Toward Hartree-Fock Calculations for Simple Crystals

  • Frank E. Harris
  • Hendrik J. Monkhorst
Part of the The IBM Research Symposia Series book series (IRSS)

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.

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References

  1. 1.
    F. E. Harris and H. J. Monkhorst, “Complete Calculations of the Electronic Energies of Solids”, Phys. Rev. Letters 23, 1026 (1969).CrossRefGoogle Scholar
  2. 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. 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
  4. 4.
    See for example R. A. Bonham, J. L. Peacher, and H. L. Cox, Jr., “On the Calculation of Multicenter Two-Electron Repulsion Integrals Involving Slater Functions”, J. Chem. Phys. 40, 3083 (1964).CrossRefGoogle Scholar
  5. 5.
    F. E. Harris and H. J. Monkhorst, “Lattice Sums and Madelung Constants”, Chem. Phys. Letters 4, 181 (1969).CrossRefGoogle Scholar
  6. 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
  7. 7.
    L. P. Bouckaert, R. Smoluchowski, and E. Wigner, “Theory of Brillouin Zones and Symmetry Properties of Wave Functions in Crystals”, Phys. Rev. 50, 58 (1936).CrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1971

Authors and Affiliations

  • Frank E. Harris
    • 1
  • Hendrik J. Monkhorst
    • 1
  1. 1.Department of PhysicsUniversity of UtahSalt Lake CityUSA

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