ab initio and density functional calculations of conformational energies and interconversion...

Journal of Molecular Structure 970 (2010) 66–74

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Journal of Molecular Structure

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Ab initio and density functional calculations of conformational energiesand interconversion pathways in 1,2,3,6-tetrahydropyridine

Tung Tran, Thomas B. Malloy Jr. *

Department of Chemistry, University of St. Thomas, 3800 Montrose Blvd, Houston, TX 77006, USA

a r t i c l e i n f o a b s t r a c t

Article history:Received 3 December 2009Received in revised form 15 February 2010Accepted 15 February 2010Available online 19 February 2010

Keywords:ConformationsBarriersInterconversion

0022-2860/$ - see front matter � 2010 Elsevier B.V. Adoi:10.1016/j.molstruc.2010.02.035

* Corresponding author. Tel.: +1 713 525 6915; faxE-mail address: [email protected] (T.B. Malloy

Hartree–Fock with and without MP2 (frozen core and full) corrections and density functional calculationshave been performed on 1,2,3,6-tetrahydropyridine with basis sets 6-31G*, 6-31+G* and 6-311+G**. Forall methods which included diffuse functions, the half-chair equatorial N–H conformer was found to beslightly more stable than the half-chair axial conformer, in agreement with experimental results. Adetailed comparison for all the methods and basis sets was made with experimental data. These includedrotational constants for both the normal and N–D isotopic species, dipole moments and dipole momentcomponents. In addition, several interconversion pathways and barriers between the axial and equatorialconformations were explored by Hartree–Fock and B3LYP with the 6-31+G* basis set. The lowest energypathway between was found to be via the N–H inversion (�4–5 kcal/mol); via a bent (boat) axial form(�6–7 kcal/mol) and finally via a bent (boat) equatorial form (�7–8 kcal/mol). The planar form was foundto be �10 kcal/mol less stable than the two half-chair forms.

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1. Introduction

It is well known that cyclohexene and most mono-unsaturatedheterocyclic six-membered rings exist in a half-chair conformation[1]. The parent molecule exists in this conformation and undergoesring inversion via the boat conformation as the transition state.Calculations with ab initio quantum mechanical methods, molecu-lar mechanics (MM3) methods and NMR measurements show thatthe ring-inversion barrier is of the order of 5–6.5 kcal/mol [2].Analysis of vibrational data involving the anharmonicity of the ringbending and twisting modes yields higher barrier heights, 8.4–12.1 kcal/mol [3,4]. Oxygenated analogs have also been shown toexist in the half-chair form and have experimentally determinedinterconversion barriers of the same order [5–10]. More recently,molecular orbital calculations on oxygenated analogs of cyclohex-ene have shown the half-chair conformation as the stable confor-mation of these compounds [11,12] in agreement with theexperimental studies.

A previous theoretical study of the molecule addressed in thiswork, 1,2,3,6-tetrahydropyridine, along with the isomeric 2,3,4,5-terahydropyridine and 1,2,3,4-tetrahydropyridines, optimized atMP2/6-31G* has been published some time ago [13]. In each case,the conformation of the ring was found to be half-chair. The1,2,3,6-isomer was found to exist with two conformers, almost equalin energy, with the N–H axial conformer found to be slightly more

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stable (0.32 kcal/mol) than the N–H equatorial conformer. 1,2,3,6-Tetrahydropyridine is also listed in the Computational ChemistryComparison and Benchmark Database [14]. Although very extensivecalculations have been done, only the axial conformer is listed.However, definitive experimental data showing the existence oftwo conformers and unequivocal evidence that the equatorialconformer is slightly more abundant (0.15 ± 0.10 kcal/mol) havelong been available [15].

In this work, we have repeated the calculations on the 1,2,3,6-isomer [13] and have extended the basis sets and also applied den-sity functional methods to both the axial and equatorial conformer.We have also compared properties for the stable conformers calcu-lated by a variety of methods and basis sets to the experimentaldata from the previously published microwave study [15]. Theseinclude rotational constants, dipole moments and dipole momentcomponents as well as rotational constants from N–D isotopic spe-cies. In addition to calculating the energies of the stable conforma-tions, we have calculated interconversion pathways and barriersbetween the ring conformations via bent (boat) axial and equato-rial transition structures; via planar ring structures and intercon-version via N–H inversion. In these latter calculations, we usedthe 6-31+G* basis set and both Hartree–Fock and density func-tional (B3LYP) methods.

