Molecular modeling of the surface charging of hematite - I. The calculation of proton affinities and acidities on a surface

Calculation of the energy of a charged defect on a surface in supercell geometry is discussed. An important example of such a calculation is evaluation of surface proton affinities and acidities, as adding or removing a proton creates a charged unit cell. Systems with periodic boundary conditions in three spatial directions and a vacuum gap between slabs are demonstrated to be inadequate for unit cells having non-zero ionic charge and uniform neutralizing background. In such a system the calculated energy diverges linearly with the thickness of the vacuum gap. A system periodic in two directions and finite in the direction perpendicular to the surface (2-D PBC) with the neutralizing background distributed as the surface charge density is free from this problem. Furthermore, the correction for the interaction of the charged defect with its own translational images is needed to speed up the convergence to the infinite dilution limit. The expression for the asymptotic correction for the energy of interaction of a charged defect with its translational images in 2-D PBC geometry has been developed in this study. The asymptotic correction is evaluated as the interaction energy of a 2-D translationally periodic array of point charges located above and below the plate of non-uniform dielectric. This is a generalization of the method of M. Leslie and M.J. Gillan [J. Phys. C, 18 (1985) 973] for the calculation of the energy of a charged defect in bulk crystals. The usefulness of this correction was demonstrated on two test cases involving the calculation of proton affinity and acidity at the (012) surface of hematite. The proposed method is likely to be important in ab initio calculations of the energy effect of the surface protonation reactions, where computational limitations dictate a small size for the unit cell. (C) 1999 Elsevier Science B.V. All rights reserved.