Origin of threefold symmetric torsional potential of methyl group in 4methylstyrene
Rajeev K. Sinha, B. Pradhan, Bhanu P. Singh, T. Kundu, Partha Biswas et al.
Citation: J. Chem. Phys. 124, 144316 (2006); doi: 10.1063/1.2189233
View online: http://dx.doi.org/10.1063/1.2189233
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THE JOURNAL OF CHEMICAL PHYSICS 124, 144316 共2006兲
Origin of threefold symmetric torsional potential of methyl group
in 4-methylstyrene
Rajeev K. Sinha, B. Pradhan, Bhanu P. Singh, and T. Kundua兲
Department of Physics, Indian Institute of Technology Bombay, Mumbai 400076, India
Partha Biswas and T. Chakraborty
Department of Chemistry, Indian Institute of Technology Kanpur, Kanpur UP-208016, India
共Received 27 October 2005; accepted 28 February 2006; published online 14 April 2006兲
To understand the effect of the para position vinyl group substitution in toluene on methyl torsion,
we investigated 4-methylstyrene, a benchmark molecule with an extended ␲ conjugation. The
assignment for a 33 cm−1 band in the excitation spectrum to the 3a2 torsional transition, in addition
to the assignments suggested previously for the other bands in the excitation spectrum, leads to the
model potentials for the ground as well as excited states with V3⬙ = 19.6 cm−1, V6⬙ = −16.4 cm−1 and
V3⬘ = 25.6 cm−1, V6⬘ = −30.1 cm−1, respectively. These potentials reveal that both in ground and
excited states, the methyl group conformations are staggered with a 60° phase shift between them.
MP2 ab initio calculations support the ground state conformations determined from experiments,
whereas Hartree-Fock calculations fail to do so. The origin of the modified ground state potential
has been investigated by partitioning the barrier energy using the natural bond orbital 共NBO兲
theoretical framework. The NBO analysis shows that the local delocalization 共bond-antibond
hyperconjugation兲 interactions of the methyl group with the parent molecule is sixfold symmetric.
The threefold symmetric potential, on the other hand, stems from the interaction of the vinyl group
and the adjacent ring ␲ bond. The threefold symmetric structural energy arising predominantly from
the ␲ electron contribution is the barrier forming term that overwhelms the antibarrier contribution
of the delocalization energy. The observed 60° phase shift of the excited state potential is attributed
to the ␲*-␴* hyperconjugation between out of plane hydrogens of the methyl group and the benzene
ring. © 2006 American Institute of Physics. 关DOI: 10.1063/1.2189233兴
I. INTRODUCTION
In methylated aromatic molecules, the rotation of the
methyl group experiences a periodic potential barrier in accordance with the symmetry of the parent molecule. This
hindered motion of the methyl group is an important factor
in intramolecular dynamics and hence makes the investigation on the origin of the potential barrier to its rotation interesting. An excellent review on the nature of the methyl internal rotation barrier for aromatic molecules was presented
by Ito.1 In the simple methylated aromatic molecule toluene,
the methyl group experiences a very small sixfold symmetric
barrier to its rotation2 due to six different equivalent methyl
group conformations with respect to the benzene plane. The
magnitude of this barrier depends mainly on the local chemical environment experienced by the methyl group during its
rotation.3–5 The ortho and meta substitutions in toluene2,3,5,6
reduce this sixfold symmetry, and the threefold symmetry in
the barrier becomes dominant. Yan and Spangler4,7 and Lu et
al.5 have shown that the interactions vicinal to the methyl
group play an important role in the determination of the
phase and the magnitude of the torsional potential barrier.
With the local geometry of the methyl group having a purely
sixfold symmetry, the barrier is small due to the cancellation
of two large threefold symmetric terms, as observed in the
a兲
Electronic mail: [email protected]
0021-9606/2006/124共14兲/144316/10/$23.00
case of para-fluorotoluene 共p-FT兲,3 para-tolunitrile 共p-TN兲,6
and p-xylene,2 and the conformation of the methyl group
having a CH-bond cis to the higher order C–C bond is favored when the repulsive steric interaction is unimportant.5
The asymmetric substitution at the para position is interesting in the sense that it retains the sixfold symmetry of the
methyl group with respect to the benzene ring, and the important aspect is to understand the symmetry of the electronic distribution over the benzene frame and its consequences to the potential barrier of the methyl rotation, as
observed in the case of p-methylanisole,8 in which a threefold barrier term appears in the potential function.
