Semi-infinite jellium: Thermodynamic potential, chemical potential, and surface energy

A general expression for the thermodynamic potential of the model of semi-infinite jellium is obtained. By using this expression, the surface energy for the infinite barrier model is calculated. The behavior of the surface energy and of the chemical potential as functions of the Wigner-Seitz radius and the influence of the Coulomb interaction between electrons on the calculated values is studied. It is shown that taking into account the Coulomb interaction between electrons leads to growth of the surface energy. The surface energy is positive in the entire area of the Wigner-Seitz radius. It is shown that taking into account the Coulomb interaction between electrons leads to a decrease of the chemical potential.

Figure 1

The chemical potential of the interacting electrons $\mu$ (solid line) and the chemical potential of the noninteracting electrons ${\mu }_0$ (dashed line) as a function of the Wigner-Seitz radius.

Figure 2

The parameter $d$ as a function of the Wigner-Seitz radius (solid line is for interacting electrons whereas the dashed line is for noninteracting electrons).

Figure 3

The one-particle distribution function of electrons as a function of the electron coordinate normal to the dividing plane at $r_{\mathrm{s}}=2a_{\mathrm{B}}$ (left) and $r_{\mathrm{s}}=6a_{\mathrm{B}}$ (right) (the solid line is for interacting electrons whereas the dashed line is for noninteracting electrons).

Figure 4

The surface energy as a function of the Wigner-Seitz radius (the solid line is for the interacting system, the dashed line is for the noninteracting system, whereas the dash-dotted line is the result of Lang and Kohn [5]).