  We investigate two-site electronic correlations within generalized Hubbard
model, which incorporates the conventional Hubbard model (parameters: $t$
(hopping between nearest neighbours), $U$ (Coulomb repulsion (attraction))
supplemented by the intersite Coulomb interactions (parameters:
$J^{(1)}$(parallel spins), $J^{(2)}$ (antiparellel spins)) and the hopping of
the intrasite Cooper pairs (parameter: $V$). As a first step we find the
eigenvalues $E_{\alpha} $ and eigenvectors $|E_{\alpha}>$ of the dimer and we
represent each partial Hamiltonian $E_{\alpha} |E_{\alpha} > < E_{\alpha} |$
($\alpha =1,2,..,16$) in the second quantization with the use of the Hubbard
and spin operators. Each dimer energy level possesses its own Hamiltonian
describing different two-site interactions which can be active only in the case
when the level will be occupied by the electrons. A typical feature is the
appearence of two generalized $t-J$ interactions ascribed to two different
energy levels which do not vanish even for $% U=J^{(1)}=J^{(2)}=V=0$ and their
coupling constants are equal to $\pm t$ in this case. The competition between
ferromagnetism, antiferromagnetism and superconductivity (intrasite and
intersite pairings) is also a typical feature of the model because it persists
in the case $U=J^{(1)}=J^{(2)}=V=0$ and $t\neq 0$. The same types of the
electronic, competitive interactions are scattered between different energy
levels and therefore their thermodynamical activities are dependent on the
occupation of these levels. It qualitatively explains the origin of the phase
diagram of the model. We consider also a real lattice as a set of interacting
dimers to show that the competition between magnetism and superconductivity
seems to be universal for fermonic lattice models.
