Finite-difference Newton--Raphson solution of the multiconfiguration Hartree--Fock problem

Journal Article · Wed Dec 01 04:00:00 EST 1976 · J. Comput. Phys.; (United States)

DOI:https://doi.org/10.1016/0021-9991(76)90042-5· OSTI ID:5421669

Fimple, W R; McKenzie, B J; White, S P

The finite-difference Newton--Raphson algorithm coupled with a self-consistent field iteration, which recently has proved to be very successful in solving the atomic Hartree--Fock equations for a single configuration, was extended to treat the multiconfiguration case. The problem is algebraicized through the introduction of finite-difference variables, treating the multipliers on normalization and orthogonality on an equal footing with the other variables, and the resulting large system of nonlinear algebraic equations is solved by means of a generalized Newton--Raphson iteration. Because of the particular ordering of the variables and equations and the coupled SCF iteration employed, the unit operation of the method involves the inversion of a partly block tridiagonal Jacobian matrix and can be solved rapidly by means of a partitioning. A solution of the 1s2s/sup 1/S excited state of helium is presented as an example.

• Research Organization: Univ. of Canterbury, Christchurch, N.Z.
• OSTI ID: 5421669
• Journal Information: J. Comput. Phys.; (United States), Journal Name: J. Comput. Phys.; (United States) Vol. 4; ISSN JCTPA
• Country of Publication: United States
• Language: English

Related Subjects

640302* -- Atomic
Molecular & Chemical Physics-- Atomic & Molecular Properties & Theory
74 ATOMIC AND MOLECULAR PHYSICS
ALGEBRA
CRYOGENIC FLUIDS
ELEMENTS
ENERGY LEVELS
FINITE DIFFERENCE METHOD
FLUIDS
FUNCTIONS
HARTREE-FOCK METHOD
HELIUM
ITERATIVE METHODS
JACOBIAN FUNCTION
MATHEMATICS
NONLINEAR PROBLEMS
NONMETALS
NUMERICAL SOLUTION
RARE GASES
SELF-CONSISTENT FIELD