Approximate calculation of femtosecond pump-probe spectra monitoring nonadiabatic excited-state dynamics

An approximate theory of femtosecond spectroscopy of nonadiabatically coupl ed electronic states is developed. Neglecting the commutators of vibrationa l Hamiltonians pertaining to different diabatic electronic states, the form ulation represents a generalization of the semiclassical Franck-Condon appr oximation to the case of nonadiabatic dynamics. Explicit expressions for va rious time- and frequency-resolved spectra are derived which allow for a si mple interpretation of femtosecond spectroscopy of vibronically coupled mol ecular systems. Employing multidimensional model problems describing (i) th e nonadiabatic cis-trans isomerization of an electronic two-state system, a nd (ii) the S-2--> S-1 internal conversion of pyrazine, exact reference dat a are compared to approximate calculations of transient absorbance and emis sion as well as time-resolved photoelectron spectra. In all cases considere d, the approximation is shown to be appropriate for probe-pulse durations t hat are shorter than the period of the fastest relevant vibrational mode of the molecular system. Reducing the numerical costs of pump-probe simulatio ns to the costs of a standard time-dependent wave-packet propagation, the a pproximate theory leads to substantial computational savings. (C) 2000 Amer ican Institute of Physics. [S0021-9606(00)01310-6].