Spectral Moments Dynamics of a Fluorophore in Solution

The analysis of the spectral moments behavior is one of the common methods for assessing solvation dynamics of a fluorescent system in a polar media. Spectral moments contain information about the position and shape of the emission intensity distribution. A model is necessary that combines the accuracy of describing physical phenomena with computational efficiency. The approach proposed in this work accounts for the parameters of the pump pulse and the duration of the probe signal. It accurately reproduces solvation dynamics and also demonstrates the influence of intramolecular vibrational relaxation on the fluorescence spectrum behavior. This model does not require numerical methods and is based on a simple construction using basis functions combined with a complementary error function. The effect of all key parameters on system relaxation is illustrated. It is shown that temporal delocalization of the probe-pulse suppresses oscillatory behavior in the first moment and obscures information about the damped intramolecular vibrational mode. The effect of a low-frequency intramolecular vibrational mode on the spectral width and asymmetry is also demonstrated. Finally, inverse problem solution is proposed. Dynamics and shape of the spectral distribution are derived from information on the evolution of spectral moments.