vapor-phase raman spectra, theoretical calculations, and the vibrational and structural properties...

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Article

Vapor-Phase Raman Spectra, Theoretical Calculations and theVibrational and Structural Properties of cis- and trans-Stilbene

Toru Egawa, Kiyoaki Shinashi, Toyotoshi Ueda, Esther J. Ocola, Whe-Yi Chiang, and Jaan LaaneJ. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/jp410271h • Publication Date (Web): 13 Jan 2014

Downloaded from http://pubs.acs.org on January 18, 2014

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Vapor-Phase Raman Spectra, Theoretical Calculations and the Vibrational

and Structural Properties of cis- and trans-Stilbene

Toru Egawaa*, Kiyoaki Shinashib,c, Toyotoshi Uedad,

Esther J. Ocolab, Whe-Yi Chiangb, and Jaan Laaneb*

a College of Liberal Arts and Sciences, Kitasato University, Kitasato 1-15-1, Minami-ku, Sagamihara,

Kanagawa 252-0373, Japan

b Department of Chemistry, Texas A&M University, College Station, Texas 77843-3255, U.S.A.

c Department of Law, Chuogakuin University, Kujike 451, Abiko, Chiba 270-1196, Japan

d Department of Interdisciplinary Sciences and Engineering, Meisei University, Hodokubo 2-1-1, Hino, Tokyo

191-8506, Japan

Abstract

The vapor-phase Raman spectra of cis- and trans-stilbene have been collected at high

temperatures and assigned. The low-frequency skeletal modes were of special interest. The

molecular structures and vibrational frequencies of both molecules have also been obtained

using MP2/cc-pVTZ and B3LYP/cc-pVTZ calculations, respectively. The two-dimensional

potential map for the internal rotations around the two Cphenyl–C(=C) bonds of cis-stilbene

was generated by using a series of B3LYP/cc-pVTZ calculations. It was confirmed that the

molecule has only one conformer with C2 symmetry. The energy level calculation with a

two-dimensional Hamiltonian was carried out, and the probability distribution for each level

was obtained. The calculation revealed that the "gearing" internal rotation in which the two

phenyl rings rotate with opposite directions has a vibrational frequency of 26 cm–1, while that

of the "antigearing" internal rotation in which the phenyl rings rotate with the same direction

is about 52 cm–1. In the low vibrational energy region the probability distribution for the

gearing internal rotation is similar to that of a one-dimensional harmonic oscillator, and in the

higher region the motion behaves like that of a free rotor.

*Corresponding Authors, Email address: [email protected], Phone: 979-845-3352; E-mail address: [email protected], Phone/Fax: +81-42-778-8088.

Keywords: cis-stilbene, trans-stilbene, Raman spectra, DFT calculations, internal rotation, potential energy surface, two-dimensional analysis, gearing internal rotation.

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1. Introduction

There have been many experimental and theoretical reports about the cis-trans

isomerization of stilbene (see Ref. 1 and references therein). Among the most recent studies,

Nakamura and co-workers2 measured fluorescence of cis-stilbene in a solution after

excitation at 270 nm with a time resolution of 270 fs to investigate the reaction path of the

cis-trans isomerization via the S1 state. Han and co-workers3 obtained the potential energy

curves for the torsion around the C=C double bond of stilbene, which enables the cis-trans

isomerization, in the electronic excited states as well as the ground state by using the DFT

method. A similar investigation was carried out by Improta and Santoro,4 where the potential

surfaces of stilbene as a function of the C=C torsional angle and other torsional or bending

angles in some electronic states were obtained by using the time-dependent DFT method.

Improta's group5 also investigated the dependence of the excitation energies from the ground

state to some excited states of trans-stilbene on its Cphenyl–C(=C) torsional angle.

In addition to the internal rotation around the C=C double bond, the phenyl internal

rotations around the two Cphenyl–C(=C) bonds are a subject of interest. In considering the

nature of the internal rotation of the phenyl groups, it is not a safe assumption that the two

phenyl rings can rotate independently of each other. It is possible that the internal-rotation

potential function for one phenyl ring more or less depends on the torsional angle of the other

(so-called cog-wheel effect6) because of the conjugation among the π electrons of the two

phenyl rings and the C=C bond. In the case of cis-stilbene the steric repulsion between the

phenyl rings would be another source of the cogwheel effect.

In contrast with trans-stilbene, for which the internal rotations have been investigated

extensively,7 there have been fewer reports for the cis-stilbene. The gas-phase molecular

structures of the both isomers of stilbene have been investigated by Traetteberg and co-

workers by means of gas electron diffraction.8,9 The gas phase Raman spectrum of trans-

stilbene was measured by the Laane group10 and will be discussed more extensively in the

present paper. Arenas and co-workers11 measured infrared and Raman spectra of solid trans-

stilbene and pure liquid cis-stilbene and assigned the observed vibrational frequencies using

theoretical calculations of the force constants.11,12 In 2002 Watanabe and co-workers13

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reported a thorough infrared and Raman investigation of trans-stilbene in solution and

complemented the study with theoretical calculations. Extensive theoretical calculations

were carried out by Choi and Kertesz14 to obtain the vibrational frequencies of cis- and trans-

stilbene as well as their structural parameters by using various basis sets and methods,

including MP2 and DFT (B3LYP). Simulated infrared and Raman spectra of cis- and trans-

stilbene have been provided by Negri and Orlandi15 and Baker and Wolinski.16 The

theoretical one-dimensional torsional potential of the phenyl ring was obtained by Chen and

Chieh17 for the trans-stilbene. In that study, the geometrical parameters were also calculated

for the cis and trans isomers.

