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Phonon and the intramolecular motions in crystalline trans-stilbene
Physica B 219&220 (1996) 417-419
ELSEVIER
Phonon and the intramolecular motions in crystalline trans-stilbene Kazuya Saito*, Isao Ikemoto Department of Chemist~, Faculty of Science, To~.'o Metropolitan Unit:ersiO', Hachioji, Tolo,o 192-03, Jupan
Abstract
Lattice-dynamics calculations have been performed on crystalline trans-stilbene using a flexible and a rigid molecular model. The intramolecular twisting of the benzene rings strongly couples with the overall rotation of the molecule. The coupled modes form phonon branches and show little dispersion.
1. Introduction
Intramolecular (internal) degrees of freedom are often ignored when the lattice vibrations of molecular crystals are considered. There are, however, a few examples where the intramolecular degrees of freedom strongly couple to the lattice degrees of freedom and modifies the lattice vibration. Indeed a structural phase transition in crystalline biphenyl (C6Hs-C6Hs) is driven by the softening of such a coupled mode [1 3]. trans-Stilbene (C6H s CH=:CH-C6Hs) is one of the compounds on which the intramolecular degrees of freedom have been extensively studied. The spectroscopic studies on the molecular vibration in gas [4], liquid [5] and crystalline [5, 6] states have revealed that the characteristic energy of the intramolecular twisting degrees of freedom is low and within the range of the external lattice vibration of the crystal [4, 5]. It is also widely observed that the central C=C bonds show anomalously short length in derivatives of trans-stilbene and trans-azobenzene. Recently this apparent shortening of the bond lengths has been suggested being due to some molecular motion [7]. The motion suggested is a combination of * Corresponding author. Present address: Microcalorimetry Research Center, Faculty of Science, Osaka University, Toyonaka, Osaka 560, Japan.
the overall rotation of a molecule and the intramolecular twisting of the benzene rings to keep the orientation of the rings, as shown in Fig. 1. Namely, two benzene rings are twisted by some angle keeping the inversion symmetry of the molecule and simultaneously the molecule itself (as described by the plane on which the central CH =CH moiety lies) also twisted by the same angle in the opposite sense. There is, however, no direct evidence of such a motion, though its experimental verification will be indirect in any way. It will therefore be valuable to make lattice-dynamics calculation to see whether the motion suggested is, in the crystal, possibly excited or not.
2. Calculation
The molecule of trans-stilbene (C6H 5 CH=CH C6Hs) has two "soft" intramolecular twisting degrees of freedom of the benzene rings (-C6H5). Combination of the motions of two benzene rings forms a 9erade and an ungerade intramolecular motional modes, which are adopted as only elementary motions besides translational and librational degrees of freedom in the lattice-dynamics calculation, resulting in total eight degrees of freedom per molecule. The intramolecular rotations in an isolated state are assumed being free based on the spectroscopic results [4].
0921-4526/96/$15.00 1996 Elsevier Science B.V. All rights reserved SSDI 0 9 2 1 - 4 5 2 6 ( 9 5 ) 0 0 7 6 3 - 6
418
K. Saito, L ikemoto / Physica B 219&220 (1996) 417-419 ,, ;i,
X
p
i /'
"','', /~ 5 kJ/mo
,,i"
,
>,
",,,L,,
,/'/"
B
iU.l
-20
0
20
Angle / degree Fig. 1. Molecular motion suggested for the explanation of the abnormally short bond-length of the central C=C bond of trans-stilbene molecule,
An idealized molecular model is assumed in the calculation: The benzene ring is a regular hexagon with a bond length of 1.397 A. The lengths of single and double bonds o between carbon atoms are 1.474 and 1.353 A, respectively. The C - H bond is assumed being 0.995 A. All the bond angles are 120 °. The intermolecular interaction is approximated by the sum of the a t o m - a t o m potential of Buckingham type [8]. The parameters for the cross interaction (between carbon and hydrogen atoms) were obtained by the standard mixing rule. The lattice-dynamics calculations were made based on the formulation by Venkataraman and Sahni [9] for the idealized perfect crystal, though apparent orientational disorder is known to exist in the crystal [10-14]. The calculation under the rigid molecular model is also made for comparison.
Fig. 2. One-particle potential energy for the molecules A and B in crystalline trans-stilbene for the overall rotation (dotted line) and the composite motion (solid line) suggested for the explanation of the abnormally short length of the central C =C bond.
