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Experiments on the 3Blu state of benzene in the past have established that this state is conformationally unstable due to vibronic coupling with the 3Elu state and that this instability is critically dependent on the influence of a crystal field and substituents. For the 3Blu state of the free molecule, however, the energy differences and sizes of distortion are not known. Since these quantities are of importance for the interpretation of the spectroscopic and photochemical behavior of benzene, the potential energy surface of the )B1, state along the two-dimensional deformation coordinate s8 was calculated with large ab initio MRDCI calculations, including u-u and u-T correlation. The results show the hexagonal conformation to be unstable and to lie 800 cm-' above an almost cylindrical trough. Calculation of spectroscopic observables yields good agreement with the experimentally observed vibrational spacing and Franck-Condon factors. The geometry of benzene in its lowest triplet state (3Bl,) has received considerable attention since Moffit and Liehr pointed out that, in a static picture, the hexagonal conformation might be unstable because of vibronic coupling between the 3Blu and 3Elu states through eZg modes.' Low-temperature EPR experiments on benzene in a glassy matrixZa and subsequent EPRZb and END OR^^ experiments on the C6H6 in C6D6 crystal established that in the solid state the electron spin distribution in the 3Blu state, indeed, is nonhexagonal. Spectroscopic observations3 supported this result; most remarkable amongst these was the strong doublet, 245 f 6 cm-' above the 0-0 in the 3Blu-IAlg absorption spectrum of the C6H6 in C6D6 crystal.3f The idea that this feature corresponds to us, at 1584 cm-I in the ground state, was corroborated by Zeeman s t ~ d i e s . ~ ~ , ~ ' The EPR experiments further revealed that the size and even the kind of distortion are critically dependent on the nature of the environment into which benzene is incorp ~ r a t e d . ~ A large number of calculations on vibronic coupling in the 3Blu state have been made, which helped the qualitative interpretation of spectroscopic and EPR result^.^ Because of their semiempirical nature, however, no clear picture exists of the energy differences and sizes of distortion involved in the deformation of the free molecule in the 3Blu state. In view of its importance for the interpretation of the spectroscopic and photochemical behavior of benzene, we have performed a b initio configuration interaction (CI) calculations to determine the 3Blu potential energy surface as a function of the S8 coordinate. A detailed account of these calculations and of the effects of a crystal field and substituents will be given elsewhere. Here, we report the principal conclusions regarding the free molecule. The calculation shows that in the 3Blu state the hexagonal conformation corresponds to an energy maximum, about 800 cm-' above a flat, almost cylindrical trough. When the first vibrational excitation for the 3Blu potential surface is calulated, the low-frequency doublet of Burland et al.3f is nicely recovered, indicating that even for large molecules as benzene accurate energy surfaces are calculable. The nuclear coordinate chosen is s8, dominant in the Q8(p,p) normal coordinate6 (see Figure I ) . For the hexagonal conformation the experimental ground-state C-H distance of 2.0539 bohr is taken, and a C-C distance of 2.722 bohr, optimized for the triplet state. The atomic orbital basis set is a slightly modified (9~5p15~)-[4s2p12s] set of Fischer-Hjalmars,' which in view of recent results of Matos et al. and Kitao aL8 should be adequate for the description of the lowest triplet state. The molecular orbitals used in the C I are the S C F orbitals for a state in which ' Huygens Laboratory. * Gorlaeus Laboratories. 