The two-dimensional potential surface of stilbene as a function of phenyl torsional

angles, Cphenyl–C(=C), has been obtained only for the trans isomer. Chiang and Laane7

measured the fluorescence excitation spectrum and dispersed fluorescence spectrum of trans-

stilbene, and the observed transition frequencies were used to determine the parameters of the

two-dimensional potential surfaces for the S0 and S1 states.7 The potential parameters

obtained for the S0 state were further refined by Melandri and co-workers.18 Orlandi and co-

workers19 carried out B3LYP/6-31G* calculations to obtain the theoretical two-dimensional

potential surface, which was further refined by using the observed energy level spacings

taken from the literature. There has been no similar study for cis-stilbene, for which only a

one-dimensional potential function for torsion has been obtained from the B3LYP/6-31+G(d)

calculations.20

In the present study the equilibrium structures and the vibrational frequencies of both

trans- and cis-stilbene have been obtained by means of theoretical calculations, and these

frequencies have been compared to the vapor-phase Raman spectra. For the cis isomer its

two-dimensional potential map for the internal rotations of the phenyl rings has been made.

Then, the energy levels and the corresponding probability distributions have been calculated

by using a two-dimensional Hamiltonian with a particular interest in investigating the gear-

like concerted internal rotations. A large number of basis functions have to be used in order

for the analysis with a multi-dimensional Hamiltonian to provide a reliable result. In

addition, huge amounts of computation have to be performed to get the corresponding multi-

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dimensional probability distributions. The computer resources that are available today have

made such a process possible.

2. Experimental section

The samples of trans- and cis-stilbene were purchased from Aldrich Chemical Co. without

further purification. Vapor-phase Raman spectra were recorded at right angle scattering

geometry using an Jobin Yvon U-1000 monochromator equipped with 1800 groves mm-1

holographic grating and PMT or CCD detection. The resolution was 1 cm-1. A Coherent

Radiation Innova 20 argon ion laser operating at 6W at 514.5 nm (2 W at the sample) was

used as the excitation source. Polarization measurements utilized a scrambler along with the

polarizing film oriented in either the parallel or perpendicular orientation. A homemade

single-pass gas cell10,21 was used to contain 760 torr of the trans-stilbene, achieved by

heating the solid sample to 330°C. The liquid cis-stilbene was heated in a similar cell to

obtain approximately 1 atm of vapor pressure of the sample. The spectra of trans-stilbene

were recorded at 330°C using PMT detection, while the spectra of cis-stilbene at 240°C were

recorded using a CCD. Because of the high temperatures used, not all attempts to record the

spectra were successful since sample decomposition or decolorization would sometimes

occur. As a consequence, we were not able to record the spectrum of the cis-stilbene in the

higher frequency region. It should also be noted that no Raman bands below 100 cm-1 could

be observed due to the high laser power used and the scattering from the glass cell and

windows.

3. Theoretical calculations

Structure optimization. The geometrical parameters of cis- and trans-stilbene were

optimized without structural constraints by using Gaussian 09 software.22 The method used

was MP223-26 with a cc-pVTZ27 basis set. For the investigation of the conformational

properties, the structural optimization of planar (C2v symmetry) cis-stilbene was also carried

out. Additional calculations were carried out for cis-stilbene using MP2 level of theory and

the aug-cc-pVTZ basis set in order to test whether this augmented basis set would produce

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different results. Previous calculations on trans-stilbene28 concluded that the augmented

basis set was not needed, and we have confirmed that here. All the calculated distances from

the MP2/cc-pVTZ and the MP2/aug-cc-pVTZ calculations agreed within ±0.001Å and all of

the angles agreed within ±0.2°.

Frequency calculations. The vibrational frequencies of cis- and trans-stilbene with

their IR and Raman intensities were calculated by using the same software suite. The method

used was B3LYP 29,30 with a cc-pVTZ basis set. The scaling factors used were 0.985 for

frequencies below 1500 cm-1, 0.973 for 1500 cm-1 to 2000 cm-1 and 0.961 above. The

descriptions of the normal modes were given according to their potential energy distributions

calculated by using the force constants obtained from the B3LYP calculations.

Potential energy calculations. The two-dimensional potential map for the internal

rotations around the two Cphenyl–C(=C) bonds of cis-stilbene was obtained by means of a

series of geometry optimizations in which only the torsional angles of the phenyl rings,

��(C2=C1–C3–C4) and ��(C1=C2–C9–C10), were fixed independently at 0° to 90° with

intervals of 15° (see Figure 1 for the atom numberings). Gaussian 0922 was also used for this

purpose as was the B3LYP method with a cc-pVTZ basis set. This combination of the

method and basis set, B3LYP/cc-pVTZ, was used in calculating the two dimensional

potential surface of ethoxybenzene with successful reproduction of the experimental result.31

Natural bond orbital (NBO) calculations. NBO calculations were performed at the

MP2 level of theory and the cc-pVTZ basis set using Gaussian 09 linked to the NBO 5.9

program.32 These calculations were done for the trans-stilbene and cis-stilbene both with C2

symmetry (conformational minimum) and with C2v symmetry (totally planar skeleton). The

AMPAC/AGUI software33 was used to visualize the structures, vibrations and results of the

NBO calculations.

4. Symmetry

The above-mentioned theoretical calculations revealed that cis-stilbene has only one

unique conformer with C2 symmetry on the potential surface. Accordingly, the symmetry

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species for the normal modes should be 37A + 35B. The ν37 mode of the A species and the ν72

mode of the B species consist mainly of the internal rotations of the two phenyl rings. In ν37,

the two phenyl rings rotate with the same direction, and in ν72, they rotate with the opposite

directions like a pair of gears. In the following sections, the motions for the ν37 and ν72 modes

are referred to the "antigearing" and "gearing" motions, respectively.

