Most modern calculations of many-electron atoms use basis sets of atomic orbitals. An accurate account for electronic correlations in heavy atoms is a very difficult computational problem, and an optimization of the basis sets can reduce computational costs and increase final accuracy. Here, we propose a simple differential ansatz to form virtual orbitals from the Dirac–Fock orbitals of the core and valence electrons. We use basis sets with such orbitals to calculate different properties in Cs including hyperfine structure constants and QED corrections to the valence energies and to the E1 transition amplitudes.