0002-7863/89/1511-0086$0l.50/0 the T electrons are coupled to the quintet (la2,)2(le1,)2(le2,)2('Al,). The CI calculations have been performed with the CRAY X M P version of the Wuppertal-Bonn MRDCI program^,^ in which the energy corresponding to the full-CI space within the A 0 basis is estimated with a formula given in ref 10. The correlation of 20 electrons and use of 15 reference configurations leads to MRDCI spaces of 3-8 configurations of BI, symmetry, of which 3000-8000 are selected using a threshold of 15 fiH and selection on the two lowest roots. The resulting 3Blu energy surface is depicted in Figure 1 for three values of the parameter p. For comparison, this figure also contains the surface calculated for the 3Elu component to which 3Blu is coupled. I t is clear from this figure that the surface for the lowest triplet state is extremely flat and that the hexagonal conformation is unstable, lying 800 cm-' above the conformations of minimal energy. The dependence on p, if it exists a t all, is very small and much smaller than the stabilization energy. With this (1) (a) Moffitt, W.; Liehr, A. D. Phys. Reu. 1957, 106, 1195-l200. (b) Liehr, A. D. Z . Naturforsch., A: Astrophys., Phys. Phys. Chem.-Chim. B i d . 1961, 16A, 641. (2) (a) de Groot, M. S.; van der Waals, J. H. Mol. Phys. 1963,6, 545-562. ( b ) de Groot, M. S.; Hesselmann, I. A. M.; van der Waals, J. H. Mol. Phys. 1967, 13, 583-586; Ibid. 1969, 16, 45-60. (c) Ponte Goncalves, A. M.; Hutchison, C. A. J . Chem. Phys. 1968, 49, 4235-4236. (3) (a) Leach, S.; Lopez-Delgado, R. J . Chim. Phys. Phys.-Chim. B i d . 1964, 61, 1636. (b) King, G. W.; Pinningfon, E. H. J . Mol. Spectrosc. 1965, 1 5 , 394-404. (c) Nieman, G. C.; Tinti, D. S . J . Chem. Phys. 1967, 46, 1432-1443. (d) Bernstein, E. R.; Colson, S. D.; Tinti, D. S.; Robinson, G. W. J . Chem. Phys. 1968,48,4632-4659. (e) Nieman, G. C. J . Chem. Phys. 1969, 50, 1674-1683. (0 Burland, D. M.; Castro, G.; Robinson, G. W. J . Chem. Phys. 1970,52,41OCk4108. (g) Gwaiz, A. A,; El-Sayed, M. A.; Tinti, D. S. Chem. Phys. Lett. 1971, 9, 454-456. (h) Hochstrasser, R. M.; Wessel, J. E.; Zewail, A. H. J . Chem. Phys. 1971,55, 3596-3597. ( i ) van Egmond, J.; Burland, D. M.; van der Waals, J . H. Chem. Phys. Lett. 1971, 9,454-456. (j) Johnson, P. M.; Ziegler, L. D. J . Chem. Phys. 1972,56, 2169-2175. (k) van Egmond, J.; van der Waals, J. H. Mol. Phys. 1973, 26, 1147-1167. (4) (a) El-Sayed, M. A.: Moowaw, W. R.; Chodak, J. B. J . Chem. Phys. 1972,57,4061-4063. (b) Pruyssen, J . M.; Colson, S . D. Chem. Phys. 1974, 6, 382-402. (c) Vergragt, P. J.; van der Waals, J. H. Chem. Phys. Lett. 1976, 42, 193-196; Ibid. 1975, 36, 283-289. (5 ) (a) Donath, W. E. J . Chem. Phys. 1965, 42, 118-126. (b) van der Waals, J. H.; Berghuis, A. M. D.; de Groot, M. S . Mol. Phys. 1967, 13, 301-321; Ibid. 1971, 21, 497-521. (c) van Egmond, J.; van der Waals, J. H. Mol. Phys. 1974, 28, 457-467. (d) Langhoff, S. R.; Davidson, E. R.; Kern, C. W. J . Chem. Phys. 1975, 63, 4800-4807. (e) Vergragt, P. J.; van der Waals, J . H. Mol. Phys. 1977, 33, 1507-1521. (6) Wilson, E. B. Phys. Rev. 1934, 45, 706-714. (7) Fischer-Hjalmars, I . ; Siegbahn, J. Theor. Chim. Acta 1973, 31, 1-17. ( 8 ) (a) Matos, J. M. 0.; Roos, B. 0.; Malmqvist, P. A. J . Chem. Phys. 1987, 86, 1458-1466. (b) Kitao, 0.; Nakatsuji, H. J . Chem. Phys. 1988, 87, (9) Buenker, R. J.; Peyerimhoff, S. D.; Butscher, W. Mol. Phys. 1978,35, ( I O ) Bruna, P. J.; Peyerimhoff, S. D.; Buenker, R. J. Chem. Phys. Lett. 1169-1 182.

Conformational instability of the lowest triplet state of benzene: the result of ab initio calculations