Relativistic Effects on the Topology of the Electron Density

The topological analysis of electron densities obtained either from X-ray diffraction experiments or from quantum chemical calculations provides detailed insight into the electronic structure of atoms and molecules. Of particular interest is the study of compounds containing (heavy) transition-metal elements, which is still a challenge for experiment as well as from a quantum-chemical point of view. Accurate calculations need to take relativistic effects into account explicitly. Regarding the valence electron density distribution, these effects are often only included indirectly through relativistic effective core potentials. But as different variants of relativistic Hamiltonians have been developed all-electron calculations of heavy elements in combination with various electronic structure methods are feasible. Yet, there exists no systematic study of the topology of the total electron density distribution calculated in different relativistic approximations. In this work we therefore compare relativistic Hamiltonians with respect to their effect on the electron density in terms of a topological analysis. The Hamiltonians chosen are the four-component Dirac-Coulomb, the quasi-relativistic two-component zeroth-order regular approximation, and the scalar-relativistic Douglas-Kroll-Hess operators.