Evaluation of Hylleraas-CI atomic integrals by integration over the coordinates of one electron. IV: An improved algorithm for three-electron kinetic energy integrals

DOI10.1007/S10910-016-0608-9zbMATH Open1345.81133arXiv1207.7294OpenAlexW3099895525MaRDI QIDQ298064

María Belén Ruiz

Publication date: 20 June 2016

Published in: Journal of Mathematical Chemistry (Search for Journal in Brave)

Abstract: An improved algorithm to evaluate the nonrelativistic three-electron Hylleraas-Configuration Interaction (Hy-CI) kinetic energy integrals over Slater orbitals and the Hamiltonian in Hylleraas coordinates is shown. The resulting analytical expressions are general for all quantum numbers of the orbitals. From there, the restriction of employing orbitals with quantum numbers $lle2$ of the above algorithm presented in paper I of this series has been removed. With the new algorithm it is possible, in the direct integration method described in this series, to carry out Hy-CI atomic structure calculations including $f$-, $g$-, $ldots$ , $l$ and higher angular-momentum Slater orbitals and to determine $F$, $G$, $ldots$ , $L$ and states of higher order symmetry.

Full work available at URL: https://arxiv.org/abs/1207.7294

zbMATH Keywords

two-electron integralsHylleraas-configuration interactionkinetic-energy integralsSlater orbitals

Mathematics Subject Classification ID

Molecular structure (graph-theoretic methods, methods of differential topology, etc.) (92E10) Numerical integration (65D30) Other fundamental interactions in quantum theory (81V19)

Cites Work

• Title not available (Why is that?)
• Evaluation of Hylleraas-CI atomic integrals. III: Two-electron kinetic energy integrals
• Evaluation of Hylleraas-CI atomic integrals by integration over the coordinates of one electron. I: Three-electron integrals
• Evaluation of Hylleraas-CI atomic integrals by integration over the coordinates of one electron. II: Four-electron integrals
• On the overlap integral of associated Legendre polynomials

Related Items (2)

Analysis of atomic integrals involving explicit correlation factors for the three-electron case. I: Connection to the hypergeometric function \(_{3}F_{2}\) ⋮ Numerical evaluation of three-center two-electron Coulomb and hybrid integrals over \(B\) functions using the \(HD\) and \(H\overline{D}\) methods and convergence properties

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