Vapor-Phase Raman Spectra, Theoretical Calculations, and the

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Vapor-Phase Raman Spectra, Theoretical Calculations and the Vibrational and Structural Properties of cis- and trans-Stilbene Toru Egawa, Kiyoaki Shinashi, Toyotoshi Ueda, Esther J. Ocola, Whe-Yi Chiang, and Jaan Laane J. 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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The Journal of Physical Chemistry 1

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

c

d

Department of Chemistry, Texas A&M University, College Station, Texas 77843-3255, U.S.A. Department of Law, Chuogakuin University, Kujike 451, Abiko, Chiba 270-1196, Japan 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. Keywords: cis-stilbene, trans-stilbene, Raman spectra, DFT calculations, internal rotation, potential energy surface, two-dimensional analysis, gearing internal rotation. *Corresponding Authors, Email address: [email protected], Phone: 979-845-3352; E-mail address: [email protected], Phone/Fax: +81-42-778-8088.

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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 coworkers by means of gas electron diffraction.8,9 The gas phase Raman spectrum of transstilbene 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 transstilbene 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 transstilbene 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 transstilbene 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 transstilbene, 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 coworkers19 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 gearlike 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,

,

,

,

cos 2 2 , sin 2 sin 2 . 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

,

,

, , '.,/ , '.,/ cos 2 2 '.,/ sin 2 sin 2 , 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. , cos 2 2

3. , sin 2 sin 2 , 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 cisstilbene 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 transstilbene. 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 twodimensional 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 cisstilbene (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


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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 lowfrequency 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 (1)

Waldeck, D. H. Photoisomerization Dynamics of Stilbenes. Chem. Rev. 1991, 91, 415436.

(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.

(3)

Han, W.-G.; Lovell, T.; Liu, T.; Noodleman, L. Density Functional Studies of the Ground-

and

Excited-State

Potential-Energy

Curves

of

Stilbene

cis-trans

Isomerization. ChemPhysChem 2002, 3, 167-178. (4)

Improta, R.; Santoro, F. Excited-State Behavior of trans and cis Isomers of Stilbene and Stiff Stilbene: A TD-DFT Study. J. Phys. Chem. A 2005, 109, 10058-10067.



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Page 14 of 29 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 Stiff-Stilbenes. Chem. Phys. Lett. 2004, 387, 509-516.

(6)

Senent, M. L.; Moule, D. C.; Smeyers, Y. G. Ab Initio and Spectroscopic Study of Dimethyl Sulfide. An Analysis of the Torsional Spectra of (CH3)2S and (CD3)2S. J. Phys. Chem. 1995, 99, 7970-7976.

(7)

Chiang, W.-Y.; Laane, J. Fluorescence Spectra and Torsional Potential Functions for trans-Stilbene in its S0 and S1(π,π) Electronic States. J. Chem. Phys. 1994, 100, 87558767.

(8)

Traetteberg, M.; Frantsen, E. B. A Gas Electron Diffraction Study of the Molecular Structure of cis-Stilbene. J. Mol. Struct. 1975, 26, 69-76.

(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.

(10)

Haller, K.; Chiang, W.- Y.; del Rosario, A.; Laane, J. High-Temperature Vapor-Phase Raman Spectra and Assignment of The Low-Frequency Modes of trans-Stilbene and 4-Methoxy-trans-stilbene. J. Mol Struct. 1996, 379, 19-23.

(11)

Arenas, J. F.; Tocón, I. L.; Otero, J. C.; Marcos, J. A Priori Scaled Quantum Mechanical Vibrational Spectra of trans- and cis-Stilbene. J. Phys. Chem. 1995, 99, 11392-11398.

(12) Arenas, J. F.; Tocón, I. L.; Otero, J. C.; Marcos, J. I. Vibrational Spectra of cisStilbene. J. Mol. Struct. 1995, 349, 29-32. (13) Watanabe, H.; Okamoto, Y.; Furuya, K.; Sakamoto A.; Tasumi M. Vibrational Analysis of trans-Stilbene in the Ground and Excited Singlet Electronic States Revisited. J. Phys. Chem. A. 2002, 106, 3318-3324. (14) Choi, C. H.; Kertesz, M. Conformational Information from Vibrational Spectra of Styrene, trans-Stilbene, and cis-Stilbene. J. Phys. Chem. A 1997, 101, 3823-2831. (15) Negri, F.; Orlandi, G. Infrared and Raman Spectra of Binuclear Aromatic Molecules: A Density Functional Theory Study. J. Raman. Spectrosc. 1998, 29, 501-509.


