A simple model for the calculation of nonlinear optical response functions and femtosecond time-resolved spectra

A simple model is developed for the calculation of optical response functions for electronically nonadiabatic systems coupled to a heat bath. A phenomenological dissipation ansatz is suggested which describes the major bath-induced relaxation processes, namely excited-state population decay, optical dephasing, and vibrational relaxation. The model is constructed in such a way that it allows one to express the nonlinear response functions for a dissipative system in terms of those for the corresponding bath-free system. The explicit formulas for the third order response functions are given. Several special cases are considered for which the evaluation of the response functions simplifies considerably. To illustrate the performance and validity of the theory, the response functions have been used for the calculation of time and frequency gated spontaneous emission spectra. The time-dependent spectra derived from the model have been compared with those calculated (i) for the standard damped harmonic oscillator model and (ii) for a model nonadiabatic electron-transfer system with Redfield theory. It is concluded that the present model provides qualitatively correct response functions and, therefore, may be useful for the interpretation of observed time-resolved spectra.