  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 J. Chem.
Theory Comput. 14, 4151 (2018). 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 wavefunction. Notably, we find that the
second natural orbital presents an extra node very far out on the side of the
more electronegative atom.
