Time-dependent electron transfer and energy dissipation in condensed media

We study a moving adsorbate interacting with a metal electrode immersed in a solvent using the time-dependent Newns-Anderson-Schmickler model Hamiltonian. We have adopted a semiclassical trajectory treatment of the adsorbate to discuss the electron and energy transfers that occur between the adsorbate and the electrode. Using Keldysh Green's function scheme, we found a non-adiabatically suppressed electron transfer caused by the motion of the adsorbate and coupling with bath phonons that model the solvent. The energy is thus dissipated into electron-hole pair excitations, which are hindered by interacting with the solvent modes and facilitated by the applied electrode potential. The average energy transfer rate is discussed in terms of the electron friction coefficient and given an analytical expression in the slow-motion limit.