Inter-site Coulomb interaction and Heisenberg exchange
  Based on exact diagonalization results for small clusters we discuss the effect of inter-site Coulomb repulsion in Mott-Hubbard or charge transfer insulators. Whereas the exchange constant J for direct exchange is substantially enhanced by inter-site Coulomb interaction, that for superexchange is suppressed. The enhancement of J in the single-band models holds up to the critical value for the charge density wave (CDW) instability, thus opening the way for large values of J. Single-band Hubbard models with sufficiently strong inter-site repulsion to be near a CDW instability thus may provide `physical' realizations of t-J like models with the `unphysical' parameter ratio J/t=1. 
R. Eder, J. van den Brink, and G. A. Sawatzky