Heisenberg Dirac Van Vleck Research Articles

On the importance of the biquadratic terms in exchange coupled systems: A post-HF investigation

The importance of the many-body interactions was studied both at the experimental and theoretical level. However, no definitive proofs of their presence as high order terms in the Heisenberg–Dirac–Van Vleck (HDVV) Hamiltonian, as far as we know, were presented. The present work wants to reanalyze the HDVV Hamiltonian at the Full CI level on the two model systems N 2He and N 3He 3.

Microscopic origin of isotropic non-Heisenberg behavior inS=1magnetic systems

We have reanalyzed the microscopic origin of the isotropic deviations that are observed from the energy spacings predicted by the Heisenberg--Dirac--van Vleck (HDVV) Hamiltonian. Usually, a biquadratic spin operator is added to the HDVV Hamiltonian to account for such deviations. It is shown here that this operator cannot describe the effect of the excited atomic non-Hund states which brought the most important contribution to the deviations. For systems containing more than two magnetic centers, non-Hund states cause additional interactions that are of the same order of magnitude as the biquadratic exchange and should have significant effects on the macroscopic properties of extended systems.

Magnetic Investigation of an Unusual Dissymmetric Binuclear Manganese Carboxylate Complex

The magnetic susceptibility (χT) of an unusual dissymmetric binuclear manganese corboxylate complex has been measured from 2 to 300K. The magnetic data which have been fitted with help of the Heisenberg Dirac Van Vleck HDVV spin-exchange Hamiltonian H = − J S 1 S 2 , indicate that an antiferromagnetic interaction equal to J = -0.90(1) cm-1 is present. A correlation between J values and Mn-H2O-Mn angles has been tempted.

A MONTE CARLO SIMULATION OF MAGNETIC ORDERING IN ISING CUBIC FERROSPINELS

This work signifies the next step in our way in the magnetic properties simulation of spin clusters and extended networks containing quantum spins, by original FORTRAN codes based on Heisenberg–Dirac–VanVleck (HDVV) or Ising approaches, using Full Diagonalization Heisenberg Matrix (FDHM) or Monte Carlo–Metropolis (MCM) procedure, respectively. We present the results of magnetic Monte Carlo studies on a magnetite type lattice, Ising model ferrimagnet that provide insight into the exchange interactions involved in Cubic Ferrospinels. We have demonstrated that a comparatively simple model can reproduce ferrimagnetic behavior of ferrospinels, particularly for magnetite.

Synthesis, crystal structure and magnetic property of a binuclear iron(III) citrate complex

The compound (Hql)2[Fe2(cit)2(H2O)2]·4H2O (1) [ql = quinoline, cit4− = C(O−)(CO−2)(CH2CO−2)2], prepared by reacting ferric nitrate, sodium citrate and quinoline in a molar ratio of 1:1:1 in aqueous solution, was characterized by density measurements, elementary analysis, i.r., X-ray crystallography and magnetic measurements. The X-ray crystallography results reveal that the molecule (1) consists of a binuclear iron(III) citrate anionic complex [Fe2(cit)2(H2O)2]2− and two protonated quinolines [Hql]+. The anionic complex has a centro-symmetric structure, in which two Fe3+ ions are bridged by two μ2-alkoxo groups of the two deprotonated citrate ligands. The other coordination sites of the two slightly distorted octahedra are completed by all the carboxylate groups of the two cit4− ligands in a monodentate mode, and two coordinated water molecules. Magnetic measurements indicate that the two Fe3+ ions are antiferromagnetically coupled below 200 K. A least-squares fit of variable-temperature (1.5–291 K) molar susceptibility data to a dimer model gave the coupling constant J/k = −6.35(7) K and Lande factor g = 2.052(9), where the spin-only Heisenberg–Dirac–van Vleck Hamiltonian is expressed as H = −2JS1S2.

