  A combined theoretical and experimental study of the natural Cu(2+)-mineral
callaghanite is presented. Its crystal structure features well separated
Cu$_2$(OH)$_6$ structural dimers with weakly bonded carbonate groups and water
molecules in between. Susceptibility, field-dependent magnetization and
specific heat measurements reveal a compound with a small spin gap of about 7
K. The observed magnetic properties are well described by a model of isolated
antiferromagnetic spin dimers. Possible ferromagnetic interactions between the
dimers amount to -1.5 K, at most. Different flavors of electronic structure
calculations have been employed to locate the magnetic dimers in the crystal
structure, i.e., to determine whether they coincide with the structural dimers
or not. Calculations of the coupling between the structural dimers clearly show
that magnetic and structural dimers are the same. For the intradimer coupling,
however, the computational results confirmed a coupling strength close to zero
but the sign of the coupling could not be determined unambiguously. Based on
this finding, we then discuss how the reliability of the numerical methods
depends on the characteristics of exchange pathways and on structural features
of the compound in general. Eventually, we try to provide a minimum coupling
strength that is needed for a reliable computational description.
