A study of the basis set dependence of the bifunctional expression of the non-interacting kinetic energy for atomic systems

The non-interacting kinetic energy is divided into the von Weizsacker term and the Pauli kinetic energy. Whereas the von Weizsacker energy is known in terms of the density, the Pauli kinetic energy is not. Consequently, its functional derivative can only be determined formally, at the solution point, from a given set of Kohn-Sham eigenfunctions. Since in a practical calculation the solution point is never reached exactly, the formal functional derivative is evaluated only in proximity of the solution point. Therefore, bifunctional expressions involving the corresponding potential are approximate. In this study the atoms from H - Xe are examined, showing that the energy deviation between the bifunctional expression and the orbital-based kinetic energy density is of a few hundred millihartrees for a quadruple basis set, while it can reach the order of a few hartrees when employing basis sets of less quality.