2. Minimum energy conformations

The programs used were GaussViewW 3.09 and Gaussian 03WVersion 6.0 [16]. The computer had an Intel 2.8 MHz processor

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T. Tran, T.B. Malloy Jr. / Journal of Molecular Structure 970 (2010) 66–74 67

with 1 GB of RAM with Windows� XP. The input files were gener-ated with the GaussView program. It was necessary to start from astructure with the correct orientation of the N–H, either axial orequatorial. This was fairly straightforward for the lower energyhalf-chair conformations, but more challenging for some of theconformations involved in the interconversions from one form toanother. In all cases, complete geometry optimizations were per-formed. Hartree–Fock calculations were performed with the fol-lowing basis sets: 6-31G*, 6-31+G*, 6-311+G** (6-31G(d), 6-31G+(d), 6-311G+(d,p)). Each of these basis sets was also used withdensity functional B3LYP calculations and with Moeller–PlessetMP2 calculations with both frozen core and full optimization.The calculations took as few as 2.5 min to several hours of CPUtime.

Table 1 gives the results of the energy calculations in hartreesfor the axial and the equatorial conformers without and with theinclusion of zero-point energy (ZPE). The ZPEs are as calculated,uncorrected. The results agreed exactly with those reported in ref-erence 11 for those calculations that were repeated. In addition,regardless of the method used, the 6-31G* basis set yielded aslightly lower energy for the axial conformer. For the more exten-sive basis sets, 6-31+G*and 6-311+G**, Hartree–Fock, B3LYP andMP2/FC and Full calculations are all consistent with the N–H equa-torial conformer being the lowest energy form, in agreement withthe experimental results [15].

The experimental energy difference has a large uncertainty, ofthe same order as its value [15] (0.15 ± 0.10 kcal/mol). The energydifference was measured by comparing intensities of correspond-ing pairs of rotational transitions in the microwave spectrum foraxial and equatorial conformers at ambient temperature and withthe waveguide packed in dry-ice. While this method resulted in arelatively large uncertainty in the energy difference, there wasabsolutely no uncertainty in the identification of the most stableconformer. In every case, lowering the temperature increased the

Table 1Comparison of the total energy for the axial and equatorial N–H conformers of 1,2,36-tetr

Model HF 6-31G*

Axial (hartree) �248.99842405w/ZPE (hartree) �248.85285405Equatorial (hartree) �248.99822917w/ZPE (hartree) �248.85269317ax-eq (kcal/mol) �0.12w/ZPE (kcal/mol) �0.10

B3LYP 6-31G*


MP2FC 6-31G*


MP2Full 6-31G*


a The experimental energy difference was determined to be 0.15 ± 0.10 kcal/mol, with

intensity of the equatorial form rotational transitions comparedto the corresponding transitions for the axial form. The identifica-tion of the conformers was confirmed by the values of the rota-tional constants, by measurement of the different dipole momentcomponents in the principal axis systems for each conformer,and by the changes in the rotational constants measured for thedeuterated (ND) species.

Table 2 compares the rotational constants (in MHz) calculatedby the various methods and basis sets to the experimental values.All of the models do a reasonable job of reproducing the experi-mental rotational constants. The % differences (calc–exp) are listedin the Tables. The Hartree–Fock method is the only one where the% differences exceed 1% and all of the deviations are positive. Thismay be a result of HF calculations resulting in bonds that are stron-ger and shorter than those calculated where electron correlation isexplicitly or implicitly included. Considering that the calculationsyield equilibrium values of the principal moments of inertia, whilethe experimental values represent the vibrationally averaged reci-procal moments of inertia, the correspondence is excellent. Table 3is a comparison of the shift in the rotational constants on exchangeof the imino hydrogen with deuterium. The calculated values are ingood agreement for all the models. The most striking thing is thelarge difference in the changes in rotational constants betweenthe two conformers due to the very different position of the hydro-gen in the principal axis system for the two conformers.

