Origin of methyl torsional barrier in 1-methyl-2(1H)-pyridinimine and 3methyl-2(1H)-pyridone: II. Ground state
B. Pradhan, Rajeev K. Sinha, Bhanu P. Singh, and T. Kundu
Citation: J. Chem. Phys. 126, 114313 (2007); doi: 10.1063/1.2566602
View online: http://dx.doi.org/10.1063/1.2566602
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THE JOURNAL OF CHEMICAL PHYSICS 126, 114313 共2007兲
Origin of methyl torsional barrier in 1-methyl-2„1H…-pyridinimine
and 3-methyl-2„1H…-pyridone: II. Ground state
B. Pradhan, Rajeev K. Sinha, Bhanu P. Singh, and T. Kundua兲
Department of Physics, Indian Institute of Technology Bombay, Mumbai 400076, India
共Received 16 October 2006; accepted 17 January 2007; published online 21 March 2007兲
To get the insight into the electronic structure-methyl torsion correlation in nitrogen heterocyclic
molecules, a comparative study on torsion of the methyl group in 1-methyl-2共1H兲pyridone 共1MPY兲,
1-methyl-2共1H兲pyridinimine 共1MPI兲, and 3-methyl-2共1H兲pyridone 共3MPY兲 was carried out using
ab initio calculations. To understand the barrier forming mechanism in the ground state and its
consequence on the molecular structure, the ground state torsional potential has been investigated by
partitioning the barrier energy using the natural bond orbital 共NBO兲 theoretical framework. The
NBO analysis reveals that the delocalization energy is the barrier forming term whereas the Lewis
energy is always antibarrier for all these molecules. To get further insight into the effect of local
electronic structure on the methyl torsional barrier, the individual bond-antibond interactions and
structural energy contributions have been investigated. It was found that when the bond order
difference between the vicinal bonds does not change appreciably during the course of methyl
rotation, the local electronic interactions with the methyl group do not play any decisive role in
barrier formation as observed in the case of 1MPY and 1MPI. In these cases, it is the skeletal
relaxation during methyl rotation that plays an important role in determining the barrier. On the
other hand, if the bond order change is appreciable as is the case for 3MPY, the local interactions
alone suffice to describe the origin of the torsional barrier of the methyl group. © 2007 American
Institute of Physics. 关DOI: 10.1063/1.2566602兴
I. INTRODUCTION
The study of internal rotation of methyl group in aromatic and heterocyclic has important implications in understanding noncovalent forces governing the conformational
preference in polyatomic molecules. Physical quantities,
such as barrier height and phase of the methyl torsional potential, vary drastically depending on the chemical structure
and the electronic state of the molecule. There is also diversity in the behavior of methyl rotor among the different substituted molecular species. Each new example raises the
subtle structural question about variation in height of the
potential barrier and the methyl group conformation from
energetic point of view. Unlike aliphatic molecules, very few
theoretical concepts are available for aromatic molecules.
Payne and Allen1 and Villard2 have presented in-depth review of ab initio barrier calculations. Nature of methyl rotation in aromatic compounds has been reviewed by Ito,3 while
Spangler and Pratt4 have focused on the internal rotation
dynamics in their paper. Liljefors and Allinger5 proposed that
the methyl torsional barrier in the aromatic molecules originates from the difference in the ␲-bond order between the
two ring C–C bonds vicinal to the methyl group and this idea
has been extended by George et al.6 for toluene and several
other aromatic hydrocarbons. Lu et al.7 have carried out an
extensive ab initio calculations on ground and cationic states
of substituted toluenes and presented a unified picture on the
effect of the local geometry and the electronic structure on
a兲
Electronic mail: tkundu@phy.itb.ac.in
0021-9606/2007/126共11兲/114313/7/$23.00
the internal rotation of the methyl group. In ortho-substituted
toluene, by using natural bond orbital 共NBO兲 analysis, it was
shown that the repulsive steric interaction dominates over
attractive hyperconjugative interaction to favor the pseudotrans conformation of the methyl group. By the use of natural resonance theory, a correlation between the bond order
and the barrier height was found. When the steric interactions are unimportant, the major determining factor of the
rotor barrier height is the difference in ␲-bond order between
the two ring C–C bonds vicinal to the methyl group. It was
shown that the barrier height is proportional to the calculated
bond order difference, with a slope of 950 cm−1 per bond.
