VOLUME 46, NUMBER 13 PHYSICAL REVIEW LETTERS 30 M~RcH 1981 Interaction between Closed-Shell Systems and Metal Surfaces N. D. Lang IBM Thomas J. watson Research Center, Yoxktomn Heights, Nese York 10598 (Received 6 November 1980) The relationship between the van der Waals description of the binding of rare-gas atoms to metal surfaces and the description using a local approximation for exchange-correlation effects is discussed. The local-density treatment is shown to provide a good account of recent data on atomic binding energy, dipole moment, and core-level binding-energy shift. Charge rearrangement maps are used to analyze bond formation and to discuss the validity of the image picture of core-hole screening. PACS numbers: 68.45.Da, 79.60.Gs, 82.65.Jv, 82.65.Nz This paper considers the interaction between closed-shell systems, typified by rare-gas atoms, and metal surfaces. These relatively weak inter- actions are often discussed in terms of the van der Waals mechanism. The hallmark of this mechanism is the power-law dependence of the interaction strength at large metal-adatom sepa- rations, which owes its existence to the detach- ment of the adatom electron from its exchange- correlation hole (image) in the metal. Paradox- ically, I demonstrate that a variety of experimen- tal measurements on such systems are well de- scribed by a theory —the density functional for- malism with local-density approximation for ex- change-correlation" — in which the electron and its exchange-correlation hole are always attached (and which as a result gives an interaction that vanishes exponentially at large distances). Apart from the fact that the local-density theory in- cludes electrostatic and kinetic-energy terms (and hence repulsive forces), it and the van der Waals picture differ simply in the degree of at- tachment envisioned between an electron and its exchange-correlation hole. ' The essential point is that for equilibrium rare-gas-metal distances, the most important part of the valence-shell elec- tron orbit (that nearest the metal) lies sufficient- ly within the surface electron gas that it is most correct to consider the electron to be attached to the hole. I mill discuss experimental data for adsorption on simple metals, and therefore use the jellium model for the metal (ions smeared into a uniform positive background), which is an entirely ade- quate approximation mhen treating adatoms that are sufficiently large not to dig into the first lay- er of metal atoms. The only parameter in this model is the density p of the positive background, expressed via r, (~m, '= p') The t-reatm. ent for a single atom adsorbed on a semi-infinite sub- strate is fully wave mechanical and self-consis- -0.09— -0.06— C3 0 LLJ 4J -0.03— Ar (rs= 5) O 0 0.03— 0.06— I I I I I 4 5 6,7 8 d (BOHR) FIG. 1. Atomic binding energy vs distance d for Ar atom on r = 3 substrate. tent, and employs the method of Lang and Wil- liams4 for solving the Hartree-like single-parti- cle equations of the density-functional formalism. These equations contain an effective exchange- correlation potential that is a local potential, and which in the local-density approximation is taken to depend at each point only on the electron density at that point. The only parameter spec- ifying a particular adatom is its nuclear charge Z; the wave functions for the core states are ob- tained as part of the calculation. I consider first the ability of the theory to give the measured atomic binding energy. Figure 1 shows this binding energy as a function of metal- adatom distance' d, for an Ar atom' adsorbed on a substrate of r, = 3 bohrs. [This corresponds to the mean free-electron (s-p) density of Ag, which I will regard as sufficiently like a simple metal in the region of the adatom to use the jellium model for it. j d is measured from the positive- background edge (which by construction is half an interplanar spacing in front of the outermost lat- tice plane of the crystal being modeled~). The 842 Oc 1981 The American Physical Society