Fischer, Charlotte Froese A B-spline Hartree-Fock program. (English) Zbl 1262.81265 Comput. Phys. Commun. 182, No. 6, 1315-1326 (2011). 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. Cited in 2 Documents 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 Keywords:atomic structure; B-spline methods; bound states; generalized eigenvalue problem; Lagrange multipliers; Newton-Raphson method for atoms Software:HF86; HF96 PDFBibTeX XMLCite \textit{C. F. Fischer}, Comput. Phys. Commun. 182, No. 6, 1315--1326 (2011; Zbl 1262.81265) Full Text: DOI References: [1] Froese Fischer, C., Comput. Phys. Commun., 43, 355-365 (1987) [2] Gaigalas, G.; Froese Fischer, C., Comput. Phys. Commun., 98, 255 (1996) [3] Froese Fischer, C., Comput. Phys. Commun., 14, 145-153 (1978) [4] Hartree, D. R., The Calculation of Atomic Structures (1957), Wiley: Wiley New York [5] Froese Fischer, C., (Arimondo, E.; Berman, P. R.; Lin, C. C., Advances in Atomic and Molecular Physics, vol. 55 (2007)), 539-550 [6] Fletcher, C. A.J., Computational Galerkin Methods (1984), Springer: Springer New York · Zbl 0533.65069 [7] Bachau, H.; Cormier, E.; Decleva, P.; Hansen, J. E.; Martin, F., Rep. Prog. Phys., 64, 1815-1942 (2001) [8] Spline theory allows for multiple knots at any point but the present code assumes they occur only at the first and last knot.; Spline theory allows for multiple knots at any point but the present code assumes they occur only at the first and last knot. [9] Bentley, M., J. Phys. B: At. Mol. Opt. Phys., 27, 637-644 (1994) [10] Koopmans, T. A., Physica, 1, 104 (1933) [11] Slater, J. C., Quantum Theory of Atomic Structure, vol. II (1960), McGraw-Hill: McGraw-Hill New York · Zbl 0094.44702 [12] Zatsarinny, O., Comput. Phys. Commun., 174, 273-356 (2006) [13] Sapirstein, J.; Johnson, W. R., J. Phys. B, 29, 5213-5225 (1996) [14] Verdebout, S.; Jönsson, P.; Gaigalas, G.; Godefroid, M.; Froese Fischer, C., J. Phys. B, 43, 074017 (2010) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.