In this work we present a comprehensive study of analytical electric field gradients in hydrogen halides calculated within the high-order Douglas-Kroll-Hess ͑DKH͒ scalar-relativistic approach taking picture-change effects analytically into account. We demonstrate the technical feasibility and reliability of a high-order DKH unitary transformation for the property integrals. The convergence behavior of the DKH property expansion is discussed close to the basis set limit and conditions ensuring picture-change-corrected results are determined. Numerical results are presented, which show that the DKH property expansion converges rapidly toward the reference values provided by four-component methods. This shows that in closed-shell cases, the scalar-relativistic DKH͑2,2͒ approach which is of second order in the external potential for both orbitals and property operator yields a remarkable accuracy. As a parameter-dependence-free high-order DKH model, we recommend DKH͑4,3͒. Moreover, the effect of a finite-nucleus model, different parametrization schemes for the unitary matrices, and the reliability of standard basis sets are investigated.

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.

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