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Accurate and stable numerical Hartree–Fock calculations for atoms. I. The 1 s 2 ground state of H − , He, Li + , and Be ++
Author(s) -
Roothaan C. J. Clemens,
Soukup George A.
Publication year - 1979
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.560150502
Subject(s) - hartree–fock method , ground state , numerical integration , atomic physics , gaussian , stability (learning theory) , physics , numerical stability , series (stratigraphy) , generalization , helium , chemistry , quantum mechanics , numerical analysis , mathematics , mathematical analysis , machine learning , computer science , paleontology , biology
Abstract New techniques have been developed for atomic self‐consistent‐field calculations by numerical integration. For the origin and tail regions we present analytical expansions which can represent the solutions to high accuracy. For the numerical integration in the central region a five‐point generalization of the Numerov formula is used; the error term is of the order h 10 . While this formula is unstable if used in the customary way, stability is achieved by using a Gaussian elimination technique. The new procedures are tested on the ground state of the helium isoelectronic series; with 251 integration points all quantities are calculated with an inherent accuracy of better than 10 –11 .