In addition to the total energy and rotational constants, wecompiled the calculated total dipole moments for the two con-formers. These are given in Table 4 and compared to the experi-mental dipole moments determined by analysis of the Starkeffect in the microwave spectrum. All of the calculations do a rea-sonable job of reproducing the experimental dipole moments. In allcases, the calculated dipole moments are higher than the experi-mental values, by as much as 0.28 debye to as little as a few thou-sandths of a debye. The calculated dipole moments for the axial

ahydropyridine calculated by different methods and basis sets.a

HF 6-31+G* HF 6-311+G**

�249.0051791 �249.0644756�248.8598461 �248.9205286�249.0052789 �249.0645762�248.8599949 �248.9206652

0.06 0.060.09 0.09

B3LYP 6-31+G* B3LYP 6-311+G**

�250.6816297 �250.7451355�250.5463607 �250.6106805�250.6817483 �250.7452524�250.5465293 �250.6108394

0.07 0.070.11 0.10

MP2FC 6-31+G* MP2FC 6-311+G**

�249.81611071 �249.9677812�249.67857371 �249.8314452�249.81637631 �249.9678581�249.67890631 �249.8315961

0.17 0.050.21 0.09

MP2Full 6-31+G* MP2Full 6-311+G**

�249.8446295 �250.0817387�249.7069685 �249.9451657�249.8449302 �250.0818239�249.7073372 �249.9453279

0.19 0.050.23 0.10

the equatorial conformer the lowest energy form [13].

Table 2Percent differences of calculated rotational constants from experimental values (MHz) for 1,2,3,6-tetrahydropyridine.

Model Rot. Const. HF HF HF B3LYP B3LYP B3LYP EXPTLBasis 6-31G* 6-31+G* 6-311+G** 6-31G* 6-31+G* 6-311+G**

(%) (%) (%) (%) (%) (%) (MHz)

AxialN–H A 0.79 0.79 0.76 �0.47 �0.61 �0.38 4897.47

B 1.24 1.13 1.23 �0.30 �0.49 �0.11 4709.16C 0.75 0.72 0.66 �0.67 �0.89 �0.64 2641.48

N–D A 0.85 0.79 0.79 �0.38 �0.58 �0.34 4785.44B 1.19 1.10 1.17 �0.39 �0.58 �0.22 4594.74C 0.72 0.67 0.60 �0.68 �0.94 �0.72 2616.00

EquatorialN–H A 0.62 0.54 0.59 �0.45 �0.60 �0.37 4950.50

B 1.21 1.08 1.16 �0.18 �0.40 �0.04 4743.05C 0.51 0.36 0.39 �0.60 �0.85 �0.62 2647.82

N–D A 0.82 0.70 0.77 �0.36 �0.60 �0.37 4882.41B 1.02 0.92 0.98 �0.29 �0.44 �0.09 4575.05C 0.50 0.35 0.38 �0.62 �0.88 �0.65 2577.26

MP2FC MP2Full MP2FC MP2Full MP2FC MP2Full6-31G* 6-31G* 6-31+G* 6-31+G* 6-311+G** 6-311+G**(%) (%) (%) (%) (%) (%)

AxialN–H A 0.49 0.69 0.33 0.54 0.37 0.61 4897.47

B 0.16 0.36 �0.10 0.10 0.01 0.23 4709.16C 0.46 0.68 0.18 0.41 0.36 0.59 2641.48

N–D A 0.47 0.67 0.22 0.43 0.33 0.56 4785.44B 0.21 0.42 �0.05 0.16 0.07 0.30 4594.74C 0.52 0.74 0.18 0.41 0.40 0.64 2616.00

EquatorialN–H A 0.60 0.81 0.44 0.65 0.46 0.70 4950.50

B 0.22 0.42 �0.05 0.15 �0.04 0.17 4743.05C 0.64 0.85 0.35 0.57 0.39 0.62 2647.82

N–D A 0.47 0.68 0.15 0.37 0.33 0.55 4882.41B 0.31 0.51 0.17 0.37 0.06 0.29 4575.05C 0.60 0.81 0.32 0.54 0.37 0.59 2577.26

Table 3Comparison of the change in rotational constants on N-deuteration for different methods and basis sets.

Model Rot. Const. HF HF HF B3LYP B3LYP B3LYP EXPTLBasis 6-31G* 6-31+G* 6-311+G** 6-31G* 6-31+G* 6-311+G**

(%) (%) (%) (%) (%) (%) (MHz)

AxialN–D–N–H DA �1.37 1.17 �0.79 �4.45 �1.97 �2.01 �112.03

DB 3.30 2.10 3.86 3.18 3.19 4.38 �114.42DC 4.00 5.69 7.42 0.35 4.95 7.89 �25.48

EquatorialN–D–N–H DA �13.54 �10.60 �12.40 �7.39 �0.65 �0.69 �68.09

DB 6.46 5.44 6.14 2.82 0.75 1.33 �168.00DC 0.78 0.62 0.62 0.43 0.26 0.47 �70.56

MP2FC MP2Full MP2FC MP2Full MP2FC MP2Full6-31G* 6-31G* 6-31+G* 6-31+G* 6-311+G** 6-311+G**(%) (%) (%) (%) (%) (%)

