Classical calculation of transient absorption spectra monitoring ultrafast electron transfer processes

Classical formulations are considered that allow for the calculation of time- and frequency-resolved pump-probe spectra of nonadiabatically coupled molecular systems. When the semiclassical Franck-Condon approximation in the theoretical framework of the doorway-window formalism is employed, various first- and second-order expressions for the classical doorway and window functions are derived. Moreover, a classical analogue of the electronic dipole transition operator is employed. When established models describing ultrafast photoinduced electron transfer are adopted, it is found that the first- order approximations give rise to spurious structures of the time- resolved signal, which indicate that these approximations fail to correctly account for the averaging effect caused by finite pulses. The higher-order approximations, on the other hand, are shown to give a fairly accurate description of the transient absorption spectrum. By comparing to exact quantum-mechanical calculations, the merits and shortcomings of the various approaches as well as the generally achievable accuracy of a classical modeling of optical spectra is discussed.