Magnetic exchange in polynuclear metal complexes

A Discrete, Boron-Containing Triangular Triradical

A neutral boron-containing triangular triradical based on a triptycene derivative has been designed and synthesized. Its structure, bonding and physical property have been studied by EPR spectroscopy, SQUID magnetometry and single crystal X-ray diffraction, as well as theoretical calculations. The triradical has a series of isosceles triangle conformations in the solution due to the Jahn-Teller distortion, leading to the splitting of the two low-lying doublet states. This factor together with negligible spin-orbit coupling (SOC) of composing light atoms quenches the spin frustration. The work represents a rare example of a neutral through-space triangular triradical.

Distribution of Bipartite and Tripartite Entanglement within a Spin-1/2 Heisenberg Star in a Magnetic Field

The spatial distribution of entanglement within a spin-1/2 Heisenberg star composed from a single central spin and three peripheral spins is examined in the presence of an external magnetic field using the Kambe projection method, which allows an exact calculation of the bipartite and tripartite negativity serving as a measure of the bipartite and tripartite entanglement. Apart from a fully separable polarized ground state emergent at high-enough magnetic fields, the spin-1/2 Heisenberg star exhibits at lower magnetic fields three outstanding nonseparable ground states. The first quantum ground state exhibits the bipartite and tripartite entanglement over all possible decompositions of the spin star into any pair or triad of spins, whereby the bipartite and tripartite entanglement between the central and peripheral spins dominates over that between the peripheral spins. The second quantum ground state has a remarkably strong tripartite entanglement between any triad of spins in spite of the lack of bipartite entanglement. The central spin of the spin star is separable from the remaining three peripheral spins within the third quantum ground state, where the peripheral spins are subject to the strongest tripartite entanglement arising from a two-fold degenerate W-state.

Dipolar dephasing for structure determination in a paramagnetic environment

We demonstrate the efficacy of the REDOR-type sequences in determining dipolar coupling strength in a paramagnetic environment. Utilizing paramagnetic effects of enhanced relaxation rates and rapid electronic fluctuations in Cu(II)-(DL-Ala)₂.H₂O, the dipolar coupling for the methyl C-H that is 4.20 ​Å (methyl carbon) away from the Cu²⁺ ion, was estimated to be 8.8 ​± ​0.6 ​kHz. This coupling is scaled by a factor of ~0.3 in comparison to the rigid limit value of ~32 ​kHz, in line with partial averaging of the dipolar interaction by rotational motion of the methyl group. Limited variation in the scaling factor of the dipolar coupling strength at different temperatures is observed. The C-H internuclear distance derived from the size of the dipolar coupling is similar to that observed in the crystal structure. The errors in the dipolar coupling strength observed in the REDOR-type experiments are similar to those reported for diamagnetic systems. Increase in resolution due to the Fermi contact shifts, coupled with MAS frequencies of 30-35 ​kHz allowed to estimate the hyperfine coupling strengths for protons and carbons from the temperature dependence of the chemical shift and obtain a high resolution ¹H-¹H spin diffusion spectrum. This study shows the utility of REDOR-type sequences in obtaining reliable structural and dynamical information from a paramagnetic complex. We believe that this can help in studying the active site of paramagnetic metalloproteins at high resolution.

Synthesis, structure, electrochemistry and magnetism of cobalt-, nickel- and zinc-containing [M4(OH)3(H2O)2(α-SiW10O36.5)2]13- (M = Co2+, Ni2+, and Zn2+)

Interaction of the trilacunary 9-tungstosilicate [A-α-SiW₉O₃₄]^10- with cobalt(ii), nickel(ii) and zinc(ii) ions in pH 9 aqueous medium at room temperature led to the formation of the respective M₄-containing heteropolytungstates [M₄(OH)₃(H₂O)₂(α-SiW₁₀O_36.5)₂]^13- (M = Co²⁺ (1), Ni²⁺ (2), and Zn²⁺ (3)). Polyanions 1-3 were characterized in the solid state by single-crystal XRD, FT-IR spectroscopy, and thermogravimetric and elemental analyses. Electrochemical studies showed that the Co²⁺ ions in 1 can be oxidized to Co³⁺ and the CVs of the W^VI centers of the polyanions feature well-defined and chemically reversible reduction waves. Magnetic measurements on 1 and 2 showed paramagnetism with complex ferromagnetic and antiferromagnetic interactions. A model was presented for extracting the exchange constants for the magnetic exchange interaction.