AxialN–D–N–H DA 1.02 4.90 5.44 1.52 4.90 5.44 �112.03

DB �2.10 �2.45 �2.26 �1.82 �2.45 �2.26 �114.42DC �5.81 �0.04 0.31 �5.34 �0.04 0.31 �25.48

EquatorialN–D–N–H DA 9.49 20.66 21.12 9.72 20.66 21.12 �68.09

DB �2.36 �6.11 �5.82 �2.00 �6.11 �5.82 �168.00DC 1.94 1.70 2.01 2.27 1.70 2.01 �70.56

68 T. Tran, T.B. Malloy Jr. / Journal of Molecular Structure 970 (2010) 66–74

form are very slightly greater than those for the equatorial form, asare the experimental values (1.007 and 0.990 D).

We also compared the direction of the calculated dipole mo-ments to those determined experimentally insofar as possible.The output yielded the calculated components of the dipole

moment in the in the coordinate system used to define the finalatomic positions. In order to compare the calculated dipole compo-nents to the experimental, it was necessary to extract the principalaxis transformation from the calculated output and then to trans-form the calculated dipole moment components to the principal

Table 4Comparison of dipole moments calculated by different methods and basis sets.

Basis 6-31 6-31 6-311 6-31 6-31 6-311 ExperimentalSet G* +G* +G** G* +G* +G** (debye)Method HF HF HF B3LYP B3LYP B3LYP

Axiall 1.185 1.161 1.102 1.069 1.123 1.058 1.007 ± 0.006

Equatoriall 1.072 1.132 1.101 0.991 1.067 1.037 0.990 ± 0.005

MP2FC MP2FC MP2 FC MP2Full MP2Full MP2Full

Axiall 1.290 1.286 1.226 1.224 1.186 1.182 1.007 ± 0.006

Equatoriall 1.154 1.150 1.193 1.189 1.183 1.178 0.990 ± 0.005


axis system. Even then there was another issue. The analyses of theStark effects in the microwave spectrum yield the squares of theprinciple axis components. Consequently, there is a sign ambiguityin the experimental components. However, the dipole moment isdominated by the orientation of the N–H, i.e. by the lone pair onthe nitrogen and a decision as to the actual direction and the signsof the components is made fairly easily.

In order to compare the components of the dipole moment aswell as the direction, we chose to normalize the calculated dipolemoment components to reproduce the experimental total dipolemoments. We then simply compared the magnitudes of the calcu-lated and experimental components. The results are given in Table5. The angle between the experimental and calculated dipole vec-tors were also calculated and are listed in the table.

The principal axis components graphically demonstrate the dif-ference in the direction of the dipole vector in the molecule for thetwo conformers. There are significant differences for the two con-formers (equatorial: la = 0.293 D, lb = 0.428 D, lc = 0.843 D, axial:la = 0.757, lb = 0.530 and lc = 0.401 D). The c inertial axis (largestmoment of inertia) for either conformation is roughly perpendicu-lar to the C–C@C–C plane for both conformers. The lone pair ofelectrons on the nitrogen is approximately parallel to this c axis

Table 5Comparison of the principal axis dipole moment componentsa calculated by different met

Basis 6-31 6-31 6-311Set G* +G* +G**Method HF HF HF

Axial|la| 0.725 0.749 0.761|lb| 0.547 0.516 0.488|lc| 0.437 0.433 0.444Angleb 2.9 2.0 3.5

Equatorial|la| 0.275 0.268 0.270|lb| 0.264 0.348 0.362|lc| 0.914 0.887 0.881Angleb 10.4 5.5 4.6

MP2FC MP2FC MP2FC

Axial|la| 0.749 0.747 0.757|lb| 0.578 0.579 0.546|lc| 0.346 0.349 0.379Angleb 4.2 4.1 1.6

Equatorial|la| 0.255 0.258 0.250|lb| 0.255 0.258 0.362|lc| 0.922 0.920 0.887Angleb 11.2 11.0 5.2

a The dipole moment components have been normalized to reproduce the experimenb This is the inverse cosine of the scalar product of unit vectors in the directions of th

for the N–H equatorial conformer resulting in a large c-componentof the dipole moment. Correspondingly, the axial N–H will havethe N lone pair roughly in the C–C@C–C plane and result in a smal-ler c-component of the dipole for this conformer. All of the calcu-lations agree qualitatively (Table 5). In general, the basis set 6-31G* deviates more from the experimental result regardless ofthe type of calculation as judged by the angle calculated betweenthe observed and calculated dipole moments.

