Gradients in the ab initio scalar zeroth-order regular approximation (ZORA) approach

We discuss ways to obtain analytical gradients within the scalar zeroth-order regular approximation (ZORA) to the Dirac–Fock equation within an ab initio context. Simply employing the relativistic density within the non-relativistic gradient package is in error by 10−5. We introduce a new strictly atomic scheme which in addition to yielding exact gradients is also computationally inexpensive and avoids the gauge invariance problems that plague molecular ZORA approaches. We show that the total and orbital energies produced with the scaled version of this method are generally, i.e. except for very short interatomic distances, very close to the full molecular scaled ZORA results. Equilibrium geometries from full molecular scaled ZORA and strictly atomic ZORA are shown to be within 0.01 Å from Dirac–Fock.