Experimental and theoretical study of inhomogeneous electron transfer in betaine: comparisons of measured and predicted spectral dynamics

Abstract

New tunable pump and probe data are reported for the S 1 → S 0 reverse electron transfer in betaine in solution. The observed dynamics are a dramatic function of probe wavelength due to energy deposition into solute and solvent molecular degrees of freedom from the electron transfer. The data indicate that in nonpolar solvents, this energy is primarily deposited into intramolecular modes. In polar solvents, most of the energy is deposited into intramolecular modes, but some is specifically deposited into polar collective motions of the solvent, i.e. the solvent coordinate. Modern theories of electron transfer that include diffusive motion along the solvent coordinate as a driving mechanism for electron transfer predict this specific energy deposition into the solvent coordinate. In this paper, we extend a model by Walker et al. to predict the spectral dynamics due to solvent coordinate heating caused by the electron transfer and compare with experimental results. We show that the diffusive electron transfer mechanism creates a displaced distribution along the solvent coordinate that is characterized by an absorption spectrum that is red-shifted from the equilibrium ground-state distribution, in agreement with experimental observations. The model is not in quantitative agreement with experiment, however, because it neglects the contributions of vibrational heating of the intramolecular modes to the spectral dynamics. This type of vibrational heating is evident in the observed dynamics in nonpolar solvents.