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Numerical calculation of overlap and kinetic integrals in prolate spheroidal coordinates. II
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.21515
Subject(s) - eigenfunction , kinetic energy , prolate spheroidal coordinates , domain (mathematical analysis) , numerical integration , atomic orbital , hydrogen atom , basis function , basis (linear algebra) , prolate spheroid , physics , mathematical analysis , mathematics , classical mechanics , quantum mechanics , eigenvalues and eigenvectors , geometry , group (periodic table) , electron
The efficient algorithm calculating the overlap and the kinetic integrals for the numerical atomic orbitals is presented. On the basis of the prolate spheroidal coordinates, the overlap and the kinetic integral are reduced to the integral over the rectangular domain. The integration over the rectangular domain is performed by the adaptive integration scheme. The developed algorithm is applied to calculate the integrals for the pairs of hydrogen and gallium eigenfunctions. It is demonstrated that high accuracy can be obtained for small number of integrand evaluations what guarantees the efficiency of the presented algorithm. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2008