It is shown how the regularized two-component relativistic Hamiltonians of Heully et al. and Chang, Pelissier, and Durand can be viewed as arising from a perturbation expansion that unlike the Pauli expansion remains regular even for singular attractive Coulomb potentials. The performance of these approximate Hamiltonians is tested in the framework of the local density approximation and the relation of their spectrum to that of the Dirac Hamiltonian is discussed. The circumstances under which the current approximations are superior to the Pauli Hamiltonian are analyzed. Finally, it shown how the Hamiltonians could be used within the context of conventional Hartree-Fock theory. 0 1996 John Wiley & Sons, Inc. lntroduction t is well known that relativistic effects are very I important in the study of heavy elements. Instead of the Schrodinger equation, one has to solve the Dirac equation, which involves a fourcomponent Hamiltonian. Fully relativistic calculations are not intrinsically more complicated than are nonrelativistic ones, but they are very timeconsuming, even at the SCF level. One needs complex arithmetic and the dimension of the secular problem will be large due to the four components, *This article appeared earlier in limited edition in Nezu