Hartree-Fock formalism for solids. II. Application to the nearly-free-electron gas

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Abstract
In this paper, Gaussian basis functions and Fourier transforms of both the Coulomb and exchange terms are employed to simplify numerical procedures in Hartree-Fock calculations for solids. A very simple set of working equations is presented, and the advantages of this particular formalism for solids are discussed. As a test of the method the nearly-free-electron gas is solved in the Hartree and Hartree-Fock approximations. In both cases excellent agreement is obtained with the well-known exact solutions if a suitable set of Gaussian basis functions is employed. On the basis of this study it is concluded that the formalism is not only practical for real solids, but yields accurate results when properly applied.