A generator coordinate version of the closed-shell Dirac–Fock equations

Abstract

A generator coordinate version of the Dirac–Fock equations for relativistic closed-shell atoms is presented. The integration of the Dirac–Fock equations is performed through the integral discretization technique so as to preserve the continuous character of the generator coordinate formalism. With the new formalism we generate a universal Gaussian basis set for relativistic closed-shell atoms with d and f orbitals (zinc up to nobelium). The results obtained with the universal Gaussian basis set for Dirac–Fock–Coulomb self-consistent-field energies are compared with numerical-finite-difference results and Dirac–Fock–Coulomb energies obtained by using other Gaussian basis sets. The excellent performance of our universal Gaussian basis set is attributed to the integral discretization technique of the generator coordinate Dirac–Fock method, as with it we are capable of generating Gaussian-type function exponents that are able to represent properly the relativistic kinematics of an electron inside the nucleus.