This paper reports a theory of the inner sphere-type electron transfer reaction. Inner sphere reactions, as opposed to the outer sphere variety, require that the solvate or ligand shells surrounding the electron donor and acceptor species undergo considerable change in the course of the electron transfer. In this paper we assume that the electron transfer step takes place in a molecular complex which exists in equilibrium with the reactants. The electron transfer step occurs as a non-radiative charge transfer-type transition. In this manner we treat the charge transfer kinetics, in particular, the evaluation of the reaction rate constant, in the same manner as is usual for non-radiative problems. The analysis leading to the rate constant expression is based on Yamamoto’s general chemical reaction rate theory. The rate constant expressions obtained are quite general, they hold for any degree of strength of coupling between subsystems comprising the entire system. The activation energy, in the Arrhenius form for the rate constant, shows a dependence on the energy (work) of formation of the intermediate charge transfer complex, on vibrational shift energies associated with the molecular motions of the ligands, and on solvent repolarization energies. The activation energy also shows an important dependence on coupling terms which link the vibrations of the molecular inner shell with the polarization states of the (assumed) dielectric continuum which surrounds the charge transfer participants. The approach we take in developing this theory we believe points the way towards the development of a more complete theory capable of accounting for the dynamics of the molecular reorganization leading to the intermediate charge transfer complex as well as accounting for the electron transfer step itself.
Horizontal versus vertical charge and energy transfer in hybrid assemblies of semiconductor nanoparticles
