Theory of indirect interaction between chemisorbed atoms

Abstract Progress in the development of the theory of two chemisorbed atoms has been hindered by the very low symmetry of the problem. Mono-layers of adatoms are simplest since they have the full two-dimensional symmetry of the substrate. Going to a (2 × 1) or a (2 × 2) adlayer, which doubles the size of the surface primitive cell, quadruples the size of a secular matrix, raising computer time even more. At the other end of the scale, a single adatom (in a symmetric site) will at least have the point symmetry of the substrate. With jellium as a substrate, this increases to full rotational and translational symmetry. Conserved quantities (“good quantum numbers”), which make calculations simpler, are associated with these symmetries. As a result, a variety of elaborate many-body techniques have been successfully applied to these systems; there are several excellent recent reviews.1,2 For two adatoms on a surface, there is little or no symmetry, typically just a twofold rotation or mirror plane (often leading to splittings of levels).