If the gearing and antigearing motions are feasible as large amplitude internal

rotations that allow the molecule to switch from one minimum on the potential surface to

another, it is appropriate to treat the molecular symmetry by means of a permutation

inversion group rather than a point group. In that case, cis-stilbene is considered to have G16

symmetry of the permutation inversion group, which is isomorphous with the D4h point

group. According to the Longuet-Higgins' notation of the symmetry species,34 the ν37 and ν72

modes belong to A1– and B1

– of the G16 group, respectively.

For trans-stilbene the molecule is planar with C2h symmetry, which was confirmed by

the theoretical calculations.

5. Vapor-phase Raman spectra

The vapor-phase Raman spectrum of trans-stilbene has previously been reported, but the

vibrational assignments were not given.10 A complete assignment of the infrared and Raman

spectra in solution was reported by the Furuya and Tasumi groups,13 who also carried out

theoretical calculations and presented a detailed description of all of the vibrations. The

molecule is planar and has C2h symmetry for which only the 25 Ag and 11 Bg vibrations are

Raman active. The 12 Au and 24 Bu vibrations are only infrared active. Figure 2 shows the

vapor-phase spectrum and compares it to the computed spectrum. Table 1 presents a listing

of the observed frequencies and assignments and compares these to the solution work and to

our theoretical calculations. The vapor, solution, and calculated frequencies all agree quite

well with each other. The lower frequencies were discussed extensively by Chiang and

Laane.7 A particularly significant result is that the overtone of the low-frequency mode ν72 at

152 cm-1 was observed as a strong polarized band. We had previously7 assigned this as ν25,

but the theoretical calculations show that ν25 should be near 202 cm-1. We now believe that

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transitions observed at 202 and 211 cm-1 in the dispersed spectra correspond to ν25 and ν47,

respectively, and the broad Raman band at about 203 cm-1 results from contributions from

both of these. The Raman band at 120 cm-1 was previously assigned10 as ν48, but from the

phenyl torsional potential energy surface7 this band corresponds to 48��. The theoretical DFT

calculations predict a value of 67 cm-1 for ν48, but this is based on the assumption of an

harmonic force field. A listing of the infrared active frequencies can be found elsewhere.13

The experimental vapor-phase Raman spectrum of cis-stilbene is compared to the

computed spectrum in Figure 3, and Table 2 presents a listing of the assignments. Again, the

frequency agreement between the observed and calculated spectra is very good. Most of the

observed Raman bands correspond to A modes, although the B vibration predicted to have the

highest intensity at 1601 cm-1 apparently also contributes to the observed band at that value,

given that its depolarization ratio is about 0.6. Table 2 also lists the observed Raman spectra

of liquid cis-stilbene. The data are from reference 35, except where indicated they are from

reference 36. A few of the assignments have been corrected, and many assignments given in

reference 36 for the B modes are not listed since the band intensities clearly come from A

modes.

6. Analyses

Potential fitting. The potential energies obtained of the phenyl groups in cis-stilbene

internal rotations were fitted to the functional form,

��, �� ,��

�,��cos2��2�� ,�� sin2�� sin2�� .

�

�,��1�

It was necessary to adopt higher terms than those used for trans-stilbene7,18,19 to obtain a good

fitting quality. The resultant potential constants, ��,�� and ��,�� , are listed in Table 3 and the

reproduced potential surface is shown in Figure 4.

Energy level analysis. The results of the potential energy calculations revealed that

the internal rotations around the two Cphenyl–C(=C) bonds highly correlate with each other.

Therefore, it is appropriate to carry out the energy level calculations by means of the two

dimensional Hamiltonian,7

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" � #$ %%�� %%��& $

'��'��'��'�� &()*

%%��%%��+

,-� ��, ��.2�

The elements, '��, '�� and '��, in the kinetic energy term cannot be treated as

constants, and their dependences on�� and �� were approximated by the following

expansion,31

'.,/��, �� '.,/��,��

�,��cos2��2�� '.,/��,� sin2�� sin2�� ,

�

�,��3�

1, 2 � 1,1�, 1,2�, 2,2��.

The expansion coefficients, '.,/��,�and '.,/��,�, are functions of moments of inertia of the

molecule and internal rotors (i.e., the phenyl rings), and they were evaluated by using a

method similar to that described elsewhere.37 The optimized two C=C–C bond angles,

3�(C2=C1–C3) and 3�(C1=C2–C9) strongly depend on ��and �� (see Results and discussion).

Therefore, in these calculations of the '.,/��,�and'.,/��,� coefficients, these dependences were

taken into account by using the following expansion, which has the same functional form as

eq. (3)

3.��, �� 3.��,��

�,��cos2��2�� 3.��,� sin2�� sin2�� ,

�

�,��4� 1 � 1,2�.

This treatment is similar to that applied for the variation of the C=C–C, C1–C3–C4, and

C2–C9–C10 angles of trans-stilbene elsewhere.19

The products of two free rotation eigenfunctions, exp(i k ��) exp(i l ��) / 2π, for k, l = –

100 to +100 were used as a basis set in the calculation of the energy levels and the

corresponding wave functions, by means of a matrix diagonalization. The total number of the

basis functions was 40401 (201 by 201).

The probability distribution was calculated for each of the energy levels obtained by

using its wave function. Then, the vibrational quantum numbers for the antigearing and

gearing modes, ν37 and ν72, respectively, were assigned to each energy level according to the

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number of the nodes of the resultant probability distribution.

7. Results and discussions

Table 4 shows the results of the structure optimization for cis- and trans-stilbene as

well as the hypothetical planar (C2v) cis-stilbene. Figure 1 shows the calculated structures for

these isomers.

