Molecular Properties Obtained by Analysis of Electronic Spectra Containing Interference Dips. Comparisons of Analytical Equations and Exact Models Based on Coupled Potential Energy Surfaces

Interference dips in electronic absorption spectra caused by coupling between excited states are calculated and interpreted using three methods: an analytical expression, an integratable expression, and wave packet propagation. All of the analyses give similar results. The dips (distantly related to Fano's antiresonance) are caused by spin−orbit coupling between the states involved in spin-forbidden transitions with narrow bandwidths and the state involved in a spin-allowed transition with a large bandwidth caused by progressions in normal vibrational modes that are displaced between the excited and ground electronic states. The analytical expression involves the assumptions that only one vibrational eigenstate of the “forbidden” electronic state is involved and that the broad background is represented by a Lorentzian-type function. The integratable expression replaces the Lorentzian function by one that represents the band shape caused by a progression of unresolved vibronic peaks. The wave packet propagation method is exact for the model. Analytical expressions for multiple interfering states and integratable expressions for multiple electronic states and multiple vibrational modes are derived. The spectra of Ni(H2O)6 2+ and octahedral CrO6 9- units in ZrO2·33%Y2O3 doped with chromium(III) are analyzed. Physical meanings and mathematical origins of the interference dips are interpreted.