Is the non-additive kinetic potential always equal to the difference of effective potentials from inverting the Kohn-Sham equation?

The relation used frequently in the literature according to which the non-additive kinetic potential which is a functional depending on a pair of electron densities is equal (up to a constant) to the difference of two potentials obtained from inverting two Kohn-Sham equations, is examined. The relation is based on a silent assumption that the two densities can be obtained from two independent Kohn-Sham equations, i.e., are v(s)-representable. It is shown that this assumption does not hold for pairs of densities: rho(tot) being the Kohn-Sham density in some system and rho(B) obtained from such partitioning of rho(tot) that the difference rho(tot) - rho(B) vanishes on a Lebesgue measurable volume element. The inversion procedure is still applicable for rho(tot) - rho(B) but cannot be interpreted as the inversion of the Kohn-Sham equation. It is rather the inversion of a Kohn-Sham-like equation. The effective potential in the latter equation comprises a contaminant that might even not be unique. It is shown that the construction of the non-additive kinetic potential based on the examined relation is not applicable for such pairs.

Automated summary

This paper examines the frequently used relation in the literature regarding the non-additive kinetic potential. It investigates whether the assumption behind this relation holds for certain density pairs. The results show that the assumption is not applicable for these density pairs, implying that the method of constructing the non-additive kinetic potential is not suitable for such cases.