obtained the time-dependent appearance of the hydrogen atom

photoproduct by monitoring the total flux of hydrogen atoms while varying the time

delay between excitation and probe laser. This led to the spectra depicted in figure 6.4.

The transient appearance of the hydrogen atoms is recorded upon exication into the

A-state origin and the A107 band with the pump laser. The increased noise in the A1

07 is

due to the lower intensity of this band compared to the origin.

We observe the formation of the product in an unimolecular process. Plotting

product concentration vs. time should therefore result in an exponential rise. The

data points were fitted using the expression

SH(t) = N(e−k1t − e−kHt), (6.1)

which was convoluted with a 6 ns FWHM Gaussian function corresponding to the

cross-correlation of the two laser pulses. SH is the hydrogen atom signal, kH the uni-

molecular rate constant and k1 accounts for the decay of the signal at longer delay time

due to hydrogen atoms moving out of the detection volume of the probe laser. This

6.4 Dynamics 61

hyd

rog

en

ato

m s

ign

al /

arb

. u

nits

300250200150100500-50

pump-probe delay /ns

Allyl A excitation (408.3 nm)00

Allyl A 7 excitation (399.3 nm)10

kH = 3.49 ± 0.62 × 107s

-1

kH = 1.75 ± 0.47 × 107s

-1

Figure 6.4: Appearance of the hydrogen atom signal as a function of the time delay

between pump and probe laser for initial excitation to the A-state origin

and the A107 band.

decay rate, k1 depends on the geometry of the system, i. e. the spatial overlap of the

beams of pump and probe lasers, and the velocity of the formed hydrogen atoms.

It should be pointed out that in contrast with earlier measurements in the C-

state,[103,104] the signal rise can be fitted by a mono-exponential function without sig-

nificant deviation from the experimental data points. This indicates that we observe


one unimolecular process and not competing reaction channels via different interme-

diates as found at higher excitation energies.

The experimental unimolecular dissociation rates of 1.75 ± 0.47 × 107 s−1 for

A00 excitation and 3.49 ± 0.62 × 107 s−1 for A1

07 excitation are in good agreement

with statistical microcanonical rate constants obtained from RRKM calculations and

as expected, the reaction becomes faster with increasing excitation energy. H-atom

transients were recorded and analyzed for most of the prominent vibronic bands in the

spectrum. The comparison of these experimental results with RRKM calculations is

discussed in detail in section 8.3 on page 111.

6.4.2 Doppler Spectroscopy and Kinetic Energy Release

Apart from the kinetics, information about the energy distribution in the products is im-

portant in the discussion of unimolecular dissociation dynamics. We assume that the

photodissociation of the allyl radical leads to a C3H4 hydrocarbon fragment and a hy-

drogen atom. Most of the translational energy available for products will be imparted

in the hydrogen atom due to conservation of linear momentum. Therefore, the study is

restricted to the analysis of the translational energy distribution in the hydrogen atom

photofragment.

From frequency-resolved photoionization of the hydrogen atom photoproduct upon

408.5 nm excitation in the A00 origin we obtained the Doppler profile depicted in figure

6.5. The profile is broadened by the VUV laser linewidth of 0.5 cm−1 and a Gaussian

FWHM of 2.67 cm−1 resulted after proper convolution (for data fitting and deconvo-

lution, see appendix B.2 on page 155).

The translational temperature of the hydrogen atom in the laboratory coordinate

frame can be calculated using the expression

TT =∆ν2

FWHMmH

(c

ν0(H)

)2

8k ln 2, (6.2)

from which the translational energy 〈ET〉 = 32kTT can be obtained, assuming a

Boltzmann-like distribution of ET. From our measured Doppler profiles, we derive

a translational temperature of 2100 K, corresponding to an expectation value for the

translational energy of the hydrogen atom photoproduct of 6.2± 0.5 kcal/mol.

6.5 Results from Isotopically Labeled Allyl Radicals 63

-6 -4 -2 0 2 4 6

FWHM

2.67 ± 0.05 cm-1

Doppler shift Δν / cm-1

H-a

tom

sig

nal / arb

. units

Figure 6.5: Hydrogen atom Doppler profile obtained following excitation into A-state

origin at 100 ns pump-probe delay.

The high-energy wings of the Doppler profile may indicate a small contribution

of higher-order multiphoton processes. We have measuered H-atom signal intensity

at different excitation laser energies and found a linear dependence on laser power,

typical for a one photon process. Doppler profiles recorded at different laser intensities

showed no significant variation in their shape. Furthermore, two-photon processes

would lead to resonant Rydberg states around 200 nm with sharp bands, which were

not observed in the action spectrum.

6.5 Results from Isotopically Labeled Allyl Radicals

We wanted to investigate the site selectivity of the hydrogen abstraction. Therefore,

allyl radicals where selected hydrogen atoms were substituted by deuterium were pre-

pared. The synthesis of the deuterated precursor, 2-deuterioallyl iodide is specified in


appendix A on page 151.

6.5.1 Kinetic Isotope Effect

If we study the dynamics of the cleavage of a carbon-deuterium bond, a first order

kinetic isotope effect must be considered. Substitution of hydrogen with deuterium

leads to a decrease of the zero-point energy and an increase in the density of states,

caused by a lowering of the C-D frequency compared to the C-H.

deute

riu

m a

tom

sig

na

l / arb

. units

300250200150100500

pump-probe delay / ns


kD = 2.04 ± 0.42 × 107s

-1

Figure 6.6: Appearance of the deuterium atom signal as a function of the time delay

between pump and probe laser for initial excitation to the A-state origin

and the A107 band.

As a result, reaction rates involving cleavage of a C-H bond will, in general, de-

crease upon deuteration up to one order of magnitude. We measured the time de-

pendent appearance of deuterium atoms upon excitation of 2-deuterioallyl to selected

vibronic bands in the A-state. The obtained D-atom transient after excitation into

the A107 band is shown in figure 6.6. The measured unimolecular dissociation rate of

2.04± 0.42× 10−7 s−1 is roughly two times slower than the rate for hydrogen loss at


the same excitation energy as a consequence of the kinetic isotope effect. This signifi-

cant change in the reaction rate upon deuteration indicates a primary isotope effect and

consequently a direct cleavage of the C-D bond as reaction channel.

6.5.2 Site Selectivity of Hydrogen Loss and Reaction Channels

Additional evidence for the site selectivity of the hydrogen abstraction was found in the

Doppler spectra of the selectively deuterated D-2-allyl radical. From the ratio between

hydrogen and deuterium signals obtained from the Doppler profiles in figure 6.7, we

conclude that direct dissociation to allene from loss of the central deuterium atom is

the dominant reaction channel.

H/D

sig

na

l / arb

. units

8228582280822758227082265822608225582250

H/D = 1 : 5

laser energy / cm-1

D

H H

HH

Figure 6.7: Doppler profiles for 2-deuterioallyl obtained from the A-state origin at a

time delay between excitation and probe laser of 100 ns. The ratio be-

tween hydrogen (�) and deuterium (◦) is ∼ 1 : 5.


Hydrogen-deuterium Doppler profiles

The 1s-2p Lyman-α transition in deuterium is blue-shifted by only 22.4 cm−1 with

respect to hydrogen, so that both transitions could be recorded in the same scan of

the probe laser. Due to the proximity of the signals, we assume the efficiency of the

non-resonant frequency tripling for the generation of VUV laser light to be constant

over the whole scan range. If it is further presumed that both absorption and ionization

cross sections for hydrogen and deuterium are comparable, the area under the H and

D peaks is directly proportional to the number of H and D atoms lost from the parent

allyl radical.

Scheme 6.2 shows calculated reaction channels for allyl radical unimolecular dis-

sociation, which are in principle open at the energy of the A-state. The allyl radical

may dissociate directly into allene and a hydrogen atom via transition state 1 (TS 1) or

isomerize to the 2-propenly radical and subsequently dissociate into either propyne or

allene and a hydrogen atom.

The calculations predict TS 1 to be more than 2 kcal·mol−1 lower in energy than TS

2. Therefore we mainly expect allene and hydrogen as products. For the dissociation

via TS 1, one would expect loss of the hydrogen atom connected to the central carbon

atom in allyl. We would expect exclusive formation of deuterium in the experiment

with the 2-deuterioallyl radical. On the other hand, the 2-propenyl radical formed by

a 1,2-hydrogen shift can either dissociate to propyne or allene, giving rise to isotopic

scrambling.

The H/D ratio derived from the Doppler profile in figure 6.7 clearly indicates pref-

erential formation of allene via TS 1. If propyne or allene were formed from the

dissociation of the 2-propenyl radical, the probability for hydrogen release would sta-

tistically be four times higher than for deuterium release. Furthermore, the kinetic

isotope effect works in favor of cleavage of the terminal C-H bonds. The isotopic pu-

rity of the radical precursor, 2-deuterioallyl iodide, was determined by 1H-NMR and is

∼ 94%. Hence, a significant fraction of the detected hydrogen atoms is due to isotopic

impurity.


H

H H

HH

H

H H

H

+ H

H H

HH

H

reaction coordinate

59.7

55.458.1

61.8

19.8

0

20

40

60

80

TS 1TS 2

ener

gy /

kcal

mol

-1

TS 3

H

H H

H

+ HTS 4

57.2 55.453.6

H+

H

CH3

Scheme 6.2: Possible reaction pathways for allyl radical unimolecular dissocia-

tion. Given energies are zero-point corrected and are calculated at

CCSD(T)/cc-pVXZ (X = D,T,Q, extrapolated to the basis set limit)

level of theory at CCSD/cc-pVTZ geometries of these stationary points

(see section 8.2 on page 99).

Time-dependence of H/D ratio

Typically, upon increase of the energy of the system, higher lying reaction channels

may open. For this reason, the ratio between deuterium and hydrogen release was

investigated at higher excitation energies. In addition, the unimolecular rate constants

for isomerization via TS 2 and direct dissociation via TS 1 are different. The product

from the faster reaction should therefore be favorably formed at short time delays,

wheres the concentration of the product of the slower reaction should increase with

delay time.

Figure 6.8 on the next page shows the Doppler profiles for 2-deuterioallyl at differ-

ent delay times between the pump and probe laser upon excitation to the A1014 band.

Compared to the Doppler profiles obtained after excitation into the A-state origin,

significantly more hydrogen atoms are formed at the higher energy. The formation


H/D

sig

na

l / arb

. units

8230082290822808227082260

laser energy / cm-1

Δt = 25 ns

Δt = 50 ns

Δt = 75 ns

H : D = 1 : 3.6

H : D = 1 : 3.4

H : D = 1 : 3.7


Figure 6.8: Doppler profiles for 2-deuterioallyl obtained upon excitation into theA1014

band at different time delays between pump and probe laser. The ratio

between hydrogen (♦) and deuterium (◦), ∼ 1 : 3.5, is nearly constant.

6.6 The Direct Hydrogen-Loss Channel 69

of deuterium atoms is still dominant though. The concentration of hydrogen atoms

seems to increase with increasing delay time, visible at ∆t = 50 ns. If the delay time

is further extended, the formation of hydrogen atoms seems to decrease again. This

can easily be explained by the faster movement of the hydrogen atoms out of the probe

laser detection volume, which becomes significant at longer delay times.

6.6 The Direct Hydrogen-Loss Channel

The experimental data we obtained from the afore mentioned spectroscopic studies

clearly indicates that formation of allene following direct abstraction of the central hy-

drogen atom is the major reaction channel. These findings are in good agreement with

the calculated energies of the various stationary points along the reaction pathways.

The principal formation of deuterium atoms upon excitation of the partially deuterated

allyl radical further supports this thesis.

6.6.1 Product Translational Energy

The Unusually High Kinetic Energy Release

From the hydrogen atom Doppler profiles, an expectation value for the translational

energy of 6.2 ± 0.5 kcal·mol−1 upon excitation into the A-state origin was derived.

Assuming allene as the reaction product, 42% of the excess energy of 14.6 kcal·mol−1

would be released as translation. In earlier experiments on allyl C-state, only 23% of

the 59 kcal·mol−1 excess energy were released in translation.[103,104]

For hydrogen loss from unsaturated hydrocarbons, typical translational energy re-

leases between 10% and 25% have been reported.[27, 28,109] Obviously, the kinetic en-

ergy release of this reaction is exceptionally high. Already in the earlier experiments

for dissociation following excitation to the C-state, the kinetic energy release was

higher than predicted by simple statistical models such as the prior distribution ap-

proach[110] or RRKM calculations.[111]

These simple models, however, do not take into account the energy of a reverse

barrier and are thus restricted to reactions with a loose transition state. For the direct

dissociation of allyl to allene and a hydrogen atom, we obtained a reverse barrier of


Reactant

Products

TS

hν

Estat

E

reaction coordinate

Eimp

Eavail

D0

ETS

Scheme 6.3: Diagram illustrating the partitioning of the energy available to products

(Eavail = hν−D0) into the impulsive (Eimp = ETS−D0) and the statistical

reservoir (Estat = Eavail − ETS).

4.3 kcal·mol−1, which clearly indicates that the transition state cannot be considered

loose.

The more recent statistical adiabatic impulsive model[112,113] is suitable for mod-

eling unimolecular dissociations with a reverse barrier. The total energy available to

products (Eavail) is divided into two independent reservoirs as shown in scheme 6.3.

The statistical reservoir (Estat) contains the energy difference between total energy and

zero point energy of the transition state. The impulsive reservoir (Eimp) is defined

as the difference between zero point energies of the transition state and the products,

which is the reverse activation barrier. The model predicts that most of the energy

in the impulsive reservoir (60-80%) goes into translation whereas the product energy

distribution of the statistical reservoir depends on the transition state geometry.

If we assume that 70% of the impulsive reservoir (4.3 kcal·mol−1) goes into trans-

lation, 28% of the statistical reservoir (11.3 kcal·mol−1) must contribute to translation

to get the measured expectation value of 6.2 kcal·mol−1 for the translational energy re-

6.6 The Direct Hydrogen-Loss Channel 71

lease. In the A-state with small excess energy, the reverse barrier has a larger influence

on the kinetic energy release than in the photodissociation at higher excess energy be-

cause the impulsive reservoir is independent of excitation energy, as the energy of this

reservoir is defined by the constant energy of the transition state. The ratio of energy

going from the statistical reservoir into translation is in the typical range obtained for

similar reactions.[27, 28,103,104,109,114]

Product translational energy distribution

Whereas the expectation value of the product translational energy can be derived from

the hydrogen atom Doppler profile straightforward, one is often interested in the the de-

tails of the complete product translational energy distribution. Assuming an isotropic

angular distribution of the hydrogen atom photofragment, we obtained the translational

energy distribution as depicted in figure 6.9 from the Doppler profile.

This experimental distribution can be compared to predictions from statistical mod-

els. Quack suggested the use of an empirical distribution function

P (ET, E) = Cρ(E − ET)EnT , (6.3)

with E being the total available energy to products, ET being the translational energy,

ρ(E − ET) being the rovibrational density of states of the product, C being a normal-

ization constant and an adjustable parameter, 0 < n < 3, to mimic the more detailed

phase space theory and adiabatic channel model behavior.[115] A value of n = 0 cor-

responds to the case of a completely loose transition state with no barrier at all and

where the centrifugal term in the channel potential was omitted altogether. Kinsey has

proposed a distribution with n = 0.5, which corresponds to a microcanonical equi-

librium, if the collision partners are assumed to be enclosed in a box with a classical

translational density of states.[116]

The distributions for different values of n are shown together with the experimental

distribution in figure 6.9. Setting n = 1, the calculated distribution is in best agree-

ment with the experimental data. For comparison, calculated distributions for n = 0.5

and n = 1.5 are provided as well. The value of n, to some extent, is a measure for

the tightness of the transition state as well as for the degree of statistical behavior of

the reaction. A value of n = 1 is still in a range where the reaction can be consid-

ered statistical, however, it indicates a tight transition state and therefore a significant


181614121086420

translational energy / kcal mol-1

P(E

T)

n = 1.5

n = 0.5

Figure 6.9: Comparison of experimental (◦) and calculated (solid) P (ET ) distribu-

tions for allyl radical dissociation with allene and a hydrogen atom as

products. Best fit was achieved with n = 1 (see text). Calculated distribu-

tions for n = 0.5 and n = 1.5 (dashed) are given as well.

reverse activation barrier, which is in good agreement with our experimental and the-

oretical findings. The significant deviation of the experimental data points from the

prior distribution at higher translational energy can be attributed to a broadening of the

Doppler profile by the VUV laser bandwith and, to some minor extent to hydrogen

atoms originating from other photochemical reactions.

6.7 Conclusions

The action spectrum of the allyl radical in the hydrogen atom channel has been mea-

sured in the range of 380-420 nm. The observed vibronic bands correspond to those

6.7 Conclusions 73

obtained in earlier absorption experiments and were assigned with the help of calcu-

lated vibrational frequencies for the A [2B1] electronically excited state.

The diffuse character of the band system and the used linewidth in the rotational

contour simulation are in good agreement with the proposed short lifetime of the A-

state. Whereas we have no experimental information on the primary photochemical

processes leading to hot ground state radicals, the measured kinetics of the hydrogen

atom loss and Doppler profiles suggest that dissociation to the primary photoproducts,

allene and a hydrogen atom, must occur on the ground state surface.

Chapter 7

C [2B1] Allyl RadicalPhotodissociation Dynamics

7.1 Introduction

In contrast to the first electronically excited state, the A-state, the spectroscopy of

the C [2B1] state has been investigated exhaustively. Shortly after Currie and Ram-

say reported their diffuse absorption spectrum around 400 nm,[83] a more intense band

system between 210 and 250 nm was discovered by Callear and Lee in a similar ex-

periment.[87]

This spectral region was further examined in some MPI studies, but the vibronic

bands were not assigned due to the irregular spacings and intensities. Chen and

coworkers were able to assign the complete band system of the close-lying and strongly

coupled B [2A1], C [2B1] and D [2B2] states when they obtained a partially rotation-

ally resolved spectrum in a REMPI experiment of cold allyl radicals prepared by jet

flash pyrolysis.[78–80] The lifetime of these UV-states was determined by time-resolved

photoelectron spectroscopy and was found to be between 15 and 25 ps.[74, 86]

The comprehensive characterization of the C [2B1] state and its strong absorp-

tion cross-section made this electronically excited state an ideal starting point for the

investigation of the photodissociation dynamics of the allyl radical. It has been con-

cluded in two earlier studies made in our group that the allyl radical dissociates on

the ground state surface following fast internal conversion upon excitation from the

C-state and that predominantly allene and a hydrogen atom were formed as reaction

76 C [2B1] Allyl Radical Photodissociation Dynamics

products.[103,104]

The improved sensitivity and a 25-fold increase in signal-to-noise ratio compared

to our earlier experiments enabled us to investigate the C-state photodissociation dy-

namics in more detail. A better temporal resolution of the experiment facilitated the

interpretation and simulation of the hydrogen atom transients, in particular the fast rise

associated with the formation of allene via the direct H-loss channel. An investiga-

tion of the J-dependent dynamics following excitation to the small K ′a subband heads

was feasible due to the increased sensitivity for hydrogen atom detection. This was

of particular interest in respect of recent publications about centrifugal barriers in the

unimolecular dissociation of the allyl radical.[117–119]

7.2 Photofragment Action Spectroscopy

The C-state has a considerably longer lifetime than the A-state and the oscillator

strength associated with the C [2B1] ← X [2A2] transition (fosc = 0.26)[89] is more

than two orders of magnitude higher than that for the A [2B1]← X [2A2] transition.

Thus, a strong allyl ion signal is obtained in a (1+1) REMPI experiment and a scan in

the C00 origin region reveals some rotational structure.

Integration of the hydrogen ion signal for 200 laser shots as a function of excita-

tion laser wavelength led to the action spectrum depicted in figure 7.1. We used the

same detection scheme as in the A-state (scheme 6.1 on page 54) but with different

wavelength of the excitation laser. Due to the faster kinetics of the photodissociation

following C-state excitation, the delay time between pump and probe laser was set

to 50 ns. The (1+1) REMPI spectrum of allyl, recorded simultaneously in the C3H+5

(m/z = 41) mass channel is provided for comparison. For each resonance in the

REMPI spectrum, we find a corresponding resonance in the action spectrum, confirm-

ing that the hydrogen atoms are lost from C-state allyl radical.

