A Study of Selection Rules for Vibrational Spectra of Complex Crystals

Abstract

Relations are obtained for the expression of the dipole moment and polarizability matrices for a particular transition in a crystal, in terms of corresponding expressions for molecular or ionic groups within the crystal. The results show that, to the degree of approximation used (quadratic terms in the dipole moment or polarizability expansion and cubic terms in the potential energy), the only cause for the appearance of bands which would be forbidden for a given uncoupled complex ionic or molecular group is the alteration of the normal coordinates of these groups by vibrations of neighboring groups. It is also shown that the bands of fully allowed first overtones and binary combinations of frequencies that are not degenerate or near‐degenerate in a unit cell have a shape that is approximately given from the distributions of frequencies that arise from lattice coupling. As an incidental result, the dipole moment matrix elements for the first overtones and binary combinations arising from the cubic terms in the potential energy are given explicitly.