The geometry structure, dissociation energy, vibrational frequencies, and low-lying spin-state energy spectrum of Mn2+ are investigated by using ab initio CASSCF/ECP10MDF, complete active space self-consistent field/atomic natural orbital basis sets CASSCF/ANO-s, CASPT2/ECP10MDF, and second-order perturbation theory with CASSCF reference function/atomic natural orbital basis sets CASPT2/ANO-s levels of theory. For the ground state the dissociation energy of 1.397 eV calculated at the CASPT2/ANO-s level supports Jarrlod's experimental value of 1.39 eV. The equilibrium bond length and vibrational frequency are 2.940 Å calculated at the CASPT2/ANO-s level of theory and 214.4cm−1 calculated at the CASSCF/ANO-s level of theory, respectively. On the basis of the mixed-valence model, the Heisenberg exchange constant J−71.2cm−1 and the double-exchange constant B 647.7cm−1 are extracted explicitly from the low-lying energy spectrum calculated at the higher levels of theory. The magnetic competition between the weaker Heisenberg exchange interactions and the stronger double-exchange interactions makes the ground state a 12g+ state, consistent with electron paramagnetic resonance experimental observation, which explains unusual magnetic properties of Mn2+, quite different from the antiferromagnetic ground state of Mn2 and Cr2. On the other hand, the results calculated at the higher levels of theory show the consistent antiferromagnetic Heisenberg exchange interactions between 3d−3d for Cr2, Mn2+, and Mn2.

Magnetic exchange interaction for the μ-hydroxo bridged vanadium (IV) dimers is investigated based on calculations of density functional theory combined with the broken-symmetry approach. It is found that there is an exponential correlation between the V-O (hydroxo)-V angle, the V-O (hydroxo) distance and the exchange coupling constants J. Meanwhile, the calculated results reveal that the deprotonation of the bridging hydroxo ligand causes a sharp increase of the exchange coupling interaction, but the magnetic coupling constant J is insensitive to the deprotonation of the bridging aquo ligand. Moreover, simplifying each 1,2-bridging squarate ligand with two OCH2 groups almost does not influence magnetic exchange behavior between the two vanadium (IV) ions, and the principle of the shortest superex-change pathway is available for the multiplicity of the bridging ligand in the μ-hydroxo bridged vanadium (IV) di-mers.

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 construction of low-dimensional coordination polymers has received intense attention for a long time because of their structural diversity and unusual properties as well as their magneto-structural correlations.[1] Among them, some onedimensional (1D) expanded chains with exotic topologies have been reported, such as ladders,[2] ropes,[3] and clusterbased chains.[4] They provide an intermediate step from 1D chains towards 2Dnetworks, thus potentially helping the magnetic behavior at the border of 1Dto 2Dsystems to be understood. As a versatile bridging ligand, the azido ion could link two or more metal ions in various modes, for example, m-1,1 (end-on (EO)), m-1,3 (end-to-end (EE)), m-1,1,1, m-1,1,3, and so forth, thus giving rise to a variety of zero-to threedimensional polynuclear complexes.[5-9] As far as 1Dchains are concerned, many unusual alternating chains with different combinations of these modes have been obtained.[7,8]

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