On the calculation of polyatomic Franck–Condon factors: Application to the 1A1g→1B2u absorption band of benzene

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Abstract
Two methods for calculating polyatomic Franck–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 Franck–Condon integral to be written as a sum of integrals each of which is a product of one‐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 Franck–Condon integral involves evaluation of matrix elements exclusively within the ground electronic state vibrational manifold. Application of both methods is made to the A0n vibronic series of the 1A1g→1B2u symmetry‐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.