Exchange and Delocalization Effects in [Fe6S6]2+ Superclusters

A theoretical study of Heisenberg exchange and double exchange (delocalization) effects in the iron-sulphur supercluster is presented. Such clusters can play important role in biological systems (proteins and enzymes) acting as so-called active centres. The cluster with valence 2+ can be modelled by two Fe(III) and four Fe(II) ions. An idealized structure of double cubane has been considered instead of a more realistic defected double cubane structure of lower symmetry. Energies of the lowest spin states have been calculated numerically depending on the Heisenberg exchange J _i and double exchange b parameters. Possible spin ground states (S=0, 1, 2, 3, 4, 5) have been predicted. The ground state of a given total spin Sis usually achieved for the intermediate spin value of S ₅₆=4 in the case of fully antiferromagnetic as well as partially ferromagnetic spin interactions. In the case of no double exchange, the ground state with the total spin S=3 should always be observed, while a nonzero hopping effect results in narrowing a parameter region of the ground state. If the double exchange is taken into account, then the spin values depend on the Heisenberg integrals. The model results can be applied in order to interpret many structural and magnetic properties of proteins and enzymes possessing the Fe-S active centres.     

Redox potential of iron–sulfur clusters as a model of the Desulfovibrio vulgaris center

A theoretical study of Heisenberg exchange and double exchange effects in clusters with four and six iron ions has been performed for [Fe₄ S₃ O] ^m+, [Fe₄ S₄]^m+ (where m = 3, 2), and [Fe₆ S₆] ⁿ⁺ (where n = 5, 4) ions as models of the Desulfovibrio vulgaris iron–sulfur centers. Assuming that the redox potential mostly depends on the Heisenberg spin coupling and the resonance delocalization, we performed an analysis of the reduction process for the [Fe₄ S₃ O] ^3+/2+, [Fe₄ S₄] ^3+/2+, and [Fe₆ S₆] ^5+/4+ ions and showed that the redox potential can be calculated as a difference between average spin energies of the tetravalent and pentavalent double cubane superclusters. For the Heisenberg parameter of J₁ = 20 cm^-1, the redox potential amounts to about 0.03 V.It complies with close to zero experimental values of the redox potential.Electronic Supplementary Material: Supplementary material is available in the online version of this article at     

Determination of heisenberg exchange coupling constants in clusters with magnetic sites: A local spin approach

This work studies the ability of the two‐center local spin quantities, provided by the partitioning of the expectation value of the spin‐squared operator corresponding to N‐electron systems, for determining spin‐exchange coupling constants within the Heisenberg spin Hamiltonian model. The spin‐exchange parameters, which characterize this Hamiltonian for a determined system, have been evaluated in the HeH₂ aggregate and in several clusters (n = 2, 3, 4) with different geometrical arrangements, using internuclear distances larger than the equilibrium ones (beyond the bonding regions). The results found have been analyzed and compared with those arising from other approaches, showing the feasibility of our methodology. © 2014 Wiley Periodicals, Inc.     

Structural, thermal and magnetic characterization of the manganese oxyhalide layered perovskite, (MnCl)LaNb2O7

Mn-Cl sheets were inserted into the perovskite blocks of a double-layered Dion-Jacobson compound by ion exchange at low temperature (390°C). The Rietveld structural analysis of X-ray powder diffraction data (P4/mmm) indicates that the product, (MnCl)LaNb₂O₇, has the manganese coordinated by two apical oxygens from the perovskite layers and four in-plane chlorines within the interlayer space. On heating, this compound exhibits an exothermic transition between 650°C and 750°C that is consistent with metastability. Magnetic characterization shows Curie-Weiss behavior at higher temperatures (>200 K) with a magnetic moment corresponding to the presence of high-spin Mn²⁺ ion (S=5/2). At lower temperatures, antiferromagnetic interactions become significant and the broad maximum at 63 K reveals the 2-D character of the magnetic behavior. The susceptibility data, fit with the high temperature expansion for a Heisenberg square planar system, show a negative exchange interaction of J/k=−3.77 K.     

