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Accurate and fast algorithm of the molecular incomplete gamma function with a complex argument.

Kazuhiro Ishida1

  • 1Department of Chemistry and Frontier Research Center for Computational Sciences, Faculty of Science, Tokyo University of Science, Kagurazaka 1-3, Shinjuku-ku, Tokyo 162-8601, Japan. k-ishida@fancy.ocn.ne.jp

Journal of Computational Chemistry
|February 24, 2004
PubMed
Summary

New algorithms efficiently calculate the molecular incomplete gamma function (MIGF) for complex arguments. These methods offer high precision and speed, crucial for molecular integral calculations in computational chemistry.

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Area of Science:

  • Computational Chemistry
  • Quantum Chemistry
  • Numerical Analysis

Background:

  • The molecular incomplete gamma function (MIGF) is essential for accurate calculations in molecular integrals.
  • Existing methods for MIGF computation can be computationally intensive, limiting their application in complex systems.

Purpose of the Study:

  • To develop efficient algorithms for the accurate and fast calculation of the molecular incomplete gamma function (Fm(z)) with complex arguments.
  • To provide both high-precision and fast computational options for MIGF.

Main Methods:

  • Development of two distinct algorithms for calculating the molecular incomplete gamma function.
  • Implementation utilizing double-precision arithmetic for both high-precision and fast versions.

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Main Results:

  • A high-precision algorithm guarantees 15 significant figures (10^-15 relative error).
  • A fast algorithm guarantees 12 significant figures (10^-12 relative error) and is 5-20 times quicker.
  • The fast version offers sufficient precision for most molecular calculations.

Conclusions:

  • The developed algorithms significantly enhance the efficiency and accuracy of MIGF calculations.
  • The fast version provides a practical balance of speed and precision for computational chemistry applications.
  • These algorithms are valuable tools for advancing molecular integral computations.