Calculation of Franck–Condon factors and simulation of photoelectron spectroscopy of D 2CO: Including Duschinsky effects

Abstract

Calculations of Franck–Condon factors are crucial for interpreting vibronic spectra of molecules and studying nonradiative processes. On the base of the closed form expression of the Franck–Condon integrals between arbitrary multidimensional harmonic oscillators under the Duschinsky mixing effects, a more general algebraic expression for the calculation of the three-dimensional four-mode Franck–Condon factors was derived straightforwardly and applied to study the photoelectron spectrum of D 2 CO + ( B ∼ 2 A 1 ) . Geometry optimization and harmonic vibrational frequency calculations were performed on the X ∼ 1 A 1 state of D 2CO at B3LYP, QCISD, CCSD and CASSCF levels, and the B ∼ 2 A 1 state of D 2CO + at CIS, TD-B3LYP, and CASSCF levels. Franck–Condon analyses and spectral simulations were carried out on the D 2 CO + ( B ∼ 2 A 1 ) - D 2 CO ( X ∼ 1 A 1 ) photoionization process. The spectral simulations of vibrational structures based on the computed Franck–Condon factors are in excellent agreement with the observed spectrum. In addition, the equilibrium geometric parameters of the B ∼ 2 A 1 state of D 2CO + were obtained in the spectral simulations.