An Efficient Analytic Approach for Calculation of Multi-Dimensional Franck-Condon Factors and Associated Photoelectron Spectra.

The implementation, optimization, and performance of a generalized analytic treatment of multidimensional Franck-Condon Factors (FCF) within the harmonic oscillator approximation and associated photoelectron spectra (PES) for N-dimensional systems, including consideration of Eckart conditions in the displacement minimization and Cartesian coordinate handedness for evaluation of the Duschinsky Effect, is carried out in this work. A new efficient strategy for algorithmic efficiency for high dimensional systems is introduced, and demonstrated for 3-, 15-, and 30-dimensional systems. Determination of the photoelectron spectra for H2O+ (B̃2B2), vinyl alcohol, and C6H6+ (X̃2E1g) validates the capabilities with a high degree of accuracy with respect to experiment.