Styrene is one of the simple bichromophoric systems, in
which a ␲ conjugation of an aromatic ring is extended by a
vinyl substitution. 4-methylstyrene 共4MS兲, a methyl group
substituted at the para position in styrene, thus can be exploited to investigate the effect of this extended conjugation
on an aromatic system. The torsional characteristic in this
molecule was studied experimentally by Hollas and Taday9
using fluorescence excitation 共FE兲 and dispersed fluorescence 共DF兲 spectra. The sixfold torsional potential function
was enough to reproduce the observed low frequency transitions in the excitation spectrum but failed to explain the observed intensities. In the subsequent paper,10 utilizing the
threefold potential, torsional levels were reassigned in order
to explain the observed Frank-Condon intensities of these
transitions. Schmitt et al.11 used the rotationally resolved
124, 144316-1
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144316-2
Sinha et al.
spectrum of 4MS as well as ab initio calculations at B3LYP
and MP2 levels of theory with the 6-31G** basis set to explain the planarity of the molecule in both the ground and
first excited states and thus estimated the torsional potential
for the methyl rotation in the ground state. Biswas et al.12
have recently investigated this molecule to assign the vibrational levels and to understand the intramolecular vibrational
relaxation 共IVR兲 processes.
In order to investigate the relationship between the electronic structure and the methyl torsional barrier in
4-methylstyrene, we present the resolved fluorescence excitation and dispersed fluorescence spectra of this molecule. A
new assignment of a band in the excitation spectrum as a 3a2
torsional level modified the excited state 共S1兲 potential. The
ground state 共S0兲 potential has also been modified in the light
of ab initio calculations. The contribution of different interactions to the barrier energy has been analyzed using the
natural bond orbital 共NBO兲 analysis to decipher their roles in
the ground state methyl torsional barrier formation. The barrier energetics have been partitioned further into local structural and delocalization interactions to address the symmetrical aspects of this potential. The change in the methyl group
conformation in the excited state has been explained by the
␲*-␴* hyperconjugation. The role of orbital energies in the
excited state barrier formation has also been explored for this
molecule.
II. EXPERIMENTAL SECTION
The experimental setup used to measure the laserinduced FE and DF spectra has been described
elsewhere.13,14 Briefly, the 4-methylstyrene vapor at room
temperature was mixed with helium at a pressure of 2 atm
and expanded into the vacuum chamber through a magnetically controlled solenoid nozzle valve 共General Valve兲 of an
orifice diameter of 0.5 mm to generate the seeded supersonic
free jet. The jet cooled molecules were excited by a tunable
ultraviolet laser obtained as the doubled output of a dye laser
共Sirah Plasma Technik GmbH兲 pumped by the second harmonic of a Nd:YAG 共yttrium aluminum garnet兲 laser 共Spectra Physics, model: INDI兲. To measure the dispersed fluorescence spectra, a 0.75 m monochromator 共Spex, model:
750 M兲 with a grating of groove density of 2400 mm was
used to disperse the fluorescence before detection. The typical spectral resolution of the results presented here is
5 – 7 cm−1. The fluorescence was detected using a
Hamamatsu R928 photomultiplier tube, and the output signal
of the photomultiplier was averaged by a boxcar averager
共SRS 250兲. The data were stored in a personal computer.
4-methylstyrene was procured from Aldrich and purified by
vacuum distillation before use.
III. THEORETICAL BACKGROUND
Due to three equivalent hydrogen of the methyl group,
the barrier to the internal rotation is modeled as a Fourier
expansion 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 angle between the methyl
group and the benzene ring. If the parent molecule has no
rotational symmetry about the methyl rotor axis, V3 共the
J. Chem. Phys. 124, 144316 共2006兲
threefold symmetric term兲 will be nonzero, while for the
molecule having a twofold symmetry such as toluene and
p-fluorotoluene, there will be six equivalent minima and V6
共the sixfold symmetric term兲 becomes dominant. The Hamiltonian is expressed by H = −Fp2 + V, where F is the reduced
rotational constant of the methyl rotor about the methyl top
axis. The Hamiltonian is solved variationally by expanding
the wave function with the basis set of 21 one-dimensional
free rotor wave functions.
The large anharmonicity of the torsional motion and feasibility of the tunneling of the methyl group in an experimental time scale forbid the use of a point group to label these
energy levels. The permutation-inversion groups developed
by Longuet-Higgins15 and Bunker16 are useful in describing
such type of motion. The molecular states of ortho- and
meta-substituted toluenes are classified according to irreducible representations of the G6 molecular symmetry group and
para-substituted toluenes which have a twofold symmetry in
the molecular frame described by the G12 symmetry group.
Unlike p-fluorotoluene, whose energy levels are described by
the G12 symmetry, the presence of the asymmetric vinyl
group reduces the symmetry, and methyl torsional transitions
are assigned using the vibronic selection rules of the G6 molecular symmetry group for 4-methylstyrene. Within the G6
molecular symmetry group, the ordering of energy levels of
the internal rotation is 0a1 , 1e , 2e , 3a2 , 3a1 , 4e , 5e , . . ., and
selection rules are a1 ↔ a1, e ↔ e, and a2 ↔ a2. Due to different nuclear spin symmetries, 1e does not cool into 0a1 in a
supersonic jet cooled condition, and hence transitions occur
both from 0a1 and 1e levels of the ground electronic state in
the excitation spectrum.
