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The Extended Hubbard Hamiltonian used by the Condensed Matter community isnothing but a simplified version of the Pariser, Parr and Pople Hamiltonian,well established in the Quantum Chemistry community as a powerful tool todescribe the electronic structure of {\pi}-conjugated planar PolycyclicAromatic Hydrocarbons (PAH). We show that whenever the interaction potential isnon-local, unphysical charge inhomogeneities may show up in finite systems,provided that electrons are not neutralized by the ion charges. Increasing thesystem size does not solve the problem when the potential has an infiniterange, and for finite range potentials these charge inhomogeneities becomeslowly less important as the potential range decreases and/or the system sizeincreases. Dimensionality does also play a major role. Examples inbi-dimensional systems, such as planar PAH and graphene, are discussed to someextent.

Coulomb interaction and charge neutrality: Pariser, Parr and Pople Hamiltonian versus the Extended Hubbard Hamiltonian