Non-additive kinetic potential functional V^nadfrom analytic inversion: all-electron and pseudopotential calculations

The non-additive kinetic potential functional V^nad is a key issue in density-dependent embedding methods, such as Frozen Density Embedding Theory and Partition-DFT. V^nad is a bifunctional of pairs of specific electron densities ρ_A and ρ_B. We previously reported the exact analytical inversion procedure to generate reference V^nad for weakly overlapping ρ_A and ρ_B (M. Banafsheh, T.A. Wesolowski, Int. J. Quant. Chem. 118 (2018): e25410). We discuss the constraints on the choice of electron densities to ensure their admissibility. The potential is constructed for various diatomic systems of four electrons at different interatomic distances for which the atomic densities are weakly overlapped. The results are compared to common kinetic functional approximations to assess their quality in this regime. V^nad is also presented for some diatomic systems including more than 4 electrons. We investigate the behavior around the nuclei, where cusps appear in the density, and compare results for all-electron and pseudopotential calculations. We demonstrate the application in embedding theory by solving for a subsystem with V^nad as an additional potential. In addition, the well known step structure associated with molecular dissociation is studied from the analytically inverted potential.