Symmetrical “nonproduct” quadrature rules for a fast calculation of multicenter integrals

✍ Scribed by Claude Daul; Stéphane Daul

• Publisher: John Wiley and Sons
• Year: 1997
• Tongue: English
• Weight: 189 KB
• Volume: 61
• Category: Article
• ISSN: 0020-7608
• DOI: 10.1002/(sici)1097-461x(1997)61:2<219::aid-qua4>3.0.co;2-z

✦ Synopsis

A complete method of numerical integration, designed especially for density functional theory, is presented. We first refer to already known methods and then present a new development of the angular integration. A set of symmetrical quadrature rules which is equivalent to the popular Lebedev scheme has been developed for any arbitrary point group. In case of octahedral symmetry our method turns out to be exactly identical to Lebedev's. These formulas integrate exactly spherical harmonics of the highest possible order with, most probably, the least possible number of grid points. Nevertheless a rigorous mathematical proof of this statement has not yet been found. Examples of Ž . quadrature rules for noncubic point groups not covered by Lebedev's grid , e.g., the icosahedral, pentagonal, or hexagonal ones are given. The application of this method to the resolution of the Poisson's equation is also presented.