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Using a simplified one-dimensional model of a diatomic molecule, theassociated interacting density and corresponding Kohn-Sham potential have beenobtained analytically for all fractional molecule occupancies $N$ between 0 and2. For the homonuclear case, and in the dissociation limit, the exact Kohn-Shampotential builds a barrier at the midpoint between the two atoms, whosestrength increases linearly with $N$, with $1 < N \leq 2$. In the heteronuclearcase, the disociating KS potential besides the barrier also exhibits a plateauaround the atom with the higher ionization potential, whose size (but not itsstrength) depends on $N$. An anomalous zero-order scaling of the Kohn-Shampotential with regards to the strength of the electron-electron repulsion isclearly displayed by our model; without this property both the unusual barrierand plateau features will be absent.

Kohn-Sham potential for a strongly correlated finite system with fractional occupancy