On the connection between Gaussian statistics and excited-state linear response for time-dependent fluorescence.

Time-dependent fluorescence (TDF) of a chromophore in a polar or nonpolar solvent is frequently simulated using linear-response approximations. It is shown that one such linear-response-type approximation for the TDF Stokes shift derived by Carter and Hynes [J. Chem. Phys. 94, 5961 (1991)] that is based on excited-state dynamics gives the same result as that obtained by assuming Gaussian statistics for the energy gap. The derivation provides insight into the much discussed relationship between linear response and Gaussian statistics. In particular, subtle but important differences between the two approximations are illuminated that suggest that the result is likely more generally applicable than suggested by the usual linearization procedure. In addition, the assumption of Gaussian statistics directly points to straightforward checks of the validity of the approximation with essentially no additional computational effort.