For the action experiments, the excitation laser intensity was chosen so that only

a minimal allyl (1+1) REMPI signal could be detected. It was observed in earlier ex-

periments that allyl cations prepared via multiphoton ionization have sufficient excess

energy to release a hydrogen atom. This additional hydrogen source must be sup-

pressed because hydrogen atoms lost from the allyl cation have different energetics

and dynamics and would therefore distort the measurement of allyl C-state dynamics.


REMPI

Action

6

5

78

91011121314

K'a

C 00

40280 40300 40320

laser energy / cm-1

Figure 7.1: REMPI spectrum of allyl and hydrogen atom action spectrum recorded

simultaneously at a time delay of ∆t = 50 ns in the m/z = 41 and

m/z = 1 mass channel. The QP-branch is rotationally resolved in K ′a.

The rovibronic band envelopes in allyl have been analyzed in a previous study.[80]

The allyl radical can be treated as a near-prolate symmetric top with κ ≈ −0.9. The

degree of asymmetry in an asymmetric top is conveniently given by the value of

κ =2Be − Ae − Ce

Ae − Ce, (7.1)

where κ = −1 corresponds to a prolate top and κ = +1 to an oblate top.

A substantial change in the A rotational constant upon electronic excitation leads


to a long series of K-subband heads in the QP branch. The spectra in figure 7.1 show

the QP branch of a type A band with the associated selection rule ∆K = 0. The

subband heads are well resolved for the K ′a quantum numbers up to at least 14. Each

band consists of a number of ∆J transitions that could not be resolved with the lasers

employed in the experiments and which are also subject to lifetime broadening.

7.3 Dynamics

The dynamics of the photodissociation following excitation of the C-state are gov-

erned by the same factors as in the A-state. It will be demonstrated exhaustively that

the dissociation also occurs on the ground state surface of allyl radical, following fast

internal conversion upon excitation to the C-state. The wavelength for excitation into

the C00 origin corresponds to a total energy of 115 kcal·mol−1. The dynamics of com-

peting reaction channels will therefore be more important than in the case of A-state

photodissociation.

7.3.1 H-Atom transient spectroscopy

A previous study of the photodissociation dynamics following excitation to the C-state

on the basis of isotopic labeling experiments concluded that the main reaction channel

remains cleavage of the central C-H bond in allyl, leading to allene and a hydrogen

atom.

H-atom transients were recorded using the same approach described in sec-

tion 6.4.1 on page 60. The time-dependent appearance of hydrogen atoms upon exci-

tation into the C-state origin is shown in figure 7.2. The formation of the product is

roughly two orders of magnitude faster than in A-state photodissociation.

The signal curve has a fast instrument-limited rise up to a time delay of ≈ 6 ns

followed by a slow increase in signal amplitude up to a maximum around ≈ 45 ns

pump-probe delay. The signal curve was fitted using the expression

SH(t) = N(e−kH1t + e−kH2t − e−k1t), (7.2)

which was convoluted with a 6 ns FWHM Gaussian function corresponding to the

cross-correlation of the two laser pulses. SH is the hydrogen atom signal, kH1 and kH2

7.3 Dynamics 79

100806040200


H-a

tom

sig

na

l / a

rb. u

nits

kH2 = 2.29±0.80x107 s

-1

kH1 = 2.67±1.03x109 s

-1

Figure 7.2: Appearance of the hydrogen atom signal as a function of time delay be-

tween excitation and probe laser for initial excitation into the C00 origin.

The solid line represents a bi-exponential fit of the signal rise as explained

in the text. The fit is composed of two mono-exponential functions, drawn

as dashed lines.

are the unimolecular rate constants of the competing reaction channels and k1 accounts

for the decay of the signal at longer delay time due to hydrogen atoms moving out

of the detection volume of the probe laser. The details of the fitting procedure are

explained in appendix B on page 153.

We obtain an experimental rate constant kH1 = 2.67± 1.03× 109 s−1 for the initial

fast rise and a rate constant kH2 = 2.29±0.80×107 s−1 for the slower rise. The fast rate

constant, kH1, can be assigned to the direct hydrogen loss channel, leading to allene as

reaction product. This is the predominant reaction channel inA-state photodissociation

and is also the major reaction pathway at the higher energy in the C-state. The slower

rate constant, kH2, can be associated with a 1,2-hydrogen shift leading to the 2-propenyl

radical and subsequent dissociation to either propyne or allene and a hydrogen atom.


7.3.2 Doppler Spectroscopy and Kinetic Energy Release

For the discussion of product energy distribution, we obtained Doppler profiles by

scanning the probe laser while detecting the total hydrogen atom photofragment flux at

a pump-probe delay of ∆t = 50 ns that corresponds to maximum signal intensity. The

Doppler profile line shapes are independent of the polarization vector of the excitation

laser, which was aligned parallel to the time-of-flight axis, i. e. horizontally, in all the

measurements.

The Doppler profile shown in figure 7.3 is an average of ten individual probe laser

scans. The experimental data points were fitted using a Gaussian function. In contrast

to the profiles obtained following A-state excitation, there is a significant deviation of

the experimental data from the Gaussian fit, in particular in the flat top region. We

hence fitted the data points by a set of orthonormal harmonic oscillator wavefunc-

tions,[120,121] which is more flexible to adapt to different line shapes.

After deconvolution of the VUV laser linewidth of 0.5 cm−1, we obtained a Gaus-

sian FWHM of 3.98 ± 0.05 cm−1. A translational temperature of 4600 K and an

expectation value for the kinetic energy release of 14.0 kcal·mol−1 was derived in the

same fashion as previously described for A-state Doppler profiles (see section 6.4.2 on

page 62). Assuming the formation of allene and a hydrogen atom as the major reaction

products, 23.4% of the 59.8 kcal·mol−1 available energy to products (at 115 kcal·mol−1

total energy) would be released as translation. If propyne were the reaction product,

22.7% of the excess energy of 61.6 kcal·mol−1 would be released as translation.

Both values are in the typical range for hydrogen loss of unsaturated hydrocarbons,

which has been reported between 10% and 25%.[27, 28,109] Apparently, the influence of

the reverse activation barrier on the translational energy distribution is less important

at the higher excess energy.

From the independence of the polarization vector of the excitation laser and the

time scale of the reaction, we can presume an isotropic angular distribution. A long

enough lifetime and complete redistribution of the internal energy prior to dissociation

will lead to isotropic energy distribution and unstructured Doppler profiles that are

peaked in the center and can be approximately described by a Gaussian function. The

flat top in our Doppler profiles, however, may indicate a significant deviation from

a Boltzmann-like distribution of the product translational energy, likely caused by a

7.3 Dynamics 81

6420-2-4-6


FWHM

3.98 ± 0.05 cm-1

H-a

tom

sig

nal / arb

. units

Figure 7.3: Hydrogen atom Doppler profile obtained following excitation to the C-

state origin at 50 ns pump-probe delay. The experimental data is fitted

using a set of orthonormal harmonic oscillator wavefunctions. The dotted

line represents a 3.98 cm−1 FWHM Gaussian fit for comparison.

reverse activation barrier.

Figure 7.4 shows the translational energy distribution of the photoproducts from

C-state dissociation obtained from the fitted Doppler profile. The experimental dis-

tribution is compared to statistical prior distributions (Eq. 6.3 on page 71). We find a

good agreement of the experimental data with the statistical distribution setting n = 1.

This is consistent with the value we obtained from the analysis of the product trans-

lational energy distribution obtained from A-state photodissociation. Presumably, the

observed dissociation proceeds along the same reaction pathway.


6050403020100

translational energy / kcal mol-1

P(E

T)

n = 1.5

n = 0.5

Figure 7.4: Comparison of experimental (◦) and calculated (solid) P (ET ) distribu-

tions for allyl radical dissociation with allene and a hydrogen atom as

products. Best fit was achieved with n = 1 (see text). Calculated distribu-

tions for n = 0.5 and n = 1.5 (dashed) are given as well.

7.4 Centrifugal Effects in Allyl Radical Unimolecular

Dissociation

Whenever there is a change in the moments of inertia between reactant and transi-

tion state, a centrifugal barrier may arise in the reaction channel, affecting the kinetics

and energetics of the reaction. Two recent studies on the photodissociation dynam-

ics of allyl iodide have reported allyl radicals with internal energies well above the

dissociation threshold that did not dissociate within the time frame of the respective

experiment.[117–119] The increased stability of these energized allyl radicals was at least

7.4 Centrifugal Effects in Allyl Radical Unimolecular Dissociation 83

partially attributed to centrifugal effects, namely a centrifugal barrier in the direct hy-

drogen loss reaction channel. The partially rotationally resolved C-state presents an

ideal playground for probing J-dependent dynamics.

7.4.1 Rotational Effects in Unimolecular Dissociation

Rotation affects the unimolecular reaction dynamics in two ways. First, an energy

barrier, i. e. the centrifugal barrier, appears in the exit channel of the dissociation as a

result of the conservation of angular momentum. The rotational energy is not constant

during the course of the reaction because it depends on the moments of inertia of the

molecule and therefore the evolving geometry.

For reactions with a loose transition state, having no reverse activation barrier in

the J = 0 potential energy surface, rotational energy leads to a centrifugal barrier

along the reaction path. The energy of this barrier though tends to be smaller than

the reactant’s rotational energy because it is determined by the moments of inertia at a

large internuclear separation. For reactions with a tight transition state and a significant

reverse activation barrier, the rotational energy in the transition state may be larger or

smaller than the rotational energy in the reactant, thus increasing or decreasing the

activation energy.

Secondly, rotations may be strongly coupled to vibrations, e. g. via Coriolis in-

teractions. In such case, the projection of the principal quantum number J , the K

quantum number in symmetric top molecules, is no longer conserved. Rotational en-

ergy associated with this quantum number gets mixed with the molecule’s vibrational

energy, thereby increasing the density of states.

Dissociation of a diatom

Although the dissociation of a diatom differs from that of a polyatomic molecule in

two important aspects, there are some features that carry over. The reactant’s angular

momentum is completely converted into product orbital momentum, i. e. relative

translational energy, as the product atoms have no angular momentum. Furthermore,

the dissociation has no real barrier and the simple one-dimensional potential can be

expresssed as a Lennard-Jones or Morse potential.

For diatoms, the angular momentum can be expressed in terms of the rotational


p0 = J(J+1) h√

b

p0 = μνrelb

en

erg

y

internuclear distance (r)

Scheme 7.1: The effect of rotational energy on the effective potential of a diatomic

molecule. The centrifugal barrier is related to the impact parameter, b, of

the reverse association reaction. The dissociation of a diatomic molecule

is illustrated in the upper part of the scheme. Molecular angular momen-

tum is converted into orbital angular momentum.

quantum number, J , as p∅ = ~√J(J + 1). During the course of the dissociation, this

angular momentum is converted into orbital angular momentum, p∅ = µ|νrel|b, where b

is the impact parameter of the reverse association reaction. Thus, the highly quantized

angular momentum in the molecule is converted in a nearly continuos quantity. The

effective potential, given by

Veff =p2∅

2µr2+ V (r) (7.3)

is the sum of the centrifugal potential and the real, electronic, potential. Because p∅is a constant of motion, the centrifugal potential is always positive and monotonically

vanishes at large internuclear separation as depicted in scheme 7.1.

The centrifugal barriers for the loss of a hydrogen atom and a CH3 fragment in

ethane can be treated within the diatom approximation.[14] Whereas the reduced mass

associated with methyl loss remains the same at 7.5 u, it wil reduce to about 1 u for H-


atom loss. Because the extent of the centrifugal barrier depends on the reduced mass,

the barriers for H and CH3 loss will be very different. A maximum height of the barrier

of 271 cm−1 was obtained for H-loss, whereas dissociation into two CH3 fragments

only introduced a barrier of about 4 cm−1. It was concluded that H-loss reactions have

centrifugal barriers that are as high as the rotational energy in the molecule, wheras the

loss of a massive particle results in barriers much smaller than the molecular rotational

energy.

Dissociation of a polyatomic molecule

The dissociation of a polyatomic molecule may proceed via a well defined, tight, tran-

sition state with a geometry different from that of the reactant, so that its moments of

inertia may difffer as well. Moreover, the total angular momentum can be conserved

in many different ways as the departing product fragments can rotate themselves. If

the transition state has a real barrier and can be described in terms of vibrational oscil-

lators, i. e. a vibrator transition state, the conservation of angular momentum results

in a much larger rotational barrier than the previously discussed centrifugal barrier in

diatoms.

Many non linear molecules, including the allyl radical, can be treated as a symmet-

ric top, in which two moments of inertia are equal. The moment of inertia about the

symmetry axis is Iz, while the two perpendicular moments of inertia are Ix = Iy. The

molecule is called a prolate top, if Iz < Ix and oblate top, if Iz > Ix. The rotational

energy, expressed in terms of the J and K quantum numbers is given by

Er(J,K) = BJ(J + 1) + (A−B)K2 J = 0, 1, 2, ...

K = 0,±1,±2, ...,±J, (7.4)

where A = ~2/2Iz and B = ~2/2Ix. Obviously, in prolate tops, for which A > B,

the rotational energy increases with K, whereas in oblate tops, for which A < B, the

rotational energy decreases as K increases. If a molecule is a near symmetric top, e.

g. allyl with κ = −0.9, it can be converted to above by replacing Ix by the average of

Ix and Iy.[122]

A prerequisite for the quantification of rotational effects on the activation barrier is

the knowledge of the transition state geometry. As a vibrator transition state is located


en

erg

y

reaction coordinate (R)

Er(products)

Er(J,K)

Er‡(J,K)

E0(J,K)

E0(J = 0)

Scheme 7.2: Potential energy diagram for a dissociation with a saddle point and a tight

transition state. The rotational energy in the transition state (E‡r(J,K))

must not be equal to that in the reactant.

at a saddle point on the potential energy surface, ab initio calculations can determine its

geometry. Once the molecular and transition state moments of inertia are known, the

RRKM rate constant can be expressed in terms of the total energy, E = Ev+Er(J,K)

and the rotational quantum numbers as

k(E, J,K) =W ‡[E − E0 − E‡r(J,K)]

hρ[E − Er(J,K)], (7.5)

where Er and E‡r are obtained from equation 7.4. Note that equation 7.5 only takes

into account the effect of angular momentum on the energetics, rotations are presumed

to be adiabatic.

The effects of rotation on the activation barrier are illustrated in scheme 7.2.

Whether angular momentum raises or lowers the activation energy, E0(J,K), depends

upon the moments of inertia of the molecule and the transition state. If the rotational

constants are approximately the same, typical for tight transition states, the activation

energy remains independent of J . However, for a system near the dissociation thresh-

old and at constant energy, an increase in J lowers the dissociation rate because the


dynamical bottleneck at the transition state is more affected than the density of states

in the reactant.[14] On the other hand, if the transition state has significantly lower

rotational constants than the reactant (loose TS), an increase in J will not affect the

transition state sum of states as much as it does the density of states of the reactant.

The latter will decrease, thus raising the dissociation rate constant.

Equation 7.5 is only applicable to chemical systems in which the J andK quantum

numbers have been resolved and where K is conserved during the reaction. This is

possibly only the case for some small molecules like formaldehyde,[123] but it shall

be later demonstrated that a partial resolution in K can be sufficient to estimate the

boundaries of rotational effects.

7.4.2 Unusual Stability of Highly Rotationally Excited Allyl Radi-cals Towards Dissociation

In a recent publication, Fan and Pratt investigated the dissociation dynamics of allyl

radicals by velocity map imaging.[117] They prepared their radicals via photodissocia-

tion of an allyl iodide precursor at 193 nm. A considerable fraction of radicals with

internal energies well above the dissociation threshold was found, which was stable

towards dissociation within the time frame of the experiment. This supports an earlier

study on the dissociation dynamics of photolytically prepared allyl radicals by Szpunar

et al.[118,119] Both studies attributed the increased stability of these energized allyl rad-

icals at least partially to centrifugal effects, namely to a centrifugal barrier in the direct

hydrogen loss reaction channel.

Szpunar et al. used photofragment translational spectroscopy to disperse vibra-

tionally and rotationally highly energized allyl radicals produced by secondary pho-

tolysis of allyl iodide by their internal energy. They observed a considerable fraction

of allyl radicals with internal energies up to 15 kcal·mol−1 above the calculated reac-

tion barrier that did not dissociate within the time window of their experiment, which

was around 48 µs. They suggested that a centrifugal barrier, characterized by a near-

zero impact parameter for the microscopic reverse H-atom association reaction and a

small reduced mass of the system, would be responsible for the increased stability of

rotationally hot allyl radicals. The conservation of angular momentum along with the

small reduced mass and near-zero impact parameter caused most of the ally radical


angular momentum to be partitioned to allene rotation because the orbital angular mo-

mentum of the allene and hydrogen atom products, |L| = µ|νrel|b, is required to be

small.

In the more recent velocity map imaging study, Fan and Pratt also observed stable

allyl radicals with internal energies higher than the barrier for secondary dissociation.

They concluded however, that the increased stability of these radicals, to a large extent

can be explained as the result of the kinetic shift in the experiment. Nevertheless, they

also argued that a considerable centrifugal barrier may further increase the activation

energy of the reaction albeit they explained in an earlier section in the same publication

that rotation has no effect in dissociations involving H-loss because of an insignificant

change in the moments of inertia between reactant and transition state.

7.4.3 J-Dependent Dynamics in Allyl Radical Unimolecular Disso-ciation

The afore mentioned experiments stimulated us to an experiment on angular-

momentum-dependent photodissociation dynamics of the allyl radical. Although the

spectrum of the C-state as depicted in figure 7.1 on page 77 is not resolved in J , the re-

quirement that J > Ka provides a measure of J-selection in the electronic excitation.

The partially rotationally resolved spectrum in K ′a allowed us to prepare allyl radicals

that, following internal conversion to the electronic ground state, are vibrationally hot

with 115 kcal·mol−1 total energy but with selected low or high angular momentum.

Dissociation dynamics following excitation into different K ′a subband heads inC-state allyl radical

Low-J radicals were prepared by excitation into the large K ′a < 5 subband head. For

the preparation of high-J radicals, we chose excitation into theK ′a = 13 subband head,

because this the highest resolved subband head with an acceptable signal to noise ratio

in the H-atom mass channel.

The time-delayed scans obtained following excitation to the K ′a < 5 and K ′a = 13

subband heads of the C-state origin band are shown in figure 7.5. Both signal

curves are an average of ten individual scans. The experimental data was fitted

with three exponentials given in equation 7.2 on page 78. We obtained a rate con-


140120100806040200-20


Allyl C excitation00

kslow

= 2.75 ± 0.83.107s

-1

kslow

= 2.29 ± 0.80.107s

-1

K’a

=13

K’a

<5

kfast

= 2.14 ± 0.97.109s

-1

kfast

= 2.67± 1.03.109s

-1

Figure 7.5: Time-dependent appearance of the hydrogen atom signal following exci-

tation to the K ′a < 5 and K ′a = 13 subband heads of C-state allyl radical.

stant kH1 = 2.67 ± 1.03 × 109 s−1 for the initial fast rise and a rate constant

kH2 = 2.29 ± 0.80 × 107 s−1 for excitation to the K ′a < 5 subband. The rates for

K ′a = 13, kH1 = 2.14± 0.97× 109 s−1 and kH2 = 2.75± 0.83× 107 s−1 remain essen-

tially unchanged. The differences are much smaller than the experimental errors and

therefore insignificant. It should be noted that the fast rise is at the limit of the temporal

resolution of our experiment. Nevertheless, the short lifetime, even for high-J radicals,

stands in sharp contrast to the conjecture of Szpunar et al.,[119] that these radicals could

be long-lived although our experiment is not completely comparable. They observed

allyl radicals that were stable 48 µs after formation by photodissociation of allyl iodide

and concluded that both the barrier to direct H-loss and the barrier to isomerization are

increased by centrifugal effects. We suggest that centrifugal barriers are not important

in the unimolecular dissociation of allyl radicals at a total energy of 115 kcal·mol−1 as


the measured rate constants do not significantly change between rotationally cold and

warm allyl radicals.

