  To date, the Hubbard model and its strong coupling limit, the t-J model,
serve as the canonical model for strongly correlated electron systems in
solids. Approximating the Coulomb interaction by only the on-site term (Hubbard
U-term), however, may not be sufficient to describe the essential physics of
interacting electron systems. We develop a more complete model in which all the
next leading order terms besides the on-site term are retained. Moreover, we
discuss how the inclusion of these neglected interaction terms in the Hubbard
model changes the t-J model.
