Molecular statics calculations of proton binding to goethite surfaces: A new approach to estimation of stability constants for multisite surface complexation models

A new approach to estimating stability constants for proton binding in multisite surface complexation models is presented. The method is based on molecular statics computation of energies for the formation of proton vacancies and interstitials in ideal periodic slabs representing the (100), (110), (010), (001), and (021) surfaces of goethite. Gas-phase energies of clusters representing the hydrolysis products of ferric iron are calculated using the same potential energy functions used for the surface. These energies are linearly related to the hydrolysis constants for ferric iron in aqueous solution. Stability constants for proton binding at goethite surfaces are estimated by assuming the same log K-Delta E relationship for goethite surface protonation reactions. These stability constants predict a pH of zero charge of 8.9, in adequate agreement with measurements on CO2-free goethite. The estimated stability constants differ significantly from previous estimations based on Pauling bond strength. We find that nearly all the surface oxide ions are reactive; nineteen of the twenty-six surface sites investigated have log K-int between 7.7 and 9.4. This implies a site density between fifteen and sixteen reactive sites/nm for crystals dominated by (110) and (021) crystal faces.