DBSR_HF: A B-spline Dirac–Hartree–Fock program

Abstract

A B-spline version of a general Dirac–Hartree–Fock program is described. The usual differential equations are replaced by a set of generalized eigenvalue problems of the form (Ha−εaB)Pa=0, where Ha and B are the Hamiltonian and overlap matrices, respectively, and Pa is the two-component relativistic orbit in the B-spline basis. A default universal grid allows for flexible adjustment to different nuclear models. When two orthogonal orbitals are both varied, the energy must also be stationary with respect to orthonormal transformations. At such a stationary point the off-diagonal Lagrange multipliers may be eliminated through projection operators. The self-consistent field procedure exhibits excellent convergence. Several atomic states can be considered simultaneously, including some configuration-interaction calculations. The program provides several options for the treatment of Breit interaction and QED corrections. The information about atoms up to Z=104 is stored by the program. Along with a simple interface through command-line arguments, this information allows the user to run the program with minimal initial preparations. Program summaryProgram title: DBSR_HFCatalogue identifier: AEZK_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEZK_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 22643No. of bytes in distributed program, including test data, etc.: 354629Distribution format: tar.gzProgramming language: Fortran 95.Computer: No specific requirements to the computer.Operating system: Any system with a Fortran 95 compiler.Classification: 2.1.External routines: LAPACK (http://www.netlib.org/lapack/)Nature of problem:Relativistic Dirac–Hartree–Fock wavefunctions are determined for atoms in a bound state. These wavefunctions may be used to predict a variety of atomic properties.Solution method:The radial functions for large and small components of the one-electron spinor are expanded in B-spline bases. The variational principle applied to an energy functional that includes Lagrange multipliers for orthonormal constraints defines the Dirac–Hartree–Fock matrix for each orbital. Orthonormal transformations for a stationary solution were applied and Lagrange multipliers eliminated through projection operators.Restrictions:There is no restriction on calculations for the average or specific term energy of any atomic configuration with shells whose angular momenta are less than or equal to 9/2.Unusual features:The program allows the consideration of a few atomic states simultaneously. A simple interface through the command-line arguments allows the user to run the program with minimal initial preparations.Running time:From a few seconds to a few minutes depending on the atom under consideration.