IV. RESULTS AND DISCUSSIONS
The laser-induced fluorescence 共LIF兲 excitation spectrum of 4-methylstyrene in a supersonic jet around the S0
→ S1 transition is shown in Fig. 1共a兲. The spectrum is in
good agreement with that reported previously by Hollas and
Taday.9 The origin band is located at 34 279 cm−1. There are
many low frequency bands appearing within 100 cm−1 of
origin due to both methyl and vinyl group low frequency
vibrations. The bands at 17.4 and 53.4 cm−1 are the methyl
torsional 2e and 3a1 transitions in the excited state originating from 0a1 and 1e of the ground state, as assigned previously by Hollas and Taday.9 These methyl torsional bands
provide a sixfold symmetric torsional potential with V6⬘
= −17 cm−1 and F = 5.18 cm−1 to reproduce the observed energy levels in the excited state. The DF spectra upon excitation of origin, 2e, and 3a1 bands clearly showed that the
ground state methyl torsional levels were at 20.3 共2e兲, 52.8
共3a1兲, and 135.7 cm−1 共5e兲 respectively. Although a similar
kind of sixfold symmetric potential with V6⬙ = −17 cm−1 and
F = 5.20 cm−1 was enough to explain the observed ground
state energy levels, it was unable to reproduce the FrankCondon 共FC兲 intensity pattern observed both in excitation
and DF spectra. The addition of a threefold symmetric term
into the potential, with V3⬘ = −8 cm−1 and V6⬘ = −19 cm−1 for
the excited state and V3⬙ = 28 cm−1 and V6⬙ = −7 cm−1 for the
ground state,10 satisfies both the energy levels as well as the
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144316-3
J. Chem. Phys. 124, 144316 共2006兲
Methyl group in 4-methylstyrene
FIG. 2. Dispersed fluorescence spectrum of 4MS upon 33 cm−1 band
excitation.
FIG. 1. Fluorescence excitation spectrum of 4MS 共a兲 around the origin and
共b兲 expanded near the origin.
observed intensity distribution for these bands. Although 2e
and 3a1 species of the methyl torsional energy levels allow
one to reconstruct the model potential, the position of a2
species is an important factor to ascertain the parameters
which control the shape of the potential. But transitions to a2
levels are always symmetry forbidden in a jet cooled condition and hence remain absent in most cases. However, in the
case of p-fluorotoluene the band observed at 37 cm−1 in the
excitation spectrum was assigned as a torsional 3a2
transition,17 as no band near this frequency region was found
in the excitation spectrum of p-fluorostyrene18 due to the
absence of the methyl group in this molecule. Though this
transition is forbidden, sometimes it may gain intensity due
to the coupling of the internal rotation with the overall rotation or other low frequency modes present in the molecule.
In 4MS also, this is evident from the appearance of a weak
band at 45 cm−1 in the DF spectrum of the origin band 共Table
3 of Ref. 10兲 that was assigned as a 3a2 species in the ground
state from the prediction of the energy level calculation.
The fluorescence excitation spectrum near the origin
given in Fig. 1共b兲 shows two more bands appearing at 33 and
49 cm−1. To ascertain the characteristics, the DF spectra
upon excitation of these bands have been obtained. Figure 2
shows the Frank-Condon activity of the 33 cm−1 band with
the ground state vibrational modes. The transition to the origin of the ground state is most intense, as is evident from the
appearance of this band in the excitation spectrum. The band
appeared at 81 cm−1 due to the transition to the first overtone
of the vinyl torsion. A relatively weaker band at 42 cm−1
could arise due to the existence of the 3a2 torsional level of
the ground state. Since a2 ↔ a2 is an allowed transition, we
assign the 33 cm−1 band due to the transition to the 3a2 level
in the excited state. Since the vinyl torsional frequency is not
in this region,10 the assignment of the 33 cm−1 band as the
3a2 methyl torsional band of the excited state yields the best
fit potential parameters V3⬘ = 25.6 cm−1, V6⬘ = −30.1 cm−1, and
F = 4.76 cm−1. The calculated energy levels are given in
Table I. Although this parameter set fits the 2e level at
17.4 cm−1 and the 3a1 level at 53.4 cm−1, it produces the 3a2
at 37 cm−1 instead of at 33 cm−1. A better fit of the 3a2 level
requires F to be changed drastically, which implies a dramatic distortion of the conformation of the methyl group.
