Combined fourier transform and discrete variational method approach to the self-consistent solution of the electronic band structure problem within the local density formalism

This novel approach combines a discrete variational treatment of all potential terms arising from the superposition of the spherical overlapping atomic charge densities with a rapidly convergent Fourier series representation of all multicenter nonspherical potential terms. The basis set consists of the exact numerical atomic valence orbitals, augmented by charge transfer states, virtual atomic states, and single analytic Slater orbitals for increased variational flexibility. The initial potential is a non-muffin-tin overlapping atomic potential including nongradient local density exchange and correlation terms. Full self-consistency is obtained by a procedure that combines an iterative scheme within the superposition model with a self-consistent optimization of the Fourier components of the nonspherical charge density terms. Ground-state properties such as structure factors and cohesive energy are computed. The results for diamond show very good agreement with experiment. Comparison of the results with the Hartree–Fock calculation is discussed.