Theoretical studies of intramolecular electron transfer reactions: distance and free energy dependences

Electron tunneling through a square potential energy barrier is used to calculate the distance-dependent factors of electron transfer (ET) processes in metal-monolayer-metal junctions, donors and acceptors dispersed in rigid organic glasses, intramolecular ET in rigid donor-bridge-acceptor species in solution and redox centers attached to electrodes through adsorbed monolayers. This tunneling model of distance-dependent non-adiabatic factors is incorporated in the intersecting state model (ISM). The result is a simple semiclassical theory which is used to calculate the rates of non-adiabatic ET reactions. When the electron is originally located in a π* molecular orbital of the donor and the reaction free energy is no lower than approximately -50 kJ mol^-1. no adjustable parameters are necessary to calculate the intramolecular ET rates from a donor, through a rigid bridge, to an acceptor. Such calculated rates are within an order of magnitude of the experimental values. The model can also account for the ET rates of more exothermic reactions provided that the value of an empirical parameter, which is constant for structurally related reactants and solvents of similar polarity, is estimated. The physical meaning of this parameter is related to the dynamics of the reactions. The profiles of the distance and free energy dependences of photoinduced ET rates are closely reproduced. The occurrence of distance-dependent non-adiabatic factors in intermolecular σ*-d ETs is rationalized.