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Thomas-Fermi theory for atomic systems.

R G Parr1, S K Ghosh

  • 1Department of Chemistry, University of North Carolina, Chapel Hill, NC 27514.

Proceedings of the National Academy of Sciences of the United States of America
|June 1, 1986
PubMed
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This study refines the Thomas-Fermi theory for atomic electrons, ensuring continuous electron density. The improved method significantly enhances electron density and total energy calculations.

Area of Science:

  • Atomic Physics
  • Quantum Chemistry
  • Computational Chemistry

Background:

  • The classical Thomas-Fermi theory provides a foundational model for electron behavior in atoms.
  • However, this theory exhibits discontinuities in electron density, limiting its accuracy.
  • Addressing these limitations is crucial for precise atomic modeling.

Purpose of the Study:

  • To amend the classical Thomas-Fermi theory to achieve continuous electron density.
  • To improve the accuracy of electron density and total energy calculations in atomic systems.
  • To introduce a novel constraint for refining electron density.

Main Methods:

  • Imposing a constraint on the integral of e(-2kr) [unk](2) rho dr to be finite.
  • Determining the parameter k using the nuclear cusp condition.

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  • Applying optimal coordinate scaling before or after the constraint imposition.

    • Main Results:

    • The amended theory successfully produces a continuous electron density (rho).
    • Electron densities calculated using the new method show substantial improvement.
    • Total energy calculations also demonstrate significant enhancements.

    Conclusions:

    • The modified Thomas-Fermi approach offers a more accurate description of atomic electron densities.
    • This refinement leads to more reliable total energy predictions for atoms.
    • The imposed constraint and coordinate scaling are effective in overcoming classical theory limitations.