As mentioned above, it has been confirmed that cis-stilbene has no potential

minimum other than the one corresponding to the conformer with the C2 symmetry (see

Figure 4) for which Traetteberg et. al. determined the structural parameters by gas electron

diffraction.8 The phenyl torsional angles have been optimized to be ��= ��= 40.8°. This

value is consistent with the previously reported theoretical values,14,17 but smaller than the

experimental value of 43°.8 On the other hand, the calculated C=C–C angle of the present

study, 127.0°, is slightly smaller than the experimental value of 129.5°.8 This structure is, of

course, the result of the two factors, the conjugation among the rings and the C=C double

bond, and the steric repulsion between the rings, acting together. The former factor makes

the planar (�� = ��= 0°, C2v symmetry) form lower in energy than the perpendicular (�� = ��

= 90°) form, and the latter factor works oppositely.

The above mentioned dependence of the two C=C–C bond angles, 3� and 3�, on the

�� and ��torsional angles also can be attributed to steric repulsion because the theoretical 3�

and 3�angles have the largest value, 140°, in the planar (C2v) form, where the phenyl ring

suffers from the largest steric repulsion, while in the perpendicular form, where the steric

repulsion is the smallest, 3� and 3� have the smallest theoretical value, 126°.

A structural feature common for the two isomers is the deformation of the benzene

ring. The C4–C3–C8 angle is smaller than the other bond angles in the ring. On the other

hand, there is no significant difference between the bond lengths and bond angles of the

trans- and real C2 cis-stilbene with the exception of the C1–C3 bond length. The r(C1–C3) for

the C2 cis-stilbene is 0.01 Å longer than that of trans. The long C1–C3 bond length of C2 cis-

stilbene is caused by its reduced double-bond character because the corresponding bond

length of hypothetic C2v cis-stilbene, for which it is expected that the double-bond character

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of this bond is held, is not as long as that of C2 cis-stilbene.

The hypothetic C2v cis-stilbene is expected to suffer from the stronger steric repulsion

than the real C2 cis-stilbene. This effect can be seen on some structural parameters of the

former, namely, long C1=C2 bond, short C4–H bond, large C1–C3–C4 angle, small C1–C3–C8

angle and especially, extremely large C=C–C angle.

The contribution of the conjugation to the relative stability of the isomers was

investigated based on the results of the NBO calculations. Figure 5 illustrates the π and π*

orbitals the interactions between whom are dependent on the torsional angles around the C=C

and Cphenyl–C(=C) bonds, with their stabilization energies in kcal/mol unit obtained from the

NBO calculations. Clearly, C2 cis-stilbene is stabilized by the conjugation less than trans-

stilbene. However, the stabilization energies of C2v (planar) cis-stilbene are nearly as much

as those of the trans isomer. Therefore, it can be said that the relative instability of the cis

isomer is attributed primarily to the steric repulsion, but the reduction of the conjugation

caused by the nonplanarity of the molecule contributes also.

The calculated vibrational frequencies of trans-stilbene and cis-stilbene are listed and

compared with the observed values in Tables 1 and 2. These values are consistent with many

other reported theoretical frequencies using various methods and basis sets.11,13-16 It is

common in these studies, including the present one, that the theoretical vibrational

frequencies of the antigearing (ν37) and gearing (ν72) internal rotations are close to each other.

However, all these values have been obtained from the normal mode calculations based on

the small-amplitude assumption. The analysis of large amplitude vibrations by using the two-

dimensional Hamiltonian, as described above, is expected to provide more reliable frequency

values.

Because of the symmetry of the potential function, expressed as

��, �� #��, #�� 4, �� , �� 4� (5)

there are 8 equivalent minima on the entire potential surface of cis-stilbene as shown in

Figure 4. On the other hand, there are two unique potential maxima, corresponding to the

planar (C2v) and perpendicular forms. In the planar form, the molecule has the largest steric

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repulsion but the largest stabilization by conjugation. On the other hand, both of these effects

are smallest in the perpendicular form. As expected, Figure 4 also shows that there is a

significant correlation between the internal rotations around the two Cphenyl–C(=C) bonds

because of steric repulsion.

The gearing internal rotation is expressed as the motion along the "valley" connecting

the minima on the potential surface, and the barrier to this motion is about 563 cm–1 with the

saddle points located at (��= 0°, ��= 90°) etc. On the other hand, the antigearing internal

rotation corresponds to the motion that goes across the "mountain range" on the potential

surface, and the barriers to this motion are as high as around 1841 cm–1 (��= ��= 0°) and

1700 cm–1 (��= ��= 90°).

Figure 6 shows some examples of the probability distribution for the internal rotation

with the quantum numbers, ν37 and ν72. In the vibrational ground state, the probability

distribution is localized at the positions corresponding to the potential minima (Figure 6-(a)).

In Figure 6-(b), the distribution around each potential minimum is divided by one node line

running perpendicular to the potential valley. So, the vibrational quantum numbers, (ν37, ν72)

= (0, 1), are given to this state. In Figure 6-(c), there are two node lines running along with

the potential valley and one node line running perpendicular to the valley. So the

corresponding vibrational numbers are, (ν37, ν72) = (2, 1). The vibrational frequency of the

ν37 mode (antigearing internal rotation) is estimated from the energy difference between the

ground state and (ν37, ν72) = (1, 0) level to be 52 cm–1. That of the ν72 mode (gearing internal

rotation) is estimated from the energy difference between the ground state and (ν37, ν72) = (0,

1) level to be 26 cm–1. It is reasonable that the former has the larger value considering that

the barrier to the antigearing internal rotation is much higher than that of the gearing internal

rotation as mentioned above, but the normal mode calculations based on the small amplitude

assumption can not reproduce this feature. In trans-stilbene, the frequency difference

between the two phenyl internal rotation modes, ν37 and ν48, are much larger than in cis-

stilbene (8 cm–1 for ν37 and 120 cm–1 for 2ν48). In the case of trans-stilbene the difference in

frequency is caused by the kinetic energy coefficients Bi,js in eq. (2).7

As our interest is focused on the gearing internal rotation, the probability distributions

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of the levels for which the quantum number ν37 equals to 0 was investigated as follows.

