Intensities of vibrational difference bands

Abstract

It is shown that the intensity of a binary difference band in the vibrational spectrum of a polyatomic molecule is not necessarily related in any simple way to the intensity of the corresponding binary combination band. The effects of mechanical anharmonicity on the matrix elements 〈v_s,v_s′‖P‖v_s+1,v_s′+1 〉 and 〈v_s,v_s′+1‖P‖v_s+1,v_s′ 〉 are quite different and hence the relative intensities of the difference and combination bands are complex functions of the anharmonic force constants and the dipole‐moment derivatives. For this reason it is possible to find extraordinary resonance enhancements of the transition probability in difference transitions which have no counterpart in the combination transitions.