Reorganization parameters of electronic transitions in electronically delocalized systems. 1. Charge transfer reactions

This paper addresses the problem of calculating the free energy surfaces of charge transfer (CT) reactions in electronically delocalized systems involving direct electronic overlap of the donor and acceptor units. The model includes two electronic states of the solute linearly coupled to a linearly responding solvent in both the diagonal and off-diagonal terms of the Hamiltonian matrix. The exact solution for the adiabatic free energy surfaces along the CT reaction coordinate is derived as a function of the reorganization parameters invariant to the extent of electron delocalization and the parameter of electron delocalization. For dipolar solutes, the latter is defined through adiabatic differential and transition dipoles measured by optical spectroscopy. The invariant reorganization energy is the real, observable reorganization energy determining the vertical transition energy, bandwidth, and the activation energy of self-exchange transitions. The Golden Rule expression for the ET rate constant is obtained in the adiabatic electronic basis of the solute by treating the non-Condon off-diagonal coupling to the solvent as a perturbation. The ET matrix element entering the rate constant is fully determined in terms of the adiabatic vacuum splitting of the electronic levels and the delocalization parameter. The CT energy gap law is very asymmetric with a shallow branch in the inverted region due to the dependence of the delocalization parameter on the CT driving force.