Systematic study of the Ib diatomic molecules ${\mathrm{Cu}}_2,$ ${\mathrm{Ag}}_2$, and ${\mathrm{Au}}_2$ using advanced relativistic density functionals

In this paper we present results of four-component relativistic density-functional calculations for diatomic molecules with heavy constituents. The fully relativistic treatment of the electron kinematics is used for a consistent examination of the importance of gradient and relativistic corrections to the exchange-correlation energy functional. In agreement with recent scalar relativistic calculations, we find that relativistic corrections to exchange-correlation functionals give no significant contribution to the binding properties of the investigated diatomic molecules. On the other hand, the effect of gradient terms is sizable, leading to a clear improvement of dissociation energies over the standard local-density approximation. The usefulness of gradient contributions in the high-$Z$ regime is nevertheless somewhat questioned by the fact that they overcorrect the small errors in bond lengths found with the local-density approximation.