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Spherical potential functional theory.

Á Nagy1

  • 1Department of Theoretical Physics, University of Debrecen, H-4002 Debrecen, Hungary.

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|October 16, 2021
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Summary
This summary is machine-generated.

A new theorem shows spherically symmetric densities uniquely determine external potentials in materials. This resolves the set-representability problem in density functional theory by using potentials as the basic variable.

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Area of Science:

  • Quantum chemistry
  • Condensed matter physics
  • Materials science

Background:

  • A recent theorem by Theophilou states that a unique external potential is determined by a set of spherically symmetric electron densities for molecules and solids.
  • This finding offers a new perspective for formulating density functional theory (DFT).

Purpose of the Study:

  • To address the "set-representability problem" within this new DFT formulation: determining if a valid electron density exists for a given set of spherically symmetric densities.
  • To solve the set-representability problem by reformulating the theory.

Main Methods:

  • The study tackles the set-representability problem by shifting the fundamental variable from electron density to the external potential.
  • This approach leverages the unique relationship established by Theophilou's theorem.

Main Results:

  • The set-representability problem is resolved by utilizing the external potential as the primary variable.
  • This provides a constructive method for determining the existence of a ground-state density corresponding to a given set of spherically symmetric densities.

Conclusions:

  • The reformulation of DFT using potentials as the basic variable successfully overcomes the set-representability challenge.
  • This work opens new avenues for theoretical and computational investigations in electronic structure theory.