Semiempirical local spin: Theory and implementation of the ZILSH method for predicting Heisenberg exchange constants of polynuclear transition metal complexes

The local spin formalism ( 3 ) for computing expectation values 〈S_A · S_B〉 that appear in the Heisenberg spin model has been extended to semiempirical single determinant wave functions. An alternative derivation of expectation values in restricted and unrestricted cases is given that takes advantage of the zero differential overlap (ZDO) approximation. A formal connection between single determinant wave functions (which are not in general spin eigenfunctions) and the Heisenberg spin model was established by demonstrating that energies of single determinants that are eigenfunctions of the local spin operators with eigenvalues corresponding to high‐spin radical centers are given by the same Heisenberg coupling constants {J_AB} that describe the true spin states of the system. Unrestricted single determinant wave functions for transition metal complexes are good approximations of local spin eigenfunctions when the metal d orbitals are local in character and all unpaired electrons on each metal have the same spin (although spins on different metals might be reversed). Good approximations of the coupling constants can then be extracted from local spin expectation values 〈S_A · S_B〉 energies of the single determinant wave functions. Once the coupling constants are obtained, diagonalization of the Heisenberg spin Hamiltonian provides predictions of the energies and compositions of the spin states. A computational method is presented for obtaining coupling constants and spin‐state energies in this way for polynuclear transition metal complexes using the intermediate neglect of differential overlap Hamiltonian parameterized for optical spectroscopy (INDO/S) in the ZINDO program. This method is referred to as ZILSH, derived from ZINDO, Davidson's local spin formalism, and the Heisenberg spin model. Coupling constants and spin ground states obtained for 10 iron complexes containing from 2 to 6 metals are found to agree well with experimental results in most cases. In the case of the complex [Fe₆O₃(OAc)₉(OEt)₂(bpy)₂]⁺, a priori predictions of the coupling constants yield a ground‐state spin of zero, in agreement with variable‐temperature magnetization data, and corroborate spin alignments proposed earlier on the basis of structural considerations. This demonstrates the potential of the ZILSH method to aid in understanding magnetic interactions in polynuclear transition metal complexes. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2003     

Approximate solutions of Heisenberg Hamiltonians

Even when each atom of a 2n-center cluster or molecule only brings one active electron in one atomic orbital, the size of the Heisenberg Hamiltonian matrix increases as C. Simple truncations of this matrix would result in size consistence defects, as evident from the isomorphism between Heisenberg and configuration interaction (CI ) matrices. Geometry-dependent Heisenberg Hamiltonians derived from accurate ab initio calculations on the two-center systems have proved to be very efficient for conjugated hydrocarbons and for alkali metals; in order to apply this approach to intermediate size systems (10–20 centers), a rational procedure is proposed consisting of the selection of a truncated set of determinants (of low energy) and a dressing of the truncated Hamiltonian matrix under the perturbation of the other determinants. The second order dressing is analogous to a so-called “shift B_k procedure” or Generalized Degenerate Perturbation theory and is weakly dependent on an E₀ parameter. Tests performed on various 8- and 10-atom systems show the accuracy of the procedure. An iterative selection of the truncated basis set and proper choices of the E₀ values allow one to obtain the whole lower part of the spectrum. The calculated geometries are satisfactory. Some preliminary applications are reported concerning the C₁₂H₁₄ dodecahexene linear chain, perfectly fitting with previous extrapolations.     

Bond alternation in ring-shaped molecules: The stability of the Peierls instability

We investigate the phenomenon of bond alternation in ring molecules of the type (CH)_2n, which occurs due to the Peierls instability. We prove that the energy-minimizing configuration of bond lengths always has period two when n is odd. When n is even, a new instability may destroy the periodicity two as long as n is not too large. We also analyze the corresponding problem for the Heisenberg antiferromagnetic “spin-Peierls” system and prove that instabilities other than period two never occur there. © 1996 John Wiley & Sons, Inc.     