New Syntheses, Analytic Spin Hamiltonians, Structural and Computational Characterization for a Series of Tri-, Hexa- and Hepta-Nuclear Copper (II) Complexes with Prototypic Patterns

We present a series of pyrazolato-bridged copper complexes with interesting structures that can be considered prototypic patterns for tri-, hexa- and hepta- nuclear systems. The trinuclear shows an almost regular triangle with a μ3-OH central group. The hexanuclear has identical monomer units, the Cu6 system forming a regular hexagon. The heptanuclear can be described as two trinuclear moieties sandwiching a central copper ion via carboxylate bridges. In the heptanuclear system, the pyrazolate bridges are consolidating the triangular faces, which are sketching an elongated trigonal antiprism. The magnetic properties of these systems, dominated by the strong antiferromagnetism along the pyrazolate bridges, were described transparently, outlining the energy levels formulas in terms of Heisenberg exchange parameters J, within the specific topologies. We succeeded in finding a simple Kambe-type resolution of the Heisenberg spin Hamiltonian for the rather complex case of the heptanuclear. In a similar manner, the weak intermolecular coupling of two trimer units (aside from the strong exchange inside triangles) was resolved by closed energy formulas. The hexanuclear can be legitimately proposed as a case of coordination-based aromaticity, since the phenomenology of the six-spins problem resembles the bonding in benzene. The Broken-Symmetry Density Functional Theory (BS-DFT) calculations are non-trivial results, being intrinsically difficult at high nuclearities.

Insights into Nature of Magnetization Plateaus of a Nickel Complex [Ni4(μ-CO3)2(aetpy)8](ClO4)4 from a Spin-1 Heisenberg Diamond Cluster

Magnetic and magnetocaloric properties of a spin-1 Heisenberg diamond cluster with two different coupling constants are investigated with the help of an exact diagonalization based on the Kambe’s method, which employs a local conservation of composite spins formed by spin-1 entities located in opposite corners of a diamond spin cluster. It is shown that the spin-1 Heisenberg diamond cluster exhibits several intriguing quantum ground states, which are manifested in low-temperature magnetization curves as intermediate plateaus at 1/4, 1/2, and 3/4 of the saturation magnetization. In addition, the spin-1 Heisenberg diamond cluster may also exhibit an enhanced magnetocaloric effect, which may be relevant for a low-temperature refrigeration achieved through the adiabatic demagnetization. It is evidenced that the spin-1 Heisenberg diamond cluster with the antiferromagnetic coupling constants J1/kB = 41.4 K and J2/kB = 9.2 K satisfactorily reproduces a low-temperature magnetization curve recorded for the tetranuclear nickel complex [Ni4(μ-CO3)2(aetpy)8](ClO4)4 (aetpy = 2-aminoethyl-pyridine) including a size and position of intermediate plateaus detected at 1/2 and 3/4 of the saturation magnetization. A microscopic nature of fractional magnetization plateaus observed experimentally is clarified and interpreted in terms of valence-bond crystal with either a single or double valence bond. It is suggested that this frustrated magnetic molecule can provide a prospective cryogenic coolant with the maximal isothermal entropy change −ΔSM=10.6 J·K−1·kg−1 in a temperature range below 2.3 K.

Ferromagnetically Coupled Copper(II) Clusters Incorporated in Functionalized Boltorn H30 Hyperbranched Polymer Architecture: ESR, Magnetic Susceptibility Measurements, and Quantum-Chemical Calculations

The unusual temperature behavior of the electron spin resonance (ESR) spectra and magnetic properties are experimentally observed in copper(II) complexes with a dendritic ligand based on the Boltorn H30 polymer (Perstorp Specialty Chemicals AB, Sweden) functionalized with fumaric acid residues in a molar ratio of 1:6. The ESR spectra at low temperatures show signs of transition to higher spin states at temperatures below 8-10 K, and the temperature dependences of the integral ESR signal intensities and magnetic susceptibility show the positive deviation from the Curie-Weiss law, thereby pointing to the presence of ferromagnetic exchange interactions in the system under study. The values of the exchange interaction parameters are calculated by quantum-chemical simulation of the possible structure of the copper(II) complex when assuming the formation of trinuclear coordination sites embedded in the hyperbranched polymer structure. The results of density functional theory calculations indicate the possibility of ferromagnetic exchange through carboxylate bridges in the trinuclear magnetic clusters, and the calculated values of the exchange interaction parameters make it possible to construct theoretical curves of the temperature dependence of the effective magnetic moment, which satisfactorily fit the experimental data, especially considering that polymers are characterized by disperse molecular weights and chemical structures.

