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Related Experiment Videos

Legendre-transform functionals for spin-density-functional theory.

Paul W Ayers1, Weitao Yang

  • 1Department of Chemistry, McMaster University, Hamilton, Ontario L8S 4M1, Canada. ayers@mcmaster.ca

The Journal of Chemical Physics
|June 21, 2006
PubMed
Summary
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This study proves the Hohenberg-Kohn theorem for spin densities, establishing spin-density-functional theory. It offers a formal basis for using spin-density functionals in Kohn-Sham density-functional theory (DFT) calculations.

Area of Science:

  • Quantum Chemistry
  • Condensed Matter Physics

Background:

  • The Hohenberg-Kohn theorem is foundational to density-functional theory (DFT).
  • Extending DFT to incorporate spin densities has faced theoretical challenges.
  • Previous formulations lacked explicit constructions for spin potentials.

Purpose of the Study:

  • To rigorously prove the Hohenberg-Kohn theorem for spin densities.
  • To develop a spin-density-functional theory (SDFT) that resolves existing issues.
  • To provide a formal basis for spin-dependent exchange-correlation functionals in DFT.

Main Methods:

  • Extension of Lieb's Legendre-transform formulation to spin densities.
  • Development of explicit constructions for spin potentials along the adiabatic connection curve.

Related Experiment Videos

  • Analysis of implications for unrestricted Kohn-Sham DFT calculations.

    • Main Results:

    • A rigorous proof of the Hohenberg-Kohn theorem for spin densities is presented.
    • An explicit construction of spin potentials is derived.
    • The theory provides a formal foundation for spin-density-based exchange-correlation functionals.
    • A tendency for orbital energy to increase with occupation number is identified.

    Conclusions:

    • The developed SDFT resolves several theoretical issues in spin-based DFT.
    • The findings provide a computational basis for determining occupation numbers in Kohn-Sham DFT.
    • The work offers insights into Hund's rules and the phenomenon of holes below the Fermi level.