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Related Experiment Videos

Auxiliary basis expansions for large-scale electronic structure calculations.

Yousung Jung1, Alex Sodt, Peter M W Gill

  • 1Department of Chemistry, University of California, Berkeley, CA 94720, USA.

Proceedings of the National Academy of Sciences of the United States of America
|April 23, 2005
PubMed
Summary

Researchers found that auxiliary basis expansion coefficients in electronic structure calculations decay slowly, as slow as 1/r. An attenuated Coulomb metric addresses issues in extended systems, enabling linear scaling methods for large molecules.

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Area of Science:

  • Computational chemistry
  • Quantum chemistry
  • Materials science

Background:

  • Electronic structure calculations are computationally intensive.
  • Auxiliary basis expansions approximate four-center integrals to reduce cost.
  • The Coulomb metric is typically used to determine expansion coefficients.

Purpose of the Study:

  • Characterize the long-range decay behavior of auxiliary basis expansion coefficients.
  • Investigate issues with the Coulomb metric in extended systems.
  • Develop a method for efficient, linear scaling auxiliary basis calculations.

Main Methods:

  • Numerical experiments on linear alkanes and a toy model.
  • Analysis of the decay rate of auxiliary basis expansion coefficients.

Related Experiment Videos

  • Implementation and assessment of an attenuated Coulomb metric.
  • Evaluation of coefficient sparsity for hydrocarbon molecules.

    • Main Results:

    • Auxiliary basis expansion coefficients exhibit slow decay, as slow as 1/r.
    • The standard Coulomb metric leads to divergent matrix elements for periodic systems.
    • An attenuated Coulomb metric resolves these issues without significant energy degradation.
    • The attenuated metric shows early onset of linear growth in significant coefficients with system size.

    Conclusions:

    • Slow decay of coefficients necessitates careful method design.
    • The attenuated Coulomb metric is effective for periodic systems.
    • Linear scaling auxiliary basis methods are feasible without further approximations for large systems.