Hyperconjugative interactions were found to favor the conformation of the rotor C–H bond cis to the ring C–C bond of
higher order in close analogy with 2-methylpropene. Sonoda
and Iwata,8 from Mullikan population analysis on o-, m-,
p-fluorotoluene and their cations showed that the change of
barrier height from ground to cationic state is correlated with
the electron distribution of neighboring carbon atoms and the
barrier height is proportional to gross population difference.
Nakai et al.9 have been investigating the methyl rotational
barrier developing energy density analysis technique by partitioning the total energy into atomic energy densities. This
technique was able to predict the existence of hydrogen bond
between the in-plane hydrogen atom of the methyl group and
fluorine that decreases the barrier height in o-fluorotoluene.
Yan and Spangler10 have made a convincing approach to
explain the origin of barrier in aromatics by using the ␲
fragment orbital concept proposed by Hehre et al.11 The methyl group adopts a conformation that reflects the symmetry
126, 114313-1
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114313-2
Pradhan et al.
J. Chem. Phys. 126, 114313 共2007兲
FIG. 1. Molecular geometries of 共a兲 1-methyl-2共1H兲-pyridone 共1MPY兲, 共b兲 1-methyl-2共1H兲-pyridinimine 共1MPI兲, and 共c兲 3-methyl-2共1H兲-pyridone 共3MPY兲.
of the ␲ system. In aromatic systems such as toluene and
p-fluorotoluene, where the ␲ molecular orbitals of the parent
molecule are symmetric on either side of the plane perpendicular to the molecular frame containing the rotor axis,
␲CH3 orbital is favored and consequently, the molecule
adopts staggered conformation. The ␲ density on each side
of the plane contributes a threefold term to potential but the
contributions are out of phase and cancel each other to give a
small sixfold barrier. If an asymmetry exists in ␲ molecular
orbital of parent molecule, the methyl group orbital
␲CH3 appears and a large V3 term results. Recently Sinha
et al.12 have shown that even though the local geometry has
sixfold symmetry in 4-methylstyrene, the threefold contribution appears in the methyl torsional barrier from the remote
␲ interactions between the vinyl group and the benzene
frame.
While there has been an extensive study on the methyl
internal rotation in substituted aromatics, it is very sparse in
the case of methyl substituted heterocyclic compounds.
Nitrogen-containing heterocyclic compounds are ubiquitous
in nature and occupy an important position in biochemical
processes. The presence of nitrogen atom in these molecules
should play a crucial role in the barrier to internal rotation
both by way of the nitrogen lone pair and the perturbations
the nitrogen atom imposes on the ␲ molecular orbitals. In
our previous article on 1-methyl-2共1H兲-pyridone 共1MPY兲,13
we presented a systematic analysis on the origin of torsional
potential barrier using NBO framework. Here, 1-methyl2共1H兲-pyridinimine 共1MPI兲 and 3-methyl-2共1H兲-pyridone
共3MPY兲 serve as two important model systems to study the
effect of functional group and the position of methyl group
on the potential barrier in the light of 1MPY. The oxygen
atom of 1MPY is replaced by isoelectronic N-H group to
form an imino compound 1MPI. In this case methyl group
attached to ring nitrogen experiences a different electronic
environment because of N-H group in its vicinity which is
expected to reflect in the change of the potential to the internal rotation. In 3MPY the methyl group is substituted at ring
carbon atom adjacent to C v O bond instead of nitrogen
atom. In this molecule, presence of double bond adjacent to
methyl group is expected to influence the torsional barrier
differently in addition to oxygen lone pair. The main objective in this article is to establish an electronic structuremethyl torsional property relationship in N heterocycles. Toward this, we present a comparative investigation here of
these two molecules with 1MPY to bring out the barrier
forming mechanism of the methyl group and its consequences for the structure in this class of heteroatomic molecules.
