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A systematic sequence of relativistic approximations.

Kenneth G Dyall1

  • 1Eloret Corporation, 690 W. Fremont Ave., Suite 8, Sunnyvale, CA 94087, USA. dyall@pegasus.arc.nasa.gov

Journal of Computational Chemistry
|May 16, 2002
PubMed
Summary

A new systematic sequence of relativistic approximations simplifies quantum mechanical calculations. These approximations, based on the Dirac equation, offer high accuracy for atomic and molecular properties, reducing computational complexity.

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Area of Science:

  • Quantum Chemistry
  • Relativistic Quantum Mechanics
  • Computational Chemistry

Background:

  • Relativistic effects are crucial for accurate electronic structure calculations, especially for heavy elements.
  • Existing relativistic methods can be computationally intensive.
  • Developing efficient and accurate approximations is essential for broader applicability.

Purpose of the Study:

  • To review a systematic sequence of relativistic approximations.
  • To assess the accuracy of these approximations against established methods.
  • To provide computationally tractable alternatives for relativistic quantum mechanical calculations.

Main Methods:

  • Normalized elimination of the small component in the modified Dirac equation.
  • Projection onto positive energy states of isolated atoms.

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  • Partitioning atoms into relativistic and nonrelativistic groups.
  • Approximation of relativistic two-electron integrals using Foldy-Wouthuysen coefficients.

    • Main Results:

    • Approximations show extremely small errors (e.g., ~0.001 pm in bond lengths, tens of microhartrees in energies).
    • Partitioning atoms into relativistic and nonrelativistic groups is validated.
    • Errors for second and third-period atoms are within acceptable limits for chemical accuracy.
    • A scalar relativistic approximation shows accuracy comparable to Douglas-Kroll-Hess.

    Conclusions:

    • The reviewed approach provides a systematic and accurate way to develop relativistic approximations.
    • These approximations significantly reduce computational cost without sacrificing accuracy.
    • The methods are suitable for both isolated atoms and molecules, facilitating wider use in computational chemistry.