Comparison of methods for calculating Franck–Condon factors beyond the harmonic approximation: how important are Duschinsky rotations?

Abstract

Three different approaches for calculating Franck–Condon factors beyond the harmonic approximation are compared and discussed in detail. Duschinsky effects are accounted for either by a rotation of the initial or final wavefunctions – which are obtained from state-specific configuration-selective vibrational configuration interaction calculations – or by a rotation of the underlying multi-dimensional potential energy surfaces being determined from explicitly correlated coupled-cluster approaches. An analysis of the Duschinsky effects in dependence on the rotational angles and the anisotropy of the wavefunction is provided. Benchmark calculations for the photoelectron spectra of ClO₂, HS⁻₂ and ZnOH⁻ are presented. An application of the favoured approach for calculating Franck–Condon factors to the oxidation of Zn(H₂O)⁺ and Zn₂(H₂O)⁺ demonstrates its applicability to systems with more than three atoms.

Keywords:

• Franck–Condon factors
• Watson Hamiltonian
• Duschinsky rotation

Acknowledgements

We thank Prof. Robert Berger (Marburg, Germany) for many interesting and stimulating discussions about this topic. Financial support by the Konrad-Adenauer-Stiftung (KAS) and the Deutsche Forschungsgemeinschaft (DFG) is kindly acknowledged.

Disclosure statement

No potential conflict of interest was reported by the authors.

Supplemental

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Additional information

Funding

The Konrad-Adenauer-Stiftung (KAS); the Deutsche Forschungsgemeinschaft (DFG).