Calculation of Ground State Vibrational Structure and Phonons of the Isotopic Benzene Crystals

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Abstract
Using the “giant molecule” technique and existing intermolecular potentials, the normal modes, phonon and exciton structure, site shifts, site splitting, and orientational effect for the isotopic benzene crystals are calculated. The agreement between the calculations and the experimental observations is good for an H–H, C–H, and C–C potential set independently obtained by Williams from thermodynamic and structural properties of aromatic crystals. The calculation presented here serves to unify not only the thermodynamic and spectral properties, but also the diverse spectral properties themselves. This calculation emphasizes that all atom–atom interactions, not just H–H interactions, must be considered for best agreement between calculated and observed spectral data. This conclusion was also reached by Williams with respect to the thermodynamic and structural data. A discussion of the potentials, their form, and their relation to standard exciton theory integrals is presented. Future improvements in such calculations must be directed, not toward more extensive parametric data fitting of the atom–atom pair potential, but toward more general potential functions that include anharmonicities and multicenter terms. The use of actual site force constants rather than free molecule force constants is also indicated.