Electron transfer in fixed-nuclei systems: A comparison of propagator descriptions

Site-to-site electron transfer rates in a fixed-nucleus system are described using the polarization propagator, the time-dependent number operator, and the electron propagator. We show that given a proper choice of the initial state, the first two agree with each other. The number-operator expression forms an upper bound to the transfer rate given by the electron propagator. Numerical studies on two-site and three-site Hubbard models indicate that the electron propagator in the Hartree-Fock approximation provides a good approximation to the initial transfer rate, for a wide choice of electron repulsion strengths.