A new method of calculation of Franck-Condon factors which includes allowance for anharmonicity and the Duschinsky effect: Simulation of the HeI photoelectron spectrum of ClO2

A new method of Franck-Condon (FC) factor calculation for nonlinear polyato mics, which includes anharmonicity and Duschinsky rotation, is reported. Wa tson's Hamiltonian is employed in this method with multidimensional ab init io potential energy functions. The anharmonic vibrational wave functions ar e expressed as linear combinations of the products of harmonic oscillator f unctions. The Duschinsky effect, which arises from the rotation of the norm al modes of the two electronic states involved in the electronic transition , is formulated in Cartesian coordinates, as was done previously in an earl ier harmonic FC model. This new anharmonic FC method was applied to the sim ulation of the bands in the He I photoelectron (PE) spectrum of ClO2. For t he first band, the harmonic FC model was shown to be inadequate but the anh armonic FC simulation gave a much-improved agreement with the observed spec trum. The experimentally derived geometry of the (X) over tilde (1)A(1) sta te of ClO2+ was obtained, for the first time, via the iterative FC analysis procedure {R(Cl-O)=1.414 +/- 0.002 Angstrom, angle O-Cl-O=121.8 +/- 0.1 de grees}. The heavily overlapped second PE band of ClO2, corresponding to ion ization 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 th is 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. (C) 2000 American Institute of Physics. [S0021-9606(00)01337-4].