Adiabatic electrochemical electron-transfer reactions involving frequency changes of inner-sphere modes

A Hamiltonian model is formulated for electrochemical electron-transfer reactions involving frequency changes of the inner-sphere modes. The adiabatic free energy surface is calculated and it is shown that this nonlinear coupling leads to a transfer coefficient different from , and that the transfer coefficient can no longer be identified with the electron occupation probability in the transition state saddle point, as in the linear coupling case.