Effects of excluded volume and correlated molecular orientations on Förster resonance energy transfer in liquid water

Abstract

Förster theory for the survival probability of excited chromophores is generalized to include the effects of excluded volume and orientation correlation in the molecular distribution. An analytical expression for survival probability was derived and written in terms of a few simple elementary functions. Because of the excluded volume, the survival probability exhibits exponential decay at early times and stretched exponential decay at later times. Experimental schemes to determine the size of the molecular excluded volume are suggested. With the present generalization of theory, we analyzed vibrational resonance energy transfer kinetics in neat water. Excluded volume effects prove to be important and slow down the kinetics at early times. The majority of intermolecular resonance energy transfer was found to occur with exponential kinetics, as opposed to the stretched exponential behavior predicted by Förster theory. Quantum yields of intra-molecular vibrational relaxation, intra-, and intermolecular energy transfer were calculated to be 0.413, 0.167, and 0.420, respectively.