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Toward a Resolution of the Static Correlation Problem in Density Functional Theory from Semidefinite Programming.

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Density functional theory (DFT) struggles with strongly correlated systems. A new semidefinite programming (SDP) method improves static correlation but reveals limitations in modern DFT functionals.

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Area of Science:

  • Quantum Chemistry
  • Computational Physics
  • Materials Science

Background:

  • Kohn-Sham density functional theory (DFT) faces challenges in accurately describing strongly correlated and open-shell systems.
  • Existing hybrid functionals offer only minor improvements for these challenging electronic structures.

Purpose of the Study:

  • To address static correlation in DFT for systems with degenerate frontier orbitals.
  • To develop and apply a semidefinite programming (SDP) approach for improved electronic structure calculations.

Main Methods:

  • Utilized a semidefinite programming (SDP) method to minimize system energy.
  • Focused on the N-representable, non-idempotent 1-electron reduced density matrix.
  • Applied the SDP approach to local density approximation (LDA) and generalized gradient approximation (GGA) functionals.

Main Results:

  • Achieved significantly improved singlet-triplet gaps for LDA and GGA functionals.
  • The SDP procedure highlighted deficiencies in modern meta and hybrid GGA functionals.
  • Modern functionals showed no substantial improvement even with an accurate electron density.

Conclusions:

  • The SDP approach offers a promising avenue for treating static correlation in DFT.
  • Current advanced DFT functionals may require re-evaluation for strongly correlated systems.
  • Further development is needed to enhance the accuracy of DFT for challenging electronic structures.