The FC activity of this band with the vinyl torsion suggests
that this a2 species gets coupled with the vinyl motion and
could undergo a frequency shift due to this coupling. Thus,
this one-dimensional description of the methyl torsion may
not be sufficiently adequate to explain the observed frequency for this band. However, the DF spectrum from the
49 cm−1 band did not produce any band near the frequency
region 共⬃42 cm−1兲 in the ground state and could not be assigned as 3a2. This band is also not a part of the rotational
contour of the 53 cm−1 共3a1兲 band. A comparison between
dispersed fluorescence spectra of these bands is presented in
Fig. 3.
From the torsional energy levels of the ground state observed in the dispersed fluorescence spectra 共Table I兲, we
derive the torsional parameter set for the ground state as
V3⬙ = 19.6 cm−1, V6⬙ = −16.4 cm−1, and F = 5.25 cm−1. These
TABLE I. Torsional energy levels and torsional potential parameters in the
ground and excited states of 4MS.
Ground state
V⬙3 = 19.6 cm−1,
V⬙6 = −16.4 cm−1,
F = 5.25 cm−1
Excited state
V⬘3 = 25.6 cm−1,
V⬘6 = −30.1 cm−1,
F = 4.76 cm−1
Torsional
levels
Obs. 共cm−1兲
calc. 共cm−1兲
Obs. 共cm−1兲
calc. 共cm−1兲
0a1
1e
2e
3a2
3a1
4e
5e
6a2
6a1
0.0
0.0
18.0
45.0
53.0
¯
126
¯
190
0.0
4.4
18.0
44.0
53.0
80.3
127.8
190.0
190.2
0.0
0.0
17.4
33.0
53.4
¯
¯
¯
¯
0.0
3.8
17.4
37.0
53.4
75.7
118.0
173.6
174.3
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144316-4
Sinha et al.
FIG. 3. Dispersed fluorescence spectrum of 4MS upon 共a兲 49 cm−1 and 共b兲
53 cm−1 band excitations.
parameters are not very different from the previously reported values,10 however, this set produces the minimum
configuration of the methyl group at 30° instead of at 0°, as
discussed later. Although the FC intensity factors are not so
sensitive on this small change of the parameter set, we
present the simulated spectra of the dispersed fluorescence
J. Chem. Phys. 124, 144316 共2006兲
FIG. 5. Experimentally determined methyl torsional potential curves for
4MS in 共a兲 the ground state 共b兲 the excited state.
共Fig. 4兲 calculated with these modified potentials to ascertain
their relative positions. A good agreement is found with a
shift of the excited state potential by 60° relative to the
ground state 共Fig. 5兲.
There are three possible minimum energy conformations
adopted by the methyl group depending on the magnitude
and sign of the potential parameters: 共a兲 the pseudo-trans
conformation having one of the methyl CH bonds in the
plane of the ring and which lies on the other side where a
substituent is placed, 共b兲 the pseudo-cis conformation having
one of the methyl CH bonds in the plane of the ring and
which lies on the same side where a substituent is placed,
and 共c兲 the staggered conformation where one of the CH
bonds remains perpendicular to the plane. These conformations are shown in Fig. 6. For a purely V6 potential, only two
conformations are defined. Conformers. 共a兲 and 共b兲 become
equivalent and, together, are described as an eclipsed conformer. This conformation refers to the positive value of V6.
The second conformer is 共c兲, described as staggered referring
to the negative value of V6. In the case of the pure V3 potential, the minimum energy conformation for positive V3 is
pseudo-trans 共a兲 and for negative V3 is pseudo-cis 共b兲. When
the sixfold term is comparable to the threefold term, the conformational preference is energetically subtle. The large and
negative V6 indicates that an equilibrium conformation of the
methyl group in 4MS tends to attain a staggered conformation 共c兲. As evident from potential energy curves given in
Fig. 5, the potential minima occur near 30° or 90°, implying
that the conformation of the methyl group in ground and
excited states is staggered. A theoretical investigation in this
regard is presented in the next section.
V. ORIGIN OF THE THREEFOLD TERM
IN THE POTENTIAL BARRIER
FIG. 4. Comparison of experimental and simulated dispersed fluorescence
spectra upon excitation of 共a兲 3a1 and 共b兲 2e bands.
The GAUSSIAN 98 suite of programs19 was used for geometry optimization as well as for the torsional potential
determination of 4MS in both ground and excited states.
NBO calculations were performed using NBO 5.0 共Ref. 20兲
interfaced with GAUSSIAN 98. The visualization softwares
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144316-5
J. Chem. Phys. 124, 144316 共2006兲
Methyl group in 4-methylstyrene
FIG. 6. Conformations of the methyl
group in 4MS: 共a兲 pseudo-trans
共␶ = 0 ° 兲 共b兲 pseudo-cis 共␶ = 180° 兲, and
共c兲 staggered 共␶ = 90° 兲.
