SIMPLE FORMULA FOR THE SURFACE-ENERGY BY A SHIFTED-STEP-POTENTIAL APPROXIMATION

The jelliumlike free-electron model is used, and the effective one-electron potential v(eff) is approximated to be the step-function which is shifted to satisfy the neutrality of the charge. The eigenfunctions can be obtained in analytic form. Although not self-consistent, the calculated distribution of the electron density is very similar to the self-consistent field (SCF) jellium results by Lang and Kohn. A simple formula for the surface energy is obtained. The surface energy is given as a function of the Fermi energy and the work function. The formula suggests that the surface energy is sensitive to the Fermi energy and is not sensitive to the work function, i.e., the surface energy is approximately in proportion to the fourth power of the Fermi energy. The calculated surface energy approaches the SCF jellium results by Lang et al. and the structureless pseudopotential results by Perdew for small electron density.