Computation of Franck–Condon Factors in Terms of Primitive Internal Coordinates

We present a novel approach for computing the Duschinsky matrix and Franck-Condon factors of harmonic oscillators in terms of primitive internal coordinates. It is contrasted to the available approaches for computing Franck-Condon factors in terms of internal coordinates, in which nonredundant internal coordinates must be constructed, in that either redundant or nonredundant internal coordinates can be adopted. It is, therefore, a general approach free from constructing nonredundant internal coordinates from primitive internal coordinates for computing Franck-Condon factors. The photoelectron spectra of acetylene, ketene, and phosphorus trifluoride, as well as the absorption, fluorescence, and phosphorescence spectra of chlorophyll c2, were simulated to demonstrate the feasibility of this approach. All the theoretical predictions are in agreement with the experimental spectra, with the photoelectron spectra of ketene and phosphorus trifluoride being reassigned.