Relativistic universal Gaussian basis set for Dirac—Fock—Coulomb and Dirac—Fock—Breit SCF calculations on heavy atoms

On 'infinite basis set limits' in molecular electronic structure calculations

Sequences of basis sets can be constructed so as to approach the 'infinite basis set limit' in molecular electronic structure calculations. Extrapolation procedures can also be devized to provide accurate values of this limit. However, some care is required since the 'infinite basis set limit' may not correspond to the limit supported by a complete basis set. Extrapolation procedures can then lead to limiting values, which are not estimates of the exact solutions.

The generator coordinate Dirac–Fock method applied to beryllium-like atomic species

The recently formulated generator coordinate Dirac–Fock method for relativistic closed-shell atoms is applied to the Be atom and Be-like ions Ne6+, Ar14+, and Sn46+ in order to assess its efficacy for light atomic systems. The Dirac–Fock equations are integrated numerically in the generator coordinate Dirac–Fock method so as to generate Gaussian basis sets for the atomic species under study. The results obtained with the application of the generator coordinate Dirac–Fock method in this work for Dirac–Fock–Coulomb and Dirac–Fock–Breit energies for Be-like ions are in excellent agreement with Declaux's benchmark numerical calculations, and are better than the Dirac–Fock–Coulomb and Dirac–Fock–Breit energies obtained with even-tempered Gaussian-type function calculations. For the Be atom, the Dirac–Fock–Coulomb energy result obtained with the generator coordinate Dirac–Fock method is lower than the corresponding value obtained with the Declaux's numerical finite-difference program. Key words: Dirac–Fock–Coulomb energy, Dirac–Fock–Breit energy, Gaussian basis sets, generator coordinate Dirac–Fock method.

Gaussian- and Slater-type bases for ground and certain low-lying excited states of positive and negative ions of the atoms H through Xe based on the generator coordinate Hartree–Fock method

We applied a discretized version of the generator coordinate Hartree–Fock (GCHF) method to generate Gaussian- and Slater-type functions for mono positive and mono negative ions of the atoms H through Xe. The basis sizes for Slater-type functions are (12s, 10p, 10d) for positive ions, and (13s, 11p, 10d) for negative ions. In the case of Gaussian-type functions the bases are (18s, 12p, 11d) for both positive and negative species. Ground and excited state Hartree–Fock energies are calculated with these bases and the results compared with the best atom-optimized calculations and numerical HF results available. A discussion on the role of weight functions in the evaluation of electronic energies emphasizes the integral character of the GCHF method. Key words: Slater-type bases, Gaussian-type bases, generator coordinate Hartree–Fock, atomic ions.