Relativistic exchange-correlation energy functional: Gauge dependence of the no-pair correlation energy

Abstract

We analyze the gauge dependence of the relativistic electron gas correlation energy ${E}_{\mathrm{c}}$ resulting from the no-pair approximation. In particular, we evaluate the relativistic no-pair Lindhard function as the basic ingredient of the random-phase approximation (RPA) for ${E}_{\mathrm{c}}.$ The resulting gauge-dependent no-pair RPA is compared with a gauge-invariant counterpart. The implications for relativistic density functionals are examined by applying the local-density approximation based on each of these forms of ${E}_{\mathrm{c}}$ to atoms. It is found that the gauge dependence of ${E}_{\mathrm{c}}$ is irrelevant on the overall level of accuracy obtained with present density functionals.