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Generalized density-functional theory: extended weighted density approaches.

A Khein1, N W Ashcroft

  • 1Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, New York 14853, USA.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|April 24, 2002
PubMed
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A novel third-order density-functional theory (DFT) was developed using homogeneous state correlation functions. This approach improves predictions for hard sphere melting, enhancing solid phase properties and melting parameters.

Area of Science:

  • Statistical Mechanics
  • Computational Physics
  • Materials Science

Background:

  • Density-functional theory (DFT) is crucial for modeling many-body systems.
  • Higher-order accuracy in DFT functionals is needed for precise predictions.
  • Existing DFT models face challenges in accurately describing phase transitions.

Purpose of the Study:

  • To introduce a novel third-order density-functional theory.
  • To enable the development of higher-order accurate DFTs using known correlation functions.
  • To apply the new theory to understand the melting of classical hard spheres.

Main Methods:

  • Developed a third-order DFT approach requiring only a single weight function per order.
  • Utilized known homogeneous state correlation functions as input.

Related Experiment Videos

  • Applied the modified weighted density approximation (MWDA) for hard sphere melting calculations.

    • Main Results:

    • Achieved uniform improvement in solid phase free energies, pressures, and melting parameters for hard spheres.
    • Demonstrated further enhancements by optimizing functionals using the close packing limit.
    • Analyzed the sensitivity of results to different third-order direct correlation function models.

    Conclusions:

    • The developed third-order DFT offers a systematic route to higher accuracy.
    • The approach provides improved predictions for the melting of classical hard spheres.
    • The study highlights the importance of accurate correlation functions for DFT development.