Redox active mixed-valence hexamanganese double-cubane complexes supported by tetravanadates

A double-cubane-type hexamanganese complex that is reminiscent of the structure of an oxygen evolution center was synthesized using a polyoxovanadate ligand.

Magnetic Coupling Constants in Three Electrons Three Centers Problems from Effective Hamiltonian Theory and Validation of Broken Symmetry-Based Approaches

In the most general case of three electrons in three symmetry unrelated centers with Ŝ1 = Ŝ2 = Ŝ3 = 1/2 localized magnetic moments, the low energy spectrum consists of one quartet (Q) and two doublet (D1, D2) pure spin states. The energy splitting between these spin states can be described with the well-known Heisenberg-Dirac-Van Vleck (HDVV) model spin Hamiltonian, and their corresponding energy expressions are expressed in terms of the three different two-body magnetic coupling constants J12, J23, and J13. However, the values of all three magnetic coupling constants cannot be extracted using the calculated energy of the three spin-adapted states since only two linearly independent energy differences between pure spin states exist. This problem has been recently investigated by Reta et al. (J. Chem. Theory Comput. 2015, 11, 3650), resulting in an alternative proposal to the original Noodleman's broken symmetry mapping approach. In the present work, this proposal is validated by means of ab initio effective Hamiltonian theory, which allows a direct extraction of all three J values from the one-to-one correspondence between the matrix elements of both effective and HDVV Hamiltonian. The effective Hamiltonian matrix representation has been constructed from configuration interaction wave functions for the three spin states obtained for two model systems showing a different degree of delocalization of the unpaired electrons. These encompass a trinuclear Cu(II) complex and a π-conjugated purely organic triradical.

Handling Magnetic Coupling in Trinuclear Cu(II) Complexes

The problem of deriving three different two-body magnetic couplings in three electrons/three centers in a general geometric arrangement is investigated using the trinuclear Cu(II) HAKKEJ complex as a real case example. In these systems, one quartet and two doublet low lying electronic states exist, which define the magnetic spectra. However, the two possible linearly independent energy differences do not provide enough information to extract the three magnetic coupling constants. Here, we show how to obtain these parameters without making any assumption on the symmetry of the system from a combination of density functional- and wave function-based calculations. The density functional calculations explore various broken symmetry solutions and relate the corresponding energy to the expectation value of the Heisenberg Hamiltonian. This allows one to obtain all magnetic couplings, although their magnitude strongly depends on the exchange-correlation functional. Interestingly, a constant ratio between the magnetic coupling constants along a series of investigated functionals is found. This provides an additional equation to be used when relying on energy differences between spin states, which in turn allow solving the Heisenberg spectrum. The magnetic couplings thus obtained are compared to the experiment. Implications for the appropriate interpretation of the experiment and for the study of more complex systems are discussed.

Quantum chemical investigation of meta-xylylene based one-dimensional polymer chain

We have investigated unsubstituted and methyl substituted polyradical chains of meta-xylylene by using density functional theory-broken symmetry methodology (DFT-BS). Optimization of geometry in the high-spin and low-spin states have been done at B3LYP/6-31G(d,p) and M06-2X/6-31G(d,p) levels in unrestricted methodology. Single-point calculations on the high-spin optimized geometries have been done by using the 6-311G(d,p) basis set. Each polyradical has been found to be nonplanar with a high-spin ground state. Each has a coupling constant larger than thermal energy. For each group of polyradicals, the coupling constant has been found to exponentially decrease with increase in the number of phenylene groups. The B3LYP infinite chain limit has been estimated for both the unsubstituted and substituted polyradicals. The individual inter-radical-site coupling constants have been estimated for the triradicals and tetraradicals using HDVV Hamiltonian in ORCA 3.0.1 code. These are also generally large and positive, revealing a strong intersite ferromagnetic interaction. The intersite coupling constant too decreases with increasing distance between the radical centers. Finally, we have used CRYSTAL09 package for calculations on the infinitely long one-dimensional and periodic polyradical chains. The coupling constants estimated from the periodic calculations are quite large at about 500 cm(-1) and somewhat greater than the limiting values calculated for the polyradicals with an increasing number of phenylene groups. This happens as the individual polyradicals of increasing size progressively deviate from periodicity, and thereby lessens the strength of through-bond spin-spin coupling. The calculated band gap of ∼4.5 eV indicates that the infinitely long one-dimensional chains must be ferromagnetic and electron insulators.