NBOVIEW 1.0 共Ref. 21兲 and MOLDEN 共Ref. 22兲 were used for
structure and orbital plots.
A. Ground state
In the ground state, the geometry of the molecule was
optimized with HF/B3LYP/MP2 levels of theories employing Pople-type 6-31G* / 6-31G** / 6-311G** / 6-31+ G** / 6311+ + G** basis sets. The optimized geometry of the molecule with HF/ 6-31G** is pseudo-trans with one C–H bond
of the methyl group lying in the plane of the ring 关Fig. 6共a兲兴.
The potential parameters were calculated with abovementioned levels of theories and basis sets by using a fully
relaxed model.23 The numerical values of the potential parameters are summarized in Table II along with the experimental values. At HF and B3LYP levels of theory, the threefold term is in agreement with the experimental value when
basis sets without a diffused function are used. However, the
sixfold term exhibits a large deviation from the experimental
value. The incorporation of diffused functions increases the
threefold term up to some extent but has very little effect on
the sixfold term. The numerical value of the threefold term
with HF/ 6-31G** is very close to the experimental value, but
that of the sixfold term shows a large deviation. On the other
hand, MP2 calculations, as they account for the electron correlation effect, inherently predicts the observed shape of the
potential even though the threefold term is not in quantitative
agreement with the experiment. The potentials obtained for
4MS with HF/ 6-31G** and MP2 / 6-31G** are shown in
Fig. 7.
The absence of the threefold term in the torsional barrier
on para-substituted molecules such as p-fluorotoluene,3
p-tolunitrile,6 and p-xylene2 is attributed to the overall molecular symmetry of these molecules about the methyl rotor
axis, which allows six equivalent conformations for the methyl group in the course of the 2␲ rotation about the C–C
bond. Yan and Spangler and Lu et al.5 proposed a similar
argument by emphasizing the two equivalent sides of the
planar parent molecule, which cause the cancellation of the
threefold term. In order to get more insight into it, we bisected 4MS about the methyl rotor axis 关as shown in Fig.
6共a兲兴 and tried to explore the character of the threefold term
by comparing the individual orbital interactions on both
sides of the plane of bisection in pseudo-trans and pseudocis conformers using the NBO formalism. The NBO 共Ref.
24兲 analysis was quite successful in understanding the internal rotation potential barrier in many aliphatic25 as well as
aromatic5,26 molecules. Under this analysis, the total barrier
energy is partitioned into Lewis and delocalization energies
as
⌬Ebarrier = ⌬Elewis + ⌬Edeloc ,
共1兲
where ⌬Edeloc is the hyperconjugative energy contribution
that arises due to bond-antibond interactions and ⌬ELewis is
TABLE II. Ab initio methyl torsional potential parameters in the ground
state of 4MS calculated using different levels of theories.
Level of theory
V3 共cm−1兲
V6 共cm−1兲
HF/ 6-31G**
HF/ 6-31+ G**
HF/ 6-31+ + G**
HF/ 6-311+ G**
HF/ 6-311+ + G**
MP2 / 6-31G**
MP2 / 6-31+ G**
B3LYP/ 6-31G**
B3LYP/ 6-31+ G**
B3LYP/ 6-31+ + G**
B3LYP/ 6-311+ G**
B3LYP/ 6-311+ + G**
Experiment
20.1
24.1
24.3
32.0
31.2
7.3
8.2
18.7
20.1
20.2
20.15
20.3
19.6
−2.0
−1.5
−3.2
−3.0
0.5
−21.0
−30.4
−3.3
0.0
−2.6
−3.0
−1.0
−16.4
FIG. 7. Methyl internal rotational potential curve for 4MS calculated at
共a兲 HF/ 6-31G** and 共b兲 MP2 / 6-31G** levels.
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144316-6
J. Chem. Phys. 124, 144316 共2006兲
Sinha et al.
1. Delocalization energy change
FIG. 8. Torsional angle dependence of the relative total energy, Lewis energy, and delocalization energy using the HF/ 6-31G** level of calculation.
the energy contribution from the steric repulsion and the valence effect. Figure 8 shows the torsional angle dependence
of the barrier energy, the delocalization energy, and the
Lewis energy calculated with HF/ 6-31G**. The small torsional barrier energy results from the cancellation of two
large threefold symmetric interactions, and ⌬ELewis favors
the barrier energy over the energy contribution from delocalization interactions.
To get further insight into these energies, we focused on
the change in individual interactions of the molecule in the
course of the methyl rotation. In the following discussion we
explore the importance of individual orbital interactions
through non-Lewis 共delocalization兲 and Lewis energy
changes due to the rotation of the methyl group from the
equilibrium conformation to the top of the barrier. The results presented here were performed with the HF/ 6-31G**
level of theory, as the other basis sets do not show a significant change in orbital interactions. Since this level of theory
predicts the magnitude of the threefold term similar to the
experimental value, our analysis here is based on this level of
theory.
