Variation of Lattice Constant in Augmented-Plane-Wave Energy-Band Calculation for Lithium

Abstract

Two series of self-consistent energy-band calculations in lithium by the augmented-plane-wave (APW) method are reported. The first used the exchange approximation proposed by Slater; the second used two-thirds of this quantity, as proposed by Gaspar, Kohn, and Sham. In each series, the lattice constant was varied, and the total energy was found as a function of this parameter. From this, the equilibrium lattice constant, the cohesive energy, and the compressibility were found. These quantities differ markedly for the two exchange approximations used, and roughly bracket the experimental values. A virial theorem is derived which is valid for Hartree-Fock-Slater calculations in solids, and it is shown that the numerical results in fact satisfy the virial expression.