Theory of indirect interaction between chemisorbed atoms

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).