UC Merced

The non-additive kinetic potential functional is a key element in density-dependent embedding methods. The correspondence between the ground-state density and the total effective Kohn-Sham potential provides the basis for various methods to construct the non-additive kinetic potential for any pair of electron densities. Several research groups used numerical or analytical inversion procedures to explore this strategy which overcomes the failures of known explicit density functional approximations. The numerical inversions, however, apply additional approximations/simplifications. The relations known for the exact quantities cannot be assumed to hold for quantitiesobtained in numerical inversions. The exact relations are discussed with special emphasis on such issues as: the admissibility of the densities for which the potential is constructed, the choice of densities to be used as independent variables, self-consistency between the potentials and observables calculated using the embedded wavefunction, and so forth. The thesis focuses on how these issues are treated in practice. The inverted potentials are calculated for weakly overlapping pairs of electron densities – the case not studied previously.

The behaviour of Vnad at the vicinity of the nuclei has been questioned since the beginning. Available computational tools and methods in the past led to a cusp at nuclei in Vnad calculations. I analysed existence and non-existence properties of the cusp in Vnad analytically, and compare against nuclear cusps condition for the ground-state density and resulting cusp in the Kohn-Sham potential. I showed the agreement of numerical calculations with this fact for various diatomic model systems of two and four electrons. The results are compared to the von Weizsäcker functional (exact for one orbital) and other kinetic energy functionals.

In addition, I found that the well-known step structure of Vxc associated with molecular dissociation also appears in Vnad, even in local and semi-local functionals in the region where the two subsystems' densities weakly overlap.