Insight Into The Spin-Vibronic Problem of a Mixed Valence Magnetic Molecular Cell for Quantum Cellular Automata.

The effects of the vibronic coupling in quantum cellular automata (QCA) based on the square planar mixed valence (MV) molecular cells comprising four paramagnetic centers (spin cores) and two excess mobile electrons are analyzed in the important particular case when the Coulomb energy gap between the ground antipodal diagonal-type two-electron configurations and the excited side-type configurations considerably exceeds both the one-electron transfer parameter (strong U-limit) and the vibronic stabilization energy. Under such conditions the developed model involves the second-order double exchange, the Heisenberg-Dirac-Van Vleck (HDVV) exchange and the vibronic coupling of the excess electrons with the molecular B1g -vibration composed of four full-symmetric local vibrations. The latter interaction is shown to significant amplify the ability of the electric field produced by the driver-cell to polarize the excess electrons in the working cell, which can be termed "the effect of the vibronic enhancement of the cell-cell interaction". This effect leads to a redetermination of the conditions for switching between different spin-states, as well as to a significant change in the shapes of the cell-cell response functions. The obtained results demonstrate the importance of the vibronic coupling in all aspects (such as description of a free cell and cell-cell response) of the theory of molecular QCA based on MV clusters.

Insertion of single-ion magnets based on mononuclear Co(II) complexes into ferromagnetic oxalate-based networks.

The 1 : 2 and 1 : 1 Co(ii) complexes of the L ligand (L = 6-(3,5-diamino-2,4,6-triazinyl)2,2'-bipyridine) with formulas [CoII(L)2](ClO4)2·0.5MeCN·Et2O (1) and [CoII(L)(CH3CN)2(H2O)](ClO4)2·MeCN (2) have been prepared. The structural and magnetic characterization of the two compounds shows that they contain octahedral high-spin Co(ii) and present a field-induced slow relaxation of the magnetization. 1 has been inserted into a bimetallic oxalate-based network leading to a novel achiral 3D compound of formula [CoII(L)2][MnIICrIII(ox)3]2·(solvate) (3) exhibiting ferromagnetic ordering below 4.6 K. EPR measurements suggest a weak magnetic coupling between the two sublattices.

Photomagnetic properties of an Fe(ii) spin-crossover complex of 6-(3,5-diamino-2,4,6-triazinyl)-2,2'-bipyridine and its insertion into 2D and 3D bimetallic oxalate-based networks.

The Fe(ii) complex of the L1 ligand (L1 = 6-(3,5-diamino-2,4,6-triazinyl)-2,2'-bipyridine) has been used as a templating cation for the growth of oxalate-based networks. The magnetic characterization of the [FeII(L1)2](ClO4)2·CH3CN (1) precursor in the solid state has been performed for the first time showing that the low-spin (LS) state is predominating from 2 to 400 K with 10% of Fe(ii), which undergoes a gradual and irreversible spin-crossover above 350 K. 1 presents the LIESST effect with a photo-conversion close to 25% and a T(LIESST) of 49 K. During the preparation of 1, a secondary product of the formula [FeII(L1)(CH3CN)2(H2O)](ClO4)2·CH3CN (2) has been obtained. The magnetic characterization of 2 shows that it contains high-spin (HS) Fe(ii). 1 has afforded two novel oxalate-based compounds, the 2D compound of the formula [FeII(L1)2][MnIICrIII(ox)3]2·(CH3NO2)6·(CH3OH)·(H2O)2 (3) and the 3D compound of the formula [FeII(L1)2][MnIICrIII(ox)3]2·(CH3CN)3 (4), which have been obtained by changing the synthetic conditions. The magnetic properties show that in 3 the inserted Fe(ii) cation remains in the LS state from 2 to 340 K and presents a partial and irreversible spin-crossover of ∼20% at higher temperatures. In 4, most of the Fe(ii) complexes remain in the LS state from 2 to 230 K and present a partial and irreversible spin-crossover of ∼50% from 230 to 400 K. 3 and 4 do not present the LIESST effect.

Localization-Delocalization in Bridged Mixed-Valence Metal Clusters: Vibronic PKS Model Revisited.