A neutral triple-helical trinuclear oxo-centered mixed-valent iron complex: Mössbauer spectroscopic and magnetic susceptibility studies

The electronic properties of the trimeric oxo-centred [Fe3OL3] complex (L is a doubly negatively charged pentadentate ligand, providing five nitrogens for iron coordination) have been investigated by Mössbauer spectroscopy, magnetic susceptibility and a theoretical treatment including the phenomena of double-exchange interaction. Two quadrupole doublets I and II with the ratio ∼2:1 are observed at 4.2 K. By comparing the isomer shifts of these doublets (δI=0.52 mm s−1 and δII=0.99 mm s−1) with those of other mixed metal complexes with comparable iron–ligand coordination it is concluded in this study that [Fe3OL3] exhibits a partially delocalised ground state: Fe2.9+-Fe2.9+-Fe2.2+. At elevated temperatures the Mössbauer spectra of [Fe3OL3] exhibit two additional doublets III and IV (δIII=0.60 mm s−1 and δIV=0.80 mm s−1 at 20 K), which are ascribed to an additional partially delocalised state, i.e. Fe2.75+-Fe2.75+-Fe2.5+. By admitting the coexistence of two types of clusters with different delocalised valence states, it is possible to consistently fit the Mössbauer spectra over the whole temperature range (4.2–332 K) being investigated. Temperature-dependent magnetic susceptibility data of [Fe3OL3] from 2 to 295 K can be analysed by the Heisenberg–Dirac–Van Vleck model with only two exchange parameters J=−140 cm−1 and J1=−49 cm−1, describing the Fe(III)-Fe(III) and Fe(III)-Fe(II) exchange interactions and yielding a net antiferromagnetic coupling of the three paramagnetic sites with a spin-triplet ground state. In order to explain the seemingly contradictory situation that the Mössbauer spectra of [Fe3OL3] exhibit partial valence delocalisation while it is possible to analyse the magnetic data with valence-trapped ground state and exited states a theoretical treatment is presented, which includes antiferromagnetic exchange, double exchange and vibronic interactions.

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)(-).

Analysis of Exchange Interaction and Electron Delocalization as Intramolecular Determinants of Intermolecular Electron-Transfer Kinetics.

During the past decades, spectroscopic characterization of exchange interactions and electron delocalization has developed into a powerful tool for the recognition of metal clusters in metalloproteins. By contrast, the biological relevance of these interactions has received little attention thus far. This paper presents a theoretical study in which this problem is addressed. The rate constant for intermolecular electron-transfer reactions which are essential in many biological processes is investigated. An expression is derived for the dependence of the rate constant for self-exchange on the delocalization degree of the mixed-valence species. This result allows us to rationalize published kinetic data. In the simplest case of electron transfer from an exchange-coupled binuclear mixed-valence donor to a diamagnetic acceptor, the rate constant is evaluated, taking into account spin factors and exchange energies in the initial and final state. The theoretical analysis indicates that intramolecular spin-dependent electron delocalization (double exchange) and Heisenberg-Dirac-van Vleck (HDvV) exchange have an important impact on the rate constant for intermolecular electron transfer. This correlation reveals a novel relationship between magnetochemistry and electrochemistry. Contributions to the electron transfer from the ground and excited states of the exchange-coupled dimer have been evaluated. For clusters in which these states have different degrees of delocalization, the excited-state contributions to electron transfer may become dominant at potentials which are less reductive than the potential at which the rate constant for the transfer from the ground state is maximum. The rate constant shows a steep dependence on HDvV exchange, which suggests that an exchange-coupled cluster can act as a molecular switch for exchange-controlled electron gating. The relevance of this result is discussed in the context of substrate specificity of electron-transfer reactions in biology. Our theoretical analysis points toward a possible biological role of the spin-state variability in iron-sulfur clusters depending on cluster environment.

Crystal and molecular structure, magnetic properties and scattered-wave description of the electronic structure of the hexanuclear octahedral clusters [Fe6(µ3-S)8(PEt3)6][PF6]n(n= 1 or 2)

The crystal structure of [Fe6(µ3-S)8(PEt3)6][PF6]2 has been determined. It is isostructural with the parent tetraphenylborate complex. The electronic structures of [Fe6(µ3-S)8(PEt3)6][PF6] and of [Fe6(µ3-S)8(PEt3)6][PF6]2 have been investigated experimentally by measuring the temperature variation of the magnetic susceptibility between 300 and 4.2 K, the field dependence of the magnetisation at three different temperatures in the range 2–10 K and the polycrystalline powder Mossbauer spectra at variable temperature. The complex [Fe6(µ3-S)8(PEt3)6][PF6] possesses a S= 7/2 spin state well isolated from the excited states, while [Fe6(µ3-S)8(PEt3)6][PF6]2 shows a marked temperature dependence of the magnetic susceptibility. The magnetic structures of the complexes have been characterised empirically with the Heisenberg–Dirac–van Vleck exchange spin Hamiltonian. The nature of the magnetic states is rationalised in the framework of Xα-SW theory.