The low vibrational energy region is the "hindered rotation region", which lies lower

in energy than the barrier to the gearing internal rotation. Each level in this region is nearly

eight-fold degenerate because of the existence of the eight equivalent minima on the entire

potential surface. The composition of the symmetric species for the sub-level is A1+ + A1

– +

B2+ + B2

– + E+ + E–, according to the Longuet-Higgins' notation.32 In this region, the interval

of the energy levels is about 26 cm–1, as mentioned above. Figures 6-(a), (b), (d) and (e)

show that, the distribution around each potential minimum gets extended along with the

valley on the potential energy surface, as the quantum number, ν72, increases. At the same

time, the probability distribution near the classical turning points gets higher. They are

typical textbook features of a one-dimensional harmonic oscillator and hindered rotation.

The energy levels of ν37 = 0, ν72 = 0 – 21 belong to this region. The vibrational energy of the

(ν37, ν72) = (0, 21) level is 543 cm–1.

The levels with the energy close to the barrier of the gearing internal rotation (563

cm–1 high from the potential minimum) are categorized as the intermediate region. The

probability distributions for this region do not show clear common pattern.

The vibrational energy region higher than the intermediate region is the "free rotation

region". Each level in this region is nearly four-fold degenerate consisting of 2A1+ + 2B2

–,

2A1– + 2B2

+, or E+ + E–, arising from the existence of the two equivalent valleys on the entire

potential surface in addition to the possible two ways of the gearing rotation. In one way, one

phenyl group rotates clockwise and another one rotates counterclockwise. In another way,

they rotate reversely. In this region, the probability is distributed more uniformly without

clear nodes than in the hindered rotation region as shown in Figure 6-(f). This feature is close

to the classical image of the free rotation. The energy levels are spaced about 13 cm–1 apart,

and this spacing is a half of that of the hindered rotation region.

8. Conclusions

Numerous studies have previously been carried out on the stilbene molecules, often with a

focus on the photoisomerization. Their vibrational spectra have previously been reported for

Page 12 of 29



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13

the solid or liquid phases, but vapor phase data has been hard to obtain and been limited due

to the high boiling points of the two isomers. A recent high-temperature infrared study of

vapor-phase cis- and trans-stilbene for the 600-3200 cm-1 region at 2 cm-1 resolution has been

carried out38 but this provided no insight into the low-frequency vibrations. Since the low-

frequency vibrational modes play an important role in the vapor-phase photoisomerization, it

is important to have reliable data for these vibrations. We have provided that in the present

work. In addition, in the present work we have also provided a detailed analysis of the

structure and phenyl torsional modes of cis-stilbene. This nicely complements the

experimental results on trans-stilbene reported earlier.7

Acknowledgements

T.E. thanks the Research Center for Computational Science, Okazaki, Japan, for the use of

the HITACHI SR16000 computer and the Library Program Gaussian 09. JL wishes to thank

the Robert A. Welch Foundation for financial support under Grant A-0396. Computations

were also carried out on the Texas A&M University Department of Chemistry Medusa

computer system funded by the National Science Foundation, Grant No. CHE-0541587. The

Semichem AMPAC/AGUI and the NBO software was provided by the Laboratory for

Molecular Simulation of Texas A&M University.

References

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436.

(2) Nakamura, T.; Takeuchi, S.; Taketsugu, T.; Tahara, T. Femtosecond Fluorescence

Study of the Reaction Pathways and Nature of the Reactive S1 State of cis-Stilbene.

Phys. Chem. Chem. Phys. 2012, 14, 6225-6232.

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Ground- and Excited-State Potential-Energy Curves of Stilbene cis-trans

Isomerization. ChemPhysChem 2002, 3, 167-178.

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14

(5) Improta, R.; Santoro, F.; Dietl, C.; Papastathopoulos, E.; Gerber, G. Time Dependent

DFT Investigation on the Two Lowest 1Bu States of the trans Isomer of Stilbene and

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8767.

(8) Traetteberg, M.; Frantsen, E. B. A Gas Electron Diffraction Study of the Molecular

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(9) Traetteberg, M.; Frantsen, E. B.; Mijlhoff, F. C.; Hoekstra, A. A Gas Electron

Diffraction Study of the Molecular Structure of trans-Stilbene. J. Mol. Struct. 1975,

26, 57-68.

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11392-11398.

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of trans-Stilbene in the Ground and Excited Singlet Electronic States Revisited. J.

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Styrene, trans-Stilbene, and cis-Stilbene. J. Phys. Chem. A 1997, 101, 3823-2831.

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(16) Baker, J.; Wolinski, K. Isomerization of Stilbene Using Enforced Geometry

Optimization. J. Comput. Chem. 2011, 32, 43-53.

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Isotopomers on the Ground State Potential Energy Surface. Spectrochim. Acta. Part A

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(37) Harthcock, M. A.; Laane, J. Calculation of Kinetic Energy Terms for the Vibrational

Hamiltonian: Application to Large-Amplitude Vibrations Using One-, Two-, and

Three-Dimensional Models. J. Mol. Spectrosc. 1982, 91, 300-324.

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259, 11-15.

