Molecular vibrational spectra in the solid state

Abstract

The site and factor group methods of interpreting solid state vibrational spectra are compared. As examples. K2TiF6 (which has one molecular unit in a unit cell) and K2ZrF5 (which has eight in a non-primitive unit cell) are considered. Benzenetricarbonylchromium enables a distinction between site and factor group methods. The modification of the latter needed to account for the spectra of Cr(CO)6. dienMo(CO)3 and (C6H5)3SnFe(C5H5)(CO)2 are discussed and the concept of a vibrational unit cell introduced. In this paper I shall discuss some features of vibrational spectroscopy which are of importance in the understanding of the infra-red and Raman spectra of crystalline solids. The simplest way of looking at a crystal, be it ionic or molecular, is to regard it as a giant molecule. This viewpoint correctly indicates the complexity of the vibrational problem—there are an enormous number of modes associated with each crystal. For, for example, the understanding of specific heat phenomena, it is necessary to have a fairly detailed knowledge of the energy distribution of these modes. However, if one is only interested in the interpretation of the infra-red and Raman spectra of solids a considerable simplification results. This arises as a consequence of the fact that, in either form of spectroscopy, the wavelength of the incident radiation is very much greater than the distances between molecules (or ions, but we confine our discussion to the molecular case). Consider two molecules in adjacent primitive unit cells, interrelated by a simple translation operation. The effect of the electric vector associated with the incident radiation in either infra-red or Raman spectroscopy will be essentially identical for both of the molecules. That is, to a very good level of approximation, only those vibrations in which all translationally-related mOlecules move in phase will be observed. Evidently, this generalization cannot be extended to molecules interrelated by other than a pure translation because such molecules will usually be oriented differently in space. This means that a phase difference between the vibrations of two such molecules is to be expected. In a perfect crystal any two molecules are symmetry-related (ignoring the discontinuities imposed by the finite dimensions of the crystal) and so the number of operations of a space group is very large indeed. Fortunately. the fact that we are interested only in vibrations which are invariant with respect to the translational operations introduces a simplification. This is that we