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Kohn-Sham inversion for open-shell systems.

Jannis Erhard1, Egor Trushin1,2, Andreas Görling1,2

  • 1Lehrstuhl für Theoretische Chemie, Universität Erlangen-Nürnberg, Egerlandstr. 3, D-91058 Erlangen, Germany.

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Summary
This summary is machine-generated.

Density-functional theory methods often break symmetries, causing issues like spin contamination. This study introduces stable methods to construct Kohn-Sham potentials, restoring symmetries and providing reference energy values for open-shell systems.

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Area of Science:

  • Quantum Chemistry
  • Computational Physics
  • Materials Science

Background:

  • Standard density-functional theory (DFT) methods use spin-unrestricted Kohn-Sham (KS) formalism for open-shell systems.
  • This approach breaks spatial and spin symmetries, leading to spin contamination and hindering proper wave function classification.
  • Symmetry-restoring KS variants exist but are rarely implemented.

Purpose of the Study:

  • To develop numerically stable Kohn-Sham (KS) inversion methods for constructing KS potentials from reference spin-densities.
  • To investigate four symmetry treatments for open-shell systems: non-symmetrized, spin-symmetrized, space-symmetrized, and fully-symmetrized.
  • To provide reference values for energy component differences across these formalisms.

Main Methods:

  • Employed numerically stable KS inversion techniques.
  • Constructed reference KS potentials from reference spin-densities.
  • Obtained reference spin-densities using full configuration interaction and coupled cluster methods for atoms and diatomic molecules.

Main Results:

  • Successfully constructed KS potentials for all four symmetry treatments.
  • Demonstrated that energy decomposition differs across the four KS formalisms.
  • Identified that non-fully-symmetrized KS inversions can violate the Aufbau principle and, in the spin-symmetrized case, KS v-representability.

Conclusions:

  • The study provides a practical framework for applying symmetry-restoring KS formalisms.
  • Reference energy values are established for comparing different symmetry treatments.
  • Violations of physical principles like the Aufbau principle and KS v-representability highlight the importance of the fully-symmetrized approach.