Numerical simulations of electron tunneling in water

Electron tunneling through molecular layers has long been under study in conjunction with electron tunneling microscopy. More recently solvent effects on the tunneling matrix elements associated with electron transfer problems and with "underwater" electron tunneling microscopy have come under discussion. This paper describes the results of computer simulations of electron tunneling through frozen water layers. A water layer (∼10 Å) is confined between two electrodes, and is equilibrated and evolved in time in order to generate an ensemble of barrier configurations. The electron-(classical) water interaction is represented by a suitable pseudopotential. It is assumed that the water dynamics is negligible on the time scale of the tunneling process, so tunneling is studied for the resulting group of frozen configurations. Several numerical methods for evaluating the transmission through such disordered barriers are described and compared. It is shown that tunneling probabilities as low as 10^-10 can be calculated with sufficient accuracy. We find that tunneling in this system cannot be described by averaging over one-dimensional paths. Furthermore, in contrast to common practice which assumes that the barrier to tunneling may be estimated by lowering the bare (vacuum) barrier by a magnitude associated with the electronic dielectric response of water taken as a dielectric continuum, the simulations show that transmission is strongly reduced due to the fact that much of the physical barrier space is blocked by the practically impenetrable oxygen cores. The tunneling probability significantly depends on the water configuration in the barrier, in particular on the orientational distribution of the water molecules. These observations suggest that external variables such as temperature and electric field will affect the tunneling thrnuph their effect on the water demitv and orientation, in addition to the effect of these variables on the bare (vacuum) tunneling.