A computational study of the Dougherty model for the prediction of high-spin states in organic chemistry

The model proposed by Dougherty for the design of high-spin organic systems has been studied from a quantitative point of view using a Heisenberg Hamiltonian formalism. This analysis leads to a decomposition of the phenomenological coupling parameter, J, into contributions from individual active orbital sites and a decomposition of the spin multiplicity into terms from the ferromagnetic coupling unit and the spin-containing units. An analysis of the origin of quintet stability has been carried out for four molecular systems with quintet ground states that have previously been synthesized by Dougherty and by Adam. The results indicate that the ferromagnetic coupling unit plays the dominant role in determining high-spin stability as suggested by Dougherty and gives some insights that may be useful in the rational design of high-spin systems. Received: 31 July 1998 / Accepted: 21 September 1998 / Published online: 23 February 1999     

Anisotropic exchange interactions in dinuclear systems (Ln = Dy, Tm, Yb): Magnetometry and Dual Mode X-band Electron Paramagnetic Resonance spectroscopic study

A recently developed experimental and theoretical procedure is used in order to calculate the magnitude and anisotropy of interaction between a lanthanide and a 3d-metal ion. The general formula of the molecular compounds is [Ln(H₂O)₃(dmf)₄(μ-CN)Fe–(CN)₅] · nH₂O where 1  n  1,5 and dmf = N,N′-dimethylformamide, abbreviated as [LnFe] from now on. The main parts of this procedure are (a) the evaluation of the effective g-parameters of the lanthanide ion with the help of EPR measurements. (b) The use of dual mode EPR spectroscopy to define the anisotropic exchange interactions with the help of an anisotropic Hamiltonian model. (c) Use of the same magnetic model to fit magnetization and susceptibility data in order to verify the EPR findings.It was possible to define some trends concerning the exchange components of the [DyFe] dimer according to which the antiferromagnetic isotropic exchange constant is smaller than 4 cm⁻¹ and the anisotropic components are [D_exc, E_exc] = [6(1), 0.0] cm⁻¹. Also for the case of [TmFe] and [YbFe] dimers the antiferromagnetic isotropic exchange constant is smaller than 0.3 cm⁻¹ while the anisotropic components are [D_exc, E_exc] = [12.0, 0.0] cm⁻¹ and [D_exc, E_exc] = [0.4(1), 0.0] cm⁻¹, respectively.     

Single-ion anisotropy in a four-spin system: mixing of S-states

A four-spin system with s=1 and the single-ion anisotropy, D∑ _j [s _jz ] ² , is considered. When D≠0 the Hamiltonian of the system does not commute with S ² and, therefore, S cannot be used as an additional label of energy levels. In this work we concentrate on the problem of mixing states with different total spins S. The Hamiltonian matrix is transformed to the symmetry-adapted basis (with subspaces labeled by the irreducible representations of the symmetry group) and next, after solving the eigenproblem for S ², to the basis with vectors labeled by S. Each eigenproblem is solved exactly (at least numerically) and the eigenstates are expressed as ∑ _S a _S |S〉. The coefficients a_S are analyzed, especially for their D-dependence. Even in such a small system different schemes of level mixing can be observed.      

