Low temperature extension of the generalized Zusman phase space equations for electron transfer

In a previous paper J. Chem. Phys. 119, 11864 (2003)], we derived a set of two coupled equations which describe electron transfer in the presence of dissipation at high temperature. Employing the low temperature extension of the Fokker-Planck operator, suggested by Haake and Reibold Phys. Rev. A 32, 2462 (1985)] and Ankerhold Europhys. Lett. 61, 301 (2003)], we show that one may extend the generalized Zusman equations in a similar manner to low temperature. Numerical simulation shows that addition of the temperature-dependent term which couples the coordinate and momentum causes an increase in the electron transfer rate as compared to the rate obtained from the previous high temperature equations. The increase in the rate comes from the increase in the equilibrium variances of the coordinate and momentum. The low temperature quantum theory allows for higher energy portions of phase space to contribute to the electron transfer rate where the rate is higher thus enhancing the overall rate.