We followed the procedure suggested by Reed and
Weinhold27 for the calculation of the bond-antibond interaction energies. A mere comparison of orbital interactions between pseudo-trans and pseudo-cis conformers shows that
the interactions of the methyl group with the adjacent bonds
共C3C4 and C4C5 in Fig. 6兲 of the benzene ring are in one to
one correspondence, hence, canceling one another completely. On the other hand, in the case of interactions involving the vinyl group and adjacent bonds 共C1C2 and C1C6兲 of
the benzene ring, the interaction corresponding to the bonding ␲ electron of the vinyl group and the antibonding ␲* of
the benzene ring undergoes a change with a decrease in its
value from 3502 to 2837 cm−1 while going from the pseudotrans to the pseudo-cis conformation 共this result is obtained
by using a single deletion procedure25,27兲. So, in the case of
4MS, remote interactions rather than vicinal to the methyl
group are important in the determination of the threefold
term. Since there is a decrease in energy from the pseudotrans to the pseudo-cis conformation, the delocalization energy is stabilizing in nature. This is also evident from the
energy partition curve in Fig. 8. The corresponding NBO
orbital plot shown in Fig. 9 for this interaction shows an
effective increase in the overlap of orbitals in the pseudo-cis
conformation between the vinyl group and the benzene ring
than in the pseudo-trans conformation. Since this interaction
is attractive, more overlaps imply a stabilization of the
pseudo-cis conformation due to this interaction. Thus it is
evident that the delocalization interactions adjacent to the
methyl group have the sixfold symmetry, whereas the threefold symmetry considering the overall energy appears due to
the remote interactions of the ring and the vinyl group.
2. Lewis energy
The Lewis energy contribution to the barrier, ⌬Elewis, can
further be partitioned into steric energy and structural energy
changes:
FIG. 9. Orbital interactions of 共a兲 bonding 共␲C1C6兲 and
*
兲 orbitals in the pseudo-trans
antibonding 共␲C7C8
共␶ = 0 ° 兲 conformation and 共b兲 bonding 共␲C1C2兲 and an*
兲 in the pseudo-cis 共␶ = 180° 兲
tibonding 共␲C7C8
conformation.
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144316-7
J. Chem. Phys. 124, 144316 共2006兲
Methyl group in 4-methylstyrene
FIG. 10. Contribution of individual structural energies
to the torsional barrier in the ground state of 4MS.
⌬Elewis = ⌬Esteric + ⌬Estruc ,
共2兲
where ⌬Esteric is the change in steric energy 共a consequence
of the Pauli exclusion principle兲 not incorporating the valence effect and ⌬Estruc is the change in structural energy 共a
consequence of the Coulomb repulsion and the bond energy
change in the classical Lewis structure during the internal
rotation兲.
a. Steric Interactions The steric exchange energy is an
important part of the total Lewis energy of a molecule and is
very useful for the explanation of the torsional barrier formation in the case of ortho- and meta-substituted molecules.5,28
We investigated the change in the total NBO steric exchange
energy as well as the pairwise exchange energy29 in going
from the pseudo-trans to the pseudo-cis conformation. In the
case of the pseudo-cis conformer, the total NBO exchange
energy is 784.38 kcal/ mol against the 784.42 kcal/ mol in
the pseudo-trans conformation, while the pairwise exchange
energy in the pseudo-cis conformation is 224.28 kcal/ mol
against the 224.49 kcal/ mol of the pseudo-trans conformer.
The contribution to the barrier energy was obtained by
taking the difference between these two conformer energies.
A very low contribution of −0.04 kcal/ mol 共−14 cm−1兲 due
to the total steric exchange energy and −0.21 kcal/ mol
共−73.4 cm−1兲 due to the pairwise exchange energy to the
barrier are obtained. Thus the steric contribution to the barrier is much less compared to the delocalization contribution.
The negative sign of the steric energy reflects its antibarrier
nature. So, in the HF/ 6-31G* level of theory, the contribution due to the steric term only is not of utmost importance.
b. Structural energy In view of the insignificant role of
the steric interaction in barrier formation, the other Lewis
energy term, the structural term, needs to be investigated.
The change of the bond energy, which corresponds to the
structural energy, can be obtained as30
⌬ ␻ = ␧ cn c − ␧ tn t ,
共3兲
where ␧c and ␧t represent the bond energy of the pseudo-cis
and pseudo-trans conformations, respectively, and nc and nt
indicate the charge occupation of the corresponding state.
