  Most modern calculations of many-electron atoms use basis sets of atomic
orbitals. An accurate account for the electronic correlations in heavy atoms is
very difficult computational problem and optimization of the basis sets can
reduce computational costs and increase final accuracy. Here we suggest 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.
