A new method of calculation of Franck-Condon factors which includes allowance for anharmonicity and the Duschinsky effect: Simulation of the He I photoelectron spectrum of CIO₂

A new method of Franck-Condon (FC) factor calculation for nonlinear polyatomics, which includes anharmonicity and Duschinsky rotation, is reported. Watson's Hamiltonian is employed in this method with multidimensional ab initio potential energy functions. The anharmonic vibrational wave functions are expressed as linear combinations of the products of harmonic oscillator functions. The Duschinsky effect, which arises from the rotation of the normal modes of the two electronic states involved in the electronic transition, is formulated in Cartesian coordinates, as was done previously in an earlier harmonic FC model. This new anharmonic FC method was applied to the simulation of the bands in the He I photoelectron (PE) spectrum of ClO2. For the first band, the harmonic FC model was shown to be inadequate but the anharmonic FC simulation gave a much-improved agreement with the observed spectrum. The experimentally derived geometry of the X̃1A1 state of ClO2+ was obtained, for the first time, via the iterative FC analysis procedure {R(Cl-O)=1.414±0.002Å, ∠O-Cl-O=121.8±0.1°}. The heavily overlapped second PE band of ClO2, corresponding to ionization to five cationic states, was simulated using the anharmonic FC code. The main vibrational features observed in the experimental spectrum were adequately accounted for in the simulated spectrum. The spectral simulation reported here supports one of the two sets of published assignments for this band, which was based on multireference configuration interaction (MRCI) calculations. In addition, with the aid of the simulated envelopes, a set of adiabatic (and vertical) ionization energies to all five cationic states involved in this PE band, more reliable than previously reported, has been derived. This led also to a reanalysis of the photoabsorption spectrum of ClO2.