Site Effects in Isotopic Mixed Crystals—Site Shift, Site Splitting, Orientational Effect, and Intermolecular Fermi Resonance in the Vibrational Spectrum of Benzene

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Abstract
A modification of the Davydov theory of energy levels in molecular crystals is applied to experimental observations on ground-state vibrations of various isotopic substituted benzene crystals. Three distinct and characteristic crystal-induced phenomena have been observed experimentally: (1) site group splitting—involving degenerate vibrations of the molecule that map into nondegenerate site modes; (2) orientational effects—concerning isotopic benzenes of symmetry D2h or lower, and their relative positioning in two or more distinct orientations at crystal sites; and (3) intermolecular Fermi resonance—near-resonance interaction between two adjacent-site molecules of different isotopic compositions. The first two phenomena give rise to 10 cm−1 ≲ splittings. A general mechanism is proposed to account for this, and the differences and similarities between these two effects are discussed. The importance of observed gas-to-crystal energy shifts is also discussed in the light of these experimental findings. In addition to intersite Fermi resonance, solid-enhanced intrasite Fermi resonance is reported and discussed qualitatively. Applying the Davydov theory for the case of no resonance interactions, one can obtain information concerning the shape of the molecule in the site field, the symmetry of the site field, and the general nature of the intermolecular interactions.

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