Electronic structure of paramagnetic clusters of transition metal ions. 3. Magnetic properties and scattered wave description of the electronic structure of the hexanuclear octahedral cluster [Fe6(μ3−S)8(PEt3)6] (BPh4)2

AbstractSpin‐polarized Xα–SW calculations of [Fe6(μ3−S)8(PH3)6]2+ as a model of the cluster [Fe6(μ3−S)8(PEt3)6] (BPh4)2 have been performed. The highest occupied energy levels are well separated from empty levels, and up to a maximum of eight electrons can be unpaired, giving a maximum spin state with S = 4. This electronic state is consistent with the magnetic data of [Fe6(μ3−S)8(PEt3)6](BPh 4)2, which have been interpreted using the Heisenberg–Dirac–Van Vleck exchange spin Hamiltonian. The S = 4 state arises from the magnetic coupling between five low‐spin (Si = 1/2) and one intermediate‐spin (S = 3/2) iron(III) center. © 1994 John Wiley & Sons, Inc.

Synthesis, Structure, and Magnetic Property of Linear Chloro-Bridged Nickel(II) Tetramer with Dinucleating Bis-dimethylcyclam Ligand

Abstract A new nickel(II) complex with the composition of Ni2Cl2(L)(ClO4)2·1.5H2O (L = α,α′-bis(5R(S),7S(R)5,7-dimethyl-1,4,8,11-tetraazacyclotetradecan-6-yl)-o-xylene) has been prepared via a four coordinate complex [Ni2(L)] (ClO4)4·3H2O from [Ni2(μ-Br)Br2(L)]Br·H2O. The compound crystallizes in orthorhombic space group Ccm21 with cell parameters at −80 °C, a = 21.90(1), b = 20.28(1), c = 19.63(1) Å, V = 8718(1) Å3, Z = 8. The crystal consists of the cationic dinuclear unit [Ni2(μ-Cl)Cl2(L)]+, the counter anion ClO4−, and water of crystallization. In [Ni2(μ-Cl)Cl2(L)]+, three chloride ions and two nickel ions are alternately arranged in an almost linear manner, and two cyclam rings with the most stable trans-III type conformation are arranged in a face-to-face manner. This cationic dinuclear unit is further connected to each other by sharing the terminal Cl ligand to form pseudo one-dimensional chain structure of the ···Cl–Ni–Cl–Ni–Cl··· type. However, one of the Cl atoms which bridges the dinuclear units is statistically disordered at two positions along the chain and thereby the repeating unit in the chain is a chloro bridged dimer of the dinucleating ligand complex. The neighboring Ni–Cl distances range from 2.568(4) to 2.855(4) Å. The temperature dependent magnetic behavior in the range of 25—300 K has been interpreted by the usual Heisenberg–Dirac–Van Vleck model, assuming that only three Ni(II) ions in {Ni2Cl2(L)}2 are paramagnetic. The best fit parameters were J = −48.2(3) and J′ = −11.2(3) cm−1 for = −2J(S1·S1′) − 2J′(S1·S2).

2,2′-Bipyrimidine (bipym)-bridged dinuclear complexes. Part 2. Synthesis, crystal structure and magnetic properties of [Fe2(H2O)8(bipym)][SO4]2·2H2O and [Fe2(H2O)6(bipym)(SO4)2

Two new dinuclear iron(II) complexes of formulae [Fe2(H2O)8(bipym)][SO4]2·2H2O 1 and [Fe2(H2O)6-(bipym)(SO4)2]2(bipym = 2,2′-bipyrimidine) have been synthesised and their crystal structures determined by single-crystal X-ray diffraction. Crystals of 1 and 2 are monoclinic, space group P21/c with a= 8.138(1), b= 11.661(2), c= 11.886(2)A, β= 91.85(1)° and Z= 2 for 1 and space group P21/n with a= 6.275(2), b= 13.550(4), c= 10.937(2)A, β= 96.43(2)° and Z= 2 for 2. The structure of 1 consists of centrosymmetric dinuclear cations [Fe2(H2O)8(bipym)]4+, unco-ordinated sulfate anions and water of crystallization whereas that of 2 is made up of neutral dinuclear [Fe2(H2O)6(bipym)(SO4)2] units. The co-ordination geometry around each iron atom is that of a highly distorted octahedron: the FeII–N distances are longer (average value 2.22 A) than the FeII–O ones (average values 2.11 and 2.09 in 1 and 2, respectively). In both complexes, the bipyrimidine group joins two adjacent iron atoms acting in a bis(chelating) faschio. The C–C bond between the pyrimidine rings of bipym is perpendicular to the Fe ⋯ Fe vector giving two five-membered chelate rings, the bite angle of bipym being 74.9(1)° in 1 and 74.1(1)° in 2. The intramolecular metal–metal separation is 5.836(1) and 5.909(1)A in 1 and 2, respectively. Magnetic susceptibility versus temperature data for both compounds were fitted to the Heisenberg–Dirac–Van-Vleck S1=S2= 2 spin exchange model with J=–3.4 cm–1, g= 2.28 and θ=–0.7 cm–1 for 1 and J=–3.1 cm–1, g= 2.23 and θ=–1.3 cm–1 for 2. The efficiency of bipym to transmit electronic effects between iron(II) ions is compared to that of related oxygen-donor potentially bis(chelating) ligands.

