Theoretical Insights on Nonlinear Response Theory of Fluorescence Spectroscopy in Liquids

Correlations between the nonequilibrium solvation dynamics upon the photon excitation of the chromophore and a system's equilibrium fluctuations are deeply studied. As the linear response of the solvent has been linked with Gaussian statistics of the energy fluctuations in the literature, we specifically explore the cases beyond the regime of the linear response theory due to deviation from Gaussian fluctuations. As a continuation of our previous work, an analytical formalism is presented to project the energy shift with various order moments, where the non-Gaussian statistics arise from the overlap of the energy basins on the perturbed potential energy surface. It is shown that the nonequilibrium dynamics still correlate with the spontaneous regressions at equilibrium and are controlled by the decay rates of those higher order components with the prevailing contributions to the energy shift. Molecular dynamics simulations were performed in the protein Staphylococcus nuclease, in which even the dynamics of the high order moments are available. The results further verify the above relationship. Our scheme is used to evaluate Stokes shift using the information on non-Gaussian statistics at equilibrium, thus presenting a broad picture on the correlation between the nonequilibrium process and equilibrium properties in liquids.