Discrete Variational Method for the Energy-Band Problem with General Crystal Potentials

D. E. Ellis and G. S. Painter
Phys. Rev. B 2, 2887 – Published 15 October 1970
PDFExport Citation

Abstract

A general variational method for efficiently calculating energy bands and charge densities in solids is presented; the method can be viewed as a weighted local-energy procedure or alternately as a numerical integration scheme. This rapidly convergent procedure circumvents many of the difficulties associated with the evaluation of matrix elements of the Hamiltonian in an arbitrary basis and treats the general nonspherical potential with no more complication than the usual "muffin-tin" approximation. Thus the band structure of ionic and covalent materials can be calculated with realistic crystal potentials. As an example, the method is applied to the one-electron model Hamiltonian with a nonspherical local potential, using a linear combination of atomic orbitals basis. Matrix elements of the Hamiltonian are evaluated directly without decomposition into atomic basis integrals; no "tight-binding" approximations are made. Detailed calculations are presented for the band structure and charge density of bcc lithium which demonstrate the feasibility of our method, and reveal the sensitivity of the energy bands to nonspherical and exchange components of the crystal potential. Various prescriptions for the construction of crystal potentials are considered, and convenient least-squares expansions are described. The extension of these methods to nonlocal potentials such as are encountered in the Hartree-Fock self-consistent-field procedure is discussed.

  • Received 1 May 1970

DOI:https://doi.org/10.1103/PhysRevB.2.2887

©1970 American Physical Society

Authors & Affiliations

D. E. Ellis*

  • Department of Physics, University of Florida, Gainesville, Florida 32601
  • Department of Physics, Northwestern University, Evanston, Illinois 60201

G. S. Painter

  • Quantum Theory Project, University of Florida, Gainesville, Florida 32601

  • *Present address: Northwestern University, Evanston, Ill.
  • Present address: Metals and Ceramics Division, Oak Ridge National Laboratory, Oak Ridge, Tenn.

References (Subscription Required)

Click to Expand
Issue

Vol. 2, Iss. 8 — 15 October 1970

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review B

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×