Here we describe a new vibronic model of mixed valence (MV) dimer inspired by the conventional Piepho, Krausz, and Schatz (PKS) approach. We attempted to partially lift the main restriction of the PKS model dealing with the vibronically independent moieties of a MV molecule. The refined version of the PKS model in which the bridging ligands are included deals with the three main interactions: electron transfer (integral t0) related to the high-symmetric ligand configuration, on-site vibronic coupling (parameter υ) arising from the modulation of the crystal field on the metal sites by the breathing displacements of their nearest ligand surroundings, and intercenter vibronic coupling (parameter ζ) describing the dependence of the electron transfer on ligand positions in the course of their breathing movement. We apply the modified model to the analysis of the adiabatic potentials and electronic density distributions in the minima of their lower sheets for the cases of one-electron MV dimer with long and short bridges and for the two-electron MV dimer exhibiting a valence disproportionation effect. The inclusion of the intercenter interaction in addition to the conventional PKS coupling is shown to produce a strong effect on the degree of localization in MV dimers and, in particular, on the assignments to the Robin and Day classes and on the conditions of stabilization of valence disproportionated states in bielectron transfer systems.

Gd-based single-ion magnets with tunable magnetic anisotropy: molecular design of spin qubits.

We report ac susceptibility and continuous wave and pulsed EPR experiments performed on GdW10 and GdW30 polyoxometalate clusters, in which a Gd3+ ion is coordinated to different polyoxometalate moieties. Despite the isotropic character of gadolinium as a free ion, these molecules show slow magnetic relaxation at very low temperatures, characteristic of single molecule magnets. For T≲200 mK, the spin-lattice relaxation becomes dominated by pure quantum tunneling events, with rates that agree quantitatively with those predicted by the Prokof'ev and Stamp model [Phys. Rev. Lett. 80, 5794 (1998)]. The sign of the magnetic anisotropy, the energy level splittings, and the tunneling rates strongly depend on the molecular structure. We argue that GdW30 molecules are also promising spin qubits with a coherence figure of merit Q(M)≳50.

Lanthanoid single-ion magnets based on polyoxometalates with a 5-fold symmetry: the series [LnP5W30O110]12- (Ln3+ = Tb, Dy, Ho, Er, Tm, and Yb).

A robust, stable and processable family of mononuclear lanthanoid complexes based on polyoxometalates (POMs) that exhibit single-molecule magnetic behavior is described here. Preyssler polyanions of general formula [LnP(5)W(30)O(110)](12-) (Ln(3+) = Tb, Dy, Ho, Er, Tm, and Yb) have been characterized with static and dynamic magnetic measurements and heat capacity experiments. For the Dy and Ho derivatives, slow relaxation of the magnetization has been found. A simple interpretation of these properties is achieved by using crystal field theory.

Role of orbital degeneracy in the single molecule magnet behavior of a mononuclear high-spin Fe(II) complex.

To explain the single-molecule magnet behavior of the mononuclear complex [(tpaMes)Fe](-) we have developed a model that takes into account the trigonal ligand field splitting of the atomic (5)D term of the Fe(II) ion, and the spin-orbital splitting and mixing of the ligand field terms. The ground ligand field term is shown to be the orbital doublet (5)E possessing an unquenched orbital angular momentum. We demonstrate that the splitting of this term cannot be described by the conventional zero-field splitting Hamiltonian proving thus the irrelevance of the spin-Hamiltonian formalism in the present case. The first-order orbital angular momentum is shown to lead to the strong magnetic anisotropy with the trigonal axis being the easy axis of the magnetization.

MVPACK: a package to calculate energy levels and magnetic properties of high nuclearity mixed valence clusters.

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.

High-nuclearity mixed-valence clusters and mixed-valence chains: general approach to the calculation of the energy levels and bulk magnetic properties.

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.

Magnetic polyoxometalates: anisotropic antiferro- and ferromagnetic exchange interactions in the pentameric cobalt(II) cluster.

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.

Bimetallic cyanide-bridged complexes based on the photochromic nitroprusside anion and paramagnetic metal complexes. Syntheses, structures, and physical characterization of the coordination compounds [Ni(en)2]4[Fe(CN)5NO]2[Fe(CN)6]x5H2O, [Ni(en)2][Fe(CN)5NO]x3H2O, [Mn(3-MeOsalen)(H2O)]2[Fe(CN)5NO], and [Mn(5-Brsalen)]2[Fe(CN)5NO].

