An analytical approach for computing Franck-Condon integrals of harmonic oscillators with arbitrary dimensions.

We have developed an analytical approach for computing Franck-Condon integrals (FCIs) of harmonic oscillators (HOs) with arbitrary dimensions in which the mode-mixing Duschinsky effect is taken into account. A general formula of FCIs of HOs was obtained and was applied to study the photoelectron spectroscopy of vinyl alcohol and ovalene (C(32)H(14)). The equilibrium geometries, harmonic vibrational frequencies and normal modes of vinyl alcohol, ovalene, and their cations were computed at the B3LYP/aug-cc-pVTZ or the B3LYP/6-31G(d) level, from which Franck-Condon factors were calculated and photoelectron spectra were simulated.