For the [$Cr_2(H_2tmp)_2Cl_4$] compound, simplified models with two bridging methoxo ligands have been studied. The influence of the bridging Cr-O-Cr bond angles on the exchange coupling between metal atoms in the model compound has been analyzed by means of density functional calculations with the broken-symmetry approach. Coupling constant calculated for the full structure is in good agreement with the experimentally reported value, confirming the validity of the computational strategy used in this work to predict the exchange coupling in a family of related dinuclear Cr(III) compounds. The calculations indicate a good correlation between the calculated coupling constant and the sum of the squared energy gap of three pairs of metal $t_{2g}$ OMSOs with a limited variation of the Cr-O-Cr angle. The spin density distribution and the mechanism of magnetic coupling interactions are discussed.?