II. RESULTS AND DISCUSSIONS
A. Geometry and torsional potential barrier
The excited state torsional behavior of the methyl group
in 1MPI and 3MPY has been analyzed in our previous
communication.14 In order to investigate theoretically the
origin of the potential barrier for the internal rotation of the
methyl group in the ground state 共S0兲, ab initio electronic
structure calculations were carried out using the GAUSSIAN98
共Ref. 15兲 suite of program. The geometries of 1MPI and
3MPY in the ground state were optimized with different
level of theories using various basis sets. The minimum energy conformations of both the molecules shown in Fig. 1
are staggered in the sense that one C–H bond of the methyl
group is in plane with the molecular frame and is away from
the N–H bond and O atom 共staggered conformation兲. The
potential parameters for the rotation of the methyl group
were obtained by using one dimensional torsional potential
of the form, V共␶兲 = 共V3 / 2兲共1 − cos 3␶兲 + 共V6 / 2兲共1 − cos 6␶兲
+ . . ., where ␶ is the torsional coordinate, and the V3 and V6
are the three- and sixfold potential terms, respectively. The
torsional potential was calculated using fully relaxed model
introduced by Goodman et al.16 In this, the rotational angle
with respect to in-plane hydrogen of the methyl group 共␶
= 0兲 is defined for the minimum energy conformation in the
S0 state. The potential energy curve is obtained by constraining only the rotational angle 共␶兲 of the methyl rotor to the
local frame and then by optimizing the rest of the geometry
to minimize the energy. The obtained potential parameters
are listed in Table I. For 1MPI, the threefold barrier varies
between 430 to 530 cm−1 for most levels of theory and the
magnitude of sixfold term is around 30 cm−1. For 3MPY, the
variation of the threefold barrier is between 400 and
600 cm−1 whereas the magnitude of sixfold term is around
6 cm−1. Thus, the potential shows dominant contribution
from the threefold term. At Hartree-Fock 共HF兲 level of
theory, the potential barrier determining term V3 is consistent
with a deviation of 5%–6% with and without diffused function in the basis set. However, MP2 calculation including
electron correlation predicts somewhat higher value of V3 for
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114313-3
J. Chem. Phys. 126, 114313 共2007兲
Methyl torsional barrier
TABLE I. Ab initio methyl torsional potential parameters in the ground state
of 1MPI and 3MPY calculated at different level of theories.
Levels of theory
1MPI
V3 共cm−1兲
1MPI
V6 共cm−1兲
3MPY
V3 共cm−1兲
3MPY
V6 共cm−1兲
HF/ 6-31G共d兲
HF/ 6-31G共d , p兲
HF/ 6-31+ G共d , p兲
HF/ 6-311+ + G共d , p兲
MP2 / 6-31G共d , p兲
B3LYP/ 6-31G共d , p兲
B3LYP/ 6-311+ + G共d , p兲
472
454
475
482
530
428
433
35
31
−25
−32
−10
−15
−15
571
555
593
613
449
403
441
8.0
6.0
−15.0
2.0
4.0
0.0
0.0
1MPI whereas in the case of 3MPY the barrier height decreases compared to HF calculation. Barrier calculated using
density functional theory 共B3LYP兲 always predicts lower
barrier irrespective of the basis set used. In HF level of
theory, V6 is positive but with the introduction of diffuse
function it decreases. Since the threefold term, governing
barrier height, is dominant for both the molecules, the mere
importance of V6 lies in the control of potential shape. As
modest scale ab initio calculation predicts ground state methyl torsional potential energy barrier correctly as described
for 1MPY,13 further analysis of 1MPI and 3MPY to compare
with 1MPY will be based on HF/ 6-31G共d , p兲 level of theory.
as well as in aromatic molecules.7,19 Under this analysis, the
total barrier energy is partitioned into Lewis and delocalization energies as
⌬Ebarrier = ⌬Edeloc + ⌬ELewis ,
共1兲
where ⌬Edeloc is the hyperconjugative 共delocalization兲 energy
contribution that arises due to bond-antibond interactions and
⌬ELewis is the energy contribution from the steric repulsion
and the valence effect. Figure 2 presents the torsional angle
共␶兲 dependence of potential barrier energy and the contribution from its components Lewis and delocalization energy
for both the molecules. It is apparent from Fig. 2 that the
delocalization energy is positive in going from minimum energy conformation to the top of barrier conformation, in accordance with the observation of 1MPY and other small molecules such as ethane,20 methanol,21 dimethyl ether,22 etc.
However, the overall barrier energy comes from the cancellation of this barrier forming delocalization energy and the
antibarrier contribution from the Lewis energy. To get further
insight into these energies, we investigated the individual
orbital interactions in the vicinity of the methyl group 共local兲
and other interactions 共nonlocal兲 present in the molecule as
marked in Fig. 1. In the following section we explore the
importance of local and nonlocal orbital interactions of the
methyl group on torsional barrier through non-Lewis 共delocalization兲 and Lewis energy changes due to the rotation of
the methyl group from equilibrium conformation to top of
the barrier.
