Theory of vibrational overtone line shapes of polyatomic molecules

Abstract

We present a general theory for the overtone absorption line shapes of isolated polyatomic molecules. The theory is based on a separation of the molecular vibrational degrees of freedom into: (1) a few relevant CH local modes which interact directly with the radiation field, and (2) the remaining ’’bath’’ modes which induce spectral broadening and determine the line shapes. Line shapes are evaluated using the standard Fano–Zwanzig scattering formalism. A simple yet general model is put forth to illustrate some of the features exhibited by polyatomic line shapes. Specific application is made to benzene. The model adequately accounts for the overtone line shapes recently observed by Bray and Berry. Within its context we are able to understand the observed vibrational state and isotopic dependence of the line shape and to predict line shapes for related but as yet unstudied systems. To our knowledge this is the first dynamical application of local mode theories. We discuss their advantages and the extent to which polyatomic line shapes can provide information about intramolecular energy redistribution processes.