Basis set representation of the electron density at an atomic nucleus

In this paper a detailed investigation of the basis set convergence for the calculation of relativistic electron densities at the position of finite-sized atomic nuclei is presented. The development of Gauss-type basis sets for such electron densities is reported and the effect of different contraction schemes is studied. Results are then presented for picture-change corrected calculations based on the Douglas–Kroll–Hess Hamiltonian. Moreover, the role of electron correlation, the effect of the numerical integration accuracy in density functional calculations, and the convergence with respect to the order of the Douglas–Kroll–Hess Hamiltonian and the picture-change-transformed property operator are studied.