Theoretical study of the free energy curve as a function of reaction coordinate of electron transfer by the cumulant expansion method

We investigate the free energy curve as a function of the reaction coordinate of the electron transfer by the cumulant expansion method. The deviation from the linear response which gives rise to a harmonic form of the free energy curve is expressed in terms of the cumulants. The validity condition of the linear response is investigated using the l-particle correlation length λl. It is a central result that the linear response applies only when the conditions λ2 ≫ λl(l ≥ 3) and λ2≫a hold, where a is the sum of solute and solvent radii.