Structure of the correlation–kinetic component of the Kohn–Sham exchange potential in atoms and at metal surfaces

The Kohn–Sham density functional theory “exchange” potential v_x(r)=δE_x^KS[ρ]/δρ(r), where E_x^KS[ρ] is the “exchange” energy functional, is composed of a component representative of Pauli correlations and one that constitutes part of the correlation contribution to the kinetic energy. The Pauli term is the work done W_x^KS(r) in the field ℰ_x^KS(r) obtained by Coulomb's law from the Fermi hole charge distribution constructed from the Kohn–Sham orbitals. The correlation–kinetic term is the work done W⁽¹⁾(r) in the field Z⁽¹⁾(r) derived from the kinetic-energy–density tensor involving the first-order correction to the Kohn–Sham single-particle density matrix. The sum of these fields is conservative, so that the total work done is path-independent. There is no explicit correlation–kinetic contribution to the “exchange” energy E_x^KS[ρ]. Its contribution is manifested via the Kohn–Sham orbitals generated via the potential v_x(r). The functional E_x^KS[ρ] is thus expressed in virial form entirely in terms of the Pauli field ℰ_x^KS(r). In this article, we determine and study the structure of the correlation–kinetic component field Z⁽¹⁾(r) and work W⁽¹⁾(r) for the nonuniform electron density system in atoms and at metal surfaces. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 65: 893–906, 1997