20O flexible
rigid
~, loo U_
3. Results and discussion Fig. 2 shows the one-particle potentials for the overall rotation along the long molecular axis and for the composite motion suggested for the explanation of the abnormally short bond length. Since there are two molecules crystallographically inequivalent in the crystal, the depth and the shape of the potential curve are different to each other. Indeed, only molecules A show abnormally short bond length of the central C =C bond. The composite motion under consideration, however, has a potential curve significantly fiat for both the molecules. The dispersion relations along the b* axis for the flexible and the rigid molecular models are shown in Fig. 3. T h e calculation incorporating only the twisting degrees of freedom yielded similar dispersion relations to those of the most upper mode in the rigid molecular model. Since the calculation was made on the idealized
0
0
b*/2 0
b*/2
Fig. 3. Phonon dispersion relation of crystalline trans-stilbene calculated within the flexible and the rigid molecular models.
perfect crystal to see qualitatively what occurs if the intramolecular twisting degrees of freedom are allowed for, the coincidence between the calculated and the experimental [6] frequencies are rather poor, partly because of the existence of the frozen-in disorder of the orientation of the molecule B [15]. From the comparison of the dispersion relations obtained in the flexible and the rigid molecular model, it is
Ki Saito, L Ikemoto / Physica B 219&220 (1996) 417--419
roughly said that eight intramolecular twisting modes are grouped into two on mixing with the translational and the rotational degrees of freedom. One group has the frequency of around 50 c m - 1 with little dispersion. The other group lies above 100 c m - 1 and shows rather large dispersion. These results are very interesting, for not only modes in the frequency region of the bare twisting modes (above 100 c m - 1) but also those far from the region are significantly affected by and coupled to the intramolecular twisting degrees of freedom. Detailed inspection over the components of the eigenvectors reveals that two modes (53.4 and 64.3 cm-1) at the center of the Brillouin zone have the component ratio for the molecule A according well 1o the motion suggested as a possible cause of the abnormally short length of the central C = C bond. No such mode is observed for the molecule B. The results at the point imply that the motion suggested possibly exists for the molecule A, in accordance with the observation [7]. The composite motion suggested belongs to the group between 40 and 60 cm 1 as noted above. Since the correlation between motions (or vibration) of neighboring molecules plays no significant role, like molecular vibrations with much higher frequency than the lattice vibration, the motion suggested can be described as a oneparticle motion. In conclusion, the lattice-dynamics calculation on the crystalline trans-stilbene in the flexible and the rigid molecular models shows that the motion suggested for the explanation of the abnormally short length of the central C =C bond [7] exists in crystal and can be treated as a one-particle motion in a sense that there is no significant dispersion.
419
References [1] H. Cailleau, J.L. Baudour, J. Meinnel, A. Dworkin, F. Moussa and C.M.E. Zeyen, Faraday Discuss. Chem. Soc. 69 (1980) 7. [2] H. Cailleau, in: Incommensurate Phases in Dielectrics 2, Materials, eds. R. Blinc and A.P. Levanyuk (North-Holland, Amsterdam, 1985) Ch. 12. [3] N.M. Plakida, A.V. Belushkin, I. Natkaniec and T. Wasiutynski, Phys. Stat. Sol. B 118 (1983) 129. I-4] T. Suzuki, N. Mikami and M. Ito, J. Phys. Chem. 90 (1986) 6431. [5] Z. Mei'c and H. G~sten, Spectrochim. Acta A 34 (1978) 101. [6] A. Bree and M. Edelson, Chem. Phys. 51 (1980) 77. [7] K. Ogawa, T. Sano, S. Yoshimura, Y. Takeuchi and K. Toriumi, J. Am. Soc. Chem. 114 (1992) 1041 and references therein. 1-8] D.E. Williams, J. Chem. Phys. 47 (1967) 4680. 1-9] G. Venkataraman and V.C. Sahni, Rev. Mod. Phys. 42 (1970) 409. [10] C.J. Finder, M.G. Newton and N.L. Allinger, Acta Crystallogr. B 30 (1974) 41. [11] J. Bernstein, Acta Crystallogr. B 31 (1975) 1268. [12] A. Hoekstra, P. Meertens and A. Vos, Acta Crystallogr. B 31 (1975) 2813. [13] J. Bernstein and K. Mirsky, Acta Crystallogr. A 34 (1978) 161. [14] J.A. Bouwstra, A. Schouten and J. Kroon, Acta Crystallogr. C 40 (1984) 428. [15] K. Saito, Y. Yamamura and I. Ikemoto, J. Phys. Chem. Solids 56 (1995) 849.
