Relativistic regular two-component Hamiltonians

TLDR

The zeroth‑order expansion yields second‑order differential equations that already incorporate key relativistic effects such as spin–orbit coupling. The study transforms the four‑component Dirac Hamiltonian into effective two‑component regular Hamiltonians via potential‑dependent transformations. The authors apply potential‑dependent transformations and perform self‑consistent all‑electron and frozen‑core calculations, along with first‑order perturbation theory, on the uranium atom using the resulting Hamiltonians. One zero‑order Hamiltonian matches that of Chang, Pelissier, and Durand, and the calculations yield highly accurate one‑electron energies and valence orbital densities. Reference: Phys.

Abstract

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.