Calculation of crystal vibrations of benzene

Abstract

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.