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Some Fundamental Issues in Ground-State Density Functional Theory: A Guide for the Perplexed.

John P Perdew1, Adrienn Ruzsinszky1, Lucian A Constantin1

  • 1Department of Physics and Quantum Theory Group, Tulane University, New Orleans, Louisiana 70118, and Department of Inorganic and Analytical Chemistry, Budapest University of Technology and Economics, H-1521 Budapest, Hungary.

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|November 27, 2015
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This study discusses fundamental issues in ground-state density functional theory (DFT), highlighting limitations in approximations for exchange-correlation energy and spin densities. It emphasizes that DFT is not a mean-field theory and challenges common assumptions about its application.

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Area of Science:

  • Computational Chemistry
  • Quantum Mechanics
  • Materials Science

Background:

  • Standard Hohenberg-Kohn and Kohn-Sham theorems have limitations regarding exact Hamiltonians for real systems.
  • Exchange-correlation energy functionals in Density Functional Theory (DFT) require approximations due to electron interactions.
  • Spin densities offer advantages over total electron density for approximations in the absence of magnetic fields.

Purpose of the Study:

  • To critically examine fundamental issues and limitations in ground-state Density Functional Theory (DFT).
  • To analyze the behavior of approximations for exchange-correlation energy functionals, especially for open systems.
  • To clarify the relationship between DFT, mean-field theory, and the treatment of electron correlation and excited states.

Main Methods:

  • Conceptual analysis of existing theorems and approximations in Density Functional Theory (DFT).
  • Discussion of the role of spin densities and symmetry in Kohn-Sham calculations.
  • Evaluation of semilocal approximations for exchange-correlation energy in various system types (closed, open, fluctuating electron number).

Main Results:

  • Standard DFT theorems were proven for Hamiltonians not fully exact for real systems.
  • Semilocal approximations for exchange-correlation energy can fail for open systems with fluctuating electron numbers.
  • The Kohn-Sham band gap underestimates the fundamental gap, but may approximate exciton energies.

Conclusions:

  • Spin contamination in open-shell systems is a correct feature, not an error.
  • DFT is not strictly a mean-field theory; exact functionals include strong correlation.
  • Excited states are rarely accessible directly from ground-state DFT calculations.