Combined fourier transform and discrete variational method approach to the self‐consistent solution of the electronic band structure problem within the local density formalism

A. Zunger, Arthur J Freeman

Research output: Contribution to journalArticle

32 Citations (Scopus)

Abstract

This novel approach combines a discrete variational treatment of all potential terms arising from the superposition of the spherical overlapping atomic charge densities with a rapidly convergent Fourier series representation of all multicenter nonspherical potential terms. The basis set consists of the exact numerical atomic valence orbitals, augmented by charge transfer states, virtual atomic states, and single analytic Slater orbitals for increased variational flexibility. The initial potential is a non‐muffin‐tin overlapping atomic potential including nongradient local density exchange and correlation terms. Full self‐consistency is obtained by a procedure that combines an iterative scheme within the superposition model with a self‐consistent optimization of the Fourier components of the nonspherical charge density terms. Ground‐state properties such as structure factors and cohesive energy are computed. The results for diamond show very good agreement with experiment. Comparison of the results with the Hartree–Fock calculation is discussed.

Original languageEnglish
Pages (from-to)383-403
Number of pages21
JournalInternational Journal of Quantum Chemistry
Volume10
Issue number10 S
DOIs
Publication statusPublished - 1976

Fingerprint

Charge density
Band structure
Fourier transforms
formalism
Diamond
Fourier series
electronics
Charge transfer
Slater orbitals
flexibility
Experiments
diamonds
charge transfer
valence
orbitals
optimization
energy

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics
  • Condensed Matter Physics
  • Physical and Theoretical Chemistry

Cite this

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AB - This novel approach combines a discrete variational treatment of all potential terms arising from the superposition of the spherical overlapping atomic charge densities with a rapidly convergent Fourier series representation of all multicenter nonspherical potential terms. The basis set consists of the exact numerical atomic valence orbitals, augmented by charge transfer states, virtual atomic states, and single analytic Slater orbitals for increased variational flexibility. The initial potential is a non‐muffin‐tin overlapping atomic potential including nongradient local density exchange and correlation terms. Full self‐consistency is obtained by a procedure that combines an iterative scheme within the superposition model with a self‐consistent optimization of the Fourier components of the nonspherical charge density terms. Ground‐state properties such as structure factors and cohesive energy are computed. The results for diamond show very good agreement with experiment. Comparison of the results with the Hartree–Fock calculation is discussed.

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