3. Interconversion pathways

The interconversion pathways of the two equivalent stableforms of cyclohexene and its oxygenated analogs are quitestraightforward. Two equivalent half-chair (twisted) forms aremirror images and may inter-convert (a) via a planar ring or (b)through either of two identical boat (bent) forms. The lower energypathway is through the bent form.

Substitution of a CH2 group in the 4-position (cyclohexenenumbering) with an N–H group, complicates the situation. At thispoint (Fig. 1), there are two mirror image planar ring structures,depending on the orientation of the H on the nitrogen atom, above

hods and basis sets.

6-31 6-31 6-311 ExperimentalG* +G* +G** (debye)B3LYP B3LYP B3LYP

0.740 0.764 0.764 0.7570.480 0.466 0.456 0.5300.486 0.463 0.472 0.4015.7 5.1 5.9

0.321 0.292 0.286 0.2930.347 0.403 0.411 0.4280.870 0.856 0.854 0.8435.2 1.6 1.2

MP2Full MP2Full MP2Full

0.755 0.785 0.782 0.7570.547 0.527 0.529 0.5300.380 0.348 0.352 0.4011.5 3.4 3.1

0.253 0.260 0.262 0.2930.366 0.359 0.363 0.4280.884 0.885 0.883 0.8434.9 5.1 4.8

tal total dipole moments.e experimental and calculated dipole moments.

N

H

N H

N HN

H

N

H

N HN

H

N H

NHN

H

hcNH+eq hcNH-eq hcNH+ax hcNH-ax

bNH+ax bNH-axbNH+eq bNH-eq

pNH- pNH+

2

3

4 5

6

Fig. 1. Different forms of 1,2,3,6-tetrahydropyridine: N–H±, above/below plane; p, planar, b, bent (or boat); hc, half-chair. Mirror images are indicated by ?.


or below the plane. The boat (bent) forms now comprise two pairsof non-equivalent axial and equatorial conformers. The two axialforms are a pair of mirror images, while the two equatorial formsare a pair of mirror images, but not equivalent to the axial-bentforms. It is tempting to refer to members of equivalent pairs asenantiomers and the others as diastereomers. The relationship isanalogous, if not exact. The situation regarding the more stablehalf-chair (twisted) form is the same. There is a pair of mirror im-age axial forms and a pair of mirror image equatorial forms. Tosimplify the discussion below, we have designated the ring struc-tures as p-planar; b-bent (or boat); hc – half-chair and the N–H ori-entation as ± meaning above or below the plane and finally ax or eqto designate the axial or equatorial orientation of the N–H group.These are all illustrated in Fig. 1.

An interesting part about this multitude of conformers is thatinterconversion may occur by several different pathways. The first,and simplest to consider is interconversion of a half-chair equato-rial form to a half-chair axial form via a planar form. Even then, theparticular equatorial form can only access one of the equivalent ax-ial forms via this pathway. This is illustrated in Fig. 2. This, how-ever, is a higher energy path than inverting the ring throughlower energy boat forms or by simply inverting the N–H. Fig. 3shows different pathways among the stable half-chair forms viavarious boat forms. These involve converting from axial to equato-rial or vice versa by inverting the ring. Finally, Fig. 4 shows the low-

N H N

H

NH

Fig. 2. Interconversion of (left) hcN–H + eq to hcN–H-ax via

est energy pathway, via N–H inversion. Of note is that theequivalent members of ‘‘enatiomeric” pairs of conformers cannotconvert one to another via this mechanism. Consequently, to in-ter-convert all the possible forms, both modes of interconversionare required.

After examination of the energies of the stable equatorial andaxial forms, we decided to map the pathways using the 6-31+G*basis set using both Hartree–Fock and density functional (B3LYP)methods. This basis was chosen because it was the simplest basisset that a) agreed with the relative stability of the equatorial-axialconformers and b) did a reasonable job of reproducing not only thedipole moments, but also the dipole moment components.

