EXCHANGE POTENTIALS AT A METAL-SURFACE

In this article we have determined the structure of the exchange poten tial nu(x)((0))(r) at a jellium metal surface previously derived by re stricted functional differentiation of the exchange energy functional. The potential, which depends on the Slater potential due to the Fermi hole, the density, and their gradients, is obtained analytically for the orbitals of the infinite barrier model. We have also determined th e exchange potential W-x(r) of the work formalism, which is the work d one to move an electron in the forcefield of the Fermi hole, for the s ame model effective potential, the field being derived analytically. A comparison of these potentials shows them to be close approximations. The functional derivative nu(x)((0))(r) is further provided a physica l interpretation by rewriting it in Slater-potential form. The corresp onding effective Fermi hole charge distribution, also determined analy tically, has a dynamic structure as a function of electron position si milar to that of the Fermi hole but smaller in magnitude. Finally, pro ofs are provided of the, satisfaction by nu(x)((0))(r) of the virial t heorem sum rule, the second functional derivative functional derivativ e condition, and the sum rule relating the exchange potential to its f unctional derivative. (C) 1995 John Wiley & Sons, Inc.