Intramolecular Antiferromagnetism in μ-Oxo-bis[(5,15-dimethyl-2,3,7,8,12,13,17,18-octaethylporphyrinato)iron(III)]

The magnetism of μ-oxo-bis[(5,15-dimethyl-2,3,7,8,12,13,17,18-octaethylporphyrinato)iron(III)] with bridge geometry d(Fe? O) = 1.752 Å and ?(Fe? O? Fe) = 178.6° can be explained in terms of antiferromagnetically exchange coupled iron(III)-3d⁵ pairs. The magnetochemical analysis in the temperature range 6K–295K on the basis of the isotropic Heisenberg model (spin Hamiltonian: ? = ?2J?₁ · ?₂ S₁ = S₂ = 5/2) leads to the exchange parameter J = ?125 cm^?1. With regard to the Fe? O bond length the J value corresponds to the series of data observed for other μ-oxodiiron-porphyrins and -porphycenes. Compared to the spin-spin coupling in [Fe₂Cl₆O]^2?, |J| is enhanced by ≈ 10%.     

Effect of core substituents on the intramolecular exchange interaction in N,N′‐dioxy‐2,6‐diazaadamantane biradical: DFT studies

Density‐functional theory calculations of a series of organic biradicals on the basis of the N,N′‐dioxy‐2,6‐diazaadamantane core with different substituents at carbon atoms adjacent to the nitroxyl groups have been performed by the UB3LYP/6‐311++G(2d,2p) method. Using the breaking symmetry approach, the values of the exchange interaction parameter, J, between the radical centers are calculated. It is shown that the intramolecular exchange interaction for the most part is ferromagnetic in nature, but the J parameter gradually decreases, changing its sign to antiferromagnetic interaction for the last substituent in the following sequence: CF₃(CH₃)COH > CH₂F(H)COH > CH₂OH > H > CBr₃ > CH₂F > CCl₃ > CF₃ > CH₂Br > CH₂Cl > CH₃ > C₂H₅ > C₃H₇ > i‐C₄H₉ > F > Br > OCH₃ > Cl > CH₂C₆H₅. The calculations at the UHSEH1PBE/6‐311++G(2d,2p) level with the most of substituents show nearly the same variation sequence for the J parameter. It is concluded that spin polarization effects in the diazaadamantane cage and a direct through‐space antiferromagnetic exchange interaction between the nitroxyl groups are the main mechanisms contributing to the exchange interaction parameter value in the studied series of compounds. The exchange coupling constant, J, depends on the electronic effects and geometry of the substituents, as well as on their specific interactions with the nitroxyl radical groups.     

Magnetic exchange interactions in binuclear and tetranuclear iron(III) complexes described by spin-flip DFT and Heisenberg effective Hamiltonians

Low-energy spectra of single-molecule magnets (SMMs) are often described by Heisenberg Hamiltonians. Within this formalism, exchange interactions between magnetic centers determine the ground-state multiplicity and energy separation between the ground and excited states. In this contribution, we extract exchange coupling constants (J) for a set of iron (III) binuclear and tetranuclear complexes from all-electron calculations using non-collinear spin-flip time-dependent density functional theory (NC-SF-TDDFT). For 12 binuclear complexes with J-values ranging from −6 to −132 cm⁻¹, our benchmark calculations using the short-range hybrid ωPBEh functional and 6-31G(d,p) basis set agree well with the experimentally derived values (mean absolute error of 4.7 cm⁻¹). For the tetranuclear SMMs, the computed J constants are within 6 cm⁻¹ from the experimentally derived values. We explore the range of applicability of the Heisenberg model by analyzing bonding patterns in these Fe(III) complexes using natural orbitals (NO), their occupations, and the number of effectively unpaired electrons. The results illustrate the efficiency of the spin-flip protocol for computing the exchange couplings and the utility of the NO analysis in assessing the validity of effective spin Hamiltonians.     

Synthesis, structure and magnetic properties of the one-dimensional bimetallic oxide [Cu(terpy)Mo2O7]

The hydrothermal reaction of Cu(CH₃CO₂)₂·H₂O, Na₂MoO₄ and terpyridine at 140 °C for 48 h yields [Cu(terpy)Mo₂O₇] (1), a bimetallic one-dimensional oxide. The structure consists of ruffled chains of edge- and corner-sharing {MoO₅} square pyramids, decorated with {CuN₃O₂} ‘4+1’ axially distorted square pyramids. The Cu(II) polyhedra are disposed so as to produce an alternating pattern of Cu-Cu distances across the {Mo₂O₂} rhombi of the chain of 6.25 and 6.82 Å. This structural feature is reflected in the magnetic properties which are characteristic of a dimer rather than a linear chain, consistent with an alternating antiferromagnetic Heisenberg chain.     

