The zero order regular approximation for relativistic effects:
formulation and appplication to molecular properties
Evert Jan Baerends
Scheikundig Laboratorium der Vrije Universiteit, De Boelelaan 1083,
NL-1081 HV Amsterdam, The Netherlands
The well-known Pauli relativistic correction terms to the non-relativistic
hamiltonian (mass-velocity, Darwin and spin-orbit coupling) can be obtained
from the Dirac hamiltonian. However, the derivation is only valid in
relatively smooth and in particular nonsingular potentials. This excludes
the nuclear Coulomb potential, as is evident from the singular behaviour of
the Pauli hamiltonian. It is however possible to derive approximate
relativistic hamiltonians, that take the special character of the Coulomb
potential into account. In zeroth order this regular approximation (ZORA)
already yields very accurate relativistic results, notably for the valence
electrons. The performance of the ZORA approach in combination with GGA
functionals is excellent for bond energies and related spectroscopic
properties (frequencies, bond lengths) of heavy element compounds.
Some care has to be exercised in calculations of properties that depend on
the quality of the wavefunction close to the nucleus. The ZORA approach is
inherently less accurate for (deep) core levels. More importantly, the
picture change that has occured in going from the four-component Dirac to
the two-component ZORA method has to be taken into account. We will discuss
electric field gradients at the nucleus and NMR shielding calculations.