Magnetic coupling constants J for the complete structures of heterobinuclear compounds GdCu (OTf) 3 (bdmap)2-(H2O)‚THF (1,GdIIICuII),[Gd(C4H7ON)4(H2O)3][Fe(CN)6]‚ 2H2O (2,GdIIIFeIII), and [Gd(C4H7ON) 4 (H2O)3]-[Cr(CN)6]‚2H2O (3,GdIIICrIII) have been calculated by the combination of the broken-symmetry approach with the spin project method under the DFT framework. The calculated J values (3.6 (1), 8.1 (2), and 20.3 cm-1 (3)) conform well to that of experimental findings (2.9 (2)(1), 0.74 (3)(2), and 0.40(2)cm-1 (3)) with a small difference in absolute value. The compounds 1-3, whose J values are all positive, show ferromagnetic couplings between two metal centers; thus, their ground states are all in high-spin states. The spin density distributions are discussed in detail on the basis of Mulliken population analysis, taking into account the coexistence of spin delocalization and spin polarization mechanisms. For 1, the spin distribution in the ground state may be understood as a result of the competition between two mechanisms: a spin delocalization from Cu (II) and a spin polarization of GdIII, and the former is dominant. In the cases of 2 and 3, both transition metal (FeIII or CrIII) and rare earth GdIII display a spin polarization effect on the surrounding atoms, where a counteraction of the opposite polarization effects leads a low spin density on the bridging ligand C1N1. In the ground state of 3, the stronger polarization effect of Cr (III) even causes the positive spin density on the adjacent bridging atom N1, different from the situation in 2.

The calculations on magnetic exchange interaction of Cl3FeOFeCl3 2- and the related modeling compounds were performed by using the density functional theory coupling the broken symmetry approach. The calculated results show the absence of a direct Cl3Fe-FeCl3 magnetic coupling and the effect of the terminal Cl ligands on magnetic exchange interaction in [Fe-O-Fe]4+, while the protonation of

The theoretical calculations on magnetic exchange of the title complex are carried out by using multiconfigurational second-order perturbation theory, CASPT2, and density functional theory combined with broken-symmetry approach, DFT-BS. The CASPT2 calculated quartet ground state, stabilized by 8.02 cm1 compared with the nearest excited doublet state, is close to 5cm 1 of the experimental measurement. The dependence of energy levels on the ratio J23/J12,13 validates occurrence of the spin frustration phenomenon. Both CASPT2 and DFT-BS calculations reproduce well experimentally coupling constants of J12, 13=9.35cm 1, J23=3.95cm 1, for CASPT2 J12, 13=6cm 1, J23=2cm 1 and for DFT-BS J12, 13=11.31cm 1, J23=4.20m 1. The methodological comparison is briefly discussed.

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.

The ferromagnetic coupling behavior in oxo-bridged bis (bis(cyclopentadienyl) titanium (III)) complex (Cp2Ti)2-(Ì-O) is investigated on the basis of calculations of density functional theory combined with the brokensymmetry approach. The magnetic coupling constants calculated for the experimental and optimized geometries are 11.41 and 1.29cm-1, respectively, comparable with the experimentally measured J value (8.3 cm-1). The calculated results show that the magnetic coupling constant J slightly decreases with the increase of the Ti-(Ì-O)-Ti angle and decreases exponentially with the increase of the Ti-(Ì-O) distance. In variation of the dihedral angle‚ between the two Cp2Ti fragments the transition of the magnetic coupling property occurs near B=45°ForB>45°, the coupling is ferromagnetic, and it is antiferromagnetic forB<45°. The ferromagnetic coupling interaction between the magnetic centers is almost not affected by the protonation of the oxo-bridge ligand. Molecular orbital analysis reveals that, because of the nonbonding character and electronic location character of the single-occupied molecular orbitals (SOMO), there is no antiferromagnetic coupling pathway through superexchange via the bridging atom. However, when‚ varies from 90° to 0°, the throughspace interaction between the two magnetic centers in the SOMOs occurs, leading to a gradually increscent antiferromagnetic contribution, JAF. As soon as the antiferromagnetic contribution exceeds the ferromagnetic contribution, JF, the transition of the magnetic coupling properties for the molecule occurs. The spin population analysis is briefly discussed.