Rational Approximation of Incomplete Gamma Function for the Sake of Effective Molecular Orbital Calculations

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  • 分子軌道計算のための不完全ガンマ関数の有理式近似
  • ブンシ キドウ ケイサン ノ タメ ノ フカンゼン ガンマ カンスウ ノ ユウリシキ キンジ

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A method has been developed for an efficient approximation of incomplete gamma function that occurs in molecular orbital calculation with Gaussian-type basis sets. The method employs rational Chebyshev approximation and forward and backward recurrence relations to reduce the memory-space requirement without compromising accuracy. An example is illustrated for the cases wherein the sum of quantum numbers of orbitals is less than or equal to 8 and the rational functions are evaluated using double-precision numbers. In sucha case, results accurate to 50 significant bits can be obtained.

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