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17

TABLE 1: Observed and Calculated Raman Spectra (cm-1

) of trans-Stilbene

Observed Calculatedb Mode Vapor Solutiona Frequencyc ρ Frequencyd ρ Frequencyc ρ

Ag 1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

3059 (17)

--- ---

--- ---

--- ---

--- ---

3000 (3)

1636 (132)

1596 (100)

--- ---

1489 (11)

1446 (9)

1334 (17)

1316 (16)

1281 (1)

1189 (125)

--- ---

--- ---

--- ---

--- ---

999 (97)

863 (1)

638 (3)

617 (3)

273 (13)

~203e (1) sh

0.1

---

---

---

---

---

0.3

0.4

---

0.4

0.4

0.3

0.4

~ 0.5

0.2

---

---

---

---

0.1

---

0.3

~0.7

0.3

~0.7

--- ---

--- ---

--- ---

--- ---

--- ---

--- ---

1639 vs

1600 vs

1577 w

1492 w

1448 w

1336 w

1320 w

1293 vw

1194 s

1183 w

1157 vw

--- ---

1028 w

1001 s

869 vw

641 vw

620 vw

291 vw

203 vw

---

---

---

---

---

---

0.30

0.41

0.37

0.35

0.32

0.26

0.26

0.39

0.27

0.22

0.72

---

0.08

~0.1

0.42

0.13

0.68

---

---

3069 (19)

3061 (4)

3052 (7)

3042 (5)

3036 (1)

3016 (1)

1643 (75)

1592 (100)

1570 (8)

1488 (7)

1443 (5)

1350 (12)

1333 (6)

1311 (2)

1197 (23)

1191 (23)

1167 (1)

1092 (0.1)

1036 (1)

1003 (10)

872 (0.5)

647 (0.1)

625 (0.5)

284 (0.04)

202 (0.05)

0.13

0.46

0.73

0.63

0.75

0.34

0.32

0.37

0.36

0.36

0.36

0.31

0.32

0.38

0.32

0.28

0.75

0.21

0.13

0.21

0.74

0.14

0.65

0.58

0.28 Bg 38

39

40

41

42

43

44

45

46

47

48

--- ---

--- ---

--- ---

907 (1)

840 (1)

--- ---

--- ---

465 (1)

406 (3)

211e --- 120e (30)

---

---

---

---

---

---

---

~0.7

~0.6

---

~0.6

985 ---

969 ---

914 vw

848 vw

821 vw

736 vw

--- ---

464 vw

406 vw

227 w

--- ---

---

---

---

0.69

0.59

---

---

---

~0.6

0.66

---

989 (0.06)

969 (0.01)

926 (0.1)

873 (0.3)

837 (0.06)

745 (0.01)

696 (0.006)

470 (0.003)

408 (0.001)

217 (0.2)

67 (0.05)

0.75

0.75

0.75

0.75

0.75

0.75

0.75

0.75

0.75

0.75

0.75 Overtone and combination bands Ag 2ν23 1231 (1) ~0.5 2 x 617 = 1234

ν21+ ν25 1058 (8) ~0.1 863 + 203 = 1066

ν41+ ν48 848 + 118 = 966

ν27+ ν37 976 (5) 0.2 959 + 8 = 967

ν32+ ν35 691 + 286 = 977

ν33+ ν34 939 (9) 0.4 526 + 208 = 934

2ν72 152 (68) 0.3 2 x 76 = 152

aRef. 13.

bB3LYP/cc-pVTZ calculations. Scaling factors: 0.985 below 1500 cm-1, 0.973 between 1500 and 2000 cm-1 and 0.961 above 2000 cm-1.

cRelative intensities are indicated in parenthesis.

d s-strong, w-weak, v-very

eThe dispersed fluorescence spectra show bands at 202 and 118 cm-1 .

7 The broad Raman band ~203 cm-1 is likely an overlap of ν25 and ν47. The

120 cm-1 Raman band is 2ν48.

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18

TABLE 2: Observed and Calculated Raman Spectra (cm-1

) of cis-Stilbene

Observed Calculatedb Assignment Vapor Liquida Frequencyc ρ Frequencyd ρ Frequencyc ρ

A ν1

ν2

ν3

ν4

ν5

ν6

ν7

ν8

ν9

ν10

ν11

ν12

ν13

ν14

ν15

ν16

ν17

ν18

ν19

ν20

ν21

ν22

ν23

ν24

ν25

ν26

ν27

ν28

ν29

ν30

ν31

ν32

ν33

ν34

ν35

ν36

ν37

Cring–H s-str.

Cring –H a-str.

Cring –H a-str.

Cring –H a-str.

Cring –H s-str.

C–H str.

C=C str.

Cring – Cring s-str.

Cring – Cring a-str.

Cring –H s-bend

Cring –H a-bend

Cring –H a-bend


C–H bend

Cring –H s-bend

Cring –H a-bend

C–Ph str.



ring deform.

Cring –H s-opl.

C–H opl.

Cring –H a-opl.

Cring –H s-opl.

Cring –H a-opl.

Phenyl wag

Ring deform.

Chair bend

Ring deform.

C=C torsion

Ring deform.

Ring twist

Boat bend

C=C–C bend

Phenyl rock

Boat bend

C–Ph torsion

--- ---

--- ---

--- ---

--- ---

--- ---

--- ---

1632 (100)

1601e

(51)

1575 (22)

1488 (7)

1442 (4)

1377 (11)

1315 (13)

1232 (13)

1184 (24)

--- ---

1150 (31)

--- ---

1030 (36)

1003 (222)

998 (13)

964 (42)

--- ---

--- ---

841 (4)

768 (16)

752 (18)

--- ---

619 (11)

558 (29)

520 (13)

416 (27)

403 (18)

253 (8)

154 (116)

