A polynomial version of the Generator Coordinate Dirac-Fock (p-GCDF) method is introduced and applied to develop Adapted Gaussian Basis Sets (AGBS) for helium- and beryllium-like atomic species (He, Ne +8, Ar +16, Sn +48, Be, Ne +6, Ar +14, and Sn +46) and for Kr and Xe atoms. The Dirac-Fock-Coulomb and Dirac-Fock-Breit energies obtained with these basis sets are in excellent agreement with numerical finite-difference calculations. Moreover, the sizes of the AGBS generated here with the p-GCDF method are significantly smaller than the size of previous relativistic Gaussian basis sets.

No abstract

ABSTRACT:The purpose of this work is to analyze the relativistic Gaussian basis sets obtained with a recently developed polynomial version of the generator coordinate Dirac-Fock method. The atomic systems chosen to evaluate the basis sets are some alkaline earth and noble gas atoms: He, Be, Ne, Mg, Ar, and Ca. Hartree-Fock, relativistic, and electronic correlation contributions to the atomic total energy of the neutral and ionized atomic species were estimated using these relativistic Gaussian basis sets. The basis sets developed were able to attain energies that deviate at most by 0.47 and 0.65 mHartree, respectively, from numerical Hartree-Fock and Dirac-FockCoulomb results and are also competitive with fully optimized relativistic Gaussian basis sets of similar sizes. The electronic correlation energy contributions were obtained after two nonrelativistic calculations: a Hartree-Fock and a full quadratic configuration interaction, including single and double substitutions. The uncontracted basis sets obtained here along with polarization functions chosen to have equal exponents to selected functions already present in the original set were adequate in describing not only the neutral but also the highly ionized atomic species. The comparison of some calculated shell ionization energies with experimental results presented a maximum deviation of 3% (for a total of 15 ionization values ranging from 18 to 10,599 eV), reinforcing the quality of the basis sets developed in this work.

The polynomial Generator Coordinate Hartree-Fock Gaussian basis sets, pGCHF, for the atoms Na, Mg, Al, Si, P, S, and Cl were generated using the generator coordinate method based on polynomial...

ABSTRACT:The generator coordinate Dirac-Fock (GCDF) method and the downhill simplex algorithm were applied to generate new adapted Gaussian basis sets for relativistic closed shell atoms from He (Z ϭ 2) to Ba (Z ϭ 56). These new basis sets have a size reduction of about 30% when compared to previous GCDF adapted basis sets, and are as compact as some corresponding nonrelativistic Gaussian basis sets. The truncation error is in a millihartree order of magnitude and the optimization scheme adopted here allowed the l -and l ϩ relativistic symmetries to be different.