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Calculation of Gaussian integrals using symbolic manipulation

✍ Scribed by Paul Bracken; Rodney J. Bartlett

Publisher: John Wiley and Sons
Year: 1997
Tongue: English
Weight: 191 KB
Volume: 62
Category: Article
ISSN: 0020-7608
DOI: 10.1002/(sici)1097-461x(1997)62:6<557::aid-qua1>3.0.co;2-v

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✦ Synopsis

The calculation of molecular integrals is extremely important for applications to such diverse areas as statistical mechanics and quantum chemistry. A careful derivation of a method for calculating primitive Gaussian integrals originally proposed by Obara and Saika is presented. The basic recursion relations for the two-and three-center overlap integrals is derived using a simple technique. Several new horizontal recursion relations are given. Finally, an innovative method for implementing these recursion relations is discussed. The recursion relations in this form are suited for programming using a symbolic manipulation language. There are several reasons why it is of interest to consider programming with symbolic manipulation. It has been found that it is possible to write algorithms that will generate values for Gaussian integrals for very large values of angular momentum automatically. Calculations can be done to arbitrary precision in Maple. Having these recursions programmed in Maple allows for the possibility of using the Maple programs to help in the writing of similar programs in other languages which are, numerically, much faster.

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