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Density functional theory from spherically symmetric densities.

Á Nagy1

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

The Journal of Chemical Physics
|December 4, 2018
PubMed
Summary

A new theorem shows that spherically symmetric electron densities uniquely determine the external potential in molecules and solids. This work provides an alternative derivation and a more general proof using constrained search methods.

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Area of Science:

  • Quantum Chemistry
  • Condensed Matter Physics
  • Computational Chemistry

Background:

  • Theophilou's theorem establishes a unique relationship between electron densities and external potentials.
  • Understanding this relationship is crucial for electronic structure calculations.

Purpose of the Study:

  • To present an alternative derivation of Theophilou's theorem.
  • To prove a more general version of the theorem using constrained search.
  • To derive Euler and Kohn-Sham equations for spherically symmetric densities.

Main Methods:

  • Constrained search approach
  • Variational principles
  • Derivation of fundamental equations in density functional theory

Main Results:

  • An alternative, more general proof of Theophilou's theorem was established.
  • The derivation confirms that spherically symmetric densities uniquely determine the external potential.
  • Euler and Kohn-Sham equations were successfully derived for this specific density symmetry.

Conclusions:

  • The unique determination of external potential by spherically symmetric densities is robust.
  • The generalized theorem and derived equations offer new avenues for theoretical and computational studies.
  • This work contributes to the foundational understanding of density functional theory.