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

✍ Scribed by Kazuhiro Ishida

Publisher
John Wiley and Sons
Year
2004
Tongue
English
Weight
131 KB
Volume
25
Category
Article
ISSN
0192-8651

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✦ Synopsis

Several efficient algorithms for the accurate and fast calculation of the molecular incomplete gamma function Fm(z) with a complex argument z are developed. The complex incomplete gamma function is arising in molecular integrals over the gauge-including atomic orbitals. Two kinds of algorithms are recommended: (1) a high-precision version and (2) a fast version. The high-precision version is able to guarantee 15 significant figures (10(-15) in the relative error) and the fast version is able to guarantee 12 significant figures (10(-12) in the relative error), at worst, within the double-precision arithmetic. The fast version is about 5-20 times faster than the high-precision version. For most molecular calculations, the fast version will give a satisfied precision.

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