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(16) Baker, J.; Wolinski, K. Isomerization of Stilbene Using Enforced Geometry Optimization. J. Comput. Chem. 2011, 32, 43-53. (17) Chen, P. C.; Chieh, Y. C. Azobenzene and Stilbene: A Computational Study. Theochem 2003, 624, 191-200. (18) Melandri, S.; Maccaferri, G.; Favero, P. G.; Caminati, W.; Orlandi, G.; Zerbetto, F. Stilbenoid molecules: An Experimental and Theoretical Study of trans-1-(2-pyridyl)-2(4-pyridyl)-ethylene and the Parent Molecule. J. Chem. Phys. 1997, 107, 1073-1078. (19) Orlandi, G.; Gagliardi, L.; Melandri, S.; Caminati, W. Torsional Potential Energy Surfaces and Vibrational Levels in trans-Stilbene. J. Mol. Struct. 2002, 612, 383-391. (20) Lalevee, J.; Allonas, X.; Fouassier, J. P. Triplet–Triplet Energy Transfer Reaction to cis-Stilbene: A Dual Thermal Bond Activation Mechanism. Chem. Phys. Lett. 2005, 401, 483-486. (21) Laane, J.; Haller, K.; Sakurai, S.; Morris, K.; Autrey, D.; Arp, Z.; Chiang, W.-Y.; Combs, A. Raman Spectroscopy of Vapors at Elevated Temperatures. J. Mol Struct. 2003, 650, 57-68. (22) Frisch, M. J.; Trucks, G.W.; Schlegel, H. B.:, Scuseria, G.E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A. et al. Gaussian 09, Revision A.02, Gaussian, Inc., Wallingford CT, 2009. (23)

Simons, J.; Nichols, J. Quantum Mechanics in Chemistry, Oxford University Press, New York, 1997.

(24)

Møller, C.; Plesset, M. S. Note on the Approximation Treatment for Many-Electron Systems. Physical Review 1934, 46, 618-622.

(25)

Frisch, Æ.; Frisch, M. J.; Trucks, G. W. Gaussian 03 User's Reference, Gaussian Inc., Carnegie, PA, 2003.

(26)

Császár, A. G.; Allen, W. D.; Yamaguchi, Y.; Schaefer III, H. F. Ab initio Determination of Accurate Ground Electronic State Potential Energy Hypersurfaces for Small Molecules. In Computational Molecular Spectroscopy; Jensen, P., Bunker, P., Eds.; John Wiley and Sons: Chichester, England, 2000; pp 15-68.

(27) Dunning Jr., T. H. Gaussian Basis Sets for Use in Correlated Molecular Calculations. I.



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Page 16 of 29 16

The Atoms Boron through Neon and Hydrogen. J. Chem. Phys. 1989, 90, 1007-1023. (28) Kwasniewski S.P.; Claes L.; François J. –P.; Deleuze M. S.. High Level Theoretical Study of the Structure and Rotational Barriers of trans-Stilbene. J. Chem. Phys. 2003, 118, 7823-7836. (29) Becke, A. D. Density-Functional Thermochemistry. III. The Role of Exact Exchange. J. Chem. Phys. 1993, 98, 5648-5652 . (30) Lee, C.; Yang, W.; Parr, R. G. Development of the Colle-Salvetti Correlation-Energy Formula into a Functional of the Electron Density. Phys. Rev. B 1988, 37, 785-789. (31) Egawa, T.; Yamamoto, D.; Daigoku, K. Conformational Property of Ethoxybenzene as Studied by Laser-Jet Spectroscopy and Theoretical Calculations. J. Mol. Struct. 2010, 984, 282-286. (32) NBO 5.9, E. D. Glendening, J.K. Badenhoop, A. E. Reed, J. E. Carpenter, J.A. Bohmann and F. Weinhold, Theoretical Chemistry Institute, University of Wisconsin. (33) AGUI program from Semichem, Inc.: Shawnee, KS 66216: www.semichem.com. (34) Longuet-Higgins, H. C. The Symmetry Groups of Non-Rigid Molecules. Mol. Phys. 1963, 6, 445-460. (35)

Bree, A.; Zwarich, R. Vibrational Spectra of cis-Stilbene and 1,1-Diphenylethene. J. Mol. Struct. 1981, 75, 213-224.

