B-Spline Dirac-Hartree-Fock Program (DBSR HF)

In the B-spline version of a general Dirac-Hartree-Fock program, the usual differential equations are replaced by a set of generalized-eigenvalue problems of the form (Hᵃ − εₐₐB)Pₐ = 0 where Hₐ and B are the Hamiltonian and overlap matrices, respectively, and Pₐ is the 2-component relativistic orbital expanded in a 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 be stationary with respect to orthogonal transformations. At such a stationary point, the off-diagonal Lagrange multipliers may be eliminated through projection operators. However, the default is to omit rotations. 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.

Information about atoms up to Z = 104 (subshells and their occupation, for example) 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. The command dbsr hf Be computes the relativistic DHF results for the atom Be (Z = 4) using default parameters. By definition, a Hartree-Fock calculation is for a single configuration (possibly in non-relativistic notation), but with a non-default option, the program will perform an Extended Average Level (EAL) calculation for all the configurations in an input file. The Virial Theorem is displayed as a final check the final total energy. For relativistic calculations, V/T = -1 for an exact calculation.