Crystal and molecular structure and magnetic properties of tris{di-µ-methoxo-bis[4,4,4-trifluoro-1-(2-thienyl)butane-1,3-dionato]dicopper(II)}

The crystal and molecular structure of [{Cu2(OMe)2(tftbd)2}3][tftbd = 4,4,4-trifluoro-1-(2-thienyl)butane-1,3-dionate] has been determined from single-crystal X-ray diffraction data and refined to R 0.058 for 3 241 independent reflections. The compound crystallizes in the triclinic space group P with one hexameric molecule in a cell of dimensions a= 11.212(7), b= 11.079(7), c= 15.315(9)A, α= 92.71 (5), β= 116.80(5), and γ= 95.56(5)°. The molecule consists of three roughly planar methoxo-bridged dimeric units: a centrosymmetric ‘dimer’ with average Cu–O 1.94(1)A and Cu–O–Cu 99.5(3)° within the Cu2O2 bridging group, and two inversion-related non-centrosymmetric ‘dimers’ having a slightly non-planar Cu2O2 group with Cu-O ranging from 1.90(1) to 1.96(1)A and two different Cu–O–Cu angles, 98.9(3) and 102.8(3)°. The dimers are joined by axial copper-oxygen bonds. The geometry around the copper atoms is approximately square pyramidal. Magnetic susceptibility data in the range 4.2–350 K indicate overall antiferromagnetic spin coupling. The magnetism of the complex can be explained using the isotropic Heisenberg–Dirac–van Vleck model for three non-interacting dimers. The resulting values for the exchange parameters indicate a stronger antiferromagnetic interaction in the non-symmetric ‘dimer’(J=–440 cm–1) than in the centrosymmetric one (J=–214 cm–1). The magnetism of both ‘dimers’ is discussed in relation to the structural data.

Magnetic behaviour of tetrakis[(2-diethylaminoethanolato)isocyanatocopper(II)], a complex with an antiferromagnetic ground state; the crystal and molecular structure of the triclinic modification

The crystal and molecular structure and magnetic behaviour of [{Cu(NCO)(OCH2CH2NEt2)}4](B) from benzene have been determined. The crystal structure determination was carried out by single-crystal X-ray diffraction methods and refined to R= 0.066 for 4 379 independent reflections: triclinic, space group P, with unit-cell dimensions a= 13.478(3), b= 12.873(3), c= 11.542(3)A, α= 84.020(5), β= 80.263(5), and γ= 86.863(5)°. Each copper atom is five-co-ordinated by three oxygen and two nitrogen atoms. The magnetic susceptibility measured over the temperature range 5.0–302.5 K shows a maximum at 94 K and thus indicates that antiferromagnetic spin coupling is dominant. The magnetic behaviour can be explained on the basis of the isotropic Heisenberg–Dirac–van Vleck model. The results are compared with the structural and magnetic properties of the tetragonal form (A) of this complex. No phase transition between the two modifications could be found up to the melting point.