(36) Baranović, G.; Meić, Z.; Maulitz A. H. Vibrational Analysis of Stilbene and its Isotopomers on the Ground State Potential Energy Surface. Spectrochim. Acta. Part A 1998, 54, 1017-1039. (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. (38) Biemann, L.; Braun, M.; Kleinermanns, K. Gas Phase Infrared Spectra and Corresponding DFT Calculations of α, ω-Diphenylpolyenes. J. Mol. Spectrosc. 2010, 259, 11-15.


Page 17 of 29

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TABLE 1: Observed and Calculated Raman Spectra (cm-1) of trans-Stilbene Calculatedb

Observed Mode Ag

1

ρ

0.1

---

---

---

3069

(19)

0.13

-----

-----

-----

-----

3061 3052

(4) (7)

0.46 0.73

4 5

-----

-----

-----

-----

-----

-----

3042 3036

(5) (1)

0.63 0.75

6 7

3000 (3) 1636 (132)

--0.3

--- --1639 vs

--0.30

3016 1643

(1) (75)

0.34 0.32

8 9

1596 (100) -----

0.4 ---

1600 vs 1577 w

0.41 0.37

1592 1570

(100) (8)

0.37 0.36

10 11

1489 (11) 1446 (9)

0.4 0.4

1492 1448

w w

0.35 0.32

1488 1443

(7) (5)

0.36 0.36

12 13

1334 (17) 1316 (16)

0.3 0.4

1336 1320

w w

0.26 0.26

1350 1333

(12) (6)

0.31 0.32

14 15

1281 (1) 1189 (125)

~ 0.5 0.2

1293 vw 1194 s

0.39 0.27

1311 1197

(2) (23)

0.38 0.32

16 17

-----

-----

-----

1183 w 1157 vw

0.22 0.72

1191 1167

(23) (1)

0.28 0.75

18 19

-----

-----

-----

--- --1028 w

--0.08

1092 1036

(0.1) (1)

0.21 0.13

20 21

999 (97) 863 (1)

0.1 ---

1001 s 869 vw

~0.1 0.42

1003 872

(10) (0.5)

0.21 0.74

22 23

638 617

0.3 ~0.7

641 vw 620 vw

0.13 0.68

647 625

(0.1) (0.5)

0.14 0.65

0.3 ~0.7

291 vw 203 vw

-----

284 202

(0.04) (0.05)

0.58 0.28

(3) (3)

273 (13) ~203e (1) sh

38 39

-----

-----

-----

985 --969 ---

-----

989 969

(0.06) (0.01)

0.75 0.75

40 41

--907

--(1)

-----

914 vw 848 vw

--0.69

926 873

(0.1) (0.3)

0.75 0.75

42 43

840 ---

(1) ---

-----

821 vw 736 vw

0.59 ---

837 745

(0.06) (0.01)

0.75 0.75

44 45

--465

--(1)

--~0.7

--- --464 vw

-----

696 470

(0.006) (0.003)

0.75 0.75

46 47

406 (3) e 211 ---

~0.6 ---

406 vw 227 w

~0.6 0.66

408 217

(0.001) (0.2)

0.75 0.75

120 (30)

~0.6

--- ---

---

67

(0.05)

0.75

1231 (1) 1058 (8)

~0.5 ~0.1

2 x 617 = 1234 863 + 203 = 1066

976 (5)

0.2

848 + 118 = 966 959 + 8 = 967

939 (9)

0.4

691 + 286 = 977 526 + 208 = 934

152 (68)

0.3

2 x 76 = 152

e

Overtone and combination bands

2ν23

B3LYP/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.

Relative intensities are indicated in parenthesis.

d e

Frequencyc

Ref. 13.

b c

ρ

-----

ν21+ ν25 ν41+ ν48 ν27+ ν37 ν32+ ν35 ν33+ ν34 2ν72 a

ρ

-----

48

Ag

3059 (17)

Solution Frequencyd

2 3

24 25

Bg

Vapor Frequencyc

a

s-strong, w-weak, v-very 7

The dispersed fluorescence spectra show bands at 202 and 118 cm-1 . The broad Raman band ~203 cm-1 is likely an overlap of ν25 and ν47. The 120 cm-1 Raman band is 2ν48.