B. Natural bond orbital „NBO… analysis
To understand the origin of potential barrier and the
structure in the ground state, we analyzed the energetic consequences of NBO decomposition of the barrier for methyl
rotation.17 NBO’s are the localized set of Lewis-type 共␴ and
␲ bonds, lone pair, and core兲 and non-Lewis 共␴* and ␲*
antibond and Rydberg兲 orbitals formed by transformation of
molecular wave functions into one-center 共lone pair兲 and
two-center 共bond兲 representations. This analysis in a way
provides deeper understanding of noncovalent interactions
causing the torsional barrier in such big molecules. The NBO
calculations were performed using NBO 3.1 module of GAUSSIAN98.
The NBO analysis was quite successful for understanding the internal rotation potential barrier in many aliphatic18
1. Energy partitioning in 1MPI
a. Delocalization energy contribution. We first consider
hyperconjugative interactions comprising pairwise interactions of all the methyl C–H bonds and antibonds with N1C2
and N1C6 共Fig. 1兲 bonds and antibonds along with the outof-plane lone pair of ring nitrogen and in-plane lone pair of
imine nitrogen. We evaluate the energetic importance of this
set of interactions by simultaneously deleting corresponding
Fock matrix elements and reevaluating the energy at ␶ = 0°
共staggered conformation兲 and ␶ = 180° 共eclipsed conformation兲, following the procedure suggested by Reed and
Weinhold.23 The barrier contribution of these hyperconjugative interactions with the methyl group calculated with different levels of theory is given in Table II. It was found that
FIG. 2. Total barrier energy and their Lewis and non-Lewis components for 共a兲 1MPI and 共b兲 3MPY. The calculation was performed at HF/ 6-31G共d , p兲 level
of theory.
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114313-4
J. Chem. Phys. 126, 114313 共2007兲
Pradhan et al.
TABLE II. Total delocalization and delocalization 共interactions with the methyl group only兲 energy contributions to torsional barrier in ground state for 1MPI and 1MPY calculated at different level of theories.
1-methyl-2共1H兲-pyridinimine
1-methyl-2共1H兲-pyridone
Levels of theory
Total
delocalization
共cm−1兲
Methyl interaction
deletion
共cm−1兲
Total
delocalization
共cm−1兲
Methyl interaction
deletion
共cm−1兲
HF/ 6-31G共d , p兲
HF/ 6-31+ G共d , p兲
HF/ 6-311+ + G共d , p兲
473
773
856
−456
−423
133
495
563
570
−137
−10
164
these hyperconjugative interactions favor the eclipsed conformation by more than 350 cm−1 at HF/ 6-31G共d , p兲 and
HF/ 6-31+ 共d , p兲 levels of calculation. For detailed analysis,
we followed the single deletion procedure to get the delocalization energy barrier contribution from the individual interactions. Table III includes the dominant local and nonlocal
contributions to the barrier with respect to methyl group as
partitioned in Fig. 1. Calculations for both the molecules
1MPI and 1MPY are listed in Table III for comparison. The
analysis shows that the interaction of nitrogen lone pair
with antibonding orbital of the methyl group
关N7共LP兲-C8H14共␴*兲兴 is attractive and favors eclipsed conformation by 457 cm−1. The oxygen lone pairs 共both ␴ and
␲兲 in 1MPY have also the same antibarrier effect on barrier
to internal rotation. In ortho-fluorotoluene24 and
ortho-chlorotoluene,25 the interaction between the halogen
lone pair and antibond orbital of methyl C-H was also found
to mildly favor the eclipsed conformation. Hence the interactions between lone pair and antibond of the in-plane methyl C-H are always attractive and favor the in-plane C-H to
form eclipsed conformation. The other local hyperconjugative interactions cancel each other and the total contribution
to the barrier was calculated to be −813 cm−1 for 1MPI.
