Relevance of relativistic exchange-correlation functionals and of finite nuclei in molecular density-functional calculations

Two types of relativistic corrections in molecular electronic structure calculations that are based on the Kohn-Sham approach to density-functional theory have been studied: (1) relativistic corrections to the exchange-correlation functional, both in the local density and in the generalized gradient approximation; (2) a description of the nuclear charge distribution that avoids the Coulomb singularity. The diatomics AuH, AuCl, ${\mathrm{Au}}_2$, ${\mathrm{Ag}}_2$, and ${\mathrm{Cu}}_2$ were chosen as examples. Although significant effects on the total energy and on core-level energies are found, only the relativistic correction to local-density approximation has a noticeable impact on molecular observables: it induces changes of bond lengths by up to 0.005 Å, of vibrational frequencies by up to 10 ${\mathrm{cm}}^{\mathrm{-}1}$, and of binding energies by up to 0.05 eV. Thus, taken together, the relativistic corrections discussed here are much smaller than those obtained with density-gradient corrections to the exchange-correlation functional. Therefore, the common practice to neglect these relativistic corrections in molecular density-functional calculations is justified, at least for compounds without superheavy elements. © 1996 The American Physical Society.