  The Extended Hubbard Hamiltonian used by the Condensed Matter community is
nothing but a simplified version of the Pariser, Parr and Pople Hamiltonian,
well established in the Quantum Chemistry community as a powerful tool to
describe the electronic structure of {\pi}-conjugated planar Polycyclic
Aromatic Hydrocarbons (PAH). We show that whenever the interaction potential is
non-local, unphysical charge inhomogeneities may show up in finite systems,
provided that electrons are not neutralized by the ion charges. Increasing the
system size does not solve the problem when the potential has an infinite
range, and for finite range potentials these charge inhomogeneities become
slowly less important as the potential range decreases and/or the system size
increases. Dimensionality does also play a major role. Examples in
bi-dimensional systems, such as planar PAH and graphene, are discussed to some
extent.