Thus, the overall change 共743 cm−1兲 in hyperconjugative interactions is arising from the nonlocal interactions. Like the
case of 1MPY, C2C3共␴兲-C4C5共␴*兲, C4C5共␴兲-C6N7共␴*兲,
C2C3共␴兲-N1C8共␴*兲, and N1共LP兲-C2C3共␲*兲 interactions
give positive contribution to barrier formation and over-
TABLE III. Dominant contributions of individual pairwise bond-antibond and lone pair-antibond interactions to
barrier in 1MPI compared with 1MPY 共LP: lone pair兲.
Bond antibond interactions
1MPY
Barrier contribution
1MPY 共cm−1兲
Bond antibond interactions
1MPI
Barrier contribution
1MPI 共cm−1兲
N1C2共␴兲-N1C8共␴*兲
N1C2共␴兲-C6N7共␴*兲
N1C6共␴兲-C8H14共␴*兲
N1C6共␴兲-N7H13共␴*兲
C6N7共␴兲-N1C2共␴*兲
N7H13共␴兲-N1C6共␴*兲
C8H14共␴兲-N1C6共␴*兲
¯
¯
N1共LP兲-C6N7共␲*兲
¯
¯
N7共LP兲-N1C6共␴*兲
N7共LP兲-N1C8共␴*兲
¯
¯
N7共LP兲-C8H14共␴*兲
38
−67
46
53
81
−168
−66
¯
¯
−313
¯
¯
140
59
¯
¯
−457
Local interactions
N1C2共␴兲-N1C8共␴*兲
N1C2共␴兲-C6O7共␴*兲
N1C6共␴兲-C8H13共␴*兲
¯
C6O7共␴兲-N1C2共␴*兲
¯
C8H13共␴兲-N1C6共␴*兲
C8H14共␴兲-N1C2共␴*兲
C8H15共␴兲-N1C2共␴*兲
N1共LP兲-C6O7共␲*兲
N1共LP兲-C8H14共␴*兲
N1共LP兲-C8H15共␴*兲
O7共LP␴兲-N1C6共␴*兲
¯
O7共LP␲兲-N1C6共␴*兲
O7共LP␲兲-C8H13共␴*兲
¯
30
−78
90
¯
66
¯
−232
76
80
−323
−20
−29
−118
¯
65
−97
¯
N1C8共␴兲-C2C3共␴*兲
N1C8共␴兲-C5C6共␴*兲
C2C3共␴兲-N1C8共␴*兲
C2C3共␲兲-C4C5共␲*兲
C4C5共␴兲-C6N7共␴*兲
C4C5共␲兲-C6N7共␲*兲
C5C6共␴兲-N1C8共␴*兲
N1共LP兲-C2C3共␲*兲
N7共LP兲-C5C6共␴*兲
Nonlocal interactions
−118
N1C8共␴兲-C2C3共␴*兲
95
N1C8共␴兲-C5C6共␴*兲
101
C2C3共␴兲-N1C8共␴*兲
148
C2C3共␲兲-C4C5共␲*兲
67
C4C5共␴兲-C6O7共␴*兲
150
C4C5共␲兲-C6O7共␲*兲
−70
C5C6共␴兲-N1C8共␴*兲
252
N1共LP兲-C2C3共␲*兲
70
O7共LP␴兲-C5C6共␴*兲
−106
106
100
183
69
205
−65
292
70
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114313-5
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Methyl torsional barrier
whelm the antibarrier effect produced by the local methyl
group interactions to generate the overall positive delocalization term. These nonmethyl interactions are due to the effect
of molecular flexing during methyl rotation process as also
observed for 1MPY.13 Thus the overall contribution of the
delocalization energy change, the barrier forming term in this
class of molecules, cannot be understood without considering the effect induced by molecular relaxation during methyl
rotation.
b. Lewis energy contribution In view of the significant
role of molecular flexing in barrier formation, the other energy change, the Lewis energy term needs to be investigated.
The Lewis energy contribution to the barrier ⌬ELewis can
further be partitioned into structural energy and steric energy
changes as
⌬ELewis = ⌬Estruc + ⌬Esteric ,
共2兲
where ⌬Estruc is the change in structural energy, a consequence of Coulomb repulsion and the bond energy change in
the classical Lewis structure during internal rotation, and
⌬Esteric is the change in steric energy 共consequence of Pauli
exclusion principle兲 not incorporating the valence effect. The
change of bond energy, which corresponds to the structural
energy change, can be obtained as26
⌬ ␻ = ␧ en e − ␧ sn s ,
共3兲
where ␧e and ␧s represent the bond energies of the eclipsed
and staggered conformations, respectively, and ne and ns indicate the charge occupations of the corresponding states.
