dimer energy levels because in the large $U$ limit only these levels can be occupied. The Hamiltonian $\overline{\overline{H}}$, obtained in this way, contains many competing, magnetic, nonmagnetic and more complex interactions. Among them we can find a direct antiferromagnetic interaction generated by the term $%
\stackrel{\rightarrow }{S}_{I,1}\cdot \stackrel{\rightarrow }{S}_{I,2}$ (Heisenberg exchange interaction) multiplied by the positive coupling constant. Such a term appears in $\overline{H}_I^d$ (see (C.6) and (14)). Inside of $\overline{\overline{H}}$ (see (C.6) and (C.2) - (C.5)) a kind of ferromagnetic interactions between spins from different dimers, represented by (C.3), appears within the terms proportional to $\beta ^2$ and $\delta ^2$ (negative coupling constants). The antiferromagnetic interactions, however, appear again in terms proportional to $\beta \delta $. There are also many other magnetic, more exotic interactions, represented by (C.2), (C.4) and (C.5), entering into (C.6). The situation is, however, much more complicated when we consider the total Hamiltonian $\overline{H}$ (see (24)) in the large $U$ limit. $\overline{H}$ differs from $\overline{\overline{H}}$ by the multiplicative factor $P$ (a product of the projection operators $P_I$ (see (22) and (17)), standing on the left. Inside of each $P_I$ the mentioned antiferromagnetic interaction also appears (see (17)). In other words, the total Hamiltonian $\overline{H}$, we 