Time-dependent theory of Raman scattering for systems with several excited electronic states: Application to a H+3 model system

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Abstract
The time‐dependent formulation of Raman scattering theory is used to study how nonadiabatic interactions affect the Raman spectrum of a model H+3 system, which has two excited electronic states. We start with a formula derived by Heller which gives the Raman scattering cross section as the Fourier transform (over time) of a time‐dependent overlap integral. The latter is calculated with a method proposed by Fleck, Morris, and Feit, and extended to curve crossing by Alvarellos and Metiu. In performing these calculations we are especially interested in displaying effects typical of systems having more than one upper state. If the incident laser populates two electronic states there are several ways (i.e., excite to state one and emit from state two, excite to state one, and emit from state one, etc.) by which the Raman process can reach a given final state, and this leads to quantum interference. This interference is manifested in the Raman cross section as approximate selection rules controlling which final states can be reached through the Raman process. These selection rules depend on the relative orientation of the transition dipoles that radiatively couple the ground electronic state with the excited electronic states. The magnitude of the nonadiabatic contribution to the Raman emission, e.g., the contribution from absorbing to state one and emitting from state two, can be determined from the polarization dependence of the Raman emission if the transition dipoles have neither parallel nor antiparallel relative orientation.