The initial angular momentum in the parent allyl radical will be converted into

angular momentum of the allene photoproduct and orbital angular momentum, |~L| =

µ|~νrel|b. Because both, the reduced mass, µ, of the system and the impact parameter,

b, are small, |~νrel| must increase to form rotationally colder allene products. We would

therefore expect a change in the translational energy release of the hydrogen atom

fragment.

We obtained the Doppler profiles depicted in figure 7.6 following excitation to the

K ′a < 5 and K ′a = 13 subband heads of the C-state allyl radicals. Both Doppler pro-

files have a near Gaussian shape with a fitted FWHM of 3.98± 0.05 cm−1. Since |~νrel|should increase to form rotationally colder allene product, the translational energy dis-

tribution should peak at higher energies for K ′a < 5 excitation than for K ′a = 13.

The Doppler profiles obtained for K ′a < 5 and for K ′a = 13 excitation, however, are

identical.

This observation is consistent with the unchanged dissociation rates and suggests

that centrifugal effects are unimportant for allyl radical unimolecular dissociation at

115 kcal·mol−1. Our angular-momentum-selected experiment finds no discernible dif-

ference between the photodissociation of high and low-J allyl radicals. Although we

cannot exclude that species with J substantially higher than was accessible in this ex-

periment could show different behavior, we consider it unlikely that a centrifugal bar-

rier is the principal explanation for the long-lived radicals reported in the experiments

by Szpunar et al.[118,119] and Fan et al..[117]

Estimation of centrifugal barriers

As discussed in the preceeding section, the influence of angular momentum on the

dissociation dynamics in a polyatomic molecule with a tight transition state depends

on the rotational constants of the molecule and the transition state. The rotational

constants of the allyl radical ground state equilibrium geometry were determined to be

A = 1.801890 cm−1, B = 0.346320 cm−1 and C = 0.290219 cm−1 in several high-

resolution IR spectroscopy experiments.[68–70] As already mentioned, the allyl radical

can be treated as a prolate top with an averaged rotational constant B = (B +C)/2 =

0.318270 cm−1.


quantum numbers rotational energy (cm−1)K J Er(Allyl) Er(TS 1) ∆E0

1 1 2.1 2.3 0.21 3 5.3 5.2 -0.11 5 11.0 10.3 -0.71 10 36.5 33.2 -3.3

4 4 30.1 33.6 3.54 5 33.3 36.5 3.24 7 41.6 43.9 2.44 10 58.7 59.3 0.64 12 73.4 72.5 -0.94 15 100.1 96.5 -3.64 20 157.4 147.9 -9.5

13 13 308.7 346.9 38.213 14 317.6 354.9 37.313 16 337.3 372.6 35.313 20 384.4 414.9 30.513 25 457.6 480.6 23.013 30 546.7 560.6 13.913 40 772.7 763.5 -9.213 50 1062.3 1023.5 -38.8

20 20 727.1 817.9 90.820 30 889.4 963.6 74.220 40 1115.4 1166.5 51.120 60 1758.3 1743.7 -14.620 80 2655.8 2549.5 -106.3

50 50 4520.6 5090.3 569.650 60 4873.9 5407.5 533.550 70 5290.9 5781.8 490.950 100 6923.6 7247.7 324.150 150 10917.9 10833.8 -84.050 200 16503.49 15848.73 -654.75

Table 7.1: Rotational energies of allyl radical equilibrium geometry and transitionstate (TS 1) geometry for given values of the rotational quantum numbersK and J . The change in activation energy, E0, is given in the last column.


-8 -6 -4 -2 0 2 4 6 8


FWHM

3.98 ± 0.05 cm-1

FWHM

3.98 ± 0.05 cm-1

K’a

= 13

K’a

< 5

C0

0

C0

0

Figure 7.6: Doppler profiles obtained following excitation to the C-state K ′a < 5 lev-

els (top) and K ′a = 13 subband head (bottom).

Rotational constants of the transition state for direct loss of a hydrogen atom and

formation of allene (TS 1) were taken from the calculated geometry shown in figure

7.7. It is generally presumed that the loss of a hydrogen atom does not significantly

change the moments of inertia in the transition state because the hydrogen atom is

very light compared to the rest of the molecule. In the case of direct H-loss in allyl,

however, there is a considerable change in the moments of inertia arising from a large


d(CH) = 2.06 Å

d(CC) = 1.32 Å

α(CCC) = 167.1°

δ(HCCC) = 90.0°

Figure 7.7: Cs symmetric ab initio geometry, calculated at the CCSD/cc-pVTZ level

of theory, of the transition state for direct H-loss in allyl radical (TS 1).

increase in the CCC bonding angle and further modification of the molecular geometry.

Values of A = 2.030398 cm−1, B = 0.297417 cm−1 and C = 0.274081 cm−1 result

in an asymmetry parameter, κ = −0.987. Thus, the transition state can be treated as a

prolate top as well, with an averaged rotational constant B = 0.285749 cm−1.

The rotational energies of the allyl radical and the transition state for a large set

of different K and J quantum numbers have been calculated using equation 7.4 on

page 85 and are summarized in table 7.1. It is worth mentioning that for a givenK, the

change in the activation energy,E0, is decreasing with increasing values of J . Whereas

for J = K, the largest increase in activation energy is calculated, values of J � K

lead finally to a decrease in activation energy.

For an estimate of the upper boundary of a centrifugal barrier in C-state photodis-

sociation, we take the lowest value forE0 forK = 4 and the highest value forK = 13,

resulting in a total increase of the activation energy of 47.7 cm−1. We calculate a mi-

crocanonical rate constate at 115 kcal·mol−1 of 0.87 × 109 s−1 using RRKM theory.

The change in activation energy arising from increased angular momentum at K = 13

would only decrease the rate constant by less than 0.01 × 109 s−1, which far smaller

than the temporal resolution of our experiment.

For a comparison with the experiment of Szpunar et al.,[118,119] we may assume that

the 15 kcal·mol−1 internal energy above the barrier is rotational energy. This would be

reflected, e. g., by values of K = 50 and J = 70, leading to an increase in activation

energy of 490 cm−1. Even this though would only decrease an RRKM rate constant of

3.75× 107 s−1 at 75 kcal·mol−1 total energy to 2.36× 107 s−1.

Note that these calculations are only a crude estimate of rotational effects. In par-


ticular the role of an active K-rotor is completely neglected. Nevertheless, it is obvious

from these simple calculations, that a centrifugal barrier in the direct H-loss reaction

channel of the allyl radical can never affect the kinetics of the reaction to an extent as

observed in the experiments by Szpunar et al.[118,119] and Fan et al..[117]

7.5 Conclusions

The unimolecular dissociation dynamics in the allyl radical following excitation to

the C [2B1] state have been extensively investigated. The dissociation rate constants

derived from the measurement of the time-dependent appearance of the H-atom pho-

toproduct are roughly two orders of magnitude higher than in A-state dissociation.

The distribution of the translational energy in the photoproducts was obtained from

the measured Doppler profiles and is in good agreement with statistical prior distribu-

tions. An expectation value of 14 kcal·mol−1 for the kinetic energy release is consistent

with the formation of allene or propyne as photoproducts. Like in A-state photodis-

sociation, both, kinetics and translational energy release suggest a dissociation on the

ground state potential energy surface following fast internal conversion.

In light of recent studies on unusually stable, rotationally warm allyl radicals, we

investigated the angular-momentum-dependent dynamics of allyl C-state photodisso-

ciation. The partially rotationally resolved spectrum allowed the preparation of vibra-

tionally hot ground state radicals in both low and high J-states by excitation to selected

rovibronic bands followed by fast internal conversion. We could not find a discernible

difference in the unimolecular dissociation dynamics of high and low-J radicals in the

angular-momentum-selected experiment though. Thus we conclude that centrifugal

effects are not important in the photodissociation of the allyl radical at 115 kcal·mol−1

total energy.

Although we cannot exclude that radicals with J substantially higher than was

accessible in our experiment could show different behavior, we consider it unlikely

that a centrifugal barrier is the principal explanation for the long-lived population of

highly excited radicals in the experiments with allyl radical produced by allyl iodide

photodissociation by Szpunar et al.[118,119] and Fan et al..[117]

Whereas we can control the amount of initial rotational energy in our allyl radicals,

those prepared by C-I bond fission have an unknown distribution of internal energy

7.5 Conclusions 95

with likely significantly higher amounts of rotational energy. This unusual energy dis-

tribution with a large fraction of rotational energy and thus less vibrational energy is

most likely responsible for the increased stability towards dissociation of the observed

allyl radicals. The increased stability simply arises because there is not enough vi-

brational energy available for dissociation due to conservation of angular momentum,

which cannot be called a centrifugal effect however. To render the argument more

succinctly, the experiments of Fan et al. and Szpunar et al. would yield long-lived

radicals even if there were no change in the rotational constants between reactant and

transition state at all, which is then clearly not due to a centrifugal barrier.

Chapter 8

Statistical Interpretation of theDissociation Dynamics and ab initioCalculations

8.1 Introduction

Experimental data is futile without careful interpretation and discussion. We can ob-

tain dissociation rate constants and the distribution of the translational energy in the

reaction products from our experiments. However, the dissociation of a polyatomic

molecule may proceed via different reaction pathways, leading to various products.

An experienced chemist should be able to figure out potential products and reaction

channels by intuition. With increasing number of atoms in the molecule, the chemistry

is getting more complex though. Several products may be formed, which are close in

energy.

Likely candidates for allyl radical photodissociation reaction products are listed in

scheme 8.1 together with the heats of formation taken from the literature.[124] The for-

mation of allene, propyne and cyclopropene is associated with the loss of a hydrogen

atom. These reactions are enthalpically and entropically favorable reactions because

a closed-shell species is formed and the barriers for the reverse association reaction

between a molecule and an atom, in particular a hydrogen atom, are low. Loss of H2

leads to propargyl and cyclopropenyl radicals. The heat of formation is comparable to

that of the other reaction products, but the loss of a hydrogen molecule is believed to

98 Statistical Interpretation of the Dissociation Dynamics and ab initio Calculations

H H

H H

H

H

H

H

CH3H

HH

H

H H

HH

H H

H

H

H

H

allene

propyne

cyclopropene

propargyl

cyclopropenyl

acetylene

+ H

+ H

+ H

+ H2

+ H2

+ CH3

methyl

+ 57.1 kcal mol-1

+ 56.1 kcal mol-1

+ 78.6 kcal mol-1

+ 42.5 kcal mol-1

+ 64.5 kcal mol-1

+ 49.5 kcal mol-1

Scheme 8.1: Possible reaction products thermochemically accessible at an energy of

115 kcal·mol−1, corresponding to excitation to allyl radical C-state ori-

gin.

proceed via a high activation barrier, and is thus kinetically unfavorable. Sequential

loss of two hydrogen atoms is thermochemically not possible at 115 kcal·mol−1 avail-

able energy. The formation of these products is hence not considered in this study.

Finally, rupture of a C-C bond may lead to acetylene and a methyl radical. This reac-

tion can also be considered kinetically disfavored because two subsequent 1,2-H-shifts

are required before the C-C bond can break.

Allene and propyne, two products formed by loss of a hydrogen atom, are very

close in energy. Which of these two products is preferentially formed in the photodis-

sociation of the allyl radical cannot be predicted on the basis of the heats of formation.

Because the loss of a hydrogen atom in a collision-free gas phase environment can be

regarded as an irreversible process, these reactions are exclusively governed by kinet-

ics, i. e., their respective energies of activation. Obviously, we need information on

the energy and structure of the transition states. The evanescent nature of the transition

8.2 C3H5 Ground State Potential Energy Surface 99

state, passage through the transition state typically occurs on a time-scale of 10−13 to

10−15 s, severely complicates its experimental study, however, indirect spectroscopic

experiments have been reported.[125–127]

The most convenient way to reliable information on the structure and energy of the

transition state are ab initio caculations. DFT and semi-empirical methods are infe-

rior to ab initio methods for the calculation of transition states because these methods

have normally been parametrized with the equilibrium geometries of a representative

set of molecules and are hence not calibrated for the calculation of configurations

far from equilibrium. Rapid development of new theoretical methods to describe the

electronic structure of molecular systems and a dramatic increase in available compu-

tational power in the past few decades enables the calculation of these properties to

high accuracy in a reasonable time.

Information obtained from ab initio caculations can be combined with statistical

rate theories to calculate microcanonical rate constants and product energy distribu-

tions. These data may not only facilitate the interpretation of experimental results,

moreover can a comparison be a test for the validity of statistical rate theories in pho-

todissociation reactions. This chapter adresses the calculation of reaction-critical sta-

tionary points on the C3H5 ground state potential energy surface and the modeling of

allyl radical unimolecular dissociation in the framework of the RRKM theory.

8.2 C3H5 Ground State Potential Energy Surface

The allyl radical is one of the most prominent textbook examples of resonance sta-

bilization in a delocalized π-system. Due to its exceptional stability, the allyl radical

marks the global minimum on the C3H5 potential energy surface (PES). Taking the

allyl radical equilibrium geometry as a starting point, the reaction path towards the

potential products were scanned for transition states.

8.2.1 Ab initio Calculations

The latin term ab initio means ”from the beginning” and refers to a calculation from

first principles, i. e., on the basis of established laws of nature without additional

assumption or empirical corrections. The derivation of electronic structure methods


from quantum mechanics is extensively described in several textbooks[128–130] and is

hence only briefly summarized here.

The Schrodinger equation

The starting point for the description of static properties of a quantum mechanical

system is always the time-independent Schrodinger equation,[131]

Hψ = Eψ, (8.1)

with H being the Hamilton operator, ψ the wave function and E the energy of the sys-

tem. As the electrons move much faster than the nuclei, electron motion is decoupled

from the motion of the nuclei within the Born-Oppenheimer approximation.[132] This

also leads to the concept of a potential energy surface (PES), defined by the electronic

energy as a function of nuclear coordinates.

The molecular Hamiltonian used in electronic structure calculations contains the

kinetic energy of the electrons, Te, electron-electron repulsion, Vee, electron-nuclei

attraction, Vne and the nuclear repulsion energy, Vnn and is given by

H = − ~2

2me

∑i

∇2i +

∑i>j

e2

rij−∑i

∑m

e2Zmrim

+∑m>n

ZmZne2

rmn

= Te + Vee + Vne + Vnn, (8.2)

where Z denotes the nuclear charge, r is the distance between two particles, i and j

run over all electrons and m and n over the nuclei.

Given an initial trial wave function, φ =∑N

i ciϕi, as an expansion in an N-particle

basis set, the variational principle states that the expectation value for the energy,

ε =〈φ|H|φ〉〈φ|φ〉

, (8.3)

will be greater than the energy of the lowest energy eigenstate of the Hamiltonian,

E0, and will become equal if φ is exactly equal to the wave function of the ground

state, ψ0. Albeit there exists no analytical solution of the Schrodinger equation for

systems containing more than one electron, the so-called many electron problem, the

variational principle serves as the starting point for most numerical, iterative methods

in quantum chemistry.


Towards a solution of the many-electron problem

The evaluation of the electron repulsion energy is obviously the critical point because

it depends not on one electron, but instead on all possible (simultaneous) pairwise

interactions. If the molecular Hamiltonian is reduced to the terms for nuclear attraction

and one-electron kinetic energy, the operator is separable, and can be expressed as

H =N∑i=1

hi, (8.4)

where N is the number of electrons and hi is the one-electron Hamiltonian, defined by

hi = − ~2

2me

∇2i −

K∑n=1

e2Znrn

, (8.5)

where K is the total number of nuclei. The many-electron eigenfunctions can be con-

structed as products of the one-electron eigenfunctions,

ψHP = ψ1ψ2 · · ·N, (8.6)

which is called a Hartree-product wave function. Hartree-product wave functions

are fundamentally flawed, however, because they do not satisfy the Pauli exclusion

principle. This requires, that upon interchange of two electrons, the sign of the wave

function must change. Such a wave function is called antisymmetric.

Determinants change sign when any two rows or columns are interchanged. The

utility of this property for use in constructing antisymmetric wave functions was first

exploited by Slater.[133] A Slater determinental wave function is generally given by

ψSD =1√N !

∣∣∣∣∣∣∣∣∣∣∣

χ1(1) χ2(1) · · · χN(1)

χ1(2) χ2(2) · · · χN(2)...

... . . . ...

χ1(N) χ2(N) · · · χN(N)

∣∣∣∣∣∣∣∣∣∣∣, (8.7)

where N is the number of electrons and χi is a spin orbital, i. e., the product of a

spatial orbital, φi(ri), and an electron spin eigenfunction, σi(ωi). The spatial part is

normally expanded in linear combinations of atom-centered one-electron basis func-

tions χα within the LCAO (linear combination of atomic orbitals) approach and given

by

φi(ri) =∑α

cαiχα(ri). (8.8)


The favorable mathematical properties of Gaussian Type Orbitals (GTO) for integral

evaluation, i. e., no cusp condition at the nucleus, makes them the preferred choice for

χα. They are given in cartesian coordinates as

χα(r) = xlyylyzlye−ζr2

, (8.9)

where the sum of lx, ly and lz determines the type of orbital.

This many electron wave function together with the one-electron Hamiltonian leads

to the Hartree-Fock theory. We previously defined a one-electron Hamiltonian ex-

clusively made from one-electron integrals (Equation 8.5) by neglecting the electron

repulsion. Hartree proposed a Hamiltonian,

hi = − ~2

2me

∇2i −

K∑n=1

e2Znrn

+ Vi{j} (8.10)

where the final term represents an interaction potential with all of the other electrons

occupying orbitals {j)} and may be calculated as

Vi{j} =∑j 6=i

∫ρjrijdr, (8.11)

with ρj being the charge probability density associated with electron j. Since ρj =

|ψ|2, but the point of undertaking the calculation is the determination of ψ, an iterative,

self-consistent approach is necessary. Because the electron-electron repulsion is only

accounted for in an average fashion, i. e., the single determinant approximation of the

wave function cannot take into account Coulomb correlation, the Hartree-Fock (HF)

method is often referred to as a Mean Field approximation.

The Hartree-Fock limit, which is in the limit of a complete basis set (infinite num-

ber of basis functions), is not the exact solution of the Schrodinger equation, only

the best single-determinant wave function that can be obtained. The energy is always

above the exact energy and the difference is called the correlation energy.

There is a number of so called post-HF methods to calculate the correlation energy

that can be classified in three general types: (a) configuration interaction (CI) meth-

ods, (b) perturbation theory such as Møller-Plesset (MPn) and Coupled-Cluster (CC)

methods and (c) density functional theory (DFT).


Choice of the methods

The ab initio calculation of relatively large open-shell molecules still poses a consider-

able challenge to computational chemistry. The Slater determinants are given in terms

of spin orbitals (equation 8.7) being the products of a spatial orbital, φi(ri), times a

spin function (α or β). In a closed-shell system with an even number of electrons and

a singlet type of wave function, a restriction that each spatial orbital has two electrons,

one with α and one with β spin is normally made. Such a wave function is know as re-

stricted Hartree-Fock (RHF). If there are no such restrictions on the form of the spatial

orbitals, the trial function is an unrestricted Hartree-Fock (UHF) wave function. In the

case, where only the spatial part of doubly occupied orbitals is forced to be the same,

the wave function is of restricted open-shell Hartree-Fock (ROHF) type.

A severe disadvantage of the UHF description is that the wave function is normally

not an eigenfunction of the S2 operator, where the S2 operator evaluates the value of

the total electron spin squared. As a consequence, spurious higher-lying spin-states

may be mixed in the UHF wave function. This means a singlet UHF wave function

may also contain contributions from triplet, quintet etc. states. This feature is known

as spin contamination and the degree of mixing is determined by the energy difference

between the pure singlet and triplet states. This is of particular importance in disso-

ciation processes, as the energy difference between singlet and triplet states decreases

with increasing bond length and the the singlet and triplet state become degenerate at

large separation.

Schlegel et al. demonstrated, however, that the influence of spin contamination

on the electronic energy is small in coupled cluster calculations.[134] Coupled cluster

theory in conjunction with a large basis set has become somewhat ”gold standard” in

the calculation of moderate size molecules. It even proves somewhat tolerant in cases

where a single-determinant wave function cannot accurately describe an electronic

state, which is important in the allyl radical and for geometries far from equilibrium.

