Dirac-Gaunt theory

For further details the reader is referred to, e.g., a review article by Kutzel-nigg [67]. The Gaunt- and Breit-interaction is often not treated variationally but rather by first-order perturbation theory after a variational treatment of the Dirac-Coulomb-Hamiltonian. The contribution of higher-order corrections such as the vaccuum polarization or self-energy of the electron can be derived from quantum electrodynamics (QED), but are usually neglected due to their negligible impact on chemical properties. 

Here, the current density j r) is still required, but it is now uniquely determined by the electron density, j = j[p]. If magnetic interactions between the electrons are not included — that is, when the Dirac-Coulomb Hamiltonian is employed and the Breit or Gaunt terms are omitted — then also the DFT analog of the Coulomb interaction will reduce to a functional J[p] of the density only [396]. Moreover, it now becomes possible to set up theories in which not the full 4-current is used as the fundamental variable, but only those parts of it that are related to the total electron density and the spin density. 

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