The total structural energy change in 1MPI was calculated to
be −147 cm−1 when all the bonds and lone pairs were considered. The remaining contribution to the total Lewis energy
change 共−288 cm−1兲 comes from the steric energy change.
Thus both the changes, the structural and the steric energies,
are negative to form antibarrier Lewis energy term. On the
other hand, in 1MPY 共Ref. 13兲 the total structural energy
change was found to be 1255 cm−1 and the overwhelming
negative contribution from the steric interaction brought out
the total Lewis energy to be antibarrier term. The major bond
energy changes 共eclipsed-staggered兲 due to methyl rotation
are shown in Fig. 3. The effective contribution from the methyl group 共17, 18, and 19 in Fig. 3兲 is very less because of
their cancellation due to the positive and negative energy
changes. The dominant positive energy contribution comes
from the increase in bond energy of ␴N1C2 共1兲 and ␴N1C8
共3兲. The small energy contribution from the structural part is
due to the near cancellation of contributions from all bond
energies.
FIG. 3. Contributions of individual structural energies to the torsional barrier in the ground state of 1MPI.
overall barrier as the barrier energy is 555 cm−1. This implies
that the major contribution to barrier in 3MPY comes from
the local hyperconjugative interactions in contrast to 1MPY
and 1MPI where the molecular flexing induced nonlocal hyperconjugative energy change was important. To get further
insight, individual pairwise bond-antibond interaction energies were focused and these are listed in Table IV. It was
found that interactions of the vicinal ␲ and ␲* orbitals of
C-C bond 关C4C5共␲兲 , C4C5共␲*兲兴 of ring with ␴ and ␴* orbitals of out-of-plane methyl C–H bond 关C8H14共␴兲,
C8H14共␴*兲, C8H15共␴兲, C8H15共␴*兲兴 are the main factors
giving rise to this barrier energy. The hyperconjugation beTABLE IV. Dominant contributions of individual pairwise bond-antibond
and Ione pair-antibond interactions to barrier in 3MPY 共LP: lone pair兲.
Bond antibond interactions
Local interactions
C4C5共␴兲-C5C8共␴*兲
C5C6共␴兲-C8H13共␴*兲
C4C5共␲兲-C6O7共␲*兲
C4C5共␴兲-C6O7共␴*兲
C4C5共␲兲-C8H14共␴*兲
C4C5共␲兲-C8H15共␴*兲
C5C8共␴兲-C4C5共␴*兲
C8H13共␴兲-C5C6共␴*兲
C8H14共␴兲-C4C5共␲*兲
C8H14共␴兲-C4C5共␴*兲
C8H15共␴兲-C4C5共␲*兲
C8H15共␴兲-C4C5共␴*兲
2. Energy partitioning in 3MPY
As discussed in
the previous section that in the case of 3MPY, too, the delocalization energy is the barrier forming term and the Lewis
energy is antibarrier in nature sharing a small part compared
to delocalization energy. To ascertain the role of local hyperconjugative interactions in 3MPY, all the bond-antibond interactions with the methyl group were deleted followed by
the recalculation of energy. The potential barrier contribution
of these local interactions was found to be 769 cm−1 to the
a. Delocalization energy contribution.
Barrier contribution 共cm−1兲
93
226
−197
−45
300
299
85
−197
227
139
226
140
Nonlocal interactions
N1C2共␴兲-C6O7共␴*兲
C2C3共␲兲-C4C5共␲*兲
C3C4共␴兲-C5C8共␴*兲
C5C8共␴兲-N1C6共␴*兲
C5C8共␴兲-C3C4共␴*兲
N1共LP兲-C2C3共␲*兲
O7共LP␴兲-N1C6共␴*兲
O7共LP␴兲-C5C6共␴*兲
O7共LP␲兲-C5C6共␴*兲
44
−234
81
59
−77
−126
38
−72
36
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114313-6
J. Chem. Phys. 126, 114313 共2007兲
Pradhan et al.
TABLE V. Methyl group vicinal natural bond order difference of 3MPY,
1MPY, and 1MPI calculated using natural resonance theory.
