Intermolecular Coupling of Vibrations in Molecular Crystals: A Vibrational Exciton Approach

Abstract

A vibrational exciton theory is developed which parallels in many ways the electronic exciton theory originally put forward by Davydov and amplified by Craig and Hobbins and by Fox and Schnepp. The kernel of the theory is the adoption, following Davydov again, of a transition‐dipole—transition‐dipole interaction as the potential which perturbs the isolated molecule energies and which thereby couples the motions of pairs of molecules in a crystal. As a result of the quantitative application of this theory, molecular dipole derivatives of several of the parallel modes of methyl chloride are obtained from the correlation field splittings of the corresponding fundamentals in the spectrum of solid methyl chloride. An isotope effect upon correlation field splittings is reported and is accounted for in terms of the same theory. A general method of testing the theory in terms of this isotope effect is suggested. The effect of intermolecular transition dipole coupling on intensities is derived and compared with the ratio of the dipole derivatives obtained from the correlation field splittings to those obtained from absolute intensity studies in the gas phase. The possible use of other bases for correlation field splittings is also discussed.