  We present a model of equal spin $s_1$ dimer single molecule magnets. The
spins within each dimer interact via the Heisenberg and the most general set of
four quadratic anisotropic spin interactions with respective strengths $J$ and
$\{J_j\}$, and with the magnetic induction ${\bf B}$. We solve the model
exactly for $s_1=1/2, 1, 5/2$, and for antiferromagnetic Heisenberg couplings
($J<0$), present ${\bf M}({\bf B})$ curves at low $T$ for these cases. Low-$T$
$C_V({\bf B})$ curves for $s_1=1/2$ and electron paramagnetic susceptibility
$\chi({\bf B},\omega)$ for $s_1=1$ are also provided. For weak anisotropy
interactions, we employ a perturbative treatment, and show that the Hartree and
extended Hartree approximations lead to reliable analytic results at low $T$
and large $B$ for these quantities and for the inelastic neutron scattering
cross-section $S({\bf B}, {\bf q},\omega)$. Our results are discussed with
regard to existing ${\bf M}({\bf B})$ experiments on $s_1=5/2$ Fe$_2$ dimer
single molecule magnets, and suggest that one of them contains a substantial
amount of single-ion anisotropy, without any sizeable global spin anisotropy.
We urge further experiments of the above types on single crystals of Fe$_2$ and
on some $s_=9/2$ [Mn$_4$]$_2$ dimers, in order to elucidate the precise values
of the various microscopic interactions.
