The structural dependence of the singlet-triplet splitting in doubly bridged copper (II) dimers is evaluated by means of a variational CI procedure based on the theory of effective Hamiltonians which includes all the differential second order contributions. The influence of out-of-plane distortions - in twisted, folded and bifolded geometries - has been studied in [Cu2Cl6](2-) and [Cu2Br6](2-) anions. The in-plane distortion of the bridge angle has also been analyzed in the model compounds[Cu(NH3)(2)OH](2+)(2) and [CuCl2OH](2-)(2) . The sign and the magnitude of the gap are in agreement with experimental trends.