It was not necessary to calculate all of the interconversion path-ways represented in Figs. 3 and 4 because of the equivalenceamong several of them. However, it was necessary to define certainconstraints to define the pathways. The calculation of the energy ofthe planar form was accomplished by constraining dihedral angles6123, 3456 and 1234 to be zero (see Fig. 1 for numbering) andallowing all the other parameters to be adjusted. The result wasa transition state with two imaginary frequencies. The two fre-quencies corresponded to modes leading to the half-chair axial orequatorial minima or to saddle points corresponding to the bent(boat) axial or equatorial forms.

The interconversion pathways from half-chair axial and equato-rial through bent(boat) axial and equatorial intermediates

N

H

N H

NH

pN–H� and (right) hcN–H-ax to hcN–H+ eq via pN–H+.

N H N H

N HN

H

N

H

N H

N

H

N

H

N HN

H

N

H

N HhcNH+eq hcNH-ax hcNH+ax hcNH-eq

bNH-ax

bNH-eq

hcNH+eq hcNH-ax hcNH+ax hcNH-eq

bNH+eq

Fig. 3. Interconversion of half-chair forms via bent (boat) forms.

N

H

N HN H

N

H

NH

NH

hcNH+ax hcNH+eq hcNH-axial hcNH-eq

half-chair NH+transitionhalf-chair NH-transition

mirror images

mirror images

mirror images

Fig. 4. Interconversion of half-chair axisl and equatorial forms via N–H inversion.


were calculated by freezing dihedral angle 6123 at angles from�70� to +70� in 10� increments, with some 5� intervals includedto better define the shape when the energy was changing direction.We also included the fully optimized half-chair axial and equato-rial structures in the set by measuring the value of dihedral 6123for the fully optimized structures. Fig. 5 shows a plot of the energypathways between the stable half-chair axial and equatorial formscalculated by the Hartree–Fock method with the 6-31+G* basis.Fig. 6 is the same plot but calculated by a density functional meth-od (B3LYP) with the same basis set. There are several notable fea-tures of these curves. The transition via the boat-axial intermediateis almost symmetrical and is somewhat lower than the transitionvia the boat-equatorial intermediate. It is also almost flat at thetop, similar to comparable curves calculated for cyclohexene[2,3] although some calculations showed a secondary minimumfor the boat form for this latter molecule. In contrast, the transitionvia the boat-equatorial form is markedly asymmetric, and has itsdistinct maximum at a positive 6123 dihedral, i.e. on the side clos-est to the half-chair equatorial form. Another notable feature isthat the curves are quite similar for both the Hartree–Fock and

density functional calculations although the density functionalenergy barriers are approximately 1 kcal/mol lower (�7 and6 kcal/mol for B3LYP vs. 8 and 7 kcal/mol for HF). Table 6 comparessome of the calculated quantities.

In order to define a coordinate which would take the moleculethrough the planar configuration we used an improper dihedral an-gle where the atoms were not all bonded to each other. This isillustrated in Fig. 7. The dihedral angle involved is defined byatoms 4, 5, 1 and 2. This is the angle between the C@C bond (atoms4 and 5) and the N–C (atoms 1 and 2) projected onto a plane per-pendicular to the line between atom 5 (C) and atom 1 (N). The an-gle shown in the figure is positive. Similarly, a dihedral angle wasused to drive the N–H proton through the 612 (CNC) plane to effectthe conversion between equatorial and axial without changing thering configuration. The angle shown in the diagram is positive.

Figs. 8 and 9 show the energy changes as these two angles areeach taken through a sufficient range of values to effect the inter-conversion of the stable forms through the N–H transition stateand through the planar state. Each data point represents optimiza-tion of all structural parameters except for the angle in question.

Bent-Eq Transition

0123456789

10

-80 -40 0 40 80Dihedral 6123

Del

ta E

nerg

y (k

cal/m

ol)

Bent-Axial Transition

0123456789

10

-80 -40 0 40 80

Dihedral 6123

Del

ta E

nerg

y(kc

al/m

ol)

N HN

H

N H

N HN

H

N

HHartree-Fock 6-31+G*

Fig. 5. Hartree–Fock 6-31+G* calculated interconversion energies as a function of the 6123 dihedral angle.