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 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 18 of 29

18

TABLE 2: Observed and Calculated Raman Spectra (cm-1) of cis-Stilbene Calculatedb

Observed Assignment

Frequencyc

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

Liquida

Vapor ρ

Frequencyd

Cring–H s-str.

---

---

---

3079

Cring –H a-str.

---

---

---

3061

f

ρ

Frequencyc

ρ

w

---

3075

(23)

0.07

s

0.2

3065

(42)

0.09

f

Cring –H a-str.

---

---

---

3055 m

---

3053

(15)

0.63

Cring –H a-str.

---

---

---

3046 sh

---

3043

(9)

0.49

Cring –H s-str.

---

---

---

3028 sh

---

3035

(8)

0.65

C–H str.

---

---

- --

3013 m

0.25

3016

(19)

0.20

C=C str.

1632 (100)

0.4

1629 vw

0.17

1634 (100)

0.24

Cring – Cring s-str.

1601

(51)

~0.6

1599

s

0.48

1596

(50)

0.29

Cring – Cring a-str.

1575 (22)

0.3

1573 m

0.33

1570

(6)

0.37

Cring –H s-bend

1488

(7)

0.5

1496 vw

P

1488

(3)

0.36

Cring –H a-bend

1442

(4)

0.4

1444 w

0.20

1459

(1)

0.25

Cring –H a-bend

1377 (11)

0.2

1373 vw

0.28

1347

(3)

0.23


1315 (13)

0.3

1323 m

0.27

1326

(13)

0.33

C–H bend

1232 (13)

0.3

1234 m

0.24

1250

(8)

0.32

e

e

Cring –H s-bend

1184 (24)

0.3

1183 m

0.24

1190

(2)

0.27

Cring –H a-bend

---

--

1156 sh

---

1167

(0.7)

0.63

C–Ph str.

1150 (31)

0.3

1149 ms

0.14

1158

(11)

0.20


---

--

1072 vw

0.36

1088

(0.1)

0.19


1030 (36)

0.1

1029 m

0.04

1036

(3)

0.05

ring deform.

1003 (222)

0.1

1001 vs

0.05

1005

(12)

0.09

Cring –H s-opl.

998 (13)

0.4

988 w

0.1

996

(9)

0.28

C–H opl.

964 (42)

0.3

966 m

0.27

990

(6)

0.29

Cring –H a-opl.

---

---

---

---

---

975 (0.04)

0.41

Cring –H s-opl.

---

---

---

922 w

0.3

926

(0.3)

0.33

Cring –H a-opl.

841

(4)

0.3

846 w

0.33

848

(1)

0.23

Phenyl wag

768 (16)

0.2

770 w

0.26

780

(0.5)

0.73

Ring deform.

752 (18)

0.2

753 m

0.08

757

(2)

0.09

Chair bend

---

--

701 vw

0.59

703 (0.05)

0.66

Ring deform.

619 (11)

0.6

620 w

0.78

627

(0.8)

0.75

C=C torsion

558 (29)

0.3

561 m

0.28

573

(3)

0.31

Ring deform.

520 (13)

0.2

520 vw

0.14

522

(0.3)

0.20

Ring twist

416 (27)

~0.2

444 vw

0.3

412

(0.6)

0.32

Boat bend

403 (18)

0.6

405 m

0.41

407

(2)

0.43

C=C–C bend

253

---

261 w

0.32

261

(1)

0.23

Phenyl rock

154 (116)

---

167 m

0.49

158

(2)

0.51

Boat bend

---

---

---

---

---

---

77

(1)

0.73

C–Ph torsion

---

---

---

---

---

---

30

(2)

0.58

-----

---

(8)

f

---


Page 19 of 29

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19

TABLE 2: Continued Calculatedb

Observed Assignment

Frequencyc

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

Liquida

Vapor ρ

Frequencyd

ρ

Frequencyc

Cring –H s-str.

--- ---

---

--- ---

---

3074

(3)

0.75

Cring –H a-str.

--- ---

---

--- ---

---

3064

(7)

0.75

Cring –H a-str.

