Theory of rate processes and the compensation rule

The rate of intermolecular charge transfer as involved in the theory of rate processes is derived for a quadratic generalization of Holstein's one-dimensional linear polaron theory. The activation energy and the activation entropy are shown to be proportional to the number of vibrational degrees of freedom associated with each molecular site. The activation entropy is found to be negative in this model, thus decreasing the reaction rate. A spin-polaron model is introduced where the electron is coupled in a specific way to N spins at each site. In this model both the activation parameters are positive and are proportional to N. Thus, the oscillator model gives a negative and the spin model gives a positive compensation temperature.