F�rster theory for the ensemble-averaged population of excited chromophores is generalized to include the excluded volume and orientation correlation in the distribution of energy donor and acceptors. The conventional F�rster theory assumes a random distribution of energy acceptors around an excited chromophore. This leads to the well-known formula of a stretched exponential decay of population. However, when the concentration of energy acceptors is high as vibrational chromophores in liquid water, a major part of excited population decays by neighboring acceptors and the molecular correlations between a donor and adjacent acceptors should be properly considered. The primary molecular correlation is created by excluded volume in a molecular pair arising from finite molecular sizes. Within an independent pair approximation, an analytical expression for the excited population is derived and written in terms of a few simple elementary functions which can be used conveniently in the analyses of experimental data. The population decay exhibits transient non-F�rster kinetics of an exponential decay at early times and later the F�rster kinetics of a stretched exponential one. An experimental scheme to determine the size of molecular excluded volume is suggested. Effects of correlated molecular orientations are shown to be approximately represented by an effective excluded volume. Using the generalized F�rster theory, we analyzed vibrational energy transfer kinetics of excited OH bonds in liquid water. Due to the high concentration of OH bonds in neat water, a majority of intermolecular energy transfer takes place in the exponential regime rather than in the stretched exponential one as usually assumed. Time scales of intermolecular vibrational energy transfer in water was calculated to be 210 fs at early times and it becomes twice in about 500 fs while the initial time scale of intra-molecular energy transfer to be 480 fs and becomes twice more quickly in about 250 fs. Quantum yields of vibrational relaxation, intermolecular and intra-molecular energy transfer were calculated to be 0.413, 0.420, and 0.167, respectively.

Excluded volume effects in vibrational F�rster resonance energy transfer of liquid water and an experimental method to determine the size of excluded volume

248th National Meeting (2014)

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