This method was therefore chosen for the geometry optimization of stationary points

and the calculation of the respective electronic energies.

Because the zero-point energy may significantly vary for different molecular ge-

ometries, the computation of vibrational frequencies was also required. Harmonic

frequencies are usually obtained from a normal-mode analysis. If a molecular vibra-


tion is approximated as a harmonic oscillator, the second derivative of the energy with

respect to the internal coordinates corresponds to the force constant. As no analytical

second derivatives are currently available for coupled cluster methods and a numerical

evaluation of a system with a large number of internal degrees of freedom is extremely

time-consuming and not accurate, we used a DFT method for the determination of

vibrational frequencies.

All ab initio calculations were carried out using the MOLPRO[135] and Gaussian[136]

quantum chemistry software packages. Generally, optimized geometries and vibra-

tional frequencies were obtained from Gaussian and electronic energies were calcu-

lated using Molpro. The computations were performed on the linux cluster and the

alpha cluster in our group as well as the Stardust and Pegasus HP Superdome Clusters

(96 INTEL Itanium-2 dual core 1,6 GHz processors, 384 GB RAM) of the central IT

services of ETH Zuerich.

8.2.2 Coupled Cluster Calculations

Coupled cluster theory has emerged to one of the most reliable, yet computationally

affordable methods for the approximate solution of the electronic Schrodinger equation

since its introduction in the late 1960s by Cızek and Paldus.[137–139] In conjunction

with a large basis set, some well elaborated coupled cluster methods including higher

excitations can compute energies with chemical accuracy, i. e., with relative errors< 1

kcal·mol−1. Current research is aimed now at calculating energies with spectroscopic

accuracy, that is better than 1 cm−1.

Theory

Despite the apparent similarity of coupled cluster theory to configuration interaction

(see section 10.3 on page 130), there are some significant differences, which make CC

theory superior to configuration interaction (CI). Whereas perturbation methods add

all types of corrections (S, D, T, etc.) to the reference wave function to a given order

(1, 2, 3, etc.), the idea in CC methods is to include all corrections of a given type to

infinite order.[140] The coupled cluster wave function, written as an exponential ansatz


is given by

ψCC = eTΦ0 (8.12)

and corresponds to the full-CI wave function, i. e., the exact solution within the basis

set approximation. Φ0 is a Slater determinant usually constructed from Hartree-Fock

molecular orbitals and the cluster operator T is defined as

T = T1 + T2 + T3 + · · ·+ TN , (8.13)

N being the number of electrons. The excitation operators can be conveniently ex-

pressed in the formalism of second quantization as

T1 =∑r

∑a

craa†raa

T2 =∑r,s

∑a,b

crsaba†ra†saaab, (8.14)

where a† and a denote the creation and annihilation operators respectively, a and b

stand for occupied orbitals and r and s for unoccupied orbitals.

So far there is no formal difference to the CI method. The beauty of CC theory

becomes apperent once the cluster operator, T, is being truncated. If T = T1 + T2,

i. e., only single and double excitations are considered, the exponential operator from

equation 8.12 can be expanded in a Taylor series such that

eTCCSD = 1 + T1 + (T2 +T2

1

2!) + (T2T1 +

T31

3!) + (

T22

2!+

T2T21

2!+

T41

4!) + · · · (8.15)

CCSD implies coupled cluster theory with single and double-excitation operators.

Note that the first three terms, 1 + T1 + T2, correspond to the CISD method whereas

the remaining terms involve products of excitation operators. The first parenthesis

generates all doubly excited states, which may be considered as connected (T2) or

disconnected (T21). The second parenthesis generates all triply excited states, which

again may be either ”true” (T3) or ”product” triples (T2T1, T31) and the quadruple

excitations arise from the third parenthesis.

The lack of these higher excitation terms in truncated CI makes this method non-

size-extensive. The exponential ansatz in coupled cluster theory, however, ensures size

extensivity. CC theory is often referred to as size-consistent in literature, which is

actually not true and arises from an incorrect distinction of these two terms.


Size consistency and size extensivity

The correct calculation of a dissociation, i. e., the fragmentation of a large system

into two or more smaller sub-systems, requires a size-consistent method. A method

is considered size-consistent if the energy of a system made up of two subsystems A

and B at large separation is equal to the sum of the energies of A and B calculated

separately using the same method.

In the case of a closed-shell system dissociating into two open-shell fragments, A

and B, a restricted Hartree-Fock (RHF) reference function will not be size-consistent

and unrestricted Hartree-Fock (UHF) function will be required for a correct descrip-

tion. This original formulation by Pople et al.[141] is nowadays often extend so that a

method to be size-consistent not only correctly describes the non-interaction fragmen-

tation limit, but the entire dissociation process.

Size extensivity can be considered the analogue of the term extensive for thermo-

dynamic properties and refers to the correct scaling of a method with the number of

electrons in the system. This means that the energy of two molecules at large sepa-

ration with no interaction should be exactly twice the energy of one single molecule.

Moreover does it ensure that the energies of two molecules with different number of

electrons (and atoms), e. g. methanol and ethanol, are meaningful and can be com-

pared to another.[142]

Considerable confusion over the distinction of these terms arose and they are often

mistaken in literature. However it is important to point out, that these terms describe

very different properties, namely the proper scaling of a homogenous system with

size (extensivity) and correct fragmentation of a molecule into its fragments (consis-

tency). Whereas size extensivity is a prerequisite for size consistency, a size-extensive

method need not necessarily be size consistent. In fact, coupled cluster theory is only

size-consistent if the reference wavefunction, usually a restricted Hartree-Fock wave-

function, is size consistent itself.

Extrapolation to the complete basis set limit

Coupled cluster theory has evolved to become the standard approach for high-accuracy

calculations. Since the inclusion of connected triple excitation (vide ante) has been

considered important,[143,144] the CCSD(T) method,[145,146] including perturbative,


non-iterative triple excitation was chosen because it delivers highest accuracy in en-

ergy at yet affordable computational cost. A ROHF wave function has been used as

reference for the evaluation of energies as this was advocated to give a better accuracy

and a more stable wave function by Gauss,[147] however, no significant differences

between ROCCSD(T) and UCCSD(T) energies were found in practice.

The segmentally contracted, correlation-consistent cc-pVXZ basis sets by Dun-

ning and co-workers[148] were chosen because they form a hierarchical sequence of

increasing accuracy that converges uniformly to the complete basis set (CBS) limit. X

denotes the cardinal number of the basis set ,usually given as D, T or Q and refers

to a double, triple or quadruple-ζ basis set. Polarization functions on the carbon and

hydrogen atoms are intrinsically included in the basis set and need not be defined ex-

plicitly.

The extrapolation to the basis set limit was done using the exponential Dunning-

Feller approach[149–151]

E(n) = E∞ + αe−βn, (8.16)

where n denotes the cardinal number of the basis set: n = 2 for double-ζ , n = 3

for triple-ζ etc. E(n) is the energy obtained from the corresponding basis set and E∞is the asymptotic value, which is taken to approximate the CBS limit. Although this

approach has been discussed in literature to overestimate the rate of convergence,[152]

we do not calculate a significant change in energy upon application of different extrap-

olation methods.[153] In particular the relative energies between the various stationary

points remain essentially unchanged.

8.2.3 Anharmonic ab initio frequencies

As already stated afore, the calculation of vibrational frequencies requires the com-

putation of the second derivatives of the electronic energy with respect to the internal

coordinates. Out of the limited set of methods with analytical second derivatives, a

DFT method seemed most promising. The method for calculation of anharmonic fre-

quencies implemented in Gaussian[154] explicitly requires analytical second derivatives

and is therefore restricted to HF, CIS, MP2 and DFT methods.

For a classical trajectory study of ethyl radical dissociation, various ab initio

and DFT methods were screened and the HCTH14@6-31+G**/6-31G** method,


parametrized by Boese et al.,[155] was selected based on a comparison to a training

set of CCSD(T)/cc-pVXZ (X = D,T,Q, extrapolated to the CBS limit) energies

evaluated at the stationary points on the C2H5 surface and some highly distorted ge-

ometries.[156] The energy error relative to the training set was only 1.57 kcal·mol−1

rms. Anharmonic vibrational frequencies have been calculated as well at several sta-

tionary points and a rms error relative to the experiment[124] of 40 cm−1 was found.

In this study, the HCTH147 functional[157] was used with the TZ2P basis set, based

on Dunnings TZ basis set,[158] where polarized functions for hydrogen and carbon

atoms were added manually. The energies obtained at the HCTH147/TZ2P level of

theory were also compared to CCSD(T)/cc-pVXZ energies evaluated at different sta-

tionary points on the C3H5 surface and only minor errors, comparable to those for ethyl

radical were observed. The anharmonic frequencies computed at this level have an rms

error of 30 cm−1 relative to experimental values. Hence it can safely be assumed, that

the C3H5 potential energy surface is well represented by the HCTH147/TZ2P level

of theory in all important regions of phase space. Furthermore, the good agreement

between experimental and calculated vibrational frequencies provides a good basis for

accurate zero-point energies, which further increase the quality of the obtained PES.

8.2.4 Reaction Pathways

The results of the ab initio calculations for all relevant stationary points on the C3H5

potential energy surface are shown in figure 8.1. The geometries of the depicted sta-

tionary points were computed at the UCCSD/cc-pVTZ level of theory. Given energies

are calculated at the ROCCSD(T)/cc-pVXT (X = D,T,Q, extrapolated to the CBS

limit) level of theory and zero-point corrected using anharmonic frequencies obtained

at the HCTH147/TZ2P level of theory. The transition states were verified by calcula-

tion of the intrinsic reaction coordinate (IRC), that connects the transition state to the

reactant and product.

At the 115 kcal·mol−1 available energy in C-state photodissociation, all reaction

channels are in principle open and any product resulting from H-atom abstraction from

allyl radical could be formed. At the lower energy of the A-state, however, formation

of cyclopropene is thermochemically no longer possible.

The lowest activation barrier was computed for the cyclization of allyl to cyclo-


H

HH

HH

HH

HH

+H

H

HH

HH

HHH H

+H

HH

HH

H

3C

H

+H

H

rea ction coordinate

59.7

55.458.1 61.8

19.8

57.2

53.6

77.778.9

32.4

50.3

0 20

40

60 80

120

TS

6

TS

5

TS

1

TS

2

TS

4

energy / kcal mol-1

70 kcal/mol

(A-state)

115 kcal/mol

(C-state)

TS

3

Figure 8.1: Possible reaction pathways for allyl radical unimolecular dissociation.


propyl via TS 5. Unlike the hydrogen abstraction channels, this reaction is reversible

and a fast equilibrium between cyclopropyl and allyl radical can be presumed. Another

reversible isomerization reaction is the formation of the 2-propenyl radical via TS 2.

Starting from 2-propenyl, the barriers for unimolecular dissociation to either allene

(TS 3) or propyne (TS 4) are lower than for the reverse reaction to allyl radical how-

ever. Thus it can be assumed that the isomerization is the rate-determining step and

the subsequent dissociation is fast. The barriers for formation of allene and propyne

from the 2-propenyl radical are very close in energy and it is likely that both products

are formed.

Apart from the fast isomerization from allyl to cyclopropyl, the direct loss of a

hydrogen atom via TS 1 is the reaction channel with the lowest activation barrier.

The preferential loss of the deuterium atom attached to the central carbon atom in an

isotopic labeling is a clear experimental evidence for the dominant role of the direct H-

loss channel. The distribution of translational energy in the products obta0ined from

the Doppler profiles is consistent with the energies calculated for the formation of

allene and a hydrogen atom via TS 1.

Whereas the microcanonical rate constant does not directly depend on the acti-

vation energy of the transition state, but on the density of states of the reactant and

the sum of states of the product, these reaction channels were further investigated in

the framework of statistical rate theories, e. g. RRKM theory. Furthermore, model-

ing of unimolecular dissociations with statistical rate theories give additional insights,

namely about the statistical behavior of the reaction and the applicability of statistical

rate theories such as RRKM in photofragmentation studies of radical dynamics and

kinetics.

The cartesian coordinates and electronic energies of all stationary points on the

C3H5 PES are listed in appendix E.1.1. The anharmonic vibrational frequencies are

provided in appendix E.1.2.

8.3 RRKM Calculations 111

8.3 RRKM Calculations

The theoretical fundament of the RRKM theory has been outlined in section 2.2.1 and

the microcanonical unimolecular rate constant is given by

k(E) =σW ‡(E − E0)

hρ(E), (8.17)

where σ is the reaction path degeneracy, which can be evaluated with two different

approaches. The first one is based on the number of equivalent paths leading from

reactants to the transition state.[159] The second approach requires the evaluation of the

symmetry numbers of the transition state, σ‡, and of the reactant, σr.[160] The reaction

degeneracy is then given in their ratio, i. e.,

σ =σrσ‡. (8.18)

The symmetry number approach corrects for the neglect of symmetry in the partition

functions for the evaluation of the sums and density of states. Formally, the molecular

symmetry group must be incorporated in the calculation of the partition functions,

resulting in the following relationships,[161]

W (E, J,Γm)

W (E, J,Γn)' [Γm]

[Γn], (8.19)

ρ(E, J,Γm)

ρ(E, J,Γn)' [Γm]

[Γn], (8.20)

where Γn and Γm are irreducible representations of dimensions [Γn] and [Γm]. In

practice, however, it is sufficient to calculate W (E, J) and ρ(E, J) and to correct for

the symmetry factor. The symmetry number method must be used with care when

dealing with optically active reactants or transition states.

The symmetry number can be defined as the number of indistinguishable positions

into which a molecule can be turned by simple rigid rotations.[162] Thus, the symmetry

number is associated with the molecular point group and usually corresponds to n of

the n-fold principal symmetry axis in a linear molecule. The symmetry number is 2

for a C2v molecule and 1 for Cs and C1.[163]

The densities and sums of states were calculated by the direct state-count method

using the Beyer-Swineheart algorithm,[164] which was implemented in a FORTRAN

program.


8.3.1 Vibrational Frequencies of the Transition States

For the calculation of reaction rates within the framework of statistical rate theories,

reliable vibrational frequencies of both reactant and transition state are crucial as they

are required for the calculation of both density and sum of states. Whereas vibrational

frequencies for ground state molecules in equilibrium geometry can be calculated in

very high accuracy and are often available from high-resolution spectroscopy measure-

ments, things become intricate at the transition state.

As previously mentioned, we calculated the anharmonic vibrational frequencies

of all stationary points on the C3H5 surface at the HCTH147/TZ2P level of theory as

this functional proved to give reliable energies, geometries and frequencies for such

small hydrocarbon radicals. However, a serious flaw of DFT is self-interaction, the

nonzero interaction of a single electron with its own density, which leads to an artificial

stabilization of delocalized states. This problem is evident in systems with an odd

number of electrons, in particular in the dissociation of cationic radicals, the famous

example being the dissociation of H+2 .[165,166]

The harmonic frequencies of the two most important transition states in the dis-

cussion of the photodissociation in allyl radical (TS 1 and TS 2) were therefore also

obtained at CCSD/cc-pVTZ level of theory. The differences between HCTH147 and

CCSD frequencies were small though, so that the remaining frequencies were obtained

from DFT.

8.3.2 The Different Reaction Paths

The results of the RRKM calculations are summarized in table 8.1. Microcanonical

reaction rates have been calculated at the total energies of allyl A- and C-state photo-

dissociation.

The allyl radical is in a very fast equilibrium with the cyclopropyl radical. These

two species can be transformed into one another by an electrocyclic reaction. How-

ever, thermodynamics (the heat of formation for allyl is 32.4 kcal·mol−1 lower than

that for cyclopropyl) and kinetics (the rate constant of the reverse reaction is three

orders of magnitude faster than that for formation of cyclopropyl) both suggest that

this equilibrium is strongly shifted towards allyl radical. Subsequent H-loss from the

cyclopropyl radical, leading to cyclopropene was not further investigated because the


rate constants / s−1

A-state C-state70 kcal·mol−1 115 kcal·mol−1

TS 1 k1 2.52× 1007 8.50× 1008

TS 2 k2 2.44× 1005 5.62× 1007

TS 2 k−2 6.74× 1006 8.50× 1009

TS 3 k3 3.51× 1008 2.51× 1011

TS 4 k4 2.22× 1009 1.34× 1012

TS 5 k5 3.25× 1007 2.63× 1008

TS 5 k−5 2.32× 1011 3.56× 1012

Table 8.1: RRKM rate constants for the different reaction pathways. Note that the rateconstant of the reverse reaction is also given for reversible reactions.

activation barrier and the heat of formation of the product are so high.

Consequently there remain two primary reaction channels for the allyl radical, di-

rect H-loss leading to allene and isomerization to the 2-propenyl radical. As the iso-

merization to 2-propenyl is reversible, there is a another equilibrium between allyl

and 2-propenyl. The reverse reaction back to allyl is also faster than the formation.

However, 2-propenyl can rapidly dissociate to allene and propyne. These dissociation

reactions are more than two orders of magnitude faster than the reverse reaction. We

can hence assume, that once 2-propenyl is formed, it rapidly dissociates into allene

or propyne and a hydrogen atom. Out of these two possibilities, the calculated rate

constants suggest a preferential formation of propyne.

Finally, the direct formation of allene via TS 1, is between 20.9 (C-state) and

31.4 (A-state) times faster than isomerization to 2-propenyl. We hence conclude that

this is the dominant reaction channel in allyl radical photodissociation dynamics. Our

calculated rate constants correspond well to the experimentally obtained unimolecu-

lar dissociation constants. Furthermore, the experiments with isotopic labeled allyl

radicals revealed a high selectivity for loss of the central hydrogen atom, which is con-

sistent with the formation of allene. This primary photodissociation channel was hence

examined in a bit more detail.


Direct H-loss (TS 1)

The transition state of this reaction pathway was calculated with the the whole ar-

mory quantum chemistry can offer, reaching from coupled cluster methods (CCSD,

CCSD(T)) to multi-reference methods such as CASSCF and MRCI and finally DFT.

Despite the multi-reference character that was computed in the CASSCF and MRCI

calculations, the results obtained from single-reference methods were nearly the same.

Both, energies and geometries were quite consistent with the most significant differ-

ence being the bond length between the central carbon atom and the leaving hydrogen

atom, which is the actual reaction coordinate. This bond length was computed between

1.80 and 2.10 A.

A very precise energy was of great importance because the height of the reverse

reaction barrier is important in the discussion of the kinetic energy release as previ-

ously stated (see sections 7.3.2 on page 80 and 6.6.1 on page 69). Therefore both

geometry and vibrational frequencies for this transition state were computed at the

CCSD/cc-pVTZ level of theory.

Because the dynamics of A-state photodissociation was investigated by excitation

into different vibronic bands and isotopic labeling, the corresponding RRKM rate con-

stants for these experiments have been calculated as well and are listed in table 8.2.

Both increase of the rate constant with increasing excitation energy and kinetic isotope

effect are nicely reflected in the RRKM rate constants.

A barrier of 18 kcal·mol−1 was calculated for rotation of a terminal CH2 group and

a value of 15.7 kcal·mol−1 was measured in an ESR experiment.[167] Therefore, the

associated torsional modes, ν9 (as. CH2 twist) and ν12 (sym. CH2 twist) must be con-

Excited Energy Expt. dissociation rates RRKM rate constants (107 s−1)band (kcal·mol−1) kH(E)a kD(E)a kH(E)b kD(E)b

A00 0 70.0 1.75 1.09 2.52 1.34

A10 7 71.6 3.49 2.04 5.15 2.43

A10 14 73.5 6.58 3.49 9.98 4.39

Table 8.2: Experimental and RRKM rate constants for A-state photodissociation ofhydrogen and deuterium loss obtained at different excitation energies. (a)Obtained from time-dependent appearance of H/D atom signal. (b) RRKMrate constants for direct H-loss channel via TS1.


