The Franck–Condon principle, two-photon spectroscopy and the [formula omitted] system of benzene

Abstract

The application of the Franck–Condon principle to two-photon spectra is discussed, and it is shown that both simple and more complex theories suggest that much of the familiar form of the Herzberg–Teller description for one-photon spectra, and the same vibrational overlap integrals, can be applied to the corresponding two-photon spectra. The results are applied to the well-known A ̃ 1B 2u– X ̃ 1A 1g system of benzene. In the course of this it is shown that the experimental data used in the early Franck–Condon work on the one-photon spectrum are unreliable, and as a result it is necessary to question the usual assumption that a simple Franck–Condon analysis of this spectrum leads to a change in the C–C bond length on excitation similar to that found by rotational analyses. Preliminary work suggests that a single Franck–Condon theory may account for the main features of both the one- and two-photon spectra of benzene if the effective transition moments are allowed to increase with the ν 1 normal co-ordinate. In particular it appears that the capacity of the ν 14( b 2 u ) vibration to induce the two-photon spectrum increases as the carbon ring expands. Further experimental and theoretical work to confirm and understand these results is desirable.