The synthesis, crystal structure, and physical characterization of the coordination compounds [Ni(en)2]4[Fe(CN)5NO]2[Fe(CN)6]x5H2O (1), [Ni(en)2][Fe(CN)5NO]x3H2O (2), [Mn(3-MeOsalen)(H2O)]2[Fe(CN)5NO] (3), and [Mn(5-Brsalen)]2[Fe(CN)5NO] (4) are presented. 1 crystallizes in the monoclinic space group P2(1)/n (a = 7.407(4) A, b = 28.963(6) A, c = 14.744(5) A, alpha = 90 degrees, beta = 103.26(4) degrees, gamma = 90 degrees, Z = 2). Its structure consists of branched linear chains formed by cis-[Ni(en)2]2+ cations and ferrocyanide and nitroprusside anions. The presence of two kinds of iron(II) sites has been demonstrated by Mössbauer spectroscopy. 2 crystallizes in the monoclinic space group P2(1)/c (a = 11.076(3) A, b = 10.983(2) A, c = 17.018(5) A, alpha = 90 degrees, beta = 107.25(2) degrees, gamma = 90 degrees, Z = 4). Its structure consists of zigzag chains formed by an alternated array of cis-[Ni(en)2]2+ cations and nitroprusside anions. 3 crystallizes in the triclinic space group P1 (a = 8.896(5) A, b = 10.430(5) A, c = 12.699(5) A, alpha = 71.110(5) degrees, beta = 79.990(5) degrees, gamma = 89.470(5) degrees, Z = 1). Its structure comprises neutral trinuclear bimetallic complexes in which a central [Fe(CN)5NO]2- anion is linked to two [Mn(3-MeOsalen)]+ cations. 4 crystallizes in the tetragonal space group P4/ncc (a = 13.630(5) A, c = 21.420(8) A, Z = 4). Its structure shows an extended 2D neutral network formed by cyclic octameric [-Mn-NC-Fe-CN-]4 units. The magnetic properties of these compounds indicate the presence of quasi-isolated paramagnetic Ni2+ and Mn3+. Irradiated samples of the four compounds have been studied by differential scanning calorimetry to detect the existence of the long-lived metastable states of nitroprusside.

Heptanuclear hydroxo-bridged copper cluster of the dicubane-like type: structural and magnetic characterizations of [Cu7(OH)6Cl2(pn)6(H2O)2](C(CN)3)4Cl2 (pn = 1,3-diaminopropane).

A new polynuclear copper(II) complex [Cu7(OH)6Cl2(pn)6(H2O)2](C(CN)3)4Cl2 with hydroxo-bridging ligands has been prepared; the centrosymmetric cluster cation can be described as two Cu4O3Cl distorted cubane units sharing one copper cation.

Synthesis, structure, and magnetic properties of the low-symmetry tetranuclear cubane-like nickel complex [Ni4(pypentO)(pym)(mu 3-OH)2(mu- Oac)2(NCS)2(OH2)].

The tetranuclear [Ni4(pypentO)(pym)(mu 3-OH)2(mu-Oac)2(NCS)2(OH2)] cubane-like complex has been prepared, and its structure and magnetic properties have been studied (pypentO and pym are the deprotonated forms of 1,5-bis[(2-pyridylmethyl)amino]pentane-3-ol and 2-pyridylmethanol, respectively). The X-ray diffraction analysis of this novel nickel complex (C61H74N14O25.5S4Ni8, monoclinic, P2(1), a = 13.9375(14) A, b = 20.6604(18) A, c = 16.6684(19) A, beta = 110.619(12) degrees, Z = 2) showed a Ni4O4 cubane arrangement of four nickel atoms, four mu 3-O bridging ligands (one pypentO, one pym, and two OH-), two syn-syn bridging acetates, and three terminal monodentate ligands (two NCS- and one OH2). In this low-symmetry elongated cubane, the four Ni-Ni long distances (3.18 A) correspond to the faces of the cube including two mu 3-OR bridges, and the two Ni-Ni short distances (2.94 A) correspond to the faces including two mu 3-OR and one acetate bridges. The temperature dependence of the magnetic susceptibility was fitted with J1 = -3.09 cm-1, J2 = 15.0 cm-1, J3 = 6.72 cm-1, and g = 2.27. The differences in sign among the J1, J2, and J3 superexchange interactions is in good agreement with the different types of faces present in this Ni4O4 cubane core. The two faces of the cube, including two mu 3-OR bridges associated with one acetate bridge, exhibit ferromagnetic interactions, while the four faces which include only mu 3-OR bridges exhibit antiferromagnetic interactions. The very small zero field splitting may be attributed to the fact that the ground state is diamagnetic. The nature of the ground state is confirmed by the good simulation of the magnetization curves at 2 and 5 K (diagonalization of the full matrix taking into account all energy levels obtained with the parameter set resulting from the fit of the susceptibility curve). The large differences in J values resulting from small differences in Ni-O-Ni angles in this Ni4O4 core of very low symmetry reflect a quite strong magnetostructural correlation.

High-Nuclearity Magnetic Clusters: Generalized Spin Hamiltonian and Its Use for the Calculation of the Energy Levels, Bulk Magnetic Properties, and Inelastic Neutron Scattering Spectra.

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)(-).