Detection of Electronic and Vibrational Coherence Effects in Electron-Transfer Systems by Femtosecond Time-Resolved Fluorescence Spectroscopy:  Theoretical Aspects

Time- and frequency-gated spontaneous emission signals are calculated for electron-transfer systems. The electron-transfer dynamics is modeled in terms of two diabatic excited electronic states which are electronically coupled as well as strongly coupled to a reaction mode, which in turn is weakly coupled to a dissipative environment. The bath degrees of freedom are integrated out in the framework of Redfield theory. The reduced density matrix is obtained by the numerical solution of the Redfield equations of motion. For suitably chosen parameters, the model describes interesting features of ultrafast electron-transfer dynamics such as electronic beatings (due to the electronic coherence) and steplike electronic population decay (due to vibrational coherence). The relationship between the intrinsic system dynamics and the time-resolved fluorescence (from the electronically coupled excited states to the ground state) is investigated. The time- and frequency-gated fluorescence spectra are obtained for various durations of the pump and gate pulses. For suitably chosen parameters of the pump and gate pulses, the signal maps the vibrational wave packet dynamics of the electron-transfer system. The frequency-integrated time-resolved fluorescence, on the other hand, reflects directly the population dynamics of the diabatic electronic states. It is shown that the step structures in the electronic population probability due to vibrationally coherent electron transfer or the oscillatory structures due to electronic coherence can be experimentally detected, provided the duration of the pump and gate pulses is of the order of a vibrational period or electronic beating period, or shorter. When the duration of the pulses significantly exceeds the vibrational or electronic beating periods, the system-specific features are averaged out, resulting in exponential electronic population decay corresponding to the electron-transfer rate.