THEORY OF METAL SURFACES: CHARGE DENSITY 4559 Here the first two terms represent, as before, kinetic, exchange, and correlation contributions to the electronic energy [see Eq.(2. 2).The last term e is the total classical electrostatic en ergy of all positive and negative charge densities (n(F)-n,(F) n,(F) BACKGROUND =「q[;F](m()-n,()症,(219) of an electron, is given bye tic potential energy where the total electrosta pIn; r (2.20) Corresponding to(2. 18), the surface energy of FIG.2. Self-consistent charge density near metal ne uniform background model may be written urface for rs=2 and rs=5 (uniform positive background (2.21) also in the region outside of the metal surface For as we can take over the analysis presented by where it is not correct, does not introduce seri- Hunting hich gives ous errors into the density distributions. In ad dition, we shall see in Sec. Ic that the correla- tion contribution to the surface energy is a rela- 0(4-7/a)-k2)kd tively small fraction of the experimental value and thus, in discussing surface energies, errors j fvott[n; x]-vott[;-oo]] n(x)dx ue to an inadequate treatment of correlation ef (2.22) fects should not be important The other two terms are, in the present model, C Surface Energies [∈xa(x)-∈l)n(x) The surface energy o of a crystal is the energy required, per unit area of new surface formed and g=h∫。φv;x](n(x)-n,(x)dx.(2.24) to split the crystal in two along a plane. The total energy of the crystal, split or unsplit,can Table ii lists the magnitudes of ou and its three be written as a sum of three terms components for different values of rs.First,we E=Tsn]+Ere n]+eesIn observe that the kinetic-energy contribution os is negative, reflecting the fact that in the split crystal, the electron density is more spread out 0. Second, we note that over the entire density range Uxe >>0es, showing that Thomas-Fermi or Hartree calculations are completely useless for quantita TABLE I. The surface energy O, and its components in the uniform background model. 0xe 0x+Oc; O =0s+oxc 1330 1350 430 DISTANCE(FERMI WAVELENGTHS 05050 380 FIG.3. Effective one-electron potential veff, with electrostatic part near metal surface (positive back- 6.0 10 vs=5)