To study nuclear quantum effects on electron transfer reactions, the non-adiabatic rate constant is expanded in terms of Planck＇s constant. The expansion to the second order reproduces well the quantum correction in the activation free energy for a quantum Monte Carlo simulation of water. In addition, the spin-boson model is discussed using the expansion. The validity of the rate constant given by the spin-boson model is investigated in non-linear systems. Conditions for obtaining exact values of the rate constant are established in the second order of Planck＇s constant. In liquids, the conditions are satisfied if the one-body distribution function does not change during the electron transfer reaction.