Approximate relativistic Hartree-Fock equations and their solution within a minimum basis set of slater-type functions

Abstract

Relativistic closed-shell atoms are treated by the use of a specific approximation for the small component of the one-electron Dirac spinors. It is assumed that the large and the small component are interconnected by a parameter-dependent relation which is formally analogous to that of the one-electron system. Subject to this constraint, the total energy is varied with respect to the large components. The resulting eigenvalue equations for the large components contain only regular potential terms and reduce to the familiar Hartree-Fock equations in the limit of infinite velocity of light. Analytical solution of these approximate relativistic Hartree-Fock equations is achieved using a minimum basis set of Slater-type functions for the expansion of the radial part of the large components. Total relativistic energies, orbital energies, orbital exponents and mean radii are calculated for the ground states of He, Be, Ne, Mg, Ar, Kr, Xe and Cu + .

Linear approximation to relativistic minimax (LARM) applied to a LCAO description of the two-centre Coulomb problem

“…It will be of great practical importance to explore the sensitivity to the molecular potential in the denominator by replacing the full molecular potential by a number of systematic approximations to it. This seems promising as one may interpret certain results in the literature [22] in this direction.…”