First order perturbation treatments for relativistic pseudopotentials and corrections to the Hartree-Fock method

The lowest order relativistic corrections to both Hartree-Fock and Phillips-Kleinman and generalized Phillips-Kleinman pseudopotential theories are discussed by relating them to corresponding fully relativistic theories based on the Dirac equation. It is shown that the previous [2] lowest order theory breaks down for heavy atoms because the coulomb potential generated by the core electrons is asymptotically incorrect. A theory, which is more accurate for heavier systems because this incorrect asymptotic behaviour is eliminated by retaining a few specially selected terms of higher order than 1/c 2, is derived. Three further modifications also achieving the same ends by different means are presented. All four of these approaches are shown to reduce to the previous lowest order theory [2] for very light atoms in which all the orbitals show small relativistic effects.