Secondary Kinetic Peak in the Kohn–Sham Potential and Its Connection to the Response Step

We consider a prototypical 1D model Hamiltonian for a
stretched
heteronuclear molecule and construct individual components of the
corresponding KS potential, namely, the kinetic, the N – 1, and the conditional potentials. These components show
very special features, such as peaks and steps, in regions where the
density is drastically low. Some of these features are quite well-known,
whereas others, such as a secondary peak in the kinetic potential
or a second bump in the conditional potential, are less or not known
at all. We discuss these features building on the analytical model
treated in Giarrusso et al. J. Chem. Theory Comput. 2018, 14, 4151. In particular, we provide an explanation
for the underlying mechanism which determines the appearance of both
peaks in the kinetic potential and elucidate why these peaks delineate
the region over which the plateau structure, due to the N – 1 potential, stretches. We assess the validity of the Heitler–London Ansatz at large but finite internuclear distance, showing
that, if optimal orbitals are used, this model is an excellent approximation
to the exact wave function. Notably, we find that the second natural
orbital presents an extra node very far out on the side of the more
electronegative atom.