Long-range magnetic ordering of quasi-one-dimensional S=1/2 Heisenberg antiferromagnet Sr2Cu(PO4)2

Magnetic properties of quasi-one-dimensional S=1/2 Heisenberg antiferromagnet Sr₂Cu(PO₄)₂ were investigated by temperature and field dependence of AC susceptibility down to 0.03 K. A sharp peak was observed at on the temperature dependence of AC susceptibility indicating long-range magnetic ordering. Taking into account the exchange constant, (Hamiltonian =J∑S_iS_i+1), the ratio k_BT_N/J is 0.06%. Sr₂Cu(PO₄)₂ is, therefore, one of the best one-dimensional Heisenberg antiferromagnet known so far.     

Structure distortion effects in the spectrum of tunnel-exchange states of tetrahedral mixed-valence tetramers

Tunnel-exchange states of a tetrameric mixed-valence (MV) d₁–d₁–d₁–d₂ cluster are considered. Energy levels of distorted pseudotetrahedral conjiprations with rhombic and trigonal symmetry are calculated. It is demonstrated that the correlation diagrams of planar systems are symmetric with respect to the sign of the double exchange parameter. A strong double exchange always results in the ferromagnetic ground state of planar systems. The following types of spectrum defamations of the d₁–d₁–d₁–d₂ tetramer from tetrahedral to planar systems have been found: a) with a weak positive double exchange, deformation of a tetrahedral system does not lead to any change of spin of the antiferromagnetic ground state of the cluster; b) with a strong positive double exchange, the defonnation alters the antiferromagnetic ground (S = 1/2) state of the tetrahedral system to the ferromagnetic (S = 5/2) state of the planar system, or to an intermediate (S = 3/2) state; c) with a negative double exchange, irrespective of its absolute value, the tetrahedral system deformation does not alter the spin of the ground state. With a weak double exchange, this ground state remains antiferromagnetic, and with a strong double exchange, it is ferromagnetic or intermediate.Moldova State University. Translated fromZhurnal Strukturnoi Khimii, Vol. 34, No. 5, pp. 33–46, September–October, 1993.Translated by L. Chernomorskaya     

Bioadsorption and ion exchange of Cr3+ and Pb2+ solutions with algae

Heavy metals can be removed from effluents and recovered using physico-chemical mechanisms as biosorption processes. In this work “Arribada” seaweed biomass was employed to assess its biosorptive capacity for the chromium (Cr³⁺) and lead (Pb²⁺) cations that usually are present in waste waters of plating industries. Equilibrium and kinetic experiments were conducted in a mixed reactor on a batch basis. Biosorption equilibrium and fluid-solid mass transfer constants data were analyzed through the concept of ion exchange sorption isotherm. The respective equilibrium exchange constants (K _eqCr=173.42, K _eqPb=58.86) and volumetric mass transfer coefficients ((k _mCr a)′=1.13×10⁻³ s⁻¹, (k _mPb a)′=0.89×10⁻³ s⁻¹) were employed for the dynamic analysis of Cr and Pb sorption in a fixed-bed flow-through sorption column. The breakthrough curves obtained for both metals were compared with the predicted values by the heterogeneous model (K _eqCr=171.29, K _eqPb=60.14; k _mCr a=7.81×10⁻² s⁻¹, k _mPb a=2.43×10⁻² s⁻¹), taking into account the mass transfer process. The results suggest that these algae may be employed in a metal removal/recovery process at low cost. An erratum to this article can be found at     

