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 influence of the structural parameters of Cu2CO2 core on magnetic coupling is studied in model alkoxo-bridged Cu (II) dimers using the density functional method and the broken symmetry approach. The effect of the hinge distortion of the bridge and the out-of-plane displacement of alkoxo group is also analyzed. A small Cu

The synthesis, structures, and magnetic properties of four cyano-bridged MIIRuIII 2 compounds prepared from the paramagnetic RuIII building blocks, trans-[Ru(salen)(CN)2]- 1 [H2salen) N, N¢-ethylenebis(salicylideneimine)] and trans-[Ru(acac)2(CN)2]-(Hacac) acetylacetone), are described. Compound 2, {Mn(CH3OH)4[Ru(salen)(CN)2]2}‚ 6CH3OH‚2H2O, is a trinuclear complex that exhibits antiferromagnetic coupling between MnII and RuIII centers. Compound 3,{Mn(H2O)2[Ru(salen)(CN)2]2 H2O}n, has a 2-D sheetlike structure that exhibits antiferromagnetic coupling between Mn and Ru, leading to ferrimagnetic-like behavior. Compound 4,{Ni(cyclam)[Ru(acac)2(CN)2]2}‚ 2CH3OH‚2H2O (cyclam ) 1,4,8,11-tetraazacyclotetradecane), is a trinuclear complex that exhibits ferromagnetic coupling. Compound 5,{Co[Ru(acac)2(CN)2]2}n, has a 3-D diamond-like interpenetrating network that exhibits ferromagnetic ordering below 4.6 K. The density functional theory (DFT) method was used to calculate the molecular magnetic orbitals and the magnetic exchange interaction between RuIII and MII (MnII, NiII) ions.

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.

The effect of magnetic exchange, double exchange, vibronic coupling, and asymmetry on magnetic properties of d2-d3 systems is discussed. The temperaturedependent magnetic moment was calculated with the semiclassical adiabatic approach. The results show that the vibronic coupling from the out-of-phase breathing vibration on the metal sites (Piepho, Krausz, and Schatz [PKS] model) and the vibronic coupling from the stretching vibration between the metal sites (P model) favor the localization and delocalization of the "extra" electron in mixed-valence dimers, respectively. The magnetic properties are determined by the interplay among magnetic exchange, double exchange, and vibronic coupling. The results obtained by analyzing d2-d3 systems can be generalized to other full delocalized dinuclear mixed valence systems with a unique transferable electron.