The Effect of Multiphonon Processes on Vibrational Band Shapes in Molecular Solids

Abstract

The purpose of this note is to discuss multiple excitations which occur when a photon is absorbed (or scattered) and result in the excitation of two or more vibrational quanta on different molecules. The study of multiple excitations becomes of particular significance in ordered solids because of the existence of the translational symmetry. In these solids the two vibrational excitations are characterized by their frequencies ωi and ωj and wavevectors k i and k j.In the following, without much loss of generality,we shall refer only to absorption processes but the conclusions obtained will apply to scattering processes as well. For an absorption process the energy and momentum conservation requires that $${\omega _o} = {\omega _i} + {\omega _j}$$ (1) and $$\underline q = {\underline k _i} + {\underline k _j} + \underline G $$ (2) where ωO and q are the photon frequency and wavevector and G is a reciprocal lattice vector. From the conservation law (2) it is seen that in a two-phonon band we generally have contributions from phonons of all wavevectors k i and k within the Brillouin zone.Therefore two-phonon bands become of interest as possible sources of information on the phonon densities of states and on the intermolecular forces responsible for the phonon dispersion in crystals.