Synthesis,Characterization, and Crystal Structure of a Metallamacrocycle

The novel macrocyclic decanuclear manganese(III) 30‐metallacrown‐10 compound [Mn₁₀(RS‐3‐chmshz)₁₀(DMF)₁₀] · 9DMF ( 1 ) was synthesized by self‐assembly and characterized (H₃RS‐3‐chmshz = N‐((R,S)‐3‐cyclohexenoyl)‐5‐methylsalicylhydrazide). Compound 1 is a 30‐membered decanuclear metallamacrocycle and crystallizes in triclinic space group P2₁/c, in an alternating …ΔΛΔΛ…‐type chiral configuration. The decanuclear systems measure ~2.6 nm in diameter and ~1.1 nm in thickness. The racemic N‐(R,S)‐3‐cyclohexenoyl group directing into the cavity of the metallamacrocycle shows the alternate R,S chiral configuration. Magnetic measurements on the title 30‐metallacrown‐10 compound show weak antiferromagnetic exchange interaction.     

Structural,Magnetic, and Computational Correlations of Some Imidazolo‐Fused 1,2,4‐Benzotriazinyl Radicals

1,3,7,8‐Tetraphenyl‐4,8‐dihydro‐1H‐imidazolo[4,5g][1,2,4]benzotriazin‐4‐yl ( 5 ), 8‐(4‐bromophenyl)‐1,3,7‐triphenyl‐4,8‐dihydro‐1H‐imidazolo[4,5g][1,2,4]benzotriazin‐4‐yl ( 6 ), and 8‐(4‐methoxyphenyl)‐1,3,7‐triphenyl‐4,8‐dihydro‐1H‐imidazolo[4,5g][1,2,4]benzotriazin‐4‐yl ( 7 ) were characterized by using X‐ray diffraction crystallography, variable‐temperature magnetic susceptibility studies, and DFT calculations. Radicals 5 – 7 pack in 1 D π stacks made of radical pairs with alternate short and long interplanar distances. The magnetic susceptibility (χ vs. T) of radicals 5 and 6 exhibit broad maxima at (50±2) and (50±4) K, respectively, and are interpreted in terms of an alternating antiferromagnetic Heisenberg linear chain model with average exchange‐interaction values of J=?31.3 and ?35.4 cm^?1 (g_solid=2.0030 and 2.0028) and an alternation parameter a=0.15 and 0.38 for 5 and 6 , respectively. However, radical 7 forms 1 D columns of radical pairs with alternating distances; one of the interplanar distances is significantly longer than the other, which decreases the magnetic dimensionality and leads to discrete dimers with a ferromagnetic exchange interaction between the radicals (2J=23.6 cm^?1, 2zJ′=?2.8 cm^?1, g_solid=2.0028). Magnetic exchange‐coupling interactions in 1,2,4‐benzotriazinyl radicals are sensitive to the degree of slippage and inter‐radical separation, and such subtle changes in structure alter the fine balance between ferro‐ and antiferromagnetic interactions.     

Improving the Halogen–Magnesium Exchange by using New Turbo-Grignard Reagents

This Minireview describes the scope of the halogen–magnesium exchange. It shows that the use of the turbo-Grignard reagent (iPrMgCl⋅LiCl) greatly enhances the rate of the Br– and I–Mg exchange. Furthermore, this magnesium reagent allows the performance of a fast sulfoxide–magnesium exchange. Also, the use of sBuMgOR⋅LiOR (R=2-ethylhexyl) enables a Br–Mg exchange in toluene leading to various Grignard reagents in toluene. Additionally, the new exchange reagent sBu₂Mg⋅2 LiOR (R=2-ethylhexyl) further increases the rate of the halogen–magnesium exchange allowing one to perform a chlorine–magnesium exchange for aromatic chlorides bearing an ortho-methoxy substituent in toluene.