N HN

H

N H

N HN

H

N

HB3LYP 6-31+G*

Bent-axial path

0123456789

10

-80 -40 0 40 80

Dihedral 6123

Del

ta E

nerg

y kc

al/m

ol

Bent-eq Transition

0123456789

10

-80 -40 0 40 80Dihedral 6123

Del

ta E

nerg

y kc

al/m

ol

Fig. 6. B3LYP 6-31+G* calculated interconversion energies as a function of the 6123 dihedral angle.


The fully optimized structures were also included as part of thedata set. In both Figures, it is seen than the N–H bending modeleads to the lowest energy interconversion pathway between theminimum energy equatorial form and the very slightly less stableaxial form. As expected, the planar pathway represents a higherenergy path than either the N–H inversion or the ring inversionthrough either of the two bent (boat) forms. As was the case withthe interconversions in Figs. 5 and 6, the energy barriers calculatedby the density functional methods, are of the order of 1 kcal/mollower than those calculated by the Hartree–Fock method. TheN–H inversion pathway is slightly over 5 kcal/mol for HF, com-

pared to �4.5 for B3LYP while the planar barrier is slightly over10 kcal/mol for HF and below 10 kcal/mol for B3LYP. These valuesare given in Table 6.

One feature of the N–H inversion seemed a bit odd at firstglance; namely that the energy maximum occurred at a H–C–N–H dihedral angle of �20� rather than at the eclipsed conformationat 0�. Examination of the details of the conformations yielded aplausible explanation. We had chosen to drive the N–H bondthrough the plane of C(6)–N(1)–C(2) by varying a H–C–N–H dihe-dral on carbon 6. When we examined the structures in the range0–30� we found that a H–C–N–H dihedral involving a proton on

Table 6Comparison of energy differences and dihedral angles calculated by HF and B3LYPwith the 6-31+G* basis.

Conformation (see Figs.1 and 4)

HF energy difference(kcal/mol)

B3LYP energy difference(kcal/mol)

Dihedral angle (�) Dihedral angle (�)

hcN–H-eq 0.00 0.006123 hcN–H-eq 66.4 66.5

bN–H-eq(max) 8.0 7.36123 b-eq(max) 20 20hcN–H + ax 0.06 0.076123 hcN–H + ax �59.4 �58.4bN–H-eq(max) 7.06 6.36123 b-eq(max) �10a �20a

hcN–H-transition 5.19 4.52H–C–(6)–N–H 20 20pN–H+ 10.5 9.62

a The variation of the energy for this pathway is very flat near the top. Fordihedral 6123 between �20� to +20� it is less than 0.3 kcal/mol for HF and 0.7 kcal/mol for B3LYP.

6

2

34

1(N),5

2

3

45

H

H

H

1(N),6

NH1

23

4

5

6

1,2,3,6-tetrahydropyridine

Fig. 7. Dihedral angles for planar transition and for N–H inversion. Angles as shownare positive.


carbon 2, H–C(2)–N–H was in a very favorable position (�35�)when the H–C(6)–N–H was at 0� and was quite close to eclipsed(<10�) when H–C–(6)–N–H was at 20�. We concluded that the po-sition of the maximum was a combination of unfavorable dihedralangles on both sides.

4. Discussion

In the first part of this study, ab initio and density functional(B3LYP) methods were applied with increasingly complex basissets to calculate the energies of the stable half-chair axial andequatorial conformers and their rotational constants, dipole mo-ments and principal axis dipole moment components in order toperform a detailed comparison with a published experimentalstudy of this molecule. The calculations successfully reproducedthe experimental results to a high degree. As soon as diffuse func-

NH Inversion Path HF 6-31+G*

0123456789

10

-80 -60 -40 -20 0 20 40 60 80

HCNH dihedral

delt

a en

ergy

(kc

al/m

ol)

N HN

H

NH

N HN

H

NH

Fig. 8. Hartree–Fock 6-31+G* calculated interconversion energies as a function of the H–the N–H group through the C–(6)–N–C(2) plane and the latter twists the ring through a

tions were included in the basis sets, the correct order of stability,i.e. equatorial slightly more stable than axial was found in everycase. This is remarkable in that the energy differences are so small.The rotational constants for the conformers for the normal isotopicspecies and the ND species were reproduced to better than 2% forall calculations and to better than 1% for basis sets with diffusefunctions. While the dipole moments were consistently calculatedhigher than the experimental values, the directions of the dipolemoment in the principal axis system were quite reasonablyreproduced.

