A new method of calculation of Franck-Condon factors which includes allowance for anharmonicity and the Duschinsky effect : simulation of the He I photoelectron spectrum of ClO₂

Abstract

A new method of Franck-Condon (FC) factor calculation for nonlinear polyatomics, which includes anharmonicity and Duschinsky rotation, is reported. Watson's Hamiltonian is employed in this method with multidimensional ab initio potential energy functions. The anharmonic vibrational wave functions are expressed as linear combinations of the products of harmonic oscillator functions. The Duschinsky effect, which arises from the rotation of the normal modes of the two electronic states involved in the electronic transition, is formulated in Cartesian coordinates, as was done previously in an earlier harmonic FC model. This new anharmonic FC method was applied to the simulation of the bands in the He I photoelectron (PE) spectrum of C1O₂. For the first band, the harmonic FC model was shown to be inadequate but the anharmonic FC simulation gave a much-improved agreement with the observed spectrum. (See Article file for details of the abstract.)