Calculation of crystal vibrations of benzene

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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.

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