Fully analytical solution for the first spectral moment of a fluorophore in solution

One of the common methods for assessing the solvation dynamics of a fluorescent system in a polar medium is the analysis of the first spectral moment behavior. So there is a need to build a model that takes into account important physical processes and at the same time is not demanding in terms of calculations. In this paper, an approach is proposed that considers the parametersof the exciting laser pulse and intramolecular vibrational relaxation for constructing the solvation dynamics. A method for building an analytical solution for the dynamics of the first spectral moment is presented. This model is free of numerical methods using, and it is a simple construction built by basics functions and an additional error function. The influence of all key parameters on the system relaxation is illustrated. It is shown that delocalization in time of the pump pulse suppresses the oscillatory behavior of the first moment and hides information about the damped intramolecular mode. The similar effect is also observed with the diffusion and inertial processes contribution insreasion to the reorganization energy at early stages of relaxation. The presented model can be generalized to take into account quantum transitions between vibrational sublevels of high-frequency intramolecular vibrations.