Proximity effects on semiconducting mineral surfaces II: : Distance dependence of indirect interactions

In a previous study, we described proximity effects on surfaces of the semiconducting minerals galena and pyrite, whereby a chemical reaction at one surface site modifies the reactivity of a remote surface site several ?ngstroms or even nanometers away (Becker et al., 2001). The modification of interest does not arise because of a direct "through space" interaction between the two sites, but rather an indirect interaction via the electronic structure of the substrate. Here we investigate the distance and direction dependence of proximity effects using quantum mechanical modeling. The direct and indirect interactions between co-adsorbed oxygen atoms and between adsorbed oxygen atoms and point defects on vacuum-terminated galena (100) surfaces were modeled. Density functional theory cluster and plane wave pseudopotential calculations were used to calculate the modifications to the adsorption energy as a function of separation. Energy-distance plots indicate that the proximity effect energy can become very strong at separations decreasing below about 5 to 6 ?, and persist at increasing separations up to 12 ? in a slowly decaying form. A strong attractive indirect interaction out-competes direct electrostatic repulsion for Ovacancy interactions. An oscillatory asymptotic behavior is found for co-adsorbed O-O indirect interactions, which indicates that the proximity effect energy can vary with surface crystallographic direction. It implies the presence of a strong organizing force on like adatoms that may explain the progressive oxidation of certain sulfide minerals by patchwork growth. These findings begin to pave the way for improved adsorption isotherms and extended surface complexation models that will include the specific influence of semiconductor-type proximity effects.