Level of theory
3MPY
1MPY
1MPI
HF/ 6-31G共d , p兲
HF/ 6-31+ G共d , p兲
HF/ 6-311+ + G共d , p兲
0.835
0.8578
0.8070
−0.0684
−0.0128
−0.0388
0.0283
0.0548
0.0491
*
tween oxygen lone pair and in-plane ␴CH
antibonds gives a
small negative contribution to barrier similar to 1MPY. The
double bond character of one of the vicinal bond in 3MPY is
the main factor of high barrier because of the strong ␲ bondantibond interaction with the methyl group. Lu et al.7 have
shown a correlation between the local bond order and barrier
height in substituted toluene where a double bond is found to
be present on either side of methyl group during methyl rotation. To check such correlation we calculated the bond order for bonds vicinal to methyl group using natural resonance theory.27 The bond order differences between the two
vicinal bonds of the methyl group were calculated at eclipsed
and staggered conformations with various levels of theory.
The difference between these conformers is listed in Table V
along with 1MPY and 1MPI. For 3MPY a large bond order
difference 共⬃0.8兲 was found to exist whereas the bond order
differences for 1MPY and 1MPI are very small. This analysis
demonstrates that the rotational barrier can be described using only the local ␲ bond-antibond interactions in the molecules having a double bond vicinal to methyl group that
does not change appreciably due to resonance during methyl
rotation.
b. Lewis energy contribution. To understand the small
antibarrier contribution of the Lewis energy term to the barrier, the total structural energy change was calculated and
found to be highly positive and barrier forming 共5681 cm−1兲.
Since the total Lewis energy term is very small and antibarrier, the large negative contribution from the steric interactions cancels the positive contribution from structural energies as also seen in 1MPY.13 Figure 4 shows the calculated
individual contributions from the structural energy change
for 3MPY. The effective contribution from the methyl group
共16, 17, and 18 in Fig. 4兲 is very less because of their cancellation due to the positive and negative energy changes.
The dominant positive energy contribution comes from the
increase in bond energy of the C5C8 共13兲. The geometry
analysis 关HF/ 6-31G共d , p兲兴 revealed the increment of C5C8
bond length by 0.007 Å and the angle opening of C8C5C6
by 1.3° 共116.3° in staggered and 117.6° in eclipsed兲 in going
from staggered to eclipsed conformer. However, the increment of the C8N1 bond was not that significant in 1MPY
共0.003 Å兲 and in 1MPI 共0.001 Å兲. This bond lengthening 共␴
bond兲 in 3MPY brings about a substantial change in structural energy making the total structural term positive. This
kind of phenomenon was also observed in small molecules
such as acetaldehyde 共0.007 Å兲 共Ref. 16兲 and propene
共0.009 Å兲 共Ref. 28兲 where the principal contribution of the
barrier energy arises through the relaxation of the
Cmethyl – Cadjacent bond. The degree of this bond lengthening in
a way provides an indirect monitor of the strain on the methyl group in the metastable rigid rotation conformer. Thus,
these ␴ effects appear to have their origin in the partial unmaking of the bond between Cmethyl and the adjacent carbon
atom, which consequently lengthens.
III. CONCLUSION
Considering the noncovalent interactions of various parts
of the molecule, NBO analysis shows that the methyl torsional barrier predominantly arises from the delocalization
energy changes while the Lewis energy change forms the
antibarrier. However, the local hyperconjugative interactions
with the methyl group alone are not decisive in barrier formation when the methyl group is adjacent to two vicinal
single bonds as for 1MPY and 1MPI. It is the skeletal relaxation during methyl rotation that plays an important role in
strengthening the contribution of hyperconjugation and is a
key factor in determining the origin of the barrier. In contrast, when there is a double bond adjacent to the methyl
group as in 3MPY, local hyperconjugative interactions are
the major contributors to the barrier energy. However, the
lone pair-antibond interactions in all these molecules act like
antibarrier and decrease the magnitude of the barrier. In the
case of 3MPY, the relaxation of Cmethyl – Cadjacent bond is an
important factor to determine the magnitude of the barrier
energy similar to that observed in small molecules such as
propene and acetaldehyde.
ACKNOWLEDGMENTS
This work was supported by Department of Science and
Technology, India. The authors are thankful to Dr. R. B.
Sunoj for providing the facilities for some of the NBO 5.0
calculations.
1
FIG. 4. Contributions of individual structural energies to the torsional barrier in the ground state of 3MPY.
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