204060801001201401600.0

0.51.0

1.52.0

2.5

-40

-20

0

20

40

60

80

100

120

140E

ne

rgy / k

ca

l m

ol-1

θ / ° R / amu1/2 Bohr

3

1

1

2

Figure 8.2: Reaction pathway for direct H-loss via TS 1. The intrinsic reaction co-

ordinates starting from allyl radical equilibrium geometry (1) merge at a

valley ridge inflection point (VRI, 2) and proceed to the transition state

(3).

sidered free interal rotors at high excess energies.[168] Whereas the unimolecular rate

constant for A-state photodissociation corresponds well to the RRKM rate constant,

a good agreement between the calculated and experimental rate constants for C-state

dissociation could only be achieved when the frequency of the two afore mentioned

torsional modes were substituted by 80 cm−1. No changes were made to the transition

state frequencies and ab initio calculations found no further indications for hindered

rotors in other C3H5 isomers.

Figure 8.2 shows a scan of the terminal CH2 group rotation along the intrinsic re-

action coordinate for direct dissociation. The calculation of the IRC starting at the

transition state geometry lead to allene and a hydrogen atom on the product side, the

allyl radical as reactant was never reached though. A closer inspection of figure 8.2


Ally

l no

rma

l mo

de

s in

C2

vT

S 1

(ally

l/alle

ne

) mo

de

s in

Cs

Alle

ne

no

rma

l mo

de

s in

D2

d

Sy.

Nr.

Mo

de

aH

m. F

req

. (H

CT

H1

47

/TZ

P)

Sy.

Nr.

Mo

de

sc

al. F

req

. (C

CS

D/c

c-p

VT

Z)

Sy.

Nr.

Mo

de

aH

m. F

req

. (H

CT

H1

47

/TZ

P)

a1

1a

s C

H2 s

tretc

h (in

ph

ase

)3

21

0a

'1

as C

H2 s

tretc

h3

10

7e

1a

s C

H2

stre

tch

31

86

a1

2sy C

H2 s

tretc

h (in

ph

ase

)3

11

32

sy C

H2 s

tretc

h (in

ph

ase

)3

01

0a

19

sy C

H2

stre

tch

(in p

ha

se

)3

111

b2

14

sy C

H2 s

tretc

h (o

ut o

f ph

ase

)3

10

73

sy C

H2 s

tretc

h (o

ut o

f ph

ase

)3

00

5b

21

3sy C

H2

stre

tch

(ou

t of p

ha

se

)3

10

6

b2

17

as C

C s

tretc

h1

21

44

as C

C s

tretc

h1

89

0b

21

4a

s C

C s

tretc

h2

00

5

a1

4sy C

H2 s

cis

14

88

5sy C

H2

scis

14

13

a1

10

sy C

H2

scis

14

52

b2

15

as C

H2 s

cis

14

97

6a

s C

H2

scis

13

73

b2

15

as C

H2

scis

13

98

a1

6sy C

C s

tretc

h1

02

17

sy C

C s

tretc

h1

03

4a

111

sy C

C s

tretc

h1

09

4

a1

5sy C

H2 ro

ck

12

50

8C

H2

rock

97

3e

3C

H2

rock

99

2

b1

11

sy C

H2 w

ag

79

89

CH

2 w

ag

79

5e

5C

H2

wa

g8

39

a1

7C

CC

be

nd

42

111

CC

C b

en

d4

08

e7

CC

C b

en

d3

58

b2

13

as C

H2 s

tretc

h (o

ut o

f ph

ase

)3

20

8a

''1

3a

s C

H2 s

tretc

h3

10

7e

2a

s C

H2

stre

tch

31

86

b2

18

as C

H2 ro

ck

91

91

4C

H2

rock

99

7e

4C

H2

rock

99

2

a2

8a

s C

H2 w

ag

77

41

5C

H2

wa

g8

49

e6

CH

2 w

ag

83

9

a2

9a

s C

H2 tw

ist

53

81

6a

s C

H2

twis

t7

98

b1

12

CH

2 to

rs (tw

ist)

86

7

b1

12

sy C

H2 tw

ist (C

CC

be

nd

)5

20

17

CC

C b

en

d3

62

e8

CC

C b

en

d3

58

a1

3C

H s

tretc

h3

09

6a

'1

2C

H s

tretc

h-9

16

Pro

du

ct fra

gm

en

ts tra

ns

latio

n

b2

16

CH

be

nd

13

99

a'

10

CH

be

nd

51

5P

rod

uc

t frag

me

nts

rota

tion

b1

10

CH

ou

t of p

lan

e b

en

d9

93

a''

18

CH

be

nd

ou

t of p

lan

e1

89

Pro

du

ct fra

gm

en

ts ro

tatio

n

conservation

of yz

symmetry

breaking

Figure 8.3: Asymptotic correlation of TS vibrational modes for unimolecular dissoci-

ation of allyl radical.

8.4 Conclusion 117

reveals the existence of a valley ridge inflection point (VRI, marked as 2) on the re-

action coordinate. The gradient of this torsional mode, which is orthogonal to the

reaction coordinate, is zero at the transition state. The IRC calculation, as imple-

mented in Gaussian, was unable to correctly handle the VRI and continued on top of

the hill, as the gradient of the torsional mode there remains zero. A characteristic of

the VRI, however, is the change of sign of the second derivative, the force constant.

The transition state has Cs symmetry and the VRI is the point were symmetry breaks

on the intrinsic reaction coordinate due to rotation of the terminal CH2 group. The

configuration remains asymmetric until the C2v symmetric allyl radical geometry is

reached eventually. The splitting of the reaction path at the VRI into two equivalent

branches can also be regarded as a representation of the reaction path degeneracy. The

symmetry breaking also becomes apparent upon inspection of the normal modes corre-

lation for this reaction.Figure 8.3 illustrates how the vibrational modes of the reactant

translate into vibrational modes of the transition state and finally into internal and ex-

ternal degrees of freedom of the product. As is to be expected for the dissociation of

a molecule into an atom and a molecule, three internal modes translate into external

degrees of freedom. These modes are often referred to as disappearing modes. The

C-H stretch, which is also the reaction coordinate goes into product translation. The

other two disappearing C-H bend modes translate into product fragment rotation and

thus contribute to the orbital angular momentum.

8.4 Conclusion

This chapter demonstrates how theoretical calculations can be combined with experi-

mental data for an unambiguous and comprehensive discussion of reaction dynamics.

I am well aware of the fact that there exists more elaborated theoretical methods for

the modeling of unimolecular dissociations. However, the treatment with the both

conceptually and practically simple RRKM theory proved to be adequate for the un-

derstanding of allyl radical unimolecular dissociation.

For such a moderate size system, energies with so-called chemical accuracy can be

obtained from suitable ab initio calculations at reasonable cost. The characteristics of

the C3H5 PES obtained from these calculations can nicely explain the reactivity of the

investigated system and may to some extend predict the outcome of the reactions.


The good agreement of experimental unimolecular dissociation rates with micro-

canonical RRKM rate constants is a clear indication that allyl radical photodissocia-

tion can be considered a statistical process, i. e. the time scale of the reaction is slow

enough for a complete redistribution of vibrational energy in the molecule (IVR) fol-

lowing initial excitation. The slight discrepancies between statistical and experimental

rate constants at the higher excess energies in C-state photodissociation can be at-

tributed to insufficient account for internal rotors and anharmonicity in the calculation

of the vibrational density and sum of states.

Chapter 9

Outlook - Photodissociation Dynamicsof Methylallyl Isomers

9.1 Non-statistical effects in hydrocarbon radicals

The photodissociation dynamics of the allyl radical can be neatly rationalized within

the framework of statistical rate theories. There is, however, a rising number of reports

where anomalous behavior in the photodissociation of hydrocarbon radicals has been

observed.[118,119,156,169–173] The effects range from a decrease of reaction rate con-

stants with increasing energy of the system[172] to dissociations occuring many orders

of magnitude slower than predicted by RRKM theory[173] and unusual high stability of

highly energized species.[118,119]

Whereas the unusual stability reported for the secondary dissociation of allyl rad-

icals[118,119] can easily be explained in terms of an unusual initial energy distribution

with large amounts of rotational energy and thus insufficient vibrational energy avail-

able for dissociation (see section 7.4.2 on page 87), the other effects seem to be con-

nected to a general incapability of statistical rate theories for modeling of the photo-

dissociation dynamics of some hydrocarbon radicals.

Unimolecular dissociation of the ethyl radical

The photodissociation dynamics of the ethyl radical have been investigated in our

group using a similar approach as in the study of the allyl radical.[173] Experimental

120 Outlook - Photodissociation Dynamics of Methylallyl Isomers

unimolecular dissociation rates around 107 s−1 were five orders of magnitude slower

than predicted by RRKM theory. Such a large discrepancy can no longer be rational-

ized by insufficient account for anharmonicity and other flaws of the model. A recent

classical trajectory analysis of the dissociation of ethyl radical at 120 kcal·mol−1 on

the ground state surface found a significant fraction of surviving radicals that did not

dissociate within the lifetime predicted by RRKM theory.[156]

Time-frequency analysis found these radicals trapped for extended periods of time

in long-lived quasiperiodic trajectories. The long-lived trajectories were closer in-

spected with the aim of identifying periodic motions within the chaos.[169] It could

be shown that compared to the other trajectories, the long-lived ones exhibit a lower

degree of ergodicity, i. e. the internal energy is less randomized within the internal de-

grees of freedom. Moreover, it was found that the quasiperiodical motions correspond

to a counterrotation of the CH3 and CH2 groups and an associated umbrella mode.

These states were identified as extreme motion states, characterized by containing a

large number of quanta in a single degree of freedom, leading to a vanishingly small

overlap integral with other vibrational states.[174] Brumer and Shapiro explained the

weak coupling of the extreme motion states to other internal degrees of freedom by the

adiabatic separation of fast and slow motions.[175]

Non-RRKM behavior in other hydrocarbon radicals

Along with ethyl, experimental dissociation rates, some orders of magnitude lower

than RRKM rate constants have also been reported for the t-butyl[172] and the 2-

propyl[171] radicals. The photodissociation dynamics of the t-butyl radical can be mod-

eled by RRKM theory up to an excitation energy of 86 kcal·mol−1. Interestingly, at

higher energies, the reaction rate drops by an order of magnitude and the reaction is

not anymore described well by RRKM theory. In the case of the 2-propyl radical, the

dissociation in the experiment is occurring three to four orders of magnitude slower

than predicted by RRKM theory, comparable to the case of ethyl radical photodisso-

ciation.[173]

Whereas the drop of the rate constant at higher energies in the case of the t-

butyl radical was initially attributed to the coupling of the excited electronic state to a

long-lived dark state,[172] recent time-resolved photoionization and photoelectron spec-

troscopy studies do not support this conclusion.[170] It may be concluded though, that

9.2 Methylallyl radical photodissociation 121

another photochemical pathway leads to hot ground state radicals far away from equi-

librium. Similar effects as in the ethyl radical may hamper the rapid redistribution of

vibrational energy and limit the applicability of statistical rate theories.

9.2 Methylallyl radical photodissociation

The numerous examples of non-RRKM behavior observed in the photodissociation

of hydrocarbon radicals may lead to the assumption that a general feature must be

responsible for these effects. Given that the hot ground state radicals were prepared by

photoexcitation in all discussed studies, one has to take into account that there may be

some slow photochemical deactivation pathways and the general assumption of a fast

internal conversion leading to hot ground state radicals must be questioned. However,

the excited states dynamics in these systems have been investigated as well and no

indication for long lived excited states was found.

The other possible explanation is a slow energy randomization in the ground state

associated with a violation of the ergodicity assumption. As ergodicity is central

for statistical rate theories, this may explain their breakdown in the photodissocia-

tion of the afore mentioned species. A common structural feature of all hydrocarbon

radicals exhibiting non-RRKM behavior is the presence of a methyl group. Time-

frequency analysis of ethyl radical dissociation trajectories indicates that the rotation

of the methyl group might be considered as an extreme motion state, where a large

fraction of the internal energy can be trapped due to small coupling to other vibra-

tional modes.

The allyl radical, being a perhaps rare example of statistical behavior in photo-

dissociation dynamics of hydrocarbon radicals can serve as the starting point for a

systematic survey of the influence of a methyl rotor. A methyl group can be at-

tached to a terminal or the central carbon atom in allyl, leading to 1-methylallyl and

2-methylallyl radicals respectively. Some spectroscopic studies for these radicals have

been reported[87, 90,176–178] and the vibronic spectrum of 2-methylallyl around 4.6-5.2

eV has been analyzed.[177] Both isomers absorb strongly in the UV around 250 nm,

thus at energies comparable to C-state allyl radical.

The dominant reaction channel in all so far studied small hydrocarbon radicals is

the abstraction of a hydrogen atom and we can expect similar reactivity for the methy-


H2C

CH3

CH2

H2C C CH2 CH3

H2C

CH2

CH2

H

H2C

CH3

CH

H

CH2

H2CCH3

H2C C CH

CH3

CH3H

H

H

∆Hf = 89.7 kcal mol-1





H

Scheme 9.1: Possible reaction pathways for unimolecular dissociation in 1-

methylallyl and 2-methylallyl radicals.

lallyl radicals hence. Unimolecular dissociation rates should therefore be available

from time-resolved photoionization of the reaction products. Some of the possible

reaction channels thermochemically accessible for both 1- and 2-methylallyl radicals

at 110 kcal·mol−1 are summarized in scheme 9.1. The values for standard heat of

formation relative to 1- and 2-methylallyl respectively are indicated upon availabil-

ity in literature.[124,179,180] In all so far investigated cases, H-atom loss from saturated

and unsatured hydrocarbon radicals does not exhibit a significant reverse barrier (< 6

kcal·mol−1). An activation barrier not much higher than the indicated standard heats

of formation can be expected for these reactions.

The 1-methylallyl radical features the same reactivity as the allyl radical, leading

to the methylated reaction products. Direct loss of the central hydrogen atom leads to

1,2-butadiene (methylallene) and 1,2-H-shift may lead to the 2-butenyl radical, which

9.2 Methylallyl radical photodissociation 123

can subsequently dissociate into 1-butyne or 1,2-butadiene. In the 2-methylallyl rad-

ical, things are different, however. The central hydrogen atom in allyl is now substi-

tuted by a methyl group and thus, the dominant reaction channel in allyl radical is no

longer available. Furthermore, 1,2-H-shift is neither possible for the same reason. One

plausible reaction pathway would be the dissociation into allene and a methyl radi-

cal, although the rupture of a C-C bond is possibly related to a considerable reverse

barrier. The loss of a hydrogen atom from the methyl group leads to formation of

the trimethylenemethane (TMM) biradical species, a particularly stable intermediate

with an interesting electronic structure. Loss of a hydrogen atom in the terminal CH2

groups would lead to a carbene species, which has not yet been described in literature.

The reported (1+1) REMPI spectrum of 2-methylallyl radical[177] could be re-

produced in a preliminary study with an even better resolution. A hydrogen atom

photofragment could be detected and the action spectrum exhibits the same band struc-

ture as the REMPI spectrum. Investigation of the photodissociation dynamics lead to

results, which at first glance appear ambiguous. In particular the kinetic energy release

obtained from the Doppler spectrum of the H-atom photofragment is not consistent

with the formation of the afore discussed products.

To clarify the origin of the observed hydrogen atoms, a detailed study with iso-

topic labeled 2-methylradicals is underway. Detection of deuterium atoms following

excitation of d3-2-methylallyl radical, where all hydrogen atoms in the methyl group

were substituted by deuterium, would be considerable experimental evidence for the

formation of the TMM radical.

Non-RRKM behavior of the photodissociation of the methylated allyl radicals

would be a strong indication for the necessity of a methyl rotor for quasiperiodic-

ity. One should however keep in mind, that the observed non-RRKM behavior in the

photodissociation of the ethyl, 2-propyl and t-butyl radicals may also be attributed to

the inability of RRKM theory to correctly model internal (hindered) rotors. RRKM

rate constants for C-state photodissociation would also be three orders of magnitude

higher than the experimental dissociation rates if the frequencies of the two torsional

modes were not adjusted.

Part III

Excited States Dynamics

Chapter 10

Excited Electronic States of the AllylRadical

10.1 Introduction

Among spectroscopy and chemical dynamics, the allyl radical served as a benchmark

molecule for the development of quantum chemical theories. The first published cal-

culation of excited electronic states of the allyl radical appeared in a series of pa-

pers by Longuet-Higgins, Pople and Dewar about the electronic spectra of aromatic

molecules.[81, 181,182] They obtained excitation energies of 2.74 and 5.29 eV for the

two lowest doublet excited states from some very early configuration interaction (CI)

type of calculations.[81]

A later CI study by Peyerimhoff and Buenker[100] resulted in much higher exci-

tation energies for the two 2B1 states (3.79 and 8.06 eV) whereas Carsky et al.[183]

obtained values of 2.93 and 6.29 eV from their CI calculations.

Levin and Goddard investigated the electronic structure of the allyl radical within

the framework of the generalized valence bond (GVB) theory.[184] The GVB excitation

energies of 3.25 and 4.87 eV were in very good agreement with the results obtained

from their full CI calculations (3.20 and 4.70 eV). Furthermore, they derived a reso-

nance stabilization energy of the allyl radical of 11.40 kcal·mol−1 in the ground state

and 9.42 kcal·mol−1 in the first excited state.

Ha et al. reported the first multireference configuration interaction calculations of

the electronic spectrum of the allyl radical.[88] Using four reference configurations for

128 Excited Electronic States of the Allyl Radical

the 2B1 states, they computed excitation energies of 3.13 and 5.52 eV, which are nearly

in quantitative agreement with the experimental values. They also concluded that all

electronically excited states except the first 2B1 state have considerable Rydberg char-

acter. More studies using multiconfiguration SCF (CASSCF) and valence bond (VB)

methods, for which comparable results were obtained, have been reported.[82, 107,185]

Recently, a study of the first excited state using coupled cluster methods including

triple excitations have been reported by Smith et al.[186] They calculated the vertical

and adiabatic excitation energies at the CC3 and CCSD levels of theory and found no

significant dependence on the basis set, indicating a small Rydberg character of this

state. An adiabatic excitation energy of 3.037 eV obtained at the RO-CC3/cc-pVTZ

level is in quantitative agreement with the experiment.

The second part of this thesis adresses the excited electronic states of the allyl rad-

ical. The electronic structure of the ground and first excited state are discussed in

this chapter as well as the optimized geometry and the harmonic frequencies of the

A-state. The following chapter is dealing with the dynamics of the first excited state in

particular in view of possible electrocyclization to the cyclopropyl radical.

10.2 Electronic Structure of the Allyl Radical

The symmetry of the electronic ground state is C2v with both CC bonds having equal

length, as a consequence of the delocalized π-system. The electronic configuration of

the HF ground state determinant is as follows:

ΦHF = (1a1)2(1b2)2(2a1)2(3a1)2(2b2)2(4a1)2(5a1)2(3b2)2(6a1)2(4b2)2(1b1)2(1a2)1

The first three orbitals are the carbon 1s orbitals which were treated as frozen core

in most calculations. All the other orbitals except the last two are bonding σ-type

orbitals. The most interesting orbitals, however, are the last two, namely the bonding

1b1 π-orbital and the non-bonding 1a2 n-orbital. Together with the lowest unoccupied

orbital, the anti-bonding 2b1 π∗-orbital, they form the π-system of the allyl radical.

Notably, the UHF wavefunction can only recover Cs symmetry for the ground state

due to unphysical spin polarisation. The wavefunction of the allyl radical is even in its

ground state considerably multi-configurational. Electronic configurations describing

10.2 Electronic Structure of the Allyl Radical 129

a2

b1

b1

2A24A2

2B12B1

2B12B1

2A2

a1

b2

1A12A1

2B2

2p (π)

2p (n)

2p (π∗)

3s

2p (σ∗)

X A C B X+

Dspectroscopically

observed states

b2

a1

b1

2B2

3py

3pz

3px

2B1

Scheme 10.1: Electronic configuration of the excited states in allyl radical. The dia-

gram is restricted to the π-system described by Huckel orbitals, the 3s

and 3p Rydberg orbitals and the 2p σ? orbital. Note that except for the

B-state (3s Rydberg) all states are strongly mixed and must be described

as a linear combination of the indicated configurations. The assignment

of a spectroscopically observed state to an electronic configuration must

thus be regarded as zero-order.


several excited electronic states in the allyl radical are summarized in scheme 10.1.

The first seven configurations are composed of single, double and triple excitations

within the Huckel system.

