A simple approach for the calculation of femtosecond pump-probe spectra for electronically nonadiabatic systems

A standard and universal description of various nonlinear spectroscopic techniques can be given in terms of the optical response functions (RFs). These functions allow perturbative calculation of the nonlinear response of a material system to external time-dependent fields. Normally, one assumes that the Born-Oppenheimer approximation is adequate and it is sufficient to consider the ground and a certain excited electronic state of the system, which are coupled via the laser fields. One then can model the ground and excited state Hamiltonians via a collection of vibrational modes, which are usually assumed to be harmonic. The conventional damped oscillator is thus the standard model in this case. If the system under consideration possesses non-adiabatic electronic couplings within the excited-state vibronic manifold, the latter approach no longer is applicable. Recently, a simple model, which allows for the explicit calculation of RFs for electronically non-adiabatic systems coupled to a heat bath, has been developed. This model is based on a phenomenological dissipation ansatz, which describes the major bath-induced relaxation processes: excited-state population decay, optical dephasing, and vibrational relaxation. This model is applied for the calculation of the time and frequency gated spontaneous emission spectra for model non-adiabatic electron-transfer systems. The predictions of this model are tested against the more accurate calculations that are performed within the Redfield formalism. Therefore, it is natural to extend this description to time and frequency resolved pump-probe (PP) signals. This chapter describes briefly the model and gives explicit analytical expressions for the integral PP signal.