ELSEVIER
Phonon and the intramolecular motions in crystalline trans-stilbene Kazuya Saito*, Isao Ikemoto Department of Chemist~, Faculty of Science, To~.'o Metropolitan Unit:ersiO', Hachioji, Tolo,o 192-03, Jupan
Abstract
Lattice-dynamics calculations have been performed on crystalline trans-stilbene using a flexible and a rigid molecular model. The intramolecular twisting of the benzene rings strongly couples with the overall rotation of the molecule. The coupled modes form phonon branches and show little dispersion.
1. Introduction
Intramolecular (internal) degrees of freedom are often ignored when the lattice vibrations of molecular crystals are considered. There are, however, a few examples where the intramolecular degrees of freedom strongly couple to the lattice degrees of freedom and modifies the lattice vibration. Indeed a structural phase transition in crystalline biphenyl (C6Hs-C6Hs) is driven by the softening of such a coupled mode [1 3]. trans-Stilbene (C6H s CH=:CH-C6Hs) is one of the compounds on which the intramolecular degrees of freedom have been extensively studied. The spectroscopic studies on the molecular vibration in gas [4], liquid [5] and crystalline [5, 6] states have revealed that the characteristic energy of the intramolecular twisting degrees of freedom is low and within the range of the external lattice vibration of the crystal [4, 5]. It is also widely observed that the central C=C bonds show anomalously short length in derivatives of trans-stilbene and trans-azobenzene. Recently this apparent shortening of the bond lengths has been suggested being due to some molecular motion [7]. The motion suggested is a combination of * Corresponding author. Present address: Microcalorimetry Research Center, Faculty of Science, Osaka University, Toyonaka, Osaka 560, Japan.
the overall rotation of a molecule and the intramolecular twisting of the benzene rings to keep the orientation of the rings, as shown in Fig. 1. Namely, two benzene rings are twisted by some angle keeping the inversion symmetry of the molecule and simultaneously the molecule itself (as described by the plane on which the central CH =CH moiety lies) also twisted by the same angle in the opposite sense. There is, however, no direct evidence of such a motion, though its experimental verification will be indirect in any way. It will therefore be valuable to make lattice-dynamics calculation to see whether the motion suggested is, in the crystal, possibly excited or not.
2. Calculation
The molecule of trans-stilbene (C6H 5 CH=CH C6Hs) has two "soft" intramolecular twisting degrees of freedom of the benzene rings (-C6H5). Combination of the motions of two benzene rings forms a 9erade and an ungerade intramolecular motional modes, which are adopted as only elementary motions besides translational and librational degrees of freedom in the lattice-dynamics calculation, resulting in total eight degrees of freedom per molecule. The intramolecular rotations in an isolated state are assumed being free based on the spectroscopic results [4].
0921-4526/96/$15.00 1996 Elsevier Science B.V. All rights reserved SSDI 0 9 2 1 - 4 5 2 6 ( 9 5 ) 0 0 7 6 3 - 6
418
K. Saito, L ikemoto / Physica B 219&220 (1996) 417-419 ,, ;i,
X
p
i /'
"','', /~ 5 kJ/mo
,,i"
,
>,
",,,L,,
,/'/"
B
iU.l
-20
0
20
Angle / degree Fig. 1. Molecular motion suggested for the explanation of the abnormally short bond-length of the central C=C bond of trans-stilbene molecule,
An idealized molecular model is assumed in the calculation: The benzene ring is a regular hexagon with a bond length of 1.397 A. The lengths of single and double bonds o between carbon atoms are 1.474 and 1.353 A, respectively. The C - H bond is assumed being 0.995 A. All the bond angles are 120 °. The intermolecular interaction is approximated by the sum of the a t o m - a t o m potential of Buckingham type [8]. The parameters for the cross interaction (between carbon and hydrogen atoms) were obtained by the standard mixing rule. The lattice-dynamics calculations were made based on the formulation by Venkataraman and Sahni [9] for the idealized perfect crystal, though apparent orientational disorder is known to exist in the crystal [10-14]. The calculation under the rigid molecular model is also made for comparison.
Fig. 2. One-particle potential energy for the molecules A and B in crystalline trans-stilbene for the overall rotation (dotted line) and the composite motion (solid line) suggested for the explanation of the abnormally short length of the central C =C bond.