The bar plot of the structural energy change 关共pseudo-cis兲共pseudo-trans兲兴 is shown in Fig. 10. Among the contributions
involving ␴ electrons, the positive contribution from C1C6,
C4C5, and C2C3 are balanced by the negative contribution
from C1C2, C3C4, and C5C6, respectively. The three major
contributors to the structural energy change 共20, 21, and 22
in Fig. 10兲 appear due to the change in the ␲ electron cloud
of the benzene ring while going from the pseudo-trans to the
pseudo-cis conformation. This distortion in the ␲ electron
cloud of the benzene ring is due to the relaxation of the
molecule in the pseudo-cis conformer as compared to the
pseudo-trans conformer. The angle opening of C9C4C3 by
0.93° and the angle closing of C8C7C1 by 0.19° from the
pseudo-trans to the pseudo-cis state are the major structural
changes observed.
To lend further support to the above inference, we analyzed the structural energy contribution by partitioning the
energy on two sides 共side A and side B in Fig. 6兲 of the
methyl rotor axis for the pseudo-trans and pseudo-cis conformations of the methyl group into ␴ and ␲ electron contributions. Results of these calculations are presented in Table
III. It can be seen that in going from the pseudo-trans to the
pseudo-cis conformation both ␴ and ␲ electronic energy
contributions decrease for side A of the molecule, while for
side B both of these increase. The total change in the ␲
electron energies for sides A and B is 6941 cm−1 as against
208 cm−1 for ␴ electron energies. Since the total structural
change in energy is 7149 cm−1, the major contribution to the
torsional barrier seems to be appearing from the ␲ electron
energy for side B of the molecule.
Thus far, we have calculated only the threefold term 共V3兲
in the potential, as HF predicts very low values for the V6
term. On the other hand, MP2 calculations predict comparable magnitudes for both V3 and V6 terms. It thus appears
that due to the inclusion of electron correlation in MP2, the
local sixfold interactions dominate. As a consequence, the
methyl group conformation in the ground state would neither
be pseudo-cis nor pseudo-trans. The minimum energy con-
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144316-8
J. Chem. Phys. 124, 144316 共2006兲
Sinha et al.
TABLE III. Partition of structural energies between ␴ and ␲ electron energies of the ring in 4MS. 共␴CA − ␴TA
= ⌬␴A = −2102 cm−1; ␴CB − ␴TB = ⌬␴B = 2310 cm−1; ␲CA − ␲TA = ⌬␲A = −96 698 cm−1; ␲CB − ␲TB = ⌬␲B = 103 639 cm−1;
⌬␴Total = ⌬␴A + ⌬␴B = 208 cm−1; ⌬␲Total = ⌬␲A + ⌬␲B = 6941 cm−1; total structural energy= ⌬␴Total + ⌬␲Total
= 7149 cm−1兲.
Pseudo-trans
Side A
Bonds
Bond
energy
共cm−1兲
␴TA
␲TA
−1 179 526
−112 805
pseudo-cis
Side B
Bonds
Bond
energy
共cm−1兲
␴TB
␲TB
−1 183 527
−214 394
formation would rather be staggered, in agreement with the
experimental observation.
B. Excited state
Many aromatic and heterocyclic methyl-containing molecules were found to exhibit a profound change in the barrier
height and a 60° rotation of the methyl group upon excitation. To explain this behavior, Nakai and Kawai31 and Nakai
and Kawamura32 have pointed out a new type of interaction,
namely, the ␲*-␴* hyperconjugation using a molecular orbital theory. By considering such an interaction they were
able to successfully interpret the variation of the barrier magnitude and the methyl group conformation for substituted
toluenes,31 naphthalenes,32 and azabenzenes33,34 in the excited state. While a conventional hyperconjugation appears
between an occupied bond orbital or lone pair and an unoccupied antibond orbital, the ␲*-␴* hyperconjungation appears between an unoccupied ring ␲* orbital and an unoccupied CH ␴* orbital. This hyperconjugation leads to a weak
intramolecular bonding between the out-of-plane methyl hydrogen and the ring.
