RESUMEN

The first nickel(ii) complex with the heteroscorpionate-like bridging ligand DIMMAL (2-di1H-2-imidazolylmethylmalonate), [Ni(DIMMAL)(H2O)3]n·3nH2O (1), is a one-dimensional coordination polymer whose structure shows regular Ni(ii) chains with H-bonding inter-chain interactions and a rare example of a Quadruple Imidazolyl Embrace (QIE). The Ni(ii) chain shows a weak antiferromagnetic interaction that can be modelled with a regular S = 1 chain model including a zero field splitting with g = 2.270, J = -1.5 cm(-1) and D = -2.26 cm(-1).

RESUMEN

We present a FORTRAN code based on a new powerful and efficient computational approach to solve the double exchange problem for high-nuclearity MV clusters containing arbitrary number of localized spins and itinerant electrons. We also report some examples in order to show the possibilities of the program.

RESUMEN

A general approach to the problem of electron delocalization in the high-nuclearity mixed-valence (MV) clusters containing an arbitrary number of localized spins and itinerant electrons is developed. Along with the double exchange, we consider the isotropic magnetic exchange between the localized electrons as well as the Coulomb intercenter repulsion. As distinguished from the previous approaches dealing with the MV systems in which itinerant electrons are delocalized over all constituent metal sites, here, we consider a more common case of systems exhibiting partial delocalization and containing several delocalized domains. Taking full advantage of the powerful angular momentum technique, we were able to derive closed form analytical expressions for the matrix elements of the full Hamiltonian. These expressions provide an efficient tool for treating complex mixed-valence systems, because they contain only products of 6j-symbols (that appear while treating the delocalized parts) and 9j-symbols (exchange interactions in localized parts) and do not contain high-order recoupling coefficients and 3j-symbols that essentially constrained all previous theories of mixed valency. The approach developed here is accompanied by an efficient computational procedure that allows us to calculate the bulk thermodynamic properties (magnetic susceptibility, magnetization, and magnetic specific heat) of high-nuclearity MV clusters. Finally, this approach has been used to discuss the magnetic properties of the octanuclear MV cluster [Fe(8)(mu(4)-O)(4)(4-Cl-pz)(12)Cl(4)](-) and the diphthalocyanine chains [YPc(2)].CH(2)Cl(2) and [ScPc(2)].CH(2)Cl(2) composed of MV dimers interacting through the magnetic exchange and Coulomb repulsion.

Asunto(s)

RESUMEN

The ground-state properties of the pentameric Co(II) cluster [Co(3)W(D(2)O)(2)(CoW(9)O(34))(2)](12-) were investigated by combining magnetic susceptibility and low-temperature magnetization measurements with a detailed inelastic neutron scattering (INS) study on a fully deuterated polycrystalline sample of Na(12)[Co(3)W(D(2)O)(2)(CoW(9)O(34))(2)].46D(2)O. The encapsulated magnetic Co(5) unit consists of three octahedral and two tetrahedral oxo-coordinated Co(II) ions. Thus, two different types of exchange interactions are present within this cluster: a ferromagnetic interaction between the octahedral Co(II) ions and an antiferromagnetic interaction between the octahedral and the tetrahedral Co(II) ions. As a result of the single-ion anisotropy of the octahedral Co(II) ions, the appropriate exchange Hamiltonian to describe the ground-state properties of the Co(5) spin cluster is anisotropic and is expressed as H = -2 summation operator(i= x,y,z)J(1)(i)[S(1)(i)S(2)(i) + S(2)(i)S(3)(i)] + J(2)(i)[S(1)(i)S(5)(i) + S(2)(i)S(5)(i) + S(2)(i)S(6)(i) + S(3)(i)S(6)(i)], where J(1)(i) are the components of the exchange interaction between the octahedral Co(II) ions and J(2)(i) are the components of the exchange interaction between the octahedral and tetrahedral Co(II) ions (see Figure 1d). The study of the exchange interactions in the two structurally related polyoxoanions [Co(4)(H(2)O)(2)(PW(9)O(34))(2)](10)(-) and [Co(3)W(H(2)O)(2)(ZnW(9)O(34))(2)](12)(-) allowed an independent determination of the ferromagnetic exchange parameters J(1)(x) = 0.70 meV, J(1)(y) = 0.43 meV, and J(1)(z) = 1.51 meV (set a) and J(1)(x) = 1.16 meV, J(1)(y) = 1.16 meV and J(1)(z) = 1.73 meV (set b), respectively. Our analysis proved to be much more sensitive to the size and anisotropy of the antiferromagnetic exchange interaction J(2). We demonstrate that this exchange interaction exhibits a rhombic anisotropy with exchange parameters J(2)(x) = -1.24 meV, J(2)(y) = -0.53 meV, and J(2)(z) = -1.44 meV (set a) or J(1)(x) = -1.19 meV, J(1)(y) = -0.53 meV, and J(1)(z) = -1.44 meV (set b). The two parameter sets reproduce in a satisfactory manner the susceptibility, magnetization, and INS properties of the title compound.

RESUMEN

A general solution of the exchange problem in the high-nuclearity spin clusters (HNSC) containing arbitrary number of exchange-coupled centers and topology is developed. All constituent magnetic centers are supposed to possess well-isolated orbitally non-degenerate ground states so that the isotropic Heisenberg-Dirac-Van Vleck (HDVV) term is the leading part of the exchange spin Hamiltonian. Along with the HDVV term, we consider higher-order isotropic exchange terms (biquadratic exchange), as well as the anisotropic terms (anisotropic and antisymmetric exchange interactions and local single-ion anisotropies). All these terms are expressed as irreducible tensor operators (ITO). This allows us to take full advantage of the spin symmetry of the system. At the same time, we have also benefitted by taking into account the point group symmetry of the cluster, which allows us to work with symmetrized spin functions. This results in an additional reduction of the matrices to diagonalize. The approach developed here is accompanied by an efficient computational procedure that allows us to calculate the bulk magnetic properties (magnetic susceptibility, magnetization, and magnetic specific heat) as well as the spectroscopic properties of HNSC. Special attention is paid to calculate the magnetic excitations observed by inelastic neutron scattering (INS), their intensities, and their Q and temperature dependencies. This spectroscopic technique provides direct access to the energies and wave functions of the different spin states of the cluster; thus, it can be applied to spin clusters in order to obtain deep and detailed information on the nature of the magnetic exchange phenomenon. The general expression for the INS cross-section of spin clusters interacting by all kinds of exchange interactions, including also the single-ion zero-field splitting term, is derived for the first time. A closed-form expression is also derived for the particular case in which only the isotropic exchange interactions are involved. Finally this approach has been used to model the magnetic properties as well as the INS spectra of the polyoxometalate anion [Ni(9)(OH)(3)(H(2)O)(6)(HPO(4))(2)(PW(9)O(34))(3)](16)(-), which contains a central magnetic cluster formed by nine exchange-coupled Ni(II) ions surrounded by diamagnetic phosphotungstate ligands (PW(9)O(34))(9)(-).