The magnetic exchange behaviour for l-hydroxo and l-acetato double-bridged chromium (III) dimer is investigated based on calculations of density functional theory combined with the broken-symmetry approach. It is demonstrated that there is a magnetic exchange cooperative effect of the two bridging ligands in a double-bridged dimer systems with approximate equal coupling intensity. Meanwhile, the calculated results reveal that the deprotonation of the l-hydroxo ligand causes a sharp increase of the magnetic exchange interaction between the chromium centers. Replacing either the l-hydroxo bridging ligand by one water bridging ligand or the l-acetato bridging ligands by two terminal water ligands produces a relatively reasonable model to examine the contribution on the magnetic exchange interaction of another individual bridging ligand.

In order to theoretically study on the magnetic coupling interaction in the Mn-Mn dimer, quantum chemical calculations on the equilibrium Mn-Mn distance Re, total energy ET, binding energies Be and exchange interaction energies EðSÞ under dierent spin multiplets were performed at CASPT2 level of theory. It is found that the calculated Re, ET, and Be values are correlated with the spin multiplet, and with increasing the total spin S, Re increases, but ET and Be exhibit a decrease trend. The exchange interaction energies EðSÞ "deviate significantly from the Lande interval rule". This unusual magnetic phenomenon is primarily attributed to the biquadratic jðSa SbÞ2 term contribution in spin Hamiltonian for the Mn-Mn dimer.