The evaluation of multidimensional integrals

Cranley, R.

doi:10.1093/comjnl/11.1.102

Cited by 4 publications

(1 citation statement)

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“…It is usually thought that the multidimensional quadrature can te made more accurate by breaking the integration range into parts and summing the results of the application of the formulas to each subdomain. However, one has to consider that the abscissas lying on the boundaries of each partial domain of integration will never be numerically [53], the application of a subdivision of the range of integration does not necessarily produce, in any case, uniform convergence. They conclude in the probable requirement of more than one subdivision.…”

Section: Resultsmentioning

confidence: 99%

Comparative study of unconventional 1s basis functions for the ¹Σ ground state of H₂ and He

Leclerc

1976

Int J of Quantum Chemistry

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AbstractsWe investigated various nonstandard 1 s basis functions (generalized Slater-Gaussian, ellipsoidal Gaussian, floating spherical and ellipsoidal Gaussian, rational function, HulthSn approximation, two-Slater-type orbital, generalized Guillemin-Zener function, and various noninteger-n elliptical orbitals) for approximating the ' Z: ground state of H, and He: +.A CI trial wave-function including u,-type MO'S is adopted and. molecular integrals are evaluated numerically. The energy improvement on the 1s STO is small except for noninteger-n orbitals which closely approach the "SCF limit". Diverses fonctions de base non usuelles (forme gCnCralisie d'orbitale de Slater ouGaussienne, Gaussienne ellipsoidale, Gaussienne sphkrique ou ellipsoidale flottante, fonction rationelle, approximation de HulthCn, double orbitale de Slater, fonction de Guillemin-Zener gCnCralisCe, diverses orbitales a valeurs non entieres de n exprimks en coordonnCes elliptiques) sont appliquks en tant que orbitale atomique de type 1s a l'etat fondamental ' Z: de H, et He:+. On adopte une fonction d'onde incluant des orbitales moliculaires de type ug dans le cadre d'une interaction de configuration restreinte. Les intigrales molCculaires sont bvaluies numeriquement. Le gain en Cnergie est faible par rapport a l'orbitale 1s de Slater hormis le cas des orbitales a valeurs non entiires de n qui approchent fortement la "limite XF".Verschiedene nicht ubliche 1 s Grundfunktionen (VeraQgemeinertes Slater oder Gaussches Orbital, Ellipsoid-Gaussches Orbital, schwebendes spharisch-oder EllipsoidGaussches Orbital, rationelle Funktion, Hulthkn-Naherung, Doppelorbital von Slater, verallgemeinerte Funktion von Guillemin-Zener, verschiedene n-nicht ganzzahlige elliptische Orbitale) wurden zur Naherung des '2: Grundzustandes von H, und He:+ verwandt. Eine Wellenfunktion mit Molekulorbitalen des ug Types wurde als VersuchsKonfigurationswechselwirkung angenommen. Dabei wurden die Molekulintegrale numerisch geschatzt. Der Energie-Zuwachs ist gering dem Slater-1 s Orbital gegenuber, mit Ausnahme fur die n-nicht ganzzahligen Orbitalwerte, die an die "SCF Grenze" sehr nah herankommen.

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Section: Resultsmentioning

confidence: 99%