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Numerical calculation of overlap and kinetic integrals in prolate spheroidal coordinates
Author(s) -
Romanowski Zbigniew
Publication year - 2007
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.21485
Subject(s) - rectangle , kinetic energy , domain (mathematical analysis) , prolate spheroidal coordinates , gravitational singularity , atomic orbital , quadrature (astronomy) , numerical integration , physics , mathematics , mathematical analysis , prolate spheroid , classical mechanics , geometry , quantum mechanics , optics , electron
The efficient algorithm calculating the overlap and the kinetic integrals for the numerical atomic orbitals is presented. The described algorithm exploits the properties of the prolate spheroidal coordinates. The overlap and the kinetic integrals in ℝ 3 are reduced to the integrals over the rectangular domain in ℝ 2 , what substantially reduces the complexity of the problem. We prove that the integrand over the rectangular domain is continuous and does not have any slope singularities. For calculation of the integral over the rectangle any adaptive algorithm can be applied. The exemplary results were obtained by application of the adaptive Gauss quadrature. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2008