The mechanisms of the magnetic coupling interactions for two trigonal-bipyramid trinuclear Cu(II) complexes Cu3(mu3-X)2(mu-pz)3X3 (X = Cl and Br, respectively) and three trigonal trinuclear Cu(II) complexes Cu3(mu3-X)(mu-pz)3Cl3 (X = Cl, Br, and O) are investigated by the calculations based on density functional theory combined with broken-symmetry approach (DFT-BS). The research on the magneto-structural correlation reveals that the magnetic coupling interaction is sensitive to the Cu-(mu3-X)-Cu angle. With the Cu-(mu3-X)-Cu angle changing from 76 to 120 degrees, the magnetic coupling interaction is switched from ferromagnetic to antiferromagnetic. According to the analysis of the molecular orbitals and the variation of the spin-state energies versus the ratio of the magnetic coupling constants, it is found that there exists spin frustration phenomenon in these complexes.
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