Vibronic coupling quantitative theories

Much of chemistry occurs in the condensed phase solution phase ET reactions have been a major focus for theory and experiment for the last 50 years. Experiments, and quantitative theories, have probed how reaction-free energy, solvent polarity, donor-acceptor distance, bridging stmctures, solvent relaxation, and vibronic coupling influence ET kinetics. Important connections have also been drawn between optical charge transfer transitions and thennal ET. 

For a quantitative treatment of establishing connections between vibronic coupling and vibrational progressions in electronic spectra, band profiles from vibronic wavefunctions must be calculated using common procedures of time-dependent perturbation theory and Fermi s golden rule [57], For emission, e.g., the transition rate which is the transition probability per unit time summed over... 

The results obtained clearly demonstrate that the Marcus model for ECL processes may be used for qualitative as well as for quantitative descriptions of this kind of electron transfer reactions. The more sophisticated approach, taking into account the vibronic excitation in the reaction products (important in the inverted Marcus region), solvent molecular dynamics (important in the case of large values of the electronic coupling elements), as well as the changes in the electron transfer distance, should be used. The results indicate that the Marcus theory may also be used for predicting the ECL efficiency, provided that some conditions are fulfilled. Especially, during the ECL process, only the annihilation of ions should occur, without any competitive reactions. The necessary rate constants can be evaluated from pertinent electrochemical and spectroscopic data. 

Efforts to provide a quantitative model for the coupling of vibronic transitions to the phonons of the host material have been undertaken recently. The theory and first results will be published elsewhere. 

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