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Fractional spins and static correlation error in density functional theory.

Aron J Cohen1, Paula Mori-Sánchez, Weitao Yang

  • 1Department of Chemistry, Duke University, Durham, North Carolina 27708, USA.

The Journal of Chemical Physics
|December 3, 2008
PubMed
Summary

Fractional spin states in strongly correlated systems are ensembles of normal spin states. Exact functionals maintain constant energy for these states, a condition violated by approximate functionals, causing significant errors.

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Area of Science:

  • Quantum chemistry
  • Condensed matter physics
  • Computational materials science

Background:

  • Fractional spin states emerge in strongly correlated systems, characterized by large static correlation.
  • These states are understood as ensembles of degenerate ground states with integer spins.

Purpose of the Study:

  • To prove that the exact functional energy for fractional-spin states is constant.
  • To identify the source of static correlation errors in approximate functionals.
  • To guide the development of improved functionals for strongly correlated systems.

Main Methods:

  • Theoretical proof of the constancy condition for exact functionals.
  • Numerical calculations on molecular systems to demonstrate deviations in approximate functionals.
  • Analysis of chemical bond dissociation and Mott insulator band structures.

Main Results:

  • The exact functional energy for fractional-spin states is proven to be constant.
  • All currently used approximate functionals exhibit significant deviations from this constancy.
  • These deviations lead to substantial static correlation errors in describing chemical and material properties.

Conclusions:

  • The constancy of fractional-spin state energy is a crucial condition for accurate theoretical models.
  • Future functional development must approximate this constancy to improve descriptions of strongly correlated systems.
  • The findings are applicable to both density functional theory and reduced density-matrix functional theory.