Binding of an adatom to a simple metal surface

The density functional formalism of Hohenberg and Kohn is used to investigate the energies, charge densities and forces which hold an adatom on the surface of a simple metal. The valence wavefunction of the adatom is fitted to the Herman-Skillman solutions at large distance and is simplified somewhat in the core region. The field of the ion is represented by the Ashcroft pseudopotential. For the metal the jellium model is used. Detailed calculations are carried out for a sodium adatom on a sodium surface. Simply juxtaposing adatom and surface gives a binding energy of about $\text{1}\text{3}\text{eV}$. This value is approximately twice the surface energy per atom in the close-packed plane. Charge redistributions as determined variationally increase the binding energy by about 10%. The redistribution is primarily a dipole induced on the adatom at close distances, but at somewhat larger distances a prolate quadrupole also appears on the atom. A small amount of charge is also drawn from the metal toward the atom. The equilibrium distance for the adatom turns out to be 1.66 Å from the surface, as compared with 1.52 Å, the observed value for one-half the distance between the close-packed planes. Contour plots of the piling-up of electronic charge between the adatom and the metal are presented.