--- ---

--- ---

---

---

---

---

---

- --

0.4

~0.6

0.3

0.5

0.4

0.2

0.3

0.3

0.3

--

0.3

--

0.1

0.1

0.4

0.3

---

---

0.3

0.2

0.2

--

0.6

0.3

0.2

~0.2

0.6

---

---

---

---

3079f w

3061 s

3055f m

3046 sh

3028

sh

3013 m

1629 vw

1599e

s

1573 m

1496 vw

1444 w

1373 vw

1323 m

1234 m

1183 m

1156f sh

1149 ms

1072 vw

1029 m

1001 vs

988 w

966 m

--- ---

922 w

846 w

770 w

753 m

701 vw

620 w

561 m

520 vw

444 vw

405 m

261 w

167 m

--- ---

--- ---

---

0.2

---

---

---

0.25

0.17

0.48

0.33

P

0.20

0.28

0.27

0.24

0.24

---

0.14

0.36

0.04

0.05

0.1

0.27

---

0.3

0.33

0.26

0.08

0.59

0.78

0.28

0.14

0.3

0.41

0.32

0.49

---

---

3075 (23)

3065 (42)

3053 (15)

3043 (9)

3035 (8)

3016 (19)

1634 (100)

1596 (50)

1570 (6)

1488 (3)

1459 (1)

1347 (3)

1326 (13)

1250 (8)

1190 (2)

1167 (0.7)

1158 (11)

1088 (0.1)

1036 (3)

1005 (12)

996 (9)

990 (6)

975 (0.04)

926 (0.3)

848 (1)

780 (0.5)

757 (2)

703 (0.05)

627 (0.8)

573 (3)

522 (0.3)

412 (0.6)

407 (2)

261 (1)

158 (2)

77 (1)

30 (2)

0.07

0.09

0.63

0.49

0.65

0.20

0.24

0.29

0.37

0.36

0.25

0.23

0.33

0.32

0.27

0.63

0.20

0.19

0.05

0.09

0.28

0.29

0.41

0.33

0.23

0.73

0.09

0.66

0.75

0.31

0.20

0.32

0.43

0.23

0.51

0.73

0.58

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19

TABLE 2: Continued

Observed Calculatedb Assignment Vapor Liquida Frequencyc ρ Frequencyd ρ Frequencyc ρ

B ν38

ν39

ν40

ν41

ν42

ν43

ν44

ν45

ν46

ν47

ν48

ν49

ν50

ν51

ν52

ν53

ν54

ν55

ν56

ν57

ν58

ν59

ν60

ν61

ν62

ν63

ν64

ν65

ν66

ν67

ν68

ν69

ν70

ν71

ν72

Cring –H s-str.

Cring –H a-str.

Cring –H a-str.

Cring –H a-str.

Cring –H s-str.

C–H str.



Cring –H s-bend


C–H bend

Cring –H a-bend


C–Ph str.

Cring –H s-bend

Cring –H a-bend



ring deform.

Cring –H s-opl.

Cring –H a-opl.

Cring –H s-opl.

C=C–C bend

Cring –H a-opl.

C–H opl.

C–H opl.

Cring –H s-opl.

chair bend

ring deform.

ring deform.

phenyl wag

ring twist

phenyl rock

boat bend

C–Ph torsion

--- ---

--- ---

--- ---

--- ---

--- ---

--- ---

1601e (51)

--- ---

--- ---

--- ---

--- ---

--- ---

--- ---

--- ---

--- ---

--- ---

--- ---

--- ---

--- ---

--- ---

--- ---

932? ---

--- ---

--- ---

--- ---

--- ---

--- ---

--- ---

--- ---

--- ---

--- ---

--- ---

--- ---

--- ---

--- ---

---

---

---

---

---

---

~0.6

---

---

---

---

---

---

---

---

---

---

---

---

---

---

---

---

---

---

---

---

---

---

---

---

---

---

---

---

--- ---

--- ---

--- ---

3046 sh

--- ---

2968 vw

1599e s

--- ---

--- ---

--- ---

1406 w

1323f w

1287f vw

1208 w

--- ---

1157 mw

1073f m

--- ---

--- ---

983f vw

--- ---

--- ---

863 vw

--- ---

781 vw

732f m ---

---

698f

vs

--- ---

502f m

443f m

--- ---

--- ---

--- ---

--- ---

---

---

---

dp?

---

dp

0.48

---

---

---

0.72

---

---

0.74

---

dp

---

---

---

---

---

0.65

0.7

---

---

---

---

---

---

---

---

---

---

3074 (3)

3064 (7)

3053 (7)

3043 (14)

3035 (1)

2995 (2)

1600 (16)

1573 (0.1)

1492 (0.6)

1448 (0.01)

1425 (3)

1341 (0.5)

1302 (0.2)

1210 (4)

1188 (0.2)

1166 (0.2)

1092 (0.03)

1037 (0.4)

1006 (1)

993 (0.02)

976 (0.0003)

937 (0.1)

866 (0.2)

847 (0.2)

794 (1)

739 (0.6)

703 (0.03)

693 (0.2)

626 (0.2)

508 (0.1)

454 (0.1)

409 (0.1)

246 (0.6)

157 (0.2)

35 (0.1)

0.75

0.75

0.75

0.75

0.75

0.75

0.75

0.75

0.75

0.75

0.75

0.75

0.75

0.75

0.75

0.75

0.75

0.75

0.75

0.75

0.75

0.75

0.75

0.75

0.75

0.75

0.75

0.75

0.75

0.75

0.75

0.75

0.75

0.75

0.75 s-, symmetric; a-: antisymmetric, str.-stretch, deform.-deformation, opl- out of plane bend, p- polarized, dp- depolarized. a Ref. [35] unless indicated.

bB3LYP/cc-pVTZ calculations. Scaling factors: 0.985 below 1500 cm-1, 0.973 between 1500 and 2000 cm-1 and 0.961 above 2000 cm-1.

cRelative intensities are indicated in parenthesis.

ds- strong, m- medium, w-weak, v-very.

eAssigned twice.

f Ref. [36].

