The Franck-Condon principle and the structures of excited electronic states of molecules

Abstract

An approximate method is described for quantitatively applying the Franck-Condon principle to the problem of determining the structure of an excited electronic state of a simple polyatomic molecule. The method is applicable to an electronic transition for which both electronic states have structures of the same symmetry. Necessary information includes the geometrical structure and the totally symmetrical frequencies of the ground state, as well as the vibrational analysis of a vibronic band system and the resulting information about the totally symmetrical frequencies of the excited state. The relative intensities of a few selected vibronic bands must be measured. One dimensional Condon overlap integrals for these bands are expressed in terms of parameters which depend on the change of the geometrical structure with the electronic transition. A comparison of the squares of the overlap integrals with the band intensities permits the evaluation of the geometrical parameters. In an initial calculation the normal coordinates of the excited state are assumed to be parallel to those known for the ground state. The approximate excited state structure calculated on this basis is used to determine more exact normal coordinates of the excited state. A final calculation based on these coordinates yields an improved excited state structure. Actually there are always several excited state structures consistent with band intensities. It is therefore necessary to have some additional information from the band envelopes. As examples, the structures of one excited state of ClO 2 and of two excited states of SO 2 are determined.