Crystal and molecular structures and magnetic properties of tetrameric copper(II) complexes with 3-hydroxy-5-hydroxymethyl-4-(4′-hydroxy-4′-phenyl-2′-azabut-1′-en-1′-yl)-2-methylpyridine (H2L3), [Cu4L34]·9CH3OH and 3-hydroxy-5-hydroxymethyl-4-(4′-hydroxy-3′-methyl-4′-phenyl-2′azabut-1′-en-1′-yl)-2-methylpyridine (H2L1), [Cu4-L14]· 8CH3CH2OH : two complexes with ferromagnetic ground states

The crystal and molecular structures of the title compounds [Cu4L34]·9CH3OH (3) and [Cu4L14]·8CH3CH2OH (4) have been determined from single-crystal X-ray diffraction data and refined to final R values of 0.062 (R′= 0.052) using 2 191 independent reflections for (3) and 0.062 (R′= 0.055) using 2 458 independent reflections for (4). Both tetrameric complexes crystallize in the tetragonal space group P42/n with two molecules in an unit cell with dimensions a= 18.193(4) and c= 12.615(4)A for (3) and a= 17.991(4) and c= 14.296(4)A for (4). Both molecules exhibit the highest possible point symmetry . While compound (3) is comparable with its 4′-(3″,4″-dichlorophenyl) derivative [Cu4L24]·9CH3OH (2) which crystallizes in a monoclinic lattice having an infinite network of hydrogen bonds, (4) is isomorphous to [Cu4L14]·8CH3OH (1). Moreover these two forms of structures are distinguishable by the considerably larger Cu–O distance between two pseudo-monomeric units within the pseudo-dimeric unit in (1) and (4) compared with (2) and (3). The magnetism of the two complexes can be explained on the basis of the isotropic Heisenberg–Dirac–van Vleck model. Compound (4) is very similar in its magnetic behaviour [g= 2.16(2), J12= 0 (fixed), J13= 17.4(2.0) cm–1, and θ=–1.8(1.0) K] to (1). In contrast to (2), compound (3) definitely has a ferromagnetic ground state [g= 2.085(20), J12=–7.1(2.0), and J13= 28.5(2.0) cm–1]. The principal difficulties of fitting theoretical magnetic susceptibility equations to experimental ones in ferromagnetically coupled systems is discussed. The discrepancy of the magnetic exchange constants between (3) and (2) which has really C1 symmetry is discussed in order to test by which model of higher symmetry the magnetism of this compound can be optimally described. It can be shown that a C2v model leads to more plausible exchange constants for (2) with regard to the geometrical sizes of the highly distorted molecule.

Exchange interactions between orbitally degenerate ions in Ti2 X 9 3- (X=Cl, Br)

An effective hamiltonian ℋeff is developed for the treatment of exchange interactions in a pair of transition metal ions with orbitally degenerate ground states. In contrast to a Heisenberg-Dirac-van Vleck (HDvV) hamiltonian ℋeff retains a partial degeneracy of singlet and triplet pair states. The hamiltonian is applied to Ti2 X 9 3- (X=Cl, Br) dimers. The gross experimental features of Cs3Ti2Cl9 and Rb3Ti2Br9 are well reproduced by the theoretical model. The coupling is strongly antiferromagnetic and the exchange parameters can be rationalized by an approximate MO calculation.

ChemInform Abstract: CRYSTAL AND MOLECULAR STRUCTURE AND MAGNETIC PROPERTIES OF A TETRAMERIC COPPER(II) COMPLEX WITH 3‐HYDROXY‐4‐(4′‐(3′′,4′′‐DICHLOROPHENYL)‐4′‐HYDROXY‐2′‐AZABUT‐1′‐EN‐1′‐YL)‐5‐HYDROXYMETHYL‐2‐METHYLPYRIDINE (H2L2), ((CUL2)4).9CH3OH

The crystal and the molecular structure of the title compound has been determined using three-dimensional X-ray diffractometer data involving 7 045 independent reflections. The compound crystallizes in the monoclinic space group I2/c with eight formula units [(CuL2)4]·9CH3OH in a unit cell with dimensions a= 27.062(5), b= 25.062(5), c= 26.390(5)A, and β= 92.39(1)°. The structure has been calculated by direct methods and refined by least-squares methods to a final R value of 0.054. In the cubane structure (C1 symmetry) each copper atom is bonded to one deprotonated phenolic oxygen, one imine nitrogen, and three deprotonated alkoxo-oxygen atoms giving a distorted square-pyramidal co-ordination. The six copper–copper distances are in the range 3.021(1)–3.492(2)A(mean 3.254 ± 0.184 A). Within the Cu4O4 core there are eight shorter copper–oxygen distances [1.917(5)–2.057(5)A, mean 1.983 A] and four longer ones [2.327(5)–2.690(6)A, mean 2.496 ± 0.166 A]. There are 72 methanol molecules per unit cell which are easily lost in air, giving an amorphous powder. The magnetic properties of the complex can be explained using the isotropic Heisenberg–Dirac–van Vleck model. The exchange parameters for the complex with approximate S4 symmetry obtained (J12=–9.9 ± 3.0 cm–1, J13= 20.5 ± 3.0 cm–1, and g= 2.08 ± 0.02) are in good agreement with those of similar substances and show the presence of both ferromagnetic and antiferromagnetic interactions. The amorphous modification shows a predominant ferromagnetic interaction.

