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Numerical integration for polyatomic systems. (English) Zbl 0755.65026
This article describes the computation methods used in a new package for computing three-dimensional integrals that arise in electronic structure calculations for polyatomic systems. The primary focus of the article is a detailed description of how the three-dimensional space surrounding the atoms can be divided into appropriate polygonal subregions and how integrals over these subregions can be transformed into integrals over standard regions where Gauss product integration rules can be used.
There is some further discussion of how rules for integrals over the outer subregions should be applied to take advantage of symmetry. The article finishes with a discussion of test results for the package, including a discussion of the speed of convergence for the methods used by the package.
Reviewer: A.C.Genz (Pullman)

MSC:
65D32 Numerical quadrature and cubature formulas
41A55 Approximate quadratures
81V10 Electromagnetic interaction; quantum electrodynamics
81V45 Atomic physics
41A63 Multidimensional problems
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