We construct the complementary short-range correlation relativistic local-density-approximation functional to be used in relativistic range-separated density-functional theory based on a Dirac-Coulomb Hamiltonian in the no-pair approximation. For this, we perform relativistic random-phase-approximation calculations of the correlation energy of the relativistic homogeneous electron gas with a modified electron-electron interaction, we study the high-density behavior, and fit the results to a parametrized expression. The obtained functional should eventually be useful for electronic-structure calculations of strongly correlated systems containing heavy elements.
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