Theory of pressure-induced absorption by symmetric top molecules

Abstract

A theory of pressure-induced radiation absorption in a gas of linear molecules, due to Colpa and Ketelaar, is extended to symmetric top molecules. The absorption is attributed to the mutually-induced dipole moment µ(R) of a pair of molecules separated by distance R. The dependence of µ(R) on the orientations of the molecules is expressed by expanding µ(R) in terms of quantities D^λ1_µ1ν1(ϕ₁θ₁χ₁)D^λ2_µ2ν2(ϕ₂θ₂χ₂) where a D^λ_µν is a matrix element of an irreducible representation of the rotation group. This expansion permits evaluation of matrix elements of µ(R) between eigenstates of a molecular pair. The expansion coefficients are evaluated in terms of the polarizabilities and multipole moments (of any order) of the molecules. The theory performs summations over “uninteresting” magnetic quantum numbers and produces expressions for the intensity of pressure-induced absorption in terms of Clebsch-Gordan coefficients.