Relativistic total energy using regular approximations

In this paper we will discuss relativistic total energies using the zeroth order regular approximation (ZORA). A simple scaling of the ZORA one-electron Hamiltonian is shown to yield energies for the hydrogenlike atom that are exactly equal to the Dirac energies. The regular approximation is not gauge invariant in each order, but the scaled ZORA energy can be shown to be exactly gauge invariant for hydrogenic ions. It is practically gauge invariant for many-electron systems and proves superior to the (unscaled) first order regular approximation for atomic ionization energies. The regular approximation, if scaled, can therefore be applied already in zeroth order to molecular bond energies. Scalar relativistic density functional all-electron and frozen core calculations on diatomics, consisting of copper, silver, and gold and their hydrides are presented. We used exchange-correlation energy functionals commonly used in nonrelativistic calculations; both in the local-density approximation (LDA) and including density-gradient (‘‘nonlocal’’) corrections (NLDA). At the NLDA level the calculated dissociation energies are all within 0.2 eV from experiment, with an average of 0.1 eV. All-electron calculations for Au2 and AuH gave results within 0.05 eV of the frozen core calculations.