Relativistic Dirac-Fock exchange and Breit interaction energy functionals based on the local-density approximation and the self-consistent multiplicative constant method

Abstract

Local approximations, formulated in the context of a relativistic extension of the self-consistent $\ensuremath{\alpha}$ method, are advanced for the case of the relativistic exact Coulomb exchange functional---defined as the Dirac-Fock exchange---and for the Breit expression for the transverse photon exchange, given in terms of the expectation value of the Breit operator. The resulting potentials are local (multiplicative) operators, in both cases. Using these new functionals, fully relativistic calculations have been performed for selected atoms with $Z$ between 10 and 94, within the framework of relativistic density functional theory (RDFT). The total and exchange energies and ionization potentials obtained from these functionals are quite close to those of the relativistic optimized potential method (ROPM). The computational effort involved in the application of this new method is, however, significantly lower.