An Improved Calculation of the Energies of Metallic Li and Na

Abstract

The method of calculation used in the present work is a modification of that used by Wigner and Seitz in their original calculations of the energies of metallic Li and Na. The main difference lies in an improved method for the calculation of the Fermi energy. In each polyhedral cell, the wave function of an electron is taken to be of the form ${\psi }_k{\mathrm{=[u}}_0\mathrm{(r)+i(}\mathbf{k}·\mathbf{x}{\mathrm{)(v}}_1{\mathrm{(r)-u}}_0\mathrm{(r))]}\exp \mathrm{[i}\mathbf{k}·\mathbf{x}]$ , where u₀(r) and v₁(r) are radial s and p functions, respectively, which depend only on the distance from the ion in the center of the cell. Both functions are determined explicitly from the differential equations, and the energy of the electron is expressed in terms of the boundary values of the wave function. Values of the Fermi energy, and of the total energy of each metal, are tabulated as a function of the lattice spacing. Calculated values of the lattice constants, heats of sublimation, and compressibilities are in fair agreement with experiment.