Accurate and stable numerical Hartree--Fock calculations for atoms. I. The 1s/sup 2/ ground state of H/sup -/, He, Li/sup +/, and Be/sup + +/

Journal Article · Tue May 01 00:00:00 EDT 1979 · Int. J. Quant. Chem.; (United States)

DOI:https://doi.org/10.1002/qua.560150502· OSTI ID:6092664

Roothaan, C C.J.; Soukup, G A

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/sup 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/sup -11/.

• Research Organization: Battelle Columbus Labs., Columbus, OH
• OSTI ID: 6092664
• Journal Information: Int. J. Quant. Chem.; (United States), Vol. 15:5
• Country of Publication: United States
• Language: English

Related Subjects

74 ATOMIC AND MOLECULAR PHYSICS
BERYLLIUM IONS
GROUND STATES
HELIUM
HYDROGEN IONS 1 MINUS
LITHIUM IONS
ISOELECTRONIC ATOMS
NUMERICAL SOLUTION
SELF-CONSISTENT FIELD
WAVE FUNCTIONS
ANIONS
ATOMIC IONS
ATOMS
CHARGED PARTICLES
CRYOGENIC FLUIDS
ELEMENTS
ENERGY LEVELS
FLUIDS
FUNCTIONS
HYDROGEN IONS
IONS
NONMETALS
RARE GASES
640302* - Atomic
Molecular & Chemical Physics- Atomic & Molecular Properties & Theory