Variational Dirac-Hartree-Fock method: Results for the He, Be, C, and Ne isoelectronic sequences

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Abstract
A detailed presentation of an analytic variational Dirac-Hartree-Fock (VDHF) procedure that avoids the problems of spurious roots and collapse is given. The conditions for the avoidance of spurious roots are discussed, as well as the behavior of the one-electron and total energies as upper bounds under variations of the nonlinear parameters or the dimension of the basis sets. The implementation of the VDHF procedure and the Breit-interaction corrections is presented for Slater-type basis sets, with emphasis on the computational efficiency of the calculations. The Breit-interaction corrections in particular are reviewed in detail. Optimized results are presented for the He, Be, C, and Ne isoelectronic sequences.