On the calculation of polyatomic Franckndash;Condon factors: Application to the1A1grarr;1B2uabsorption band of benzene

摘要

Two methods for calculating polyatomic Franckndash;Condon integrals are reported. The first method uses a coordinate transformation on the normal coordinates of both the ground and excited electronic states. This transformation effectively removes any Duschinsky mixing and allows the multidimensional Franckndash;Condon integral to be written as a sum of integrals each of which is a product of onehyphen;dimensional harmonic oscillator overlap integrals. The second method uses contact transformation perturbation theory to construct a representation of the vibrational wavefunctions. With this representation, the calculation of a polyatomic Franckndash;Condon integral involves evaluation of matrix elements exclusively within the ground electronic state vibrational manifold. Application of both methods is made to theA0nvibronic series of the1A1grarr;1B2usymmetryhyphen;forbidden electronic transition of benzene. Relative intensities calculated by either method agree well with observed values. However, the computational efficiencies of the two methods are found to be markedly different, with the perturbation method being the least efficient.