--- ---

---

--- ---

---

3053

(7)

0.75

Cring –H a-str.

--- ---

---

3046 sh

dp?

3043

(14)

0.75

Cring –H s-str.

--- ---

---

--- ---

---

3035

(1)

0.75

dp

2995

(2)

0.75

0.48

1600

(16)

0.75

C–H str.

--- ---

---

2968 vw


1601 (51)

~0.6

1599


--- ---

---

--- ---

---

1573

(0.1)

0.75

Cring –H s-bend

--- ---

---

--- ---

---

1492

(0.6)

0.75


--- ---

---

--- ---

---

1448 (0.01)

0.75

C–H bend

--- ---

---

1406 w

0.72

1425

(3)

0.75

e

e

s

f

Cring –H a-bend

--- ---

---

1323 w

---

1341

(0.5)

0.75


--- ---

---

1287 vw

---

1302

(0.2)

0.75

C–Ph str.

--- ---

---

1208 w

0.74

1210

(4)

0.75

Cring –H s-bend

--- ---

---

--- ---

---

1188

(0.2)

0.75

Cring –H a-bend

--- ---

---

1157 mw

dp

1166

(0.2)

0.75


--- ---

---

1073 m

---

1092 (0.03)

0.75


--- ---

---

--- ---

ring deform.

--- ---

---

--- ---

f

f

f

1037

(0.4)

0.75

---

1006

(1)

0.75

Cring –H s-opl.

--- ---

---

983 vw

---

993 (0.02)

0.75

Cring –H a-opl.

--- ---

---

--- ---

---

976 (0.0003)

0.75

Cring –H s-opl.

932? ---

---

--- ---

---

937 (0.1)

0.75

C=C–C bend

--- ---

---

863 vw

0.65

866 (0.2)

0.75

Cring –H a-opl.

--- ---

---

--- ---

C–H opl.

--- ---

---

781 vw f

847 (0.2)

0.75

0.7

794

0.75

(1)

C–H opl.

--- ---

---

732 m ---

---

739 (0.6)

0.75

Cring –H s-opl.

--- ---

---

---

---

703 (0.03)

0.75

f

chair bend

--- ---

---

698 vs

---

693 (0.2)

0.75

ring deform.

--- ---

---

--- ---

---

626 (0.2)

0.75

f

ring deform.

--- ---

---

502 m

---

508 (0.1)

0.75

phenyl wag

--- ---

---

443 m

---

454 (0.1)

0.75

ring twist

--- ---

---

--- ---

---

409 (0.1)

0.75

phenyl rock

--- ---

---

--- ---

---

246 (0.6)

0.75

boat bend

--- ---

---

--- ---

---

157 (0.2)

0.75

C–Ph torsion

--- ---

---

--- ---

---

35 (0.1)

0.75

f

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

ρ

B3LYP/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.

Relative intensities are indicated in parenthesis. s- strong, m- medium, w-weak, v-very. e Assigned twice. f Ref. [36]. d



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 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 20 of 29

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 , , , ,5 ,6 , , ,5 ,6 , ,5 ,6

5,5 5,6 6,6

a

Parametersa 783.5 -146.2 72.3 -9.1 1.9 490.0 91.4 19.0 -3.2 138.7

, , ,5 , , ,5 ,6

5,5 5,6 6,6

-642.3 -117.5 -12.8 4.4 -119.3 -68.5 -12.9 -73.5 -38.5 -51.8

61.1 10.0 76.0 41.1 55.0

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

, , , , .


Page 21 of 29

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21

TABLE 4: Calculated MP2/cc-pVTZ Structural Parameters of cis- and trans-Stilbene. Bond lengths (Å)

cis-Stilbene

Angles (degrees)

trans-Stilbene

C2v

C2

C2h

C1=C2

1.362

1.348

1.348

C1−C3

1.464

1.469

C3−C4

1.404

C3−C8

cis-Stilbene

trans-Stilbene

C2v

C2

C2h

C4-C5-C6

120.8

120.3

120.5

1.459

C5-C6-C7

119.0

119.6

119.4

1.402

1.404

C6-C7-C8

120.0

120.0

120.0

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)

a

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

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) cisstilbene 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) cisstilbene 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


Vapor-Phase Raman Spectra, Theoretical Calculations, and the

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