  In contrast to the Hubbard model, the extended Hubbard model, which
additionally accounts for non-local interactions, lacks systemic studies of
thermodynamic properties especially across the metal-insulator transition.
Using a variational principle, we perform such a systematic study and describe
how non-local interactions screen local correlations differently in the
Fermi-liquid and in the insulator. The thermodynamics reveal that non-local
interactions are at least in parts responsible for first-order metal-insulator
transitions in real materials.
