Low-Frequency Librations and the Vibrational Spectra of Molecular Crystals

Abstract

The effect of librations of molecules about axes perpendicular to those of the transition moments of molecular vibrations upon the dichroic ratios associated with such vibrations in the infrared spectra of molecular crystals is considered. It is demonstrated that if such librations are harmonic and of small amplitude, the root-mean-square deviation of the molecular orientation from its equilibrium orientation is sufficient to account for the deviation of observed dichroic ratios from those predicted by the ``oriented gas model.'' Deviations of this type previously reported from the polarized infrared spectra of iodoform, brucite, para-dichloro-benzene and benzene are reviewed. From a knowledge of the libration frequencies determined by examination of infrared or Raman spectra of molecular crystals, and of the observed dichroic ratios of polarized infrared spectra, the orientations of molecules and/or functional groups of molecules in crystals may be quantitatively determined. It is also demonstrated that as a consequence of the model used for correction of observed dichroic ratios, a branch-type libration-vibration spectrum of such crystals is predicted. The fine structure of this spectrum is discussed and is shown to be similar, in many ways, to the rotation-vibration spectra of polyatomic gases. The relationship of this work to the interpretation of electron density maps of molecular crystals is discussed.