The configurations assigned to theA- and C-states correspond to single excitations

of the ground state configuration and would be degenerate within the Huckel approx-

imation due to the known limitations of the model. A large splitting of the A- and

C-state of 2.5 eV has been predicted in early CI calculations however.[81] Whereas the

multi-reference character of the ground state is relatively small, it is dominant in the

excited states. Both A- and C-state must be described as a linear combination of the

four indicated 2B1 configurations. Only the B-state, formally a 3s Rydberg state, is

of single-determinental character due to the lack of an energetically close lying con-

figuration of the same symmetry. The A-state is the only pure valence excited state,

significant Rydberg character has been calculated in all higher excited states.[88] Thus,

the D-state must be considered as a linear combination of the indicated 2B2 configu-

rations, furthermore the 3px 2B1 configuration can mix with the C-state and and add

some Rydberg character.

10.3 Ab initio Calculations

The principles of ab initio electronic structure calculations have been derived in sec-

tion 8.2.1 on page 99 and are extended here for the treatment of excited electronic

states. All calculations of excited states in this thesis have been performed using

multi-configuration SCF and multi-reference configuration interaction (MRCI) meth-

ods. These methods are thus briefly explained here. The interested reader can find a

comprehensive description and the mathematical details in the literature.[128–130]

10.3.1 Configuration Interaction (CI)

In order to account for dynamical electron correlation, CI uses a variational wave func-

tion, which is a linear combination of Slater determinants,

ψCI = c0ΦHF +∑S

cSΦS +∑D

cDΦD +∑T

cTΦT + · · · =∑i

ciΦi, (10.1)

10.3 Ab initio Calculations 131

where ΦHF is the Slater determinant from a Hartree-Fock calculation. The subscripts

S, D and T indicate Slater determinants that are singly, doubly and triply excited rela-

tive to the HF ground state configuration, the MO’s are taken from the HF-calculation

and held fixed. In CI calculations, Slater determinants are normally replaced by con-

figuration state functions (CSF), which are symmetry adapted linear combinations of

Slater determinants with equal electron configuration but different spin states. The

CI-coefficients, ci, are obtained by diagonalization of the CI-matrix.

The lowest energy eigenvalue of the CI wave function corresponds to the ground

state energy and the other eigenvalues correspond to the energy of the excited states.

Since the CI method is variational, the obtained energy is an upper limit of the exact

energy.

If all possible determinants in a given basis set are included, all the electron corre-

lation (in the given basis set) can be recovered. This so-called full CI leads to an exact

Solution of the non-relativistic Schrodinger equation in the limit of an infinite basis

set and within the Born-Oppenheimer approximation. As the number of CSFs grows

factorially with the size of the basis set, full CI is computationally not feasible but for

the smallest systems. Therefore, the CI wavefunction is usually truncated, i. e., only

CSFs up to a certain degree of excitation are included. Common methods include only

singly excited determinants (CIS) and singly and doubly excited determinants (CISD).

An important drawback of the truncated CI method is, however, that it is no longer

size-extensive, but still variational.

10.3.2 Multi-Reference Methods

In many cases, the HF wave function by itself may be even qualitatively incorrect due

to near-degeneracy effects caused by a strong interaction of low-lying configurations.

The resulting wave function is of multi-reference nature and the effect is termed non-

dynamical electron correlation. Whereas this is often unimportant for closed-shell

molecules close to their equilibrium geometry, the effect may rapidly gain importance

for open-shell systems, excited states and bond dissociation processes. In these cases,

the electronic state cannot be represented by a single determinental wave function and

a so called multi-configuration description is necessary.


Multi-Configuration SCF (MCSCF)

The MCSCF method can be considered as a configuration interaction, where not only

the CI-coefficients in front of the determinants are optimized variationally, but also the

MOs used for the construction of the determinants. Thus, the MCSCF wave function

can be written as a truncated CI expansion,

ψMCSCF =∑i

ciΦi, (10.2)

in which both the CI expansion coefficients and the orthonormal orbitals contained in

Φi are optimized.

Note that MCSCF is not suitable for the calculation of the correlation energy be-

cause the orbital relaxation does not recover much of the correlation energy. This can

more efficiently be done by inclusion of additional determinants and keeping the MOs

fixed (CI). Since the CSFs entering an MCSCF expansion are pure spin states, MCSCF

wave functions do not suffer from spin contamination.

The most popular approach is the complete active space self-consistent field

method (CASSCF). The orbitals are divided into active and inactive orbitals, where

inactive orbitals are always unoccupied or doubly occupied. Within the active orbitals,

a full CI is performed and all the proper symmetry adapted configurations are included

in the MCSCF optimization. The major difficulty with MCSCF methods is the se-

lection of the necessary orbitals and electrons to include in the active space to model

the properties of interest. Such calculations are normally noted as [n,m] CASSCF,

indicating that n electrons are distributed among m orbitals in all possible ways.

Multi-Reference Configuration Interaction (MRCI)

The CI methods previously discussed only consider excitations from a single reference

(usually HF) determinant. However, an MCSCF wave function can also be chosen

as the reference, so that excitations out of all determinants included in the MCSCF

wavefunction must be considered. Compared to single reference CI, the number of

configurations is increased by a factor equal to the number of configurations included

in the MCSCF wave function.

Even a truncation of the MRCI expansion at the singles and doubles level generates

so many configurations, that only small systems can be handled computationally. The


lack of size extensitivity in CI is resolved by a posteriori Davidson correction,

∆EDavidson = (EMRCI − E0)(1− c20), (10.3)

where E0 denotes the energy of the reference wave function and c20 is the weight of the

relaxed reference wave function in the final CI expansion.[187]

10.3.3 Choice of the Active Space

As already mentioned, the right choice of the active space is crucial for multi-reference

calculations. The necessity of including the π-system of the allyl radical (1b1, 1a2,

2b1), corresponding to a [3,3] CASSCF, can readily be derived from chemical intuition.

It is generally considered reasonable to include the HOMO and LUMO in the active

space in nearly any MCSCF calculation.

To make sure that no other important configurations contributing to the multi-

configurational wave function are dismissed, a so-called full valence active space cal-

culation was performed. All 17 valence electrons were distributed among 15 orbitals,

leading to 32’207’175 configuration state functions in the full CI calculation. A desir-

able [17,17] active space was not feasible because the number of CSFs was simply too

large to be handled by the program.

It was found that the ground state at equilibrium geometry can be accu-

rately described by a wave function composed of two 2A2 configurations, namely

0.955[(1b1)2(1a2)1(2b1)0] and 0.044[(1b1)0(1a2)1(2b1)2]. All other configurations con-

tribute less than 0.1% to the wave function and can thus easily be neglected. The fact

that the ground state wave function is to 95.5% composed of one configuration, which

corresponds to the ROHF wave function, justifies the calculation of the ground state

PES with single-reference methods. An analysis of the transition state geometry with a

large [7,7] active space revealed, however, that the multi-reference character increases

away from the equilibrium geometry.

Since the A-state can be described by excitations of the 2A2 ground state CSF to

some of the 2B1 configurations depicted in scheme 10.1, the same [3,3] active space

should also account for the multi-reference character in the first excited state. The

calculation of higher excited states requires significantly larger active spaces.


10.4 Results of the Calculations

10.4.1 Geometry of the A 2B1 State

The equilibrium geometry of the A-state was calculated using the CASSCF method

since this was the only method, where analytical gradients and second derivatives were

available. Preliminary studies, starting the geometry optimization from the ground

stateC2v geometry, lead to a stationary point with an imaginary frequency in a torsional

mode corresponding to the asymmetric twisting of the terminal CH2 groups, indicating

a non-planar equilibrium geometry.

Thus, the start geometry was slightly distorted by a conrotatory rotation of the

terminal CH2 groups out of plane by 5◦ with an associated symmetry reduction to C2.

A geometry optimization starting from this distorted geometry lead to a true minimum

on the A-state PES with no more imaginary frequencies. The obtained C2 symmetric

minimum geometry is depicted in figure 10.1

d(CC) = 1.47 Å

α(CCC) = 123.3°

δ(HCCC) = 42.6°

Figure 10.1: Allyl A-state C2-symmetric equilibrium geometry obtained at the

CASSCF[3,3]/6-311+G(3df,3pd) level of theory.

The most significant changes in geometry compared to the ground state are the

non-planar structure with the terminal CH2 groups rotated out of plane by a dihedral

angle of 43◦ and the lengthening of the CC bonds from 1.39 A in the ground state

to 1.47 A. The remaining internal coordinates remain essentially unchanged. Both

lengthening of the CC bond and the out of plane twisting of the CH2 groups can be

explained by the promotion of electrons from the bonding π-orbital to the non-bonding

n and anti-bonding π∗-orbital.

10.4 Results of the Calculations 135

10.4.2 Vibrational Frequencies in the A 2B1 State

The harmonic vibrational frequencies were calculated at the same level of theory as

the geometry optimization. Several different triple-zeta basis sets were applied (cc-

pVTZ, aug-cc-pVTZ, 6-311G(3df,3pd), 6-311G+(3df,3pd), 6-311++G(3df,3pd)), but

no significant differences were observed. Since the addition of diffuse functions had

no influence on the frequencies (as well as the energy and the geometry), we conclude

that theA-state has no significant Rydberg character, which is in agreement with earlier

studies.

The obtained frequencies are listed in appendix E.2.2. Frequency scaling factors

around 0.91 were obtained by linear regression to experimental frequencies obtained

from the action spectrum. The scaled harmonic frequencies are listed together with the

experimental frequencies in table 6.1 on page 58.

10.4.3 Adiabatic Excitation Energy of the A 2B1 State

The calculation of the geometry of a molecule is generally much less sensitive to the

level of theory than the energy. Since the geometry optimization requires convergence

of an SCF and the calculation of the first derivatives in every optimization step, it is

common to calculate the geometry at a lower level of theory than the energy.

We calculated the adiabatic excitation energy of the A [2B1]← X [2A2] transition

at the MRCI/cc-pVXZ (X = D,T,Q, extrapolated to the CBS limit) level of theory

at the CASSCF/6-311+G(3df,3pd) geometry of the A state and the CCSD/cc-pVTZ

geometry of the ground state.

The anharmonic HCTH147/VTZ2P frequencies of the ground state and the

CASSCF/6-311+G(3df,3pd) frequencies of the excited state were taken for zero-point

energy correction. Since the effect of anharmonicity is less severe for the zero-point

energy, the scaling factors were adjusted as xZPE = (1 + xfund)/2, which seems com-

monly accepted in the literature.[154]

We obtained an adiabatic excitation energy of 3.043 eV, which is in quantitative

agreement with the experiment and also corresponds to the value obtained from the

coupled cluster calculations.[186] Although the combination of so many different theo-

retical methods (MRCI, CASSCF, CCSD, HCTH147) seems not very consistent, their

application is justified because one is only interested in the relative energy between the


two states. The essential point is that the electronic energy of the two different states

is calculated with exactly the same method. All frequencies and energies used for this

calculation are listed in appendix E.2.

10.4.4 Vertical Excitation Energies of Higher Excited States

Within the scope of this work, the vertical excitation energies of higher lying electronic

states have been calculated at the MRCI/cc-p-VTZ level of theory and are summarized

in table 10.1. The energies obtained for the 1 2A1 and the 1 2B1 states correspond very

well to the experiment. Since both of them are the lowest lying states in the given

symmetry and thus correspond to the lowest energy eigenvalue, it is no surprise that

one obtains the best results for these states.

State El. Energy Vert. Excitation Spectroscopic Transition(Hartree) Energy (eV) State

1 2A2 -116.89 0.00 X1 2A1 -116.71 4.91 B (n, 3s)2 2A1 -116.69 5.49 (n, 3pz)1 2B1 -116.77 3.14 A (π, n)2 2B1 -116.65 6.56 (n, π∗ / n, 3dxy)3 2B1 -116.63 7.09 (n, 3px)1 2B2 -116.68 5.61 (n, 3py)

Table 10.1: Vertical excitation energies of several electronic states in the allyl radical.

The other calculated states, however, cannot be assigned to a spectroscopic state.

In particular the higher lying 2B1 states strongly interfere with another and the MCSCF

and MRCI calculations only converged upon including all these states in a state aver-

aged calculation. Certainly, these higher lying states request a closer investigation, but

we were mainly concerned about the A-state.

10.5 Conclusion

We could calculate the geometry and the vibrational frequencies of A-state allyl rad-

ical. The obtained C2 symmetric equilibrium geometry confirms the experimental

findings, namely the lower symmetry in the excited state that was deduced from the

10.5 Conclusion 137

rotational contour analysis. The calculated frequencies correspond well to the experi-

mental frequencies and the vibronic band system could be assigned.

A combination of these geometry optimization and frequency calculations with

some state of the art multi-reference configuration interaction (MRCI) calculations

resulted in an adiabatic excitation energy of 3.043 eV, which is in excellent agreement

with the experiment.

Chapter 11

Electrocyclic Reactions

11.1 Introduction

In 1965, Woodward and Hoffmann introduced the concept of conservation of orbital

symmetry in electrocyclic reactions.[188] They demonstrated the application of their

rules, nowadays known to every chemist as the Woodward-Hoffmann rules, with sev-

eral examples, among them the transformation of the allyl radical to the cyclopropyl

radical, being the smallest possible system to study this type of reaction. Based on their

frontier orbitals approach, they predicted a conrotatory cyclization to be thermally al-

lowed, i. e. in the ground state.

In the same year, however, Longuett-Higgins et al. demonstrated that the right

outcome of this reaction cannot be predicted only by consideration of the HOMO of

the reactant.[189] They could show that the ground state of each radical is correlated to

an excited state of the other in both conrotatory and disrotatory electrocyclization.

Ever since, this simplest of all electrocyclization reactions gave rise to specula-

tion.[83, 100,101] Given the fact that both reactant and product are transient species, ex-

perimental evidence is very rare. It was assumed that the diffuse character of the

A-state in the allyl radical could be attributed to fast excited state cyclization to the

cyclopropyl radical. Ab initio calculations on the ground state surface predict a bar-

rier to cyclization of 50.3 kcal·mol−1 and 17.9 kcal·mol−1 for the reverse reaction,

the ring-opening of the cyclopropyl radical. The dynamics of this reaction have been

investigated by Mann and Hase in an ab initio quasi-classical trajectories simulation

on the ground state PES using a CASSCF[3,3]/6-31G(d) potential and a slight prefer-

140 Electrocyclic Reactions

ence (57%) for disrotatory ring-opening was found.[190] A similar study using a DFT

potential in a He and Ar condensed phase came to the same result.[191]

The only experimental evidence for formation of cyclopropyl radical in the excited

state was found upon irradiation of allyl radicals in an argon matrix[65] and in some

ESR experiments of silica-surface bound allyl radicals.[66]

11.2 Allyl-Cyclopropyl Interconversion

11.2.1 Experimental Evidence

Holtzhauer et al. investigated the photochemistry of the allyl radical around 410 nm

in an argon matrix.[65] When they compared IR spectra of the matrix-trapped radicals

before and after irradiation at 410 nm, they observed that IR bands assigned to the allyl

radical decreased in intensity and new bands were formed.

Since no experimental IR frequencies of the cyclopropyl radical were available,

they calculated the vibrational frequencies at the UHF/6-31G* level of theory. Upon

scaling the ab initio frequencies they could indeed find an agreement and assigned

the newly formed IR bands to cyclopropyl radical. Since the error of UHF frequency

calculations is quite large and the vibrational frequencies of the allyl radical are not

much different, we recalculated the cyclopropyl radical frequencies at a higher level of

theory. They are listed together with the the calculated and experimental frequencies

of Holtzhauer et al. in table 11.1. The experimental frequencies of the allyl radical

are added for comparison. Obviously, the IR bands assigned to the cyclopropyl radical

correspond well to the calculated UCCSD frequencies. However, for most modes,

the frequency in the allyl radical is not much different. Only the frequencies of the

ν9, ν15 and ν18 differ significantly from the allyl radical frequencies. Nevertheless, a

substancial fraction of the initial allyl radicals was transformed to new species upon

irradiation at 410 nm and it is quite likely that the cyclopropyl radical is among them.

During our studies on the A-state photodissociation dynamics of the allyl radical,

we made several control experiments to assure the origin of the observed hydrogen

atoms. Therefore we irradiated potential photochemical reaction products, including

allene, propyne and the cyclopropyl radical, at 400 nm and checked if they would lose

a hydrogen atom. Whereas we found no hydrogen for allene and propyne, irradiation

11.2 Allyl-Cyclopropyl Interconversion 141

Experimentala UCCSD UHFa Allylb

frequency cc-pVTZ 6-31*G expt.a’ ν1 3118 3086 3032 3114

ν2 3045 3052 2998 3052ν3 2980 2975 2930 3027ν4 1440 1431 1464 1478ν5 1237 1203 1192 1242ν6 1077 1068 1109 1068ν7 997 997 1040 983ν8 825 823 828 802ν9 743 743 761 522ν10 n/a 571 627 443

a” ν11 3033 3041 2986 3111ν12 2965 2971 2925 3020ν13 1416 1399 1428 1463ν14 1229 1121 1145 1389ν15 1037 1048 1064 1182ν16 997 1028 1076 913ν17 n/a 898 897 775ν18 777 746 754 547

Table 11.1: Experimental and scaled ab initio vibrational frequencies (cm−1) of thecyclopropyl radical. a) UHF and experimental frequencies were takenfrom Ref. 65. b) Experimental frequencies of allyl radical are listed forcomparison, they were taken from Ref. 68–70

of the cyclopropyl radical, generated pyrolytically from cyclopropyl bromide, lead

to H-atoms with kinetics and translational energy distributions comparable to those

originating from allyl A-state photodissociation. Furthermore, we recorded a REMPI

spectrum of the cyclopropyl radical around 248 nm (C-state origin of the allyl radical)

in the m/z = 41 channel and obtained exactly the same band contour as for C-state

allyl radical. We conclude that the cyclopropyl radicals generated by C-Br bond fission

immediately ring-open to the allyl radical. The sharp bands in the REMPI spectrum

indicate cold radicals, thus it must be assumed that the ring-opening occured in the

pyrolysis tube prior to ultrasonic expansion.

Apparently, these two radicals can readily be converted into one another, both pho-

tochemically and thermally. However, due to the fact that both radicals have the same


mass, it is nearly impossible to gain direct experimental evidence for the formation

of cyclopropyl from A-state allyl in photofragment spectroscopical studies. Thus, we

focus on the theoretical treatment of this reaction.

11.2.2 State Correlation

Following Longuet-Higgins state correlation scheme,[189] the first excited state of the

allyl radicals correlates to the ground state of the cyclopropyl radical in both conro-

tatory and disrotatory ring closing. In a zero-order description, the photocyclization

of the allyl radical to cyclopropyl radical can be considered a purely adiabatic reac-

tion which proceeds from the excited state surface of the allyl radical all the way to

the ground state surface of the cyclopropyl radical. Such a situation can never occur

in a closed-shell molecule, where the ground state is always totally symmetric. Any

excited state molecule would need to undergo an avoided crossing or photophysical

relaxation process to return to the ground state surface.

C2 conrotatory Cs disrotatory

B

B

B

B

A

A

A'

A' A'

A'A''

A''

Scheme 11.1: Orbital correlation diagram for conrotatory and disrotatory electro-

cyclic interconversion of cyclopropyl and allyl radical.

The orbital correlation diagram in scheme 11.1 illustrates, how the π-orbitals of

the allyl radical translate into the σ-orbitals of the cyclopropyl radical. Obviously,

the ground state configuration of the allyl radical (π2n) correlates to an excited state

configuration of the cyclopropyl radical for conrotatory and disrotatory ring closure.

11.2 Allyl-Cyclopropyl Interconversion 143

This diagram also reveals, why the exclusive consideration of the HOMO (respectively

SOMO) by Woodward and Hoffmann lead to the wrong conclusion, that the reaction

would be thermally allowed in a conrotatory fashion for the allyl radical and anion.