20O flexible
rigid
~, loo U_
3. Results and discussion Fig. 2 shows the one-particle potentials for the overall rotation along the long molecular axis and for the composite motion suggested for the explanation of the abnormally short bond length. Since there are two molecules crystallographically inequivalent in the crystal, the depth and the shape of the potential curve are different to each other. Indeed, only molecules A show abnormally short bond length of the central C =C bond. The composite motion under consideration, however, has a potential curve significantly fiat for both the molecules. The dispersion relations along the b* axis for the flexible and the rigid molecular models are shown in Fig. 3. T h e calculation incorporating only the twisting degrees of freedom yielded similar dispersion relations to those of the most upper mode in the rigid molecular model. Since the calculation was made on the idealized
0
0
b*/2 0
b*/2
Fig. 3. Phonon dispersion relation of crystalline trans-stilbene calculated within the flexible and the rigid molecular models.
perfect crystal to see qualitatively what occurs if the intramolecular twisting degrees of freedom are allowed for, the coincidence between the calculated and the experimental [6] frequencies are rather poor, partly because of the existence of the frozen-in disorder of the orientation of the molecule B [15]. From the comparison of the dispersion relations obtained in the flexible and the rigid molecular model, it is
Ki Saito, L Ikemoto / Physica B 219&220 (1996) 417--419
roughly said that eight intramolecular twisting modes are grouped into two on mixing with the translational and the rotational degrees of freedom. One group has the frequency of around 50 c m - 1 with little dispersion. The other group lies above 100 c m - 1 and shows rather large dispersion. These results are very interesting, for not only modes in the frequency region of the bare twisting modes (above 100 c m - 1) but also those far from the region are significantly affected by and coupled to the intramolecular twisting degrees of freedom. Detailed inspection over the components of the eigenvectors reveals that two modes (53.4 and 64.3 cm-1) at the center of the Brillouin zone have the component ratio for the molecule A according well 1o the motion suggested as a possible cause of the abnormally short length of the central C = C bond. No such mode is observed for the molecule B. The results at the point imply that the motion suggested possibly exists for the molecule A, in accordance with the observation [7]. The composite motion suggested belongs to the group between 40 and 60 cm 1 as noted above. Since the correlation between motions (or vibration) of neighboring molecules plays no significant role, like molecular vibrations with much higher frequency than the lattice vibration, the motion suggested can be described as a oneparticle motion. In conclusion, the lattice-dynamics calculation on the crystalline trans-stilbene in the flexible and the rigid molecular models shows that the motion suggested for the explanation of the abnormally short length of the central C =C bond [7] exists in crystal and can be treated as a one-particle motion in a sense that there is no significant dispersion.
419
References [1] H. Cailleau, J.L. Baudour, J. Meinnel, A. Dworkin, F. Moussa and C.M.E. Zeyen, Faraday Discuss. Chem. Soc. 69 (1980) 7. [2] H. Cailleau, in: Incommensurate Phases in Dielectrics 2, Materials, eds. R. Blinc and A.P. Levanyuk (North-Holland, Amsterdam, 1985) Ch. 12. [3] N.M. Plakida, A.V. Belushkin, I. Natkaniec and T. Wasiutynski, Phys. Stat. Sol. B 118 (1983) 129. I-4] T. Suzuki, N. Mikami and M. Ito, J. Phys. Chem. 90 (1986) 6431. [5] Z. Mei'c and H. G~sten, Spectrochim. Acta A 34 (1978) 101. [6] A. Bree and M. Edelson, Chem. Phys. 51 (1980) 77. [7] K. Ogawa, T. Sano, S. Yoshimura, Y. Takeuchi and K. Toriumi, J. Am. Soc. Chem. 114 (1992) 1041 and references therein. 1-8] D.E. Williams, J. Chem. Phys. 47 (1967) 4680. 1-9] G. Venkataraman and V.C. Sahni, Rev. Mod. Phys. 42 (1970) 409. [10] C.J. Finder, M.G. Newton and N.L. Allinger, Acta Crystallogr. B 30 (1974) 41. [11] J. Bernstein, Acta Crystallogr. B 31 (1975) 1268. [12] A. Hoekstra, P. Meertens and A. Vos, Acta Crystallogr. B 31 (1975) 2813. [13] J. Bernstein and K. Mirsky, Acta Crystallogr. A 34 (1978) 161. [14] J.A. Bouwstra, A. Schouten and J. Kroon, Acta Crystallogr. C 40 (1984) 428. [15] K. Saito, Y. Yamamura and I. Ikemoto, J. Phys. Chem. Solids 56 (1995) 849.