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A B-spline Hartree-Fock program. (English) Zbl 1262.81265

Summary: A B-spline version of a Hartree-Fock program is described. The usual differential equations are replaced by systems of non-linear equations and generalized eigenvalue problems of the form (\(H^a-\varepsilon_{aa}B)P_a=0\), where \(a\) designates the orbital. When orbital \(a\) is required to be orthogonal to a fixed orbital, this form assumes that a projection operator has been applied to eliminate the Lagrange multiplier. When two orthogonal orbitals are both varied, the energy must also be stationary with respect to orthogonal transformations. At such a stationary point, the matrix of Lagrange multipliers, \(\varepsilon_{ab}=(P_b|H^a|P_a)\), is symmetric and the off-diagonal Lagrange multipliers may again be eliminated through projection operators. For multiply occupied shells, convergence problems are avoided by the use of a single-orbital Newton-Raphson method. A self-consistent field procedure based on these two possibilities exhibits excellent convergence. A Newton-Raphson method for updating all orbitals simultaneously has better numerical properties and a more rapid rate of convergence but requires more computer processing time. Both ground and excited states may be computed using a default universal grid. Output from a calculation for Al \(3s^{2}3p^{\,2\, p}\) shows the improvement in accuracy that can be achieved by mapping results from low-order splines on a coarse grid to splines of higher order onto a refined grid. The program distribution contains output from additional test cases.

MSC:

81V45 Atomic physics
81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
81Q10 Selfadjoint operator theory in quantum theory, including spectral analysis
81-04 Software, source code, etc. for problems pertaining to quantum theory
41A15 Spline approximation
49M15 Newton-type methods

Software:

HF86; HF96
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Full Text: DOI

References:

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