H

H H

H H

H

H H

HH

H

H H

H H

C conrotatory2 C disrotatorys

A (nπ*2) A’’

B (ππ*2) A’

B (n2π*) A’

B (π2π*) A’

B (πn2) A’

A (π2n) A’’

(nσ*2) B

(σσ*2) A

(n2σ*) B

(σ2σ*) B

(σn2) A

(σ2n) B

A’ (nσ*2)

A’ (σσ*2)

A’’ (n2σ*)

A’’ (σ2σ*)

A’ (σn2)

A’ (σ2n)

Scheme 11.2: State correlation diagram for conrotatory and disrotatory electrocyclic

interconversion of cyclopropyl and allyl radical. Note that only Huckel-

type valence excited states are considered.

The state correlation diagram depicted in scheme 11.2 can be derived from the

orbital correlations. This diagram, however, is restricted to excited states, represented

by a singly determinantal electron configuration. The calculations in the preceeding

chapter clearly demonstrate that this does not hold true for the case of the allyl radical

since all excited states except for the B-state are of considerable multi-configurational

character. Nevertheless, some qualitative conclusions can be drawn from this diagram.

Note that both diagrams presume that the cyclopropyl radical has a C2v symmetry

although it is only Cs in fact. The next section seeks to confirm the results of the state

and orbital correlation diagrams by ab initio calculations.


11.3 Ab initio Calculations

11.3.1 Conrotatory Ring-Closing of the A-state Allyl Radical

If we assume that an electrocyclic reaction proceeds in a concerted manner, we can

reduce the reaction coordinate to two internal coordinates. Upon cyclization, the CCC

bond angle is reduced from 121◦ in the allyl radical to 63◦ in the cyclopropyl radical.

Furthermore, the terminal CH2 groups are rotated by 90◦.

Figure 11.1 shows scans of the dihedral angle ϕ of the terminal CH2 groups at

different CCC bond angles. The energy of the 2A state at a CCC bond angle of 120◦ and

a dihedral angle of 0◦ corresponds to to that of allyl radical ground state. The 2B energy

2A

2B

CCC bond angle (α)

80°

100°

120°

dihedral angle (ϕ) / °

rela

tive

en

erg

y / e

V

HH

H

H

H

ϕα

2

4

6

8

0

Figure 11.1: Scan of the HCCC dihedral angle at different CCC bond angles. The

dihedral angle corresponds to a conrotatory twisting of the terminal CH2

groups.


at a CCC bond angle of 80◦ and a dihedral of 90◦ is close to that of cyclopropyl radical

ground state. The internal coordinates were chosen so that the molecule retained its C2

symmetry in all configurations, which allowed a distinction of the different electronic

states by symmetry.

Apparently, the energy of the 2B state at a dihedral angle of 90◦ is lowered with

a decreasing CCC bond angle. The A 2B1 state of the allyl radical smoothly converts

into the X 2B ground state of the cyclopropyl radical upon rotation of the terminal

CH2 groups by 90◦ and lowering of the CCC bond angle. The ab initio calculations do

not indicate a significant barrier of more than 1.0 kcal·mol−1. Notably, the ground and

excited states cross, giving rise to conical intersections and thus fast decay to the allyl

radical ground state surface without formation of the cyclopropyl radical.

rela

tive

en

erg

y / e

V

CCCH dihedral angle / °

CCC bond angle 80° 120°

20 40 60 80 100 120 140 160 18020 40 60 80 100 120 140 160 180

0

2

4

6

8

10

12

2A

2B

3s, 3pz

Figure 11.2: Scan of the HCCC dihedral angle at different CCC bond angles. Some

of the higher lying electronic states are included as well.

Figure 11.2 shows scan of the same angles as before, but now some higher lying

excited states are also included. At a CCC bond angle of 120◦, the Rydberg states show

a similar energetic dependence upon change of the dihedral angle like the ground state.

The two 2B states exhibit similar behavior, since both are π-valence excited states.

At the lower CCC bond angle of 80◦, however, the energy of the Rydberg states is

decreasing around a dihedral angle of 90◦ and there seems to be an avoided crossing


between the 3s 2A Rydberg state and the X 2A ground state.

11.3.2 2A2-2B1 Conical Intersections

The performed scans of the excited states indicate the presence of conical intersec-

tions. We performed geometry optimizations leading to the minimum geometries of

the conical intersections depicted in figure 11.3.

1

23

4

5

r( ) = 1.45 Å( C ) = 108.7°(C C C H ) = 56.2°

C CC C

1 2

1 2 3

2 3 4

a

d 1

r( ) = 1.44 Å( C ) = 97.8°(C C C H ) = 63.9°

C CC C

1 2

1 2 3

2 3 4

a

d 1

C2

Cs

1

23

4

4

1

23

(a)

(b)

Figure 11.3: Geometries at the conical intersections between the A-state and ground

state, located using the SA-CASSCF[3,3]/6-311G+(3df,3pd) method.1

The C2 geometry (a) is 1.1 kcal·mol−1 higher and the Cs geometry (b) is

3.8 kcal·mol−1 lower in energy than the A-state equilibrium geometry.

It should be mentioned that the C2 symmetric minimum energy conical intersec-

tion and the A-state equilibrium geometry are both chiral, and that there are two

enantiomeric conformations with the terminal CH2 groups simply twisted the other

way round. The two conical intersections were located when the geometry was held

in the respective symmetry (Cs and C2 as indicated) and the terminal CH2 groups

were rotated conrotatory (C2) or disrotatory (Cs). Dynamic correlation included at the1The conical intersections were calculated using the state-averaged (SA) CASSCF method. (Ref.

192) Both, the A-state and the ground state were included in the multiconifigurational wavefunction

with equal weight and optimized simultaneously.

11.4 Conclusions and Outlook 147

MRCI/CBS level of theory leads to a∼ 3 kcal·mol−1 decrease in the minimum energy

conical intersections relative to the A-state equilibrium geometry. These values should

be considered with care, as one would expect different geometries of the minimum

energy conical intersections at the MRCI level of theory. This is also reflected in the

0.5 kcal·mol−1 energy difference of the upper and lower state.

11.3.3 Photochemical Deactivation Pathways

The observed short lifetime of the A-state may be explained in terms of the flat charac-

ter of the potential energy surface along several internal coordinates, in particular the

CH2 twist motion. The three conical intersections of the A-state and the ground state

and the possibility of electrocyclic conversion to the cyclopropyl radical give rise to

various mechanism for non-radiative decay. A-state allyl radicals must thus not nec-

essarly transform to the cyclopropyl radical but may also directly return to the allyl

radical ground state via the mentioned conical intersections.

The scans depicted in figure 11.2 also indicate the existence of an accidental coni-

cal intersection between the A-state and the 3s Rydberg state. Yarkony and coworkers

located three-state conical intersections between the spectroscopically observed, ener-

getically close lying B, C and D states.[193,194] This does certainly not simplify the

nature of the primary photophysical and photochemical processes upon excitation to

the C-state, but clearly offers a distinct radiationless deactivation pathway, back to the

ground state.

11.4 Conclusions and Outlook

11.4.1 Primary Photophysical and Photochemical Processes in theAllyl Radical

The possibility of an electrocyclic reaction of the A-state allyl radical leading to the

ground state cyclopropyl radical is theoretically rationalized. The ab initio calculations

confirm Longuett-Higgins earlier predictions based on a simple state correlation dia-

gram. While there is little experimental evidence for the formation of the cyclopropyl

radical upon excitation of the allyl radical to the A-state, this mechanism can explain


the diffuse character of the spectrum, which is associated with a short-lifetime of the

excited state.

An adiabatic reaction from the A 2B allyl radical to the X 2B cyclopropyl radical

is in principle possible, but the existence of conical intersections of the 2B1 and the2A2 states in allyl radical also give rise to a direct deactivation of the A-state, leading

to ground state allyl radicals. The dynamics following excitation to the A-state can

be classified as vibrational predissociation (Herzberg type II)[13] if the reaction is adi-

abatic, leading to the cyclopropyl radical ground state. Upon change of the electronic

state via a conical intersection, leading to the allyl radical ground state, however, such

a process would rather be classified as an electronic predissociation (Herzberg type I).

11.4.2 Excited State Direct Dynamics and Surface Hopping

No quantitative predictions on the ratio between deactivation to the ground state via

conical intersections and cyclization to the cyclopropyl of the A-state allyl radical

can be made based on the calculations in this chapter. The calculated energies of

several excited states along the reaction coordinate from allyl to cyclopropyl radical

showed that none of the Rydberg states is coming lower than 5 eV. The dynamics of

the photochemical deactivation of the A-state radical can thus be treated as a two state

problem.

A simulation of these dynamics using so called ”surface-hopping” methods, e. g.

Tully’s fewest switches,[195–197] may provide more information. In particular the ques-

tion about the preference for conrotatory or disrotatory photochemical electrocycliza-

tion could finally be answered.

Part IV

Appendix

Appendix A

Synthesis of Deuterated Precursors

A.1 General Methods

All reactions were carried out in oven dried glassware under an atmosphere of argon.

For the reactions, chemicals were purified according to standard procedures, Et2O was

distilled over Na. All chemicals were purchased from FLUKA, ACROS, LANCASTER

and LT BAKER.

TLC was performed on MERCK 60 F254 TLC glass plates and visualized with UV

light or permanent stain. 1H-NMR spectra were recoreded on a VARIAN Mercury 300

MHz or a Gemini 300 MHz spectrometer in 1-D-chloroform (CDCl3). All signals are

reported in ppm with the internal chloroform signal at 7.26 ppm as standard. 13C-NMR

spectra were recorded with 1H-decoupling on a VARIAN Mercury 75 MHz spectrom-

eter in CDCl3. Signals are reported in ppm with the internal chloroform signal at 77.0

ppm as standard.

152 Synthesis of Deuterated Precursors

A.2 2-D-Allyl alcohol

OH

D

A solution of propargyl alcohol (13.8 ml, 239.0 mmol) in Et2O (80 ml) was slowly

added to a suspension of LiAlD4 (12.0 g, 285.8 mmol) in Et2O (520 ml) at 0 ◦C. The

suspension was stirred for 64 h at 34 ◦C (reflux). Then it was cooled to 10 ◦C and water

(30 ml) was added. The precipitate was filtered and washed with Et2O. The solvent

was removed by fractionated distillation. 2-D-allyl alcohol was yielded as colorless

liquid (6.32 g, 45 %). The isotopic purity was determined by 1H-NMR and found to

be ca. 94 %.

Rf 0.11 (MtB/n-Hexane, 1:4). 1H-NMR (300 MHz, CDCl3): δ 5.25 (s, 1H), 5.12

(s, 1H), 4.11 (br. s, 2 H), 2.17 (br. s, OH). 13C-NMR (75 MHz, CDCl3): δ 137.2,

114.9, 63.7. ESI-MS (m/z): calculated for [M-H]+ 58.048, found 58.039.

A.3 2-D-Allyl iodide

I

D

2-D-allyl alcohol (1.74 ml, 42.3 mmol) was added to a mixture of triphenylphos-

phite (8.5 ml, 43.6 mmol) and MeI (3.92 mmol, 42.3 mmol) at 20 ◦C. The solution

was stirred at 80 ◦C (reflux) for 28 h. Residual MeI was removed by distillation at 34◦C and 100 mbar. 2-allyl iodide was distilled at 34 ◦C and 20 mbar and condensed in a

liquid nitrogen-cooled cold trap. 2-D-allyl iodide was yielded as yellow liquid (827.9

mg, 13 %).

Rf 0.31 (MtB/n-Hexane, 1:4). 1H-NMR (300 MHz, CDCl3): δ 5.24 (br. s, 1H),

4.97 (s, 1H), 3.86 (s, 2 H). 13C-NMR (75 MHz, CDCl3): δ 117.8, 15.3, 5.7. ESI-MS(m/z): calculated for [M-H]+ 168.982, found 168.950.

Appendix B

Curve Fitting of Transients andDoppler Profiles

B.1 Hydrogen Atom Transients

The measured time-dependent appearance of the hydrogen atoms is a convolution of

the exponential rise with the instrument response function. In our experiments, the in-

strument response function is the cross-correlation of the pulse and probe laser, which

can be described by a 6 ns FWHM gaussian function.

The integrated rate laws of these first order reactions are given by

SH(t) = N(e−kH1t + e−kH2t − e−k1t) (C-state), (B.1)

SH(t) = N(e−kHt − e−k1t) (A-state), (B.2)

as described in sections 6.4.1 on page 60 and 7.3.1 on page 78. The instrument re-

sponse function can be expressed as a unit sigma Gaussian probability distribution:

R(x) =1

σ√

2πe−

x2

2σ2 . (B.3)

The measured signal can be expressed as a sum of the convolution of each exponen-

tial term in equations B.1 or B.2 and the gaussian probability distribution (eq. B.3)

resulting in

S(t) = N(F (t, kH1) + F (t, kH2)− F (t, k1)), (B.4)

154 Curve Fitting of Transients and Doppler Profiles

where the convolution of the exponential and the gaussian distribution, F (t, k), is given

by

F (t) = e−kt+σ2 (1/k)2

2 ·G(t

σ− σ

k

), (B.5)

with

G(x) =1− Γp(0.5, 0.5x

2)

2for x < 0

G(x) =1 + Γp(0.5, 0.5x

2)

2for x > 0, (B.6)

where Γp is the incomplete gamma function. The optimized fitting parameter k corre-

sponds directly to the associated microcanonical rate constant.

H-a

tom

sig

na

l / arb

. un

its

120x10-9

100806040200-20

pump-probe delay / s

Coefficient values ± one standard deviation k = 836.74 ± 4.25

a1 = 2.6727e+09 ± 4.88e+06 a2 = 2.2853e+07 ± 6.5e+05 a3 = 3.59e+06 ± 0 sigma = 3e-09 ± 0

fit_avg_4= convoluted_exponential_gauss(W_coef,x) Res_avg_4= avg_4 - (convoluted_exponential_gauss(W_coef,timex)) W_coef={-836.74,-437.11,2.6727e+09,2.2053e+07,3.59e+06,3e-09} V_chisq= 5514.75; V_npnts= 128; V_numNaNs= 0; V_numINFs= 0; W_sigma={4.25,4.58,4.88e+06,6.5e+05,0,0}

average (scan0 - scan20)

KH,1 = 2.67 ± 1.03 x 107 s

-1

KH,2 = 2.29 ± 0.80 x 107 s

-1

residuals

error band

Usually, at least ten individual H-atom transients are fitted individually and the

mean of the obtained fitting parameters is taken as unimolecular rate constants.

B.2 Doppler Profiles 155

B.2 Doppler Profiles

-4 -2 0 2 4

Doppler shift / cm-1

Tsukiyama et al. have demonstrated that the natural spectral linewidth due to life-

time broadening is negligible compared to the thermal Doppler broadening of the

2 2P1/2 ← 1 2S1/2 and 2 2P3/2 ← 1 2S1/2 transitions in atomic hydrogen (Ref. 28).

The signal can be represented as a superposition of two gaussians at the absorption

wavelengths of 82258.9206 cm−1 and 82259.2865 cm−1 for the respective transitions

with a relative intensity of 1:2.

f(ν) =1

2

√β

πe−β(ν−82258.9206)2 +

√β

πe−β(ν−82259.2865)2 (B.7)

The linewidth of the VUV laser, given by the following gaussian,

g(ν) =

√α

πe−αν

2

, (B.8)

leads to a further broadening of the signal. The measured signal, F (ν), can be ex-

pressed as a convolution of equation B.7 and equation B.8:

F (ν) =

∫ ∞−∞

g(ν − ν ′)f(ν)dν ′. (B.9)

This integral can be analytically solved and the solution is the fitting function for

the Doppler profiles:

F (ν) =

√αβπ√

α + β

[1

2eαβ(ν−82258.9206)2

α+β + eαβ(ν−82259.2865)2

α+β

]. (B.10)

156 Curve Fitting of Transients and Doppler Profiles

In the case of a gaussian profile, the parameter α can be derived from the FWHM,

∆νL, of the laser:

α =1

∆νL2

ln 2. (B.11)

Finally, the FWHM of the Doppler profile of the hydrogen atom, ∆νFWHM, can be

calculated from the fitting parameter β:

∆νFWHM = 2

√1

βln 2, (B.12)

Appendix C

Power Normalization of ActionSpectra

The action spectra obtained by measuring the total flux of hydrogen atoms as a function

of excitation laser wavelength must be power normalized because the laser intensity

varies significantly over the whole scan range.

laser wavelength / nm

sig

na

l in

ten

sity / a

rb. u

nits

The figure above shows the measured action spectrum (solid gray line), the power

normalized action spectrum (solid black line) and the laser tuning curve (dashed line).

158 Power Normalization of Action Spectra

The laser intensity was measured for the corresponding wavelength range with a stan-

dard power meter and the data points were fitted to a fifth order polynomial. The power

normalized spectrum was then simply obtained by dividing the measured spectrum by

the fitted tuning curve. The individual spectra, each obtained with a different laser dye,

were finally put together to the complete survey scan.

Appendix D

Parameters for RRKM Calculations

Erel Eavail / kcal·mol−1 Eavail / cm−1 ρ(E) / cm

(kcal·mol−1) A-state C-state A-state C-state A-state C-state

Allyl 0 70 115.2 24483 40292 1.64E+30 4.10E+34

Cyclopropyl 32.4 37.6 82.8 13151 28960 9.33E+26 4.38E+30

2-Propenyl 19.8 50.2 95.4 17558 33367 1.20E+29 1.95E+32

TS1 59.7 10.3 55.5 3602 19411

TS2 61.8 8.2 53.4 2868 18677

TS3 58.1 11.9 57.1 4162 19971

TS4 57.2 12.8 58 4477 20286

TS5 50.3 19.7 64.9 6890 22699

σ sum of states kH kH

A-state C-state A-state C-state

TS1 2 5.54E+04 1.67E+10 2.52E+07 8.50E+08

TS2 2 5.37E+02 1.10E+09 2.44E+05 5.62E+07

TS2r 1 5.37E+02 1.10E+09 6.74E+06 8.50E+09

TS3 1 2.80E+04 3.26E+10 3.51E+08 2.51E+11

TS4 1 1.77E+05 1.74E+11 2.22E+09 1.34E+12

TS5 2 7.16E+04 5.16E+09 3.25E+07 2.63E+08

TS5r 2 7.16E+04 5.16E+09 2.32E+11 3.56E+12

Parameters used for the calculation of RRKM rate constants at the total energy of

allyl radical A-state and C-state. σ is the reaction path degeneracy, ρ(E) the density

of states and r indicates the reverse reaction.