Exchange interactions between dimers of chromium(III). A cluster approach

Exchange interactions in dimers, tetramers and octamers of chromium(III) are treated with an effective Hamiltonian of the Heisenberg-Dirac-vanVleck (HDvV) type. Energies and wave functions of the cluster states are computed. The results of interdimer interactions are: (i) energy splittings and (ii) a contamination of the cluster ground state with excited configurations. The results are used for a qualitative rationalisation of the observed low-temperature properties of Cs3Cr2Cl9.

Crystal and molecular structure and magnetic properties of a tetrameric copper(II) complex with 3-hydroxy-4-[4′-(3″,4″-dichlorophenyl)-4′-hydroxy-2′-azabut-1′-en-1′-yl]-5-hydroxymethyl-2-methylpyridine (H2L2), [(CuL2)4]·9CH3OH

The crystal and the molecular structure of the title compound has been determined using three-dimensional X-ray diffractometer data involving 7 045 independent reflections. The compound crystallizes in the monoclinic space group I2/c with eight formula units [(CuL2)4]·9CH3OH in a unit cell with dimensions a= 27.062(5), b= 25.062(5), c= 26.390(5)A, and β= 92.39(1)°. The structure has been calculated by direct methods and refined by least-squares methods to a final R value of 0.054. In the cubane structure (C1 symmetry) each copper atom is bonded to one deprotonated phenolic oxygen, one imine nitrogen, and three deprotonated alkoxo-oxygen atoms giving a distorted square-pyramidal co-ordination. The six copper–copper distances are in the range 3.021(1)–3.492(2)A(mean 3.254 ± 0.184 A). Within the Cu4O4 core there are eight shorter copper–oxygen distances [1.917(5)–2.057(5)A, mean 1.983 A] and four longer ones [2.327(5)–2.690(6)A, mean 2.496 ± 0.166 A]. There are 72 methanol molecules per unit cell which are easily lost in air, giving an amorphous powder. The magnetic properties of the complex can be explained using the isotropic Heisenberg–Dirac–van Vleck model. The exchange parameters for the complex with approximate S4 symmetry obtained (J12=–9.9 ± 3.0 cm–1, J13= 20.5 ± 3.0 cm–1, and g= 2.08 ± 0.02) are in good agreement with those of similar substances and show the presence of both ferromagnetic and antiferromagnetic interactions. The amorphous modification shows a predominant ferromagnetic interaction.

Crystal and molecular structure and magnetic properties of a tetrameric copper(II) complex with 3-hydroxy-5-hydroxymethyl-4-(4′-hydroxy-3′-methyl-4′-phenyl-2′-azabut-1′-en-1′-yl)-2-methylpyridine (H2L) : [Cu4L4]·8MeOH, a complex with a ferromagnetic ground state

The crystal and molecular structure of the title compound has been determined from single-crystal X-ray diffraction data and refined to a final R value of 0.053 using 2 514 independent reflections. The compound belongs to the space group P42/n of the tetragonal system with two tetrameric molecules in a unit cell of dimensions a= 17.226(4) and c= 14.667(3)A. The tetrameric unit with a Cu4O4 core is of S4 symmetry. Copper–copper distances are 3.481(1)(two), 3.259(1)A(four) and Cu–O distances are 1.945(4)(four), 2.734(4)(four), and 1.977(4)A(four). The co-ordination about the copper atom is distorted square pyramidal with copper bonded to phenolic oxygen O(2), imine nitrogen N(1), and three alkoxo-oxygen atoms O(1). The complex crystallizes with 16 methanol molecules per unit cell. It easily loses in air the methanol molecules of crystallization giving an amorphous powder. The magnetism of the crystallized complex can be explained on the basis of the isotropic Heisenberg–Dirac–van Vleck model. Taking into account intercluster interactions, the fitting procedure yielded the values g= 2.12, J13= 17.1 cm–1, θ=–1.1 K. These parameters indicate a predominance of ferromagnetic interactions with a quintet ground state (S′= 2). The magnetic behaviour of the amorphous powder is quite different and shows weak antiferromagnetic interactions.