Theory of fluorescence excitation spectra using anharmonic-Coriolis coupling in S1 and internal conversion to S0. II. Application to the channel three problem in benzene for the 14112 band

Abstract

Rotational lines in the fluorescence excitation spectra of the 14112 band of the first excited singlet state (S1) of benzene are calculated for various J and K. For this purpose, perturbation theory is used to obtain an "eigenstate" in S1. Internal conversion to S0 via Franck–Condon (FC) factors is then calculated. A search procedure is used to obtain the important contributors to this S1 state and to this internal conversion process S1-->S0 using the perturbation theory coefficients and the FC factors in the evaluation function. At low J, the calculated lines with K=0 are sharp, other lines being broadened and diminished in intensity. The calculated K=0 lines have a linewidth proportional to J(J+1). For high J, the lines with K=J remain sharp, the other lines being broadened and diminished in intensity. These various results are in general agreement with the experimental findings. The onset of channel three in benzene occurs in the present mechanism via anharmonic-Coriolis coupling in the S1 state plus internal conversion to S0. The calculations suggest that, at low J, parallel Coriolis coupling causes mixing of the in-plane mode-excited ``light state'' with in-plane modes that are anharmonically coupled to out-of-plane modes.Dark states with certain excited out-of-plane mode contributions possess large FC factors for the internal conversion to S0. At high J, on the other hand, the in-plane modes are coupled directly to these out-of-plane modes by perpendicular Coriolis coupling. Paths involving two perpendicular Coriolis operators are important at high J in the present calculation—their matrix elements are larger at high J and so they become more competitive relative to purely anharmonic coupling operators. Such two-Coriolis paths at high J are expected to yield multiple excitation in the out-of-plane modes and further enhance the internal conversion. The perpendicular Coriolis coupling is least at J=K and so these lines survive at high J. Two-Coriolis operator paths are calculated to be relatively unimportant at low J. The present calculations, using the same electronic matrix element, account for both the low JK = 0 and high JK = J sets of lines being the dominant ones. Aspects regarding further study are discussed.

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