In the second part, the calculation of interconversion pathways,we faced a few challenges. The graphics software, GaussViewWwas essential for this purpose and made the variation of differentgeometric parameters much easier. We did, however, discover thatwe needed to start with a structure reasonably close to the finalstructure in order to obtain convergence to the correct conforma-tion. For example, it was not possible to simply increment dihedral6123 from �70� to +70� in 10� increments. If we started from a

Planar Path HF 6-31+G*

0

2

4

6

8

10

12

-40 -20 0 20 40

"dihedral" 4512

delt

a E

nerg

y (k

cal/m

ol)

NH

N HN

H

NH

N HN

H

C–(2)–N–H dihedral angle and the 4512 improper dihedral angle. The former takesplanar conformation.

NH Inversion Path B3LYP 6-

31+G*

0123456789

10

-80 -60 -40 -20 0 20 40 60 80

HCNH dihedral

delta

ene

rgy

(kca

l/mol

)

Planar path B3LYP 6-31+G*

0

2

4

6

8

10

12

-40 -30 -20 -10 0 10 20 30 40

"dihedral" 4512

delta

Ene

rgy

(kca

l/mol

)N HN

H

NH

NH

N HN

H

Fig. 9. B3LYP 6-31+G* calculated interconversion energies as a function of the H–C(2)–N–H dihedral angle and the 4512 improper dihedral angle. See Fig. 8.


structure near �70� after a few steps, the calculation would nolonger converge. What we did instead was to set up and optimizea few structures spread throughout the range and then generatedinput files from each of those where the dihedral angles were fro-zen at values near them.

The calculations all do a reasonable, and sometimes exceptionaljob of reproducing the experimental data from the microwave study[15]. The calculation of interconversion pathways by Hartree–Fockand density functional techniques with the same basis set yieldcomparable results. They also yield insight into the mechanisms ofinterconversion of the number of distinct mirror image conforma-tions. It is quite clear that the N–H inversion is the lowest energypath to inter-convert equatorial and axial conformers (4–5 kcal/mol), but that the higher barrier ring-inversion pathways are alsoaccessible (6–8 kcal/mol). These barriers are comparable to thosefor cyclohexene and related molecules [2–7,12,13]. The planar con-formations, as expected, are higher in energy (�10 kcal/mol).

Acknowledgements

Partial support for this work was provided by the National Sci-ence Foundation’s Course, Curriculum, and Laboratory Improve-ment program under Award No. 0536648. The Welch foundationis acknowledged for partial support of this research.

References

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1392–1406.[12] F. Freeman, H.N. Po, W.J. Hehre, THEOCHEM 503 (3) (2000) 145–163.[13] S.M. Bachrach, M. Liu, Tetrahedron Lett. 33 (45) (1992) 6771–6774.[14] Computational Chemistry Comparison and Benchmark DataBase Release

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[16] M.J. Frisch, G.W. Trucks, H.B. Schlegel, G.E. Scuseria, M.A. Robb, J.R. Cheeseman,J.A. Montgomery Jr., T. Vreven, K.N. Kudin, J.C. Burant, J.M. Millam, S. Iyengar, J.Tomasi, V. Barone, B. Mennucci, M. Cossi, G. Scalmani, N. Rega, G.A. Petersson,H. Nakatsuji, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T.Nakajima, Y. Honda, O. Kitao, H. Nakai, M. Klene, X. Li, J.E. Knox, H.P. Hratchian,J.B. Cross, C. Adamo, J. Jaramillo, R. Gomperts, R.E. Stratmann, O. Yazyev, A.J.Austin, R. Cammi, C. Pomelli, J.W. Ochterski, P.Y. Ayala, K. Morokuma, G.A.Voth, P. Salvador, J.J. Dannenberg, V.G. Zakrzewski, S. Dapprich, A.D. Daniels,M.C. Strain, O. Farkas, D.K. Malick, A.D. Rabuck, K. Raghavachari, J.B. Foresman,J.V. Ortiz, Q. Cui, A.G. Baboul, S. Clifford, J. Cioslowski, B.B. Stefanov, G. Liu, A.Liashenko, P. Piskorz, I. Komaromi, R.L. Martin, D.J. Fox, T. Keith, M.A. Al-Laham, C.Y. Peng, A. Nanayakkara, M. Challacombe, P.M.W. Gill, B. Johnson, W.Chen, M.W. Wong, C. Gonzalez, J.A. Pople, Gaussian 03, Revision B.01,Gaussian, Inc., Pittsburgh, PA, 2003.

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