Remarks on local and nonlocal exchange and correlation-energy calculations of surface energies and work functions

In this work we comment on the accuracy and sensitivity of metallic surface energies and work functions to the choice of local and nonlocal exchange and correlation-energy functionals used to represent the interacting inhomogeneous electron gas. For a Pauli-correlated system we compare the results of these properties as obtained within the local-density (LDA) and gradient-expansion (GEA) approximations (with the a priori gradient coefficient of Sham) with those determined by Sahni and Ma from the exact nonlocal Hartree-Fock energy functional. The proven accurate non-self-consistent procedure whereby the surface energies are determined by application of the variational principle for the energy, and the work functions by the variationally accurate "displaced-profile change-in-self-consistent-field" expression, is applied in conjunction with linear-potential model densities to each energy functional. It is observed that although the LDA surface energies are substantially in error, the corresponding work functions are within one-tenth of an eV of the exact results. The most significant fact to emerge from these calculations, however, is the remarkable equivalence of the GEA and the exact Hartree-Fock energy functionals in terms of the densities, surface energies, and work functions to which they give rise. The present conclusions about the sensitivity of the surface energy and the contrasting insensitivity of the work function to the choice of energy functional are in agreement with the results of previous work on fully correlated nonuniform systems as approximated within both the LDA for exchange-correlation and by the nonlocal-wave-vector-analysis formalism.