Chapter

Computational Methods in Band Theory

Part of the series The IBM Research Symposia Series pp 517-541

Toward Hartree-Fock Calculations for Simple Crystals

  • Frank E. HarrisAffiliated withDepartment of Physics, University of Utah
  • , Hendrik J. MonkhorstAffiliated withDepartment of Physics, University of Utah

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Abstract

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.