The paper describes the results of studying the effect of gradient corrections to the kinetic and exchange-correlation energy functional in calculating the surface energy of a metal surface; the calculations are performed within the framework of the density functional theory. The electron density distribution profile near the metal surface was calculated by the variational method for two test functions, which differ by taking into account the electron density oscillations. The exact form of the kinetic and exchange-correlation energy functional is unknown; therefore, to calculate the surface energy of the selected metals, various gradient corrections for the second and fourth order electron gas inhomogeneity are used. The effect of the discreteness of the ionic lattice and the orientation of the crystallographic planes on the spatial distribution of the electron gas is taken into account within the framework of perturbation theory; the Ashcroft pseudopotential is taken as the one to describe the electron-ion interaction. The use of a fourth-order gradient correction for the exchange-correlation and kinetic energies has little effect on the calculated values of the surface energy of alkali metals. The calculation results do not always agree well with the experimental values of the selected metals. This may be due to the fact that the relaxation of the metal surface is not taken into consideration and because of the large error in obtaining the experimental values of the surface energy
Adiabatic-connection-fluctuation-dissipation approach to long-range behavior of exchange-correlation energy at metal surfaces: A numerical study for jellium slabs