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

TL;DR

This paper analytically derives the Kohn-Sham potential for a simplified 1D diatomic molecule model with fractional occupancy, revealing how it develops barriers and plateaus during dissociation, highlighting unique scaling properties.

Contribution

It provides an exact analytical form of the Kohn-Sham potential for fractional occupancies in a model system, illustrating key features like barriers and plateaus during molecular dissociation.

Findings

Kohn-Sham potential forms a barrier at the midpoint during dissociation.

In heteronuclear cases, a plateau appears around the atom with higher ionization potential.

The potential exhibits an anomalous zero-order scaling with electron-electron interaction strength.

Abstract

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