Indirect Interaction between Adatoms on a Tight-Binding Solid

The indirect interaction between adatom pairs on the (100) surface of a simple-cubic tight-binding solid is investigated within a molecular-orbital approach. A general scheme for calculating the surface-density-of-states change and the interaction energy of one and two single-level adatoms is presented, and contact (and a correction) is made with Grimley's formulation. The method permits binding above surface atoms, at bridge sites, or at centered positions, and yields interaction energy as a function of band filling, adatom energy level, and a general hopping potential $V$ between an adatom and the nearest surface atom(s). Calculations have been carried out for $\frac{V}{W_b}$ in the range 1/12-1/2, the upper limit giving split-off states ($W_b\equiv \mathrm{bandwidth}$). The single-atom interaction shows little dependence on binding type, in all three cases being most attractive when the Fermi energy equals the noninteracting adatom level, with a strongly $V$-dependent strength. For the pair interaction, one finds a strength at nearest-neighbor separation of about an order of magnitude smaller than the absorption energy of a single adatom. This interaction has an exponentiallike dropoff and sign alternations as one moves along the $〈10〉$ direction. Under reasonable conditions, the nearest-neighbor interaction is often repulsive while the next nearest, third nearest, or fourth nearest is attractive, suggesting the patterns $c(2\mathrm{}\times 2)$, (2 × 2), and $c(4\mathrm{}\times 2)$, respectively, which are frequently observed in the adsorption of simple gases on the (100) surfaces of transition metals. On the basis of two-dimensional Ising-model calculations including second-neighbor interactions, one can estimate the strength of $V$ from the observed disordering temperature of the adatom lattice; the result is similar to that obtained from estimates based on the heat of adsorption.