The complete vibrational spectra of crystalline C6H6 and C6D6 have been calculated using semiempirical atom-atom potential functions. The calculation uses a free molecule normal coordinate basis including Eckart mass-weighted coordinates. The following factors affecting the calculated freuqencies have been investigated in some detail: (i) intermode mixing among internal vibrations and between internal and external modes, (ii) inclusion of the first derivative of the atom-atom potential with respect to interatomic distances, (iii) number of atom-atom interactions, (iv) fulfillment of equilibrium conditions, and temperature effects. The Jacobian of the crystal frequencies, equilibrium conditions, and heat of sublimation with respect to the individual atom-atom parameters have been evaluated and a refinement of the potential parameters is presented. The agreement between the calculated frequencies and available experimental data is satisfactory specially for lattice frequencies. Transition dipole-dipole calculations lead to poor agreement with observed frequencies thus showing the model to be inappropriate for crystalline benzene.
56) a n a , R.; Lang, J.; Sorba, 0.; Caulbat, A. M.; Langevin, D. J. Phys. (57) Kaneshina, S.; Ueda, I.; Kamaya, H.; Eyring, E. Biochim. Eiophys. (54) Anantaraman, A.; Walters, A.; Edmonds, P.; Pings, C.Calculations of bending energy of two different micellar forms (prolate ellipsoid and spherocylinder) were performed using the Hyde's model in order to evaluate the relative stability of both kinds of micelles in a large range of micelle length. These calculations show that (i) prolate ellipsoids are more stable than spherocylinders at lower micelle lengths, and (ii) there is a "transition" point where both kinds of micelles have the same bending energies. These results are used in the interpretation of experimental results of X-ray scattering in concentrated micellar solutions near the isotropic-hexagonal phase transition.
The high-resolution spectra in polarized light of oriented polycrystalline films of C6H6 and C6D6 at 85°K have been obtained. The observation of two different crystal faces allowed the classification of the Davydov components, according to their polarization character, into three different sets, which correspond to the three infrared-active factor-group symmetry species. The complications which arise from the presence of isotopic impurities (13C12C5H6 in 12C6H6, 13C12C5D6 and 12C6D5H in 12C6D6) are removed thanks to the use of polarized light, the aid of the correlation between C6H6 and C6D6 spectra, and solid solution information. Therefore, a complete assignment of all the observed peaks has been possible. The experimental results have been compared with exciton splittings and crystal shifts calculated by other authors.
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