A non-decomposable approximation on the complete density function space for the non-additive kinetic potential

A new non-decomposable approximation of the non-additive kinetic energy potential is constructed starting from the same exact property in the limit (ρ_A → 0 and ∫ρ_B = 2), as introduced in the work of Lastra et al. [J. Chem. Phys. 129, 074107 (2008)]. In order to cover the complete function space for exponentially decaying densities, the kernel of a differential operator D_γ[ρ] is introduced and analyzed in dependence of γ. The conclusive choice of γ = 1 assures that the solution functions span the complete space of molecular electron densities. As a result, the new approximant preserves the desired feature of the older approximation, which is the reciprocal singularity if the electron density decays exponentially, and eliminates artificial shallow wells (holes), which are responsible for an artificial "charge leak." Numerical considerations using the standard validation procedure introduced by Wesolowski and Weber [Chem. Phys. Lett. 248, 71-76 (1996)] demonstrate the numerical performance of the developed approximation, which increases the range of applicability of semilocal functionals.