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Manuscript Title: A B-spline Hartree-Fock program
Authors: Charlotte Froese Fischer
Program title: SPHF version 1.00
Catalogue identifier: AEIJ_v1_0
Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 182(2011)1315
Programming language: Fortran 95.
Computer: Any system with a Fortran 95 compiler. Tested on Intel Xeon CPU X5355, 2.66GHz.
Operating system: Any system with a Fortran 95 compiler.
Keywords: atomic structure, B-spline methods, bound states, generalized eigenvalue problem, Lagrange multipliers, Newton-Raphson method for atoms.
PACS: 02.70.Dh, 03.65.Ge, 31.15.A-.
Classification: 2.1.

External routines: LAPACK (http://www.netlib.org/lapack/)

Nature of problem:
Non-relativistic Hartree-Fock wavefunctions are determined for atoms in a bound state that may be used to predict a variety atomic properties.

Solution method:
The radial functions are expanded in a B-spline basis [1]. The variational principle applied to an energy functional that includes Lagrange multipliers for orthonormal constraints defines the Hartree-Fock matrix for each orbital. Orthogonal transformations symmetrize the matrix of Lagrange multipliers and projection operators eliminate the off-diagonal Lagrange multipliers to yield a generalized eigenvalue problem. For multiply occupied shells, a single-orbital Newton-Raphson (NR) method is used to speed convergence with very little extra computation effort. In a final step, all orbitals are updated simultaneously by a Newton-Raphson method to improve numerical accuracy.

Restrictions:
There is no restriction on calculations for the average energy of a configuration.
As in the earlier HF96 program [2], only one or two open shells are allowed when results are required for a specific LS coupling. These include:
  1. (nl)Nn′s, where l = 0, 1, 2, 3
  2. (np)Nn′l, where l = 0, 1, 2, 3, . . .
  3. (nd)(n′f)

Unusual features:
Unlike HF96, the present program is a Fortran 90/95 program without the use of COMMON. It is assumed that Lapack libraries are available.

Running time:
For Ac 7s27p2P the execution time varied from 6.9 s to 9.1 s depending on the iteration method.

References:
[1] C. Froese Fischer, Adv. At. Mol. Phys. 55 (2008) 235
[2] G. Gaigalas and C. Froese Fischer, Comput. Phys. Commun. 98 (1996) 255