An algebraic formula to calculate the three-dimensional Franck–Condon factors including the Duschinsky effect

Generalized Analytic Approach for Determination of Multidimensional Franck-Condon Factors: Simulated Photoelectron Spectra of Polynuclear Aromatic Hydrocarbons

An enhanced generalized analytic approach for determination of multidimensional Franck-Condon Factors (FCFs) enables efficient computational prediction of photoelectron spectra for large-dimensional systems. Incorporation of the automated assignment of Cartesian coordinate handedness and coordinate superposition between the ground and excited electronic states satisfies the Eckart conditions and allows evaluation of the Duschinsky effect. The model shows excellent agreement with experiments for the determination of FCFs and photoelectron spectra of a series of increasing dimensions polynuclear hydrocarbons (PAHs), including naphthalene, anthracene, phenanthrene, and pyrene. In addition, a high-resolution prediction of the PES for the 84-dimensional PAH corannulene provides motivation for an additional experimental study. For FCFs, coordinate transformation between the initial and final states rather than the dimension of the systems more greatly influences the complexity of the spectral band shapes.