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Rapidly converging lattice sums for nonelectrostatic interactions.

Gwon Hee Ko1, William H Fink

  • 1Department of Chemistry, University of California-Davis, Davis, California 95616, USA.

Journal of Computational Chemistry
|March 23, 2002
PubMed
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This study introduces a novel lattice sum method for calculating Lennard-Jones particle energies in Bravais lattices. The developed formalism efficiently computes relative energies and diffusion barriers in various chemical systems.

Area of Science:

  • Computational physics and chemistry
  • Materials science
  • Solid-state physics

Background:

  • Lattice sums are crucial for calculating energies in crystalline solids.
  • Lennard-Jones potentials model interatomic interactions effectively.
  • Calculating energies at arbitrary lattice points and diffusion pathways presents computational challenges.

Purpose of the Study:

  • To develop a rapidly converging lattice sum formalism for Lennard-Jones potentials.
  • To enable calculation of relative energies at arbitrary points within general Bravais lattices.
  • To apply the method to hexagonal close-packed (hcp) and face-centered cubic (fcc) Lennard-Jonesium systems.

Main Methods:

  • Manipulation of lattice sum expressions for accelerated convergence.

Related Experiment Videos

  • Development of a general formalism for lattice potential calculations.
  • Application to hcp and fcc Lennard-Jonesium for binding energy and diffusion pathway analysis.

    • Main Results:

    • A generalized method for calculating lattice potential at arbitrary points was established.
    • Relative binding energies for hcp and fcc Lennard-Jonesium were computed.
    • Diffusion barriers between interstitial sites in Lennard-Jonesium were quantified (e.g., 752.600 and 1035.614 in units of 4 epsilon).

    Conclusions:

    • The developed formalism offers an efficient alternative for calculating relative energies in diverse chemical systems.
    • The method accurately determines diffusion barriers, providing insights into atomic mobility.
    • This approach is valuable for understanding surface and bulk properties of crystalline materials.