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20

TABLE 3: Potential Constants for the Internal Rotations of cis-Stilbene Estimated by the

Least Squares Fitting on the Potential Energies Obtained from B3LYP/cc-pVTZ

Calculations (cm–1

)

Parametersa Parametersa

��,�� 783.5 ��,�� -642.3

��,�� -146.2 ��,�� -117.5

��,�� 72.3 ��,5� -12.8

��,5� -9.1 ��,�� 4.4

��,6� 1.9 ��,�� -119.3

��,�� 490.0 ��,5� -68.5

��,�� 91.4 ��,6� -12.9

��,5� 19.0 �5,5� -73.5

��,6� -3.2 �5,6� -38.5

��,�� 138.7 �6,6� -51.8

��,5� 61.1

��,6� 10.0

�5,5� 76.0

�5,6� 41.1

�6,6� 55.0

a See Eq. (1) for the definition of the potential constants (��,�� ,�� , ��,�� ,�� .

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TABLE 4: Calculated MP2/cc-pVTZ Structural Parameters of cis- and trans-Stilbene.

Bond lengths (Å) Angles (degrees) cis-Stilbene trans-Stilbene cis-Stilbene trans-Stilbene

C2v C2 C2h C2v C2 C2h C1=C2 1.362 1.348 1.348 C4-C5-C6 120.8 120.3 120.5

C1−C3 1.464 1.469 1.459 C5-C6-C7 119.0 119.6 119.4

C3−C4 1.404 1.402 1.404 C6-C7-C8 120.0 120.0 120.0

C3−C8 1.410 1.401 1.403 C3-C8-C7 122.2 120.9 121.3

C4−C5 1.391 1.391 1.389 C4-C3-C8 116.7 118.6 118.0

C5−C6 1.393 1.395 1.396 C3-C4-C5 121.4 120.6 120.8

C6−C7 1.393 1.393 1.393 C1-C3-C4 128.4 121.7 123.4

C7−C8 1.389 1.392 1.391 C1-C3-C8 114.9 119.7 118.6

C1−H25 1.086 1.085 1.085 C2=C1-C3 139.7 127.0 126.3

C4−H15 1.073 1.082 1.081 C3-C4-H15 120.8 119.3 120.0

C5−H16 1.082 1.082 1.082 C5-C4-H15 117.9 120.1 119.2

C6−H17 1.081 1.081 1.081 C4-C5-H16 119.2 119.7 119.6

C7−H18 1.081 1.082 1.082 C6-C5-H16 120.0 120.0 119.9

C8−H19 1.083 1.083 1.083 C5-C6-H17 120.4 120.2 120.2

C7-C6-H17 120.5 120.2 120.3

C6-C7-H18 120.3 120.1 120.2

C8-C7-H18 119.7 119.8 119.8

C7-C8-H19 119.3 120.0 119.8

C3-C8-H19 118.6 119.2 118.9

C3-C1-H25 109.7 115.8 114.8

C2=C1-H25 110.6 117.1 118.8 Dihedral angles (degrees) C2=C1-C3-C4 0.0 40.8 0.0

C2=C1-C3-C8 180.0 -141.4 180.0

C3-C1=C2-C9 0.0 5.9 180.0

a See Fig. 1 for the atom numbering.

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Figure captions

Figure 1. Calculated structures and atom numberings of planar (C2v) cis-stilbene, equilibrium (C2) cis-

stilbene and trans-stilbene. The relative energies were obtained from the MP2/cc-pVTZ calculations.

Figure 2. Vapor-phase Raman spectrum of vapor-phase trans-stilbene at 330°C compared to its

calculated spectrum.

Figure 3. Vapor-phase Raman spectrum of vapor-phase cis-stilbene at 240°C compared to its

calculated spectrum.

Figure 4. Potential surfaces of cis-stilbene as a function of ��(C2=C1–C3–C4) and ��(C1=C2–C9–C10)

torsional angles obtained from the B3LYP/cc-pVTZ calculations. See Fig. 1 for the atom numberings.

The contour interval is 200 cm–1 and × symbols represent the positions of the eight equivalent potential

minima.

Figure 5. Interacting pairs of bonding (π) and antibonding (π*) natural bond orbitals whose

interactions are dependent on the torsional angles, with the stabilization energies in kcal/mol unit

obtained from the NBO calculations.

Figure 6. Probability distributions for some selected energy levels of cis-stilbene with the assignments

and the energy values. The numbers in parentheses represent the vibrational quantum numbers, ν37 and

ν72. The ν72 for (f) is not specified. The vibrational energies are measured from the potential

minimum.

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Figure 1. Calculated structures and atom numberings of planar (C2v) cis-stilbene, equilibrium (C2) cis-stilbene and trans-stilbene. The relative energies were obtained from the MP2/cc-pVTZ calculations.

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Figure 2. Vapor-phase Raman spectrum of vapor-phase trans-stilbene at 330°C compared to its calculated spectrum.

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Figure 3. Vapor-phase Raman spectrum of vapor-phase cis-stilbene at 240°C compared to its calculated spectrum.

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Figure 4. Potential surfaces of cis-stilbene as a function of ��(C2=C1–C3–C4) and ��(C1=C2–C9–C10) torsional angles obtained from the B3LYP/cc-pVTZ calculations. See Fig.1 for the atom numberings. The contour interval is 200 cm–1 and × symbols represent the positions of the eight equivalent potential minima.

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Figure 5. Interacting pairs of bonding (π) and antibonding (π*) natural bond orbitals whose interactions are dependent on the torsional angles, with the stabilization energies in kcal/mol unit obtained from the NBO calculations.

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Figure 6. Probability distributions for some selected energy levels of cis-stilbene with the assignments and the energy values. The numbers in parentheses represent the vibrational quantum numbers, ν37 and ν72. The ν72 for (f) is not specified. The vibrational energies are measured from the potential minimum.

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TOC/Abstract Graphic

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vapor-phase raman spectra, theoretical calculations, and the vibrational and structural properties...

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