Toward Hartree-Fock Calculations for Simple Crystals
Hartree-Fock equations are formulated for LCAO wavefunctions whose atomic-orbital composition may depend upon location in the energy band. Computationally practical procedures are described for all quantities entering the formulation, and preliminary results for a simple-cubic atomic-hydrogen lattice are quoted to illustrate the convergence properties of the method. The procedure depends crucially upon reciprocal-lattice transformations and the point-group symmetry about a lattice point; exploitation of these concepts helps provide a natural understanding of the success of independent-particle schemes for solids, and of the structure of the exchange energy contributions.
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- 2.A. A. Abrikosov, “The Equations of State of Hydrogen at High Pressures”, U. S. S. R. Astronomical J. 31, 112 (1954).Google Scholar
- 3.F. C. Von der Lage and H. A. Bethe, “A Method for Obtaining Electronic Eigenfunctions and Eigenvalues in Solids with an Application to Sodium”, Phys. Rev. 71, 612 (1947); see also D. D. Betts, “Solid Harmonics as Basis Functions for Cubic Crystals”, Can. J. Phys. 37, 350 (1959).CrossRefGoogle Scholar
- 6.J. C. Slater, “Symmetry and Energy Bonds in Crystals”, Quantum Theory of Molecules and Solids, Vol. 2 ( McGraw-Hill, New York, 1965 ), p. 130.Google Scholar