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Connection between Hybrid Functionals and Importance of the Local Density Approximation.

Martín A Mosquera1, Carlos H Borca2, Mark A Ratner1

  • 1Department of Chemistry, Northwestern University , 2145 Sheridan Road, Evanston, Illinois 60208, United States.

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Generalized Kohn-Sham theory extends density functional theory. This study derives exact equations for hybrid functionals, showing Fock exchange improves electronic structure calculations, matching advanced functional performance.

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Area of Science:

  • Computational Quantum Chemistry
  • Materials Science
  • Theoretical Physics

Background:

  • The local density approximation (LDA) is a foundational density functional for electronic structure calculations.
  • Density-functional approximations are crucial for understanding molecular and solid-state properties.
  • Generalized Kohn-Sham (GKS) theory extends Kohn-Sham theory, enabling a wider range of density functionals.

Purpose of the Study:

  • To explore the generalized Kohn-Sham (GKS) theory of hybrid functionals.
  • To derive exact equations relating GKS exchange-correlation (XC) energies and parameters.
  • To investigate the role of Fock exchange in improving electronic structure and excitation energy predictions.

Main Methods:

  • Study of auxiliary electronic systems with parametrized interactions.
  • Derivation of exact equations for GKS XC energies in parameter space.
  • Formal relation established between parameters and the XC derivative discontinuity.

Main Results:

  • Exact equations relating GKS XC energies and parameters were derived.
  • A formal link between parameters and the XC derivative discontinuity was established.
  • Inclusion of Fock exchange, particularly long-range corrected, enhances fundamental gap and excitation energy estimations over generalized gradient corrections.

Conclusions:

  • The GKS formalism offers a pathway to improved density functionals.
  • Fock exchange significantly boosts the accuracy of electronic structure and excitation energy calculations.
  • The adiabatic CAM-LDA0 functional demonstrates comparable performance to CAM-B3LYP for electronic excitations.