Infrared band intensities: transition moment matrix elements for fundamentals and overtones: Part III. Isotope effect

Abstract

A theoretical analysis of the isotope effect on IR band intensities of the first threa harmonics of a diatomic oscillator is presented. The coefficients α_ij for the dipole moment derivatives appearing in the expressions for transition moment matrix elements R^iu for the transitions i→0, where i=1, 2 and 3 are calculated for OH, OD, HCl and DCl species and their dependence on the reduced mass of the oscillator is evaluated. From these studies it is concluded that, within the limits of logical approximations, the intensities of the fundamental, first overtone and second overtone are proportional to μ⁻¹, μ^-3/2 and μ⁻², respectively, where μ is reduced mass. The intensities for these three bands for OD and DCl are predicted to be approximately ½, ⅓ and ¼ times their values for OH and HCl oscillators.