The Hubbard model is a useful approximation for particles in a periodic potential at sufficiently low temperatures, where all the particles may be assumed to be in the lowest Bloch band, and long-range interactions between the particles can be ignored. If interactions between particles at different sites of the lattice are included, the model is often referred to as the "extended Hubbard model". In particular, the Hubbard term, most commonly denoted by U, is applied in first principles based simulations using Density Functional Theory, DFT. The inclusion of the Hubbard term in DFT simulations is important as this improves the prediction of electron localisation and thus it prevents the incorrect prediction of metallic conduction in insulating systems.