Inelastic effects in electron tunneling through water layers

Abstract

Calculations of tunneling matrix elements associated with electron transfer through molecular environments are usually done for given frozen nuclear configurations, with the underlying assumption being that nuclear motions are slow relative to the time scale of a tunneling event. This paper examines this issue for the case of electron tunneling through water. The motivation for this study is a recent calculation [Peskin et al., J. Chem. Phys. 111, 7558 (1999)] that indicates that electron tunneling through water may be enhanced by tunneling resonances in the range of ∼1 eV below the vacuum barrier, and finds that the lifetimes of such resonances are in the 10 fs range, same order as OH stretch periods. Our calculation is based on the absorbing-boundaryconditions-Green’s-function (ABCGF) method and proceeds in two steps. First we consider the effect of a single symmetric OH-stretch mode on electron tunneling in an otherwise frozen water environment, and establish that the inelastic tunneling probability is small enough to justify an approach based on perturbation theory limited to single phonon transitions. Next we note that on the short time scale of a tunneling event, even under resonance conditions, water nuclear dynamics may be represented in the instantaneous normal modes picture. We generalize the ABCGF method to take into account low order inelastic scattering from a continuum of such harmonic normal modes. We find that near resonance the total inelastic transmission probability is of the same order as the elastic one, and may lead to an additional ∼20–40% enhancement of the overall transmission in the range of up to 1 eV below the vacuum barrier. The absolute energy exchange is small, of the order of 1% of the incident electron energy. Surprisingly, we find that the main contribution to the inelastic transmission is associated with energy transfer into the rotational–librational range of the water instantaneous normal mode spectrum.