We also find that this ␲*-␴* hyperconjugation mechanism is well applicable to 4MS in explaining the methyl
group behavior. In this scheme, the focus is on the excitation
energy instead of on the total energy to obtain the potential
energy curve for the excited state. The excitation energies of
4MS was calculated by configuration interaction single excitation 共CIS兲 / 6-31G共d , p兲 and TDB3LYP/ 6-31G共d , p兲 methods. Although the absolute value of the excitation energy in
both CIS 共⬃5.8 eV兲 and TDB3LYP 共⬃4.8 eV兲 is somewhat
overestimated than the experimental value 共4.25 eV兲, the
relative change in the excitation energy during the methyl
rotation was focused. To determine the potential energy
curve for the excited state, we calculated the vertical excitation energy using the ground state optimized geometry at
discrete torsional angles of the methyl group and then subtracted ground state potential energies from this. The variation of these energies with respect to the minimum energy
was plotted against the torsional angle. The barrier height is
found to be 165 cm−1, overestimated than the observed value
of 18 cm−1. It is apparent from the potential curve 共Fig. 11兲
that in the excited state potential minima is shifted 60° with
respect to the ground state. While the spectroscopic results
are inadequate to specify the energetically preferred confor-
Side A
Side B
Bonds
Bond
energy
共cm−1兲
Bonds
Bond
energy
共cm−1兲
␴CA
␲CA
−1 181 628
−209 503
␴CB
␲CB
−1 181 216
−110 755
mation of the methyl group relative to the ring frame, these
results certainly predict changes in orientation accompanying
the electronic excitation. Geometry optimization at the
CIS/ 6-31G** level shows also the conformer rotated by 60°
than ground state as the minimum energy conformer. The
molecular orbital picture gives better understanding as regard
to the conformational preference adopted by methyl group in
both the electronic states. Figure 12 shows the orbital contour plot of the highest occupied molecular orbital 共HOMP兲
and the lowest unoccupied molecular orbital 共LUMO兲 of
4MS at ␶ = 0° and ␶ = 180° displaying the relative stability of
corresponding orbital energies. In 4MS, the ␲*-␴* hyperconjugation between the methyl C–H antibond and the ring ␲
antibond is found to be present in the LUMO at ␶ = 180°, thus
stabilizing the eclipsed conformer in the excited state. To
comprehend the nature of the barrier, torsional angle dependences of orbital energies were plotted. In the first order
treatment the excitation energy variation is expressed by
⌬ES0→S1 ⬇ ␧LUMO − ␧HOMO − JHOMO,LUMO + KHOMO,LUMO
= ⌬␧HOMO→LUMO − JHOMO,LUMO + KHOMO,LUMO .
Here, ⌬ES0→S1 is the excitation energy, ␧ is the orbital energy, and J and K are Coulomb and exchange integrals, respectively. Figure 13 shows the dependence of ␧HOMO,
FIG. 11. Potential energy curves for the methyl internal rotation in the
excited 共S1兲 state obtained by taking the difference of the excitation energy
and the ground state potential 共S0兲.
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144316-9
J. Chem. Phys. 124, 144316 共2006兲
Methyl group in 4-methylstyrene
FIG. 12. Contour diagrams of the HOMO and LUMO of 4MS at pseudotrans 共␶ = 0 ° 兲 and pseudo-cis 共␶ = 180° 兲 conformations using the same level
of sensitivity. The pseudo-cis conformer shows the ␲* − ␴* hyperconjugation
methyl CH␴* and the ring ␲* in LUMO, stabilizing this conformation in the
excited state.
␧LUMO, and ⌬␧HOMO→LUMO on ␶. The variation of the HOMO
energy with respect to the torsional angle is feeble compared
to that of the LUMO. Thus, the LUMO plays a key role in
determining the barrier in the excited state as compared to
the HOMO.
motion reveal that in both ground and excited states, minimum energy conformations of the methyl group are staggered with a 60° shift in phase. This is the consequence of
the admixture of threefold and sixfold symmetric interactions
with comparable magnitudes between the methyl group and
the molecular frame. For the ground state, the threefold term
in the barrier stems from the partial cancellation of two large
opposite interactions, namely, bond-antibond hyperconjugation and structural energy. A detailed investigation of these
energies in terms of various local interactions within the
NBO theoretical framework shows that there is a complete
cancellation of local threefold bond-antibond interactions
with the methyl group. However, the same is not the case for
structural energies. The origin of the barrier thus cannot be
understood without molecular flexing involving a dominant
role of ␲ electrons. This is the consequence of the extended
␲ conjugation between the ring and the vinyl group at a
remote position. The ␲ electron conjugation energy of the
two 共ring and vinyl group兲 in the pseudo-cis conformation is
more than that in the pseudo-trans conformation. The observed sixfold symmetric term, comparable to the threefold
term in the potential, arises from the local interactions between the ring and the methyl group. The staggered conformation is a manifestation of these interactions. Thus the remote para position asymmetric substitution in such
molecules facilitates tailoring of the ␲ electron conjugation
and hence the barrier. The control of such methyl torsional
barrier may have important implications for chemical and
biological processes.
ACKNOWLEDGMENTS
VI. CONCLUSION
With a view to understand the effect of asymmetric substitution at the para position on methyl rotation in toluenelike molecules, we investigated 4MS. From a highly resolved
excitation spectrum, a new band observed at 33 cm−1 is assigned as a 3a2 transition in the excited state. The model
potentials evaluated from this observation for the torsional
FIG. 13. Variation of HOMO, LUMO, and LUMO-HOMO energies as a
function of the torsional angle ␶.
This work was supported by the Department of Science
and Technology, India. The authors are thankful to Dr. R. B.
Sunoj for providing the facilities for NBO calculations.
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