Abstract: On the basis of classifying mixed-valence compounds, the dimer coupling model was extended to trinuclear magnetic coupling systems. Particular emphasis is placed on the well-localized and well-delocalized mixed-valence compounds. As a representative example, the electronic structure for well-localized and well-delocalized [Mn₃O(O₂CH)₆L₃]^z+(L=pyridine; z=0) model compounds were calculated via density functional theory, obtained the magnetic coupling constants J compared with experimental data. It is found that the density functional theory combined with broken symmetry approach can be applied to trinuclear mixed-valence systems considered. For well-delocalized mixed-valence Mn₃^Ⅱ,Ⅲ,Ⅲ system, the delocalization effect of the extra-electron on the magnetic coupling interaction must be considered, and thus the double exchange parameter B should be included in its Hamiltonian. For comparison the magnetic properties of the equivalence trinuclear [Mn₃O(O₂CH)₆L₃]^z+(L=pyridine; z=1) were also calculated.

Key words: Molecular magnetism, Mixed-valence, Trinuclear manganese, Density functional theory, Broken symmetry