General Crystalline Hartree-Fock Formalism: Diamond Results

A method is presented for performing crystalline Hartree-Fock calculations with a wave-function basis consisting of Gaussian lobe functions. The most important concepts involve (i) the utilization of crystal symmetry in characterizing the first-order density matrix, and in selective computation and efficient storage of the one- and two-electron integrals; (ii) the introduction of a charge-conserving approximation for some of the less important three- and four-center integrals over contracted Gaussian basis functions; and (iii) the imposition of monopole and dipole compensation for the most important neglected two-electron Coulomb integrals. The method is applied to diamond, and calculational results are given for various sets of parameters. The best results include a Hartree-Fock cohesive energy of 0.38 Ry/atom, a virial coefficient ($-\frac{2T}{V}$) of 1.0005 for a lattice constant of 3.56 Å, a direct band gap at $\Gamma$ of 15 eV, and an indirect band gap from $\Gamma$ to $\Delta$ of 13.7 eV. The(111) Fourier transform of the charge density is 3.29 electrons per crystallographic unit cell.