Effects of segmented contractions of Gaussian basis sets on Dirac-Fock energies

Abstract

Dirac-Fock calculations have been performed using a segmented contraction of Gaussian basis sets entirely generated from the Dirac-Fock Hamiltonian. Both Dirac-Fock-Coulomb and Dirac-FockBreit self-consistent eld calculations have been performed for Ar Z=18 , Ge Z=32 , Sn Z=50 , Xe Z=54 and Hg Z=80 . It is found that contractions of large exponent bases of s and p symmetry species have little e ect on the total and orbital energies for light atoms Ar and Ge and a large e ect for intermediate Sn and Xe and heavy Hg atoms. I IntroductionRecently, w e h a ve developed the closed-shell generator coordinate Dirac-Fock GCDF method 1,2 and applied it to perform Dirac-Fock-Coulomb DFC and Dirac-Fock-Breit DFB calculations on relativistic closed-shell atoms 1-5 . Here we w ould like to call attention for the fact that the GCDF method represents an algorithm capable of generating Gaussian-type functions GTF exponents directly from the relativistic environment a Dirac-Fock DF code , whereas the usual procedure in previous relativistic calculations was to employ GTF exponents obtained from the nonrelativistic environment a Hartree-Fock HF code , by optimization or another technique, exactly as rst performed by Matsuoka and Huzinaga 6 .Thus, due to the recent progress in the DF methods, the problem of how to contract atomic Gaussian basis sets for use in these calculations becomes relevant. The general and the segmented contraction schemes 7-11 have been used in relativistic calculations. Matsuoka 7 and Ishikawa et al. 8-10 have described some segmented schemes to contract Gaussian basis sets they employed in relativistic atomic calculations In these papers, Matsuoka and Ishikawa w orked with Gaussian basis sets that originally were generated to perform nonrelativistic calculations with a HF code .In this work, we report a DFC and DFB selfconsistent eld SCF calculations for Ar, Ge, Sn, Xe and Hg using a segmented contraction methodology for Gaussian basis sets developed recently by Jorge and da Silva 12 , in order to ascertain how contraction of the basis set a ects DF energy results. II Results and discussionTo perform the DFC and DFB calculations for Ar, Ge, Sn, Xe and Hg, we h a ve used our accurate universal Gaussian basis sets UGBSs 1,3 , developed with the characteristic of being entirely generated from the DF Hamiltonian. This point i s v ery important as all previous studies on segmented contraction of GTF for relativistic calculations were done with GTF obtained from the HF Hamiltonian 7-11 . Therefore in this work, the e ects of a segmented contraction on DF energies are studied with Gaussian basis sets entirely generated from the DF Hamiltonian. The nite nucleus model of uniform proton-charge 13 with nuclear radius equal to R = 2 :2677 10 ,5 A 1=3 A is the atomic mass number was used in our calculations. The speed of light was taken to be 137.0370 a.u. while the nonrelativistic limit was evaluated with c = 1 0 4 a.u.. Beside this, we recall that the radial small component functions are generated from the radial la...