Relativistic regular two-component Hamiltonians

In this paper, potential-dependent transformations are used to transform the four-component Dirac Hamiltonian to effective two-component regular Hamiltonians. To zeroth order, the expansions give second order differential equations (just like the Schrödinger equation), which already contain the most important relativistic effects, including spin–orbit coupling. One of the zero order Hamiltonians is identical to the one obtained earlier by Chang, Pelissier, and Durand [Phys. Scr. 34, 394 (1986)]. Self-consistent all-electron and frozen-core calculations are performed as well as first order perturbation calculations for the case of the uranium atom using these Hamiltonians. They give very accurate results, especially for the one-electron energies and densities of the valence orbitals.