160 Parameters for RRKM Calculations

Appendix E

Results of ab initio Calculations

E.1 C3H5 PES Ground State Calculations

All geometries were calculated at the UCCSD/cc-pVTZ level of theory and optimized

using tight conditions. Transition state geometries were optimized using additional

HF force constants. Anharmonic frequencies were calculated at the HCTH147/VTZ2P

level of theory unless stated otherwise. Both geometries and frequencies were calcu-

lated using the Gaussian 03 software package. (Ref. 136)

The electronic energies were calculated at the ROCCSD(T) level of theory for the

given geometries using Dunning’s hierarchy of correlation consistent basis sets: cc-

pVDZ, cc-pVTZ, and cc-pVQZ. All energy evaluations were performed using the

MOLPRO software package. (Ref. 135)

Energies at the complete basis set limit were estimated using the exponential Dunning-

Feller extrapolation:

E(n) = E∞ + αe−βn

162 Results of ab initio Calculations

E.1.1 Energies and Geometries

Allyl radical (C2v symmetry)

atomic coordinates / A

number x y z

6 .000000 .000000 .453087

6 .000000 1.236422 -.199983

6 .000000 -1.236422 -.199983

1 .000000 1.292722 -1.295402

1 .000000 .000000 1.552138

1 .000000 2.176963 .359971

1 .000000 -1.292722 -1.295402

1 .000000 -2.176963 .359971

Rotational constants (cm−1): 1.619, 0.314, 0.217

CCSD(T) energies / Hartree

cc-pVDZ: -116.91324984

cc-pVTZ: -117.03153584

cc-pVQZ: -117.06495454

CBS (est.): -117.07811400

ZPE corr: 0.064523300

2-Propenyl radical (Cs symmetry)


number x y z

6 .000000 .431550 .000000

6 -1.198336 -.453558 .000000

6 1.322938 .292246 .000000

1 -.890376 -1.519907 .000000

1 -1.823253 -.274053 .892916

1 -1.823253 -.274053 -.892916

1 1.999855 1.155741 .000000

1 1.789413 -.709157 .000000


E.1 C3H5 PES Ground State Calculations 163


cc-pVDZ: -116.88228932

cc-pVTZ: -116.99982427

cc-pVQZ: -117.03307264

CBS (est.): -117.04618810

ZPE corr: 0.064268000

Cyclopropyl radical (C2v symmetry)


number x y z

6 .029817 .902096 .000000

6 .029817 -.369614 .770597

6 .029817 -.369614 -.770597

1 -.686726 1.728456 .000000

1 -.884614 -.667188 1.301169

1 -.884614 -.667188 -1.301169

1 .959628 -.685641 1.261381

1 .959628 -.685641 -1.261381



cc-pVDZ: -116.86721303

cc-pVTZ: -116.98596647

cc-pVQZ: -117.01931718

CBS (est.): -117.02690080

ZPE corr: 0.064989540


Allene (D2d symmetry)


number x y z

6 .000000 .000000 1.324407

6 .000000 .000000 .000000

6 .000000 .000000 -1.324407

1 .000000 .940059 1.888582

1 .000000 -.940059 1.888582

1 .940059 .000000 -1.888582

1 -.940059 .000000 -1.888582



cc-pVDZ: -116.31664325

cc-pVTZ: -116.43288182

cc-pVQZ: -116.46584230

CBS (est.): -116.47888770

ZPE corr: 0.053691600

Propyne (C3v symmetry)


number x y z

6 .000000 .000000 1.442312

6 .000000 .000000 .219068

6 .000000 .000000 -1.257982

1 .000000 .000000 2.519482

1 .000000 1.032697 -1.646624

1 .894342 -.516349 -1.646624

1 -.894342 -.516349 -1.646624



cc-pVDZ: -116.31746385

cc-pVTZ: -116.43470447

cc-pVQZ: -116.46785976

CBS (est.): -116.48093310

ZPE corr: 0.052707700


Cyclopropene (C2v symmetry)


number x y z

6 .689171 -.529137 6 .000000

6 -.799772 -.213801 6 .000000

6 .000000 .827856 .000000

1 1.166492 -.895617 .923437

1 1.166492 -.895617 -.923437

1 -1.807690 -.626427 .000000

1 .138313 1.908147 .000000



cc-pVDZ: -116.28090425

cc-pVTZ: -116.39728206

cc-pVQZ: -116.43046485

CBS (est.): -116.44370000

ZPE corr: 0.053923590

TS 1 (allyl→ allene + H) (Cs symmetry)


number x y z

6 0.000000 0.056305 0.000000

1 0.167286 1.969457 0.000000

6 -1.324096 0.000108 0.000000

6 1.303416 -0.261715 0.000000

1 -1.949570 0.896642 0.000000

1 -1.818706 -0.979504 0.000000

1 1.862535 -0.327392 0.940515

1 1.862535 -0.327392 -0.940500




cc-pVDZ: -116.80594811

cc-pVTZ: -116.92463326

cc-pVQZ: -116.95827402

CBS (est.): -116.97158120

ZPE corr: 0.053067648

TS 2 (allyl→ 2-propenyl) (C1 symmetry)


number x y z

6 -1.292335 0.146356 0.009413

6 0.070060 -0.327066 -0.095371

6 1.334536 0.114380 -0.000649

1 -0.823230 -0.987078 0.585110

1 -1.557523 1.022434 0.621142

1 -2.036262 -0.246441 -0.692523

1 1.576873 1.161723 -0.244930

1 2.166576 -0.552656 0.250840



cc-pVDZ: -116.80353561

cc-pVTZ: -116.92372383

cc-pVQZ: -116.95759195

CBS (est.): -116.97088030

ZPE corr: 0.054917520


TS 3 (2-propenyl→ allene + H) (Cs symmetry)


number x y z

6 0.000000 0.148337 0.000000

6 -1.062158 -0.665021 0.000000

6 1.117854 0.849184 0.000000

1 -0.380704 -2.479781 0.000000

1 -1.575750 -0.904345 0.937866

1 -1.575750 -0.904345 -0.937866

1 1.103319 1.945661 0.000000

1 2.094708 0.347805 0.000000



cc-pVDZ: -116.80878104

cc-pVTZ: -116.92753249

cc-pVQZ: -116.96112485

CBS (est.): -116.97437590

ZPE corr: 0.053393426

TS 4 (2-propenyl→ propyne + H) (C2v symmetry)


number x y z

6 0.000000 0.205934 0.000000

6 1.002284 0.926692 0.000000

6 -1.040821 -0.839023 0.000000

1 2.532283 -0.217369 0.000000

1 1.635351 1.800771 0.000000

1 -1.680324 -0.751869 0.894867

1 -1.680324 -0.751869 -0.894867

1 -0.575761 -1.841279 0.000000




cc-pVDZ: -116.80931712

cc-pVTZ: -116.92865334

cc-pVQZ: -116.96235276

CBS (est.): -116.97561400

ZPE corr: 0.053112072

TS 5 (allyl→ cyclopropyl) (C1 symmetry)


number x y z

6 0.078923 0.707383 -0.246773

6 0.970402 -0.334311 0.037541

6 -1.049056 -0.206742 0.064597

1 0.179883 1.697879 0.210243

1 1.777871 -0.266875 0.787864

1 0.934312 -1.267596 -0.537761

1 -1.422932 -0.930990 -0.668463

1 -1.470749 -0.230401 1.075921



cc-pVDZ: -116.82729431

cc-pVTZ: -116.94675083

cc-pVQZ: -116.98034966

CBS (est.): -116.99341146

ZPE corr: 0.059919238


TS 6 (cyclopropyl→ cyclopropene + H) (C1 symmetry)


number x y z

6 0.855186 -0.270718 0.001220

6 -0.174401 0.837139 0.093907

6 -0.645622 -0.348601 -0.264358

1 1.563154 -0.269246 -0.843511

1 1.253117 -0.731468 0.918910

1 -0.348225 1.894619 0.287518

1 -1.436131 -0.913580 -0.755850

1 -1.242889 -1.287247 1.408321



cc-pVDZ: -116.77504094

cc-pVTZ: -116.89376634

cc-pVQZ: -116.92751929

CBS (est.): -116.94092998

ZPE corr: 0.053148523


E.1.2 Anharmonic Frequencies of Stationary Points on the C3H5

PES

Anharmonic frequencies were calculated by second order perturbative treatment of an-

harmonic effects using effective finite difference evaluations of third and semidiagonal

fourth derivatives. (Ref. 154)

C3H5 isomers and products

anharmonic frequencies / cm−1

allyl 2-propenyl cyclopropyl allene propyne cyclopropene

3105 2979 3071 3007 3329 3159

3031 2882 2993 1416 2913 3122

3021 2882 2940 1081 2141 3047

1450 2816 1409 868 1360 1675

1220 1681 1230 2998 926 1468

991 1391 1057 1980 2963 1089

427 1354 959 1366 2934 1030

789 1323 821 3065 1402 979

536 1045 731 3065 1479 886

976 899 452 981 1033 764

806 865 2982 981 1016 2951

531 285 2941 840 614 1083

3103 2904 1391 840 608 978

3026 1393 1108 366 343 823

1438 988 1033 366 332 587

1375 856 1006

1193 457 903

912 132 756


Transition states

anharmonic frequencies / cm−1

TS 1 TS 2 TS 3 TS 4 TS 5 TS 6

3104 3077 3080 3330 3110 3168

3012 3073 3021 2984 3080 3127

2995 2932 2994 2854 3016 2947

1896 2904 1943 2105 2971 2952

1408 2107 1408 1392 2927 1633

1362 1628 1362 1342 1443 1456

1064 1388 1066 988 1396 1107

979 1368 974 925 1297 1069

768 1084 888 651 1239 1032

447 1050 374 302 1071 980

414 984 211 195 994 971

3051 943 3148 2908 879 880

985 805 926 1413 875 616

855 801 869 995 715 735

814 655 829 621 597 12

374 389 355 334 609 265

50 299 67 27 551 178

-658 -1765 -427 -457 -903 -517


E.2 Allyl Radical Excited States Calculations

E.2.1 Energies and Geometries of Selected Points

Allyl radical A state equilibrium geometry (C2)


number x y z

6 0 0 0.513175

6 0 1.268989 -0.201252

6 0 -1.268989 -0.201252

1 0 0 1.587233

1 0.464516 1.32996 -1.166598

1 -0.727013 2.022556 0.040967

1 -0.464516 -1.32996 -1.166598

1 0.727013 -2.022556 0.040967

MRCI energies / Hartree

cc-pVDZ: -116.7455417

cc-pVTZ: -116.846988

cc-pVQZ: -116.875254

CBS(est.): -116.886171

A/X conical intersection (C2)


number x y z

6 0 0 0.622739

6 0 1.181953 -0.225158

6 0 -1.181953 -0.225158

1 0 0 1.693407

1 0.783975 1.292737 -0.951707

1 -0.908202 1.729153 -0.412263

1 -0.783975 -1.292737 -0.951707

1 0.908202 -1.729153 -0.412263

E.2 Allyl Radical Excited States Calculations 173


cc-pVDZ: -116.7475766

cc-pVTZ: -116.8488215

cc-pVQZ: -116.8770755

CBS(est.): -116.8880123

A/X conical intersection (Cs)


number x y z

6 -0.033814 0.696634 0

6 -0.033814 -0.253291 1.089818

6 -0.033814 -0.253291 -1.089818

1 -0.86473 -0.915249 1.229171

1 0.66747 1.508978 0

1 0.835316 -0.409396 1.700422

1 -0.86473 -0.915249 -1.229171

1 0.835316 -0.409396 -1.700422


cc-pVDZ: -116.7543095

cc-pVTZ: -116.8569792

cc-pVQZ: -116.8857061

CBS(est.): -116.8968665

Allyl radical ground state equilibrium geometry (C2v)


number x y z

6 .000000 .000000 .453087

6 .000000 1.236422 -.199983

6 .000000 -1.236422 -.199983

1 .000000 1.292722 -1.295402

1 .000000 .000000 1.552138

1 .000000 2.176963 .359971

1 .000000 -1.292722 -1.295402

1 .000000 -2.176963 .359971



cc-pVDZ: -116.8599566

cc-pVTZ: -116.9607401

cc-pVQZ: -116.9894626

CBS(est.): -117.000911

E.2.2 Vibrational Frequencies of the A-stateVibrational frequencies / cm−1

CASSCF(3,3) CASSCF(3,3)6-311+G(3df, 3pd) (5D, 7F) cc-pVTZ

sy. mode freq. sc. fund sc. ZPE freq. sc. fund. sc. ZPEa ν1 3357.69 3028.64 3193.16 3357.18 3055.03 3206.11

ν2 3298.81 2975.53 3137.17 3299.65 3002.68 3151.17

ν3 3258.62 2939.28 3098.95 3259.42 2966.07 3112.75

ν4 1580.19 1425.33 1502.76 1581.10 1438.80 1509.95

ν5 1199.37 1081.83 1140.60 1203.33 1095.03 1149.18

ν6 966.22 871.53 918.88 966.66 879.66 923.16

ν7 564.15 508.86 536.51 561.49 510.96 536.22

ν8 443.88 400.38 422.13 443.34 403.44 423.39

ν9 172.72 155.79 164.26 176.34 160.47 168.40

b ν10 3357.16 3028.16 3192.66 3356.78 3054.67 3205.72

ν11 3258.78 2939.42 3099.10 3259.56 2966.20 3112.88

ν12 1742.31 1571.56 1656.94 1750.95 1593.36 1672.16

ν13 1531.66 1381.56 1456.61 1532.33 1394.42 1463.38

ν14 1346.58 1214.62 1280.60 1351.45 1229.82 1290.63

ν15 1012.54 913.31 962.93 1012.65 921.51 967.08

ν16 832.37 750.80 791.58 824.10 749.93 787.02

ν17 554.33 500.01 527.17 549.70 500.23 524.96

ν18 459.78 414.72 437.25 459.05 417.74 438.39

Fund. scaling factor: 0.902 Fund. scaling factor: 0.91

ZPE scaling factor: 0.951 ZPE scaling factor: 0.955

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List of Figures

4.1 The time-of-flight mass spectrometer . . . . . . . . . . . . . . . . . . 24

4.2 Pyrolysis nozzle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

4.3 Design of ion optics . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

4.4 Electric field of new ion optics . . . . . . . . . . . . . . . . . . . . . 31

4.5 MS calibration with allyl bromide . . . . . . . . . . . . . . . . . . . 32

5.1 Allyl radical ground state structure . . . . . . . . . . . . . . . . . . . 44

6.1 Mass spectrum upon 409 nm multiphoton ionization . . . . . . . . . . 53

6.2 Allyl A state action spectrum . . . . . . . . . . . . . . . . . . . . . . 55

6.3 Rotational countour in Allyl A-state . . . . . . . . . . . . . . . . . . 57

6.4 A-state Hydrogen atom transients . . . . . . . . . . . . . . . . . . . . 61

6.5 A-state Doppler profile . . . . . . . . . . . . . . . . . . . . . . . . . 63

6.6 A-state Deuterium atom transient . . . . . . . . . . . . . . . . . . . . 64

6.7 A-state hydrogen and deuterium Doppler profiles . . . . . . . . . . . 65

6.8 Deuterium and hydrogen Doppler profiles . . . . . . . . . . . . . . . 68

6.9 Experimental and statistical product translational energy distribution . 72

7.1 C-state REMPI and action spectrum . . . . . . . . . . . . . . . . . . 77

7.2 C-state hydrogen atom transient . . . . . . . . . . . . . . . . . . . . 79

7.3 C-state Doppler profile . . . . . . . . . . . . . . . . . . . . . . . . . 81

7.4 C-state experimental and statistical product translational energy distri-

bution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

7.5 C-state hydrogen atom transients for high and low-J allyl radicals . . 89

7.6 C-state Doppler profiles for high and low-J allyl radicals . . . . . . . 92

7.7 Calculated geometry of TS 1 . . . . . . . . . . . . . . . . . . . . . . 93

188 LIST OF FIGURES

8.1 Reaction pathways for allyl radical unimolecular dissociation . . . . . 109

8.2 Reaction pathway for direct H-loss channel . . . . . . . . . . . . . . 115

8.3 Mode correlation for direct H-loss reaction channel . . . . . . . . . . 116

10.1 Allyl A state equilibrium geometry . . . . . . . . . . . . . . . . . . . 134

11.1 Scan of dihedral angle for 2A2 and 2B1 allyl radical . . . . . . . . . . 144

11.2 Scan of dihedral angle for 2A2 and 2B1 allyl radical . . . . . . . . . . 145

11.3 Geometries at conical intersections . . . . . . . . . . . . . . . . . . . 146

List of schemes

2.1 Types of direct photodissociation . . . . . . . . . . . . . . . . . . . . 8

2.2 Electronic and vibrational predissociation . . . . . . . . . . . . . . . 9

2.3 Unimolecular dissociation induced by electronic excitation . . . . . . 10

3.1 Campargue skimmer . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3.2 Types of photoionization. . . . . . . . . . . . . . . . . . . . . . . . . 19

4.1 Schematic diagram of three-field ion optics . . . . . . . . . . . . . . 28

4.2 Ion detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

4.3 Detection of atomic hydrogen . . . . . . . . . . . . . . . . . . . . . 37

4.4 Setup for pump-probe experiments . . . . . . . . . . . . . . . . . . . 39

5.1 Electronic states of the allyl radical . . . . . . . . . . . . . . . . . . . 47

6.1 Energy level diagram for pump-probe experiments . . . . . . . . . . 54

6.2 Reaction pathways for allyl radical unimolecular dissociation . . . . . 67

6.3 Statistical adiabatic impulsive model . . . . . . . . . . . . . . . . . . 70

7.1 Centrifugal barrier in diatoms . . . . . . . . . . . . . . . . . . . . . . 84

7.2 Rotational effects in the dissociation of a polyatomic molecule . . . . 86

8.1 Possible reaction products . . . . . . . . . . . . . . . . . . . . . . . 98

9.1 Reaction pathways for methylallyl radical unimolecular dissociation . 122

10.1 Electronic configuration of the allyl radical . . . . . . . . . . . . . . 129

11.1 Orbital correlation between allyl and cyclopropyl radicals . . . . . . . 142

11.2 State correlation between allyl and cyclopropyl radicals . . . . . . . . 143

190 LIST OF SCHEMES

List of Abbreviations and Acronyms

as asymmetric

BBO beta barium borate (β-BaB2O4)

CASSCF complete active space self-consistent field

CBS complete basis set

CC coupled cluster theory

CCSD coupled cluster theory with single and double excitation

CI configuration interaction

CSF configuration state function

δ chemical shift in ppm

DFT density functional theory

ESI electro spray ionization

Et2O diethyl ether

FWHM full width at half maximum

GPIB general purpose interface bus (IEEE488)

HF Hartree-Fock

HOMO highest occupied molecular orbital

HV high voltage

IP ionization potential

IC internal conversion

IRC intrinsic reaction coordinate

IVR intramolecular vibrational energy redistribution

LIF laser induced fluorescence

192 List of Abbreviations and Acronyms

LUMO lowest unoccupied molecular orbital

MCP microchannel plate

MO molecular orbital

MPI multiphoton ionization

MRCI multi-reference configuration interaction

MS mass spectrometer

Nd:YAG neodynium-doped yttrium aluminum garnet

oop out of plane

PES potential energy surface

REMPI resonance-enhanced multiphoton ionization

rms root-mean-square

RRKM Rice-Ramsberger-Kassel-Marcus (theory)

SCF self-consistent field

sci scissors

SOMO singly occupied molecular orbital

str stretch

sy symmetric

TLC thin layer chromatography

TOF time of flight

TS transition state

TTL time to loop

VUV vacuum ultraviolet

Units

1 A = 10−10 m (Angstrœm)

1 cal = 4.184 J

1 cm−1 = 1.986× 10−23 J

1 eV = 1.602× 10−19 J

1 Hartree = 4.360× 10−18 J

1 u = 1.66054× 10−27 kg (atomic mass unit)

Es leuchtet! seht! - Nun laßt sich wirklich hoffen,

Daß, wenn wir aus viel hundert Stoffen

Durch Mischung - denn auf Mischung kommt es an -

Den Menschenstoff gemachlich komponieren,

In einen Kolben verlutieren

Und ihn gehorig kohobieren,

So ist das Werk im stillen abgetan.

Es wird! die Masse regt sich klarer!

Die Uberzeugung wahrer, wahrer:

Was man an der Natur Geheimnisvolles pries,

Das wagen wir verstandig zu probieren,

Und was sie sonst organisieren ließ,

Das lassen wir kristallisieren.

Johann Wolfgang von Goethe

“Faust, der Tragodie zweiter Teil”

Curriculum Vitae

Luca Castiglioni

born January 25, 1979 in Zug, Switzerland

Citizen of Menzingen ZG, Switzerland

Education1985–1991 Primary School Menzingen, Switzerland

1991–1998 Kantonsschule Zug (Gymnasium), Switzerland

June 22, 1998 Matura Typus C (math. & science), Kantonsschule Zug

University Education10/1998–03/2003 Undergraduate studies in chemistry, ETH Zurich

10/2000–04/2001 Erasmus Exchange Program, Imperial College, London, UK

10/2002–02/2003 Diploma thesis in the group of Prof. Dr. A. Vasella, ETH Zurich,

on the subject: ”Synthesis and Binding Studies of Novel Oligonu-

cleoside Analogues”Mai 27, 2003 Diploma in Chemistry, ETH Zurich, Switzerland

10/2003-07/2007 Ph.D. thesis in the group of Prof. Dr. P. Chen, ETH Zurich, on

the subject: ”Photodissociation and Excited States Dynamics of

the Allyl Radical”

Working Experience10/1999–10/2002 Programmer and product manager at comparis.ch AG, Zurich

05/2003-09/2003 Process research and development, Novartis Pharma AG, Basel

Teaching Experience2003–2006 Teaching assistant for organic chemistry exercises and lectures

2002–2005 Teaching assistant for inorganic and physical chemistry

2004–2005 Supervision of a diploma and an undergraduate student

(all courses given at ETH Zurich)

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