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Summary form only given. The difference absorption (DA) spectra relevant to femtosecond pump-probe measurements of a chromofore within the quantum-mechanical description of the solute states is discussed in this paper. Theoretical analysis is based on the numerical solution of the equations for the reduced density matrix in the molecular states representation by considering the coherent coupling between vibrational levels in ground and excited electronic states precisely. The specific features of the of time resolved DA spectra of the molecule (such as delay-dependent Stokes shift, vibrational quantum beats) are displayed when treating interaction with a thermal environment in the framework of the Redfield theory. Such a treatment provides principal possibilities for the information on vibrational relaxation dynamics as well as electron transfer processes when using the experimentally estimated rate parameters or leaving them as parameters for the fitting with the experimental data.