Doubly TEMPO-coordinated gadolinium(iii), lanthanum(iii), and yttrium(iii) complexes. Strong superexchange coupling across rare earth ions

The X-ray crystal structure of TEMPO-coordinated lanthanide compounds was determined for the first time. The magnetic study clarified that [Gd(hfac)₃(TEMPO)₂] behaved as a ground S_total = 7/2 species. The La and Y analogues showed the superexchange interactions across the diamagnetic ions.

Synthesis, spectroscopy, magnetic and redox behaviors of copper(II) complexes with tert-butylated salen type ligands bearing bis(4-aminophenyl)ethane and bis(4-aminophenyl)amide backbones

New salen type ligands, N,N'-bis(X-3-tert-butylsalicylidene)-4,4'-ethylenedianiline [(X=H (1), 5-tert-butyl (2)] and N,N'-bis(X-3-tert-butylsalicylidene)-4,4'-amidedianiline [X=H (3), 5-tert (4)] and their copper(II) complexes 5-8, have been synthesized. Their spectroscopic (IR, (1)H NMR, UV/vis, ESR) properties, as well as magnetic and redox-reactivity behavior are reported. IR spectra of 7 and 8 indicate the coordination of amide oxygen atoms of 3 and 4 ligands to Cu(II). The solid state ESR spectra of 5-8 exhibits less informative exchange narrowed isotropic or anisotropic signals with weak unresolved low field patterns. The magnetic moments of 5 (2.92 μ(B) per Cu(II)) and 6 (2.79 μ(B) per Cu(II)) are unusual for copper(II) complexes and considerably higher than those for complexes 7 and 8. Cryogenic measurements (300-10 K) show weak antiferromagnetic exchange interactions between the copper(II) centers in complexes 6 and 8. The results of electrochemical and chemical redox-reactivity studies are discussed.

Trinuclear first row transition metal complexes of a hexapyridyl, trialkoxy 1,3,5-triarylbenzene ligand

Trinuclear complexes of Mn(II), Fe(II), Co(II), Ni(II), Cu(II), and Zn(II) were synthesized using a ligand architecture based upon a 1,3,5-triarylbenzene core decorated with six pyridines and three alkoxide moieties. Characterization via X-ray diffraction, NMR, and magnetism studies is discussed.

High-field EPR and magnetic susceptibility studies on binuclear and tetranuclear copper trifluoroacetate complexes. X-ray structure determination of three tetranuclear quinoline adducts of copper(II) trifluoroacetate

Magnetic properties and high-field EPR spectra of three previously unknown tetranuclear quinoline adducts of copper(II) trifluoroacetate were studied, and their X-ray structures were determined. Two green complexes containing a mu(4)-oxo bridge, Cu(4)O(CF(3)COO)(6)(quin)(4) x (C(6)H(5)CH(3))(0.6) (orthorhombic, Pbca, a = 15.278(3), b = 23.227(5), c = 34.895(7) A) and Cu(4)O(CF(3)COO)(6)(quin)(4) x (C(6)H(6))(0.8) (monoclinic, P2/c, a = 21.933(4), b = 11.176(2), c = 23.927(5) A, beta = 97.41(3) degrees) are ferromagnetic, whereas the blue complex [Cu(4)(OH)(2)(CF(3)COO)(8)(quin)(2)](2-)(quinH(+))(2) (monoclinic, a = 21.933(4), b = 11.176(2), c = 23.927(5) A, beta = 97.41(3) degrees), formed in humid air from the solid dimeric [Cu(CF(3)COO)(2) x (quin)](2), is antiferromagnetic, as is the tetranuclear blue product formed in humid air of the mu(4)-oxo tetramers. High-field EPR spectra allowed determination of the spin Hamiltonian parameters for the spin quintet state (S = 2) in the ferromagnetic complexes, which facilitated accurate interpretation of their magnetic susceptibility data. "Broken symmetry" DFT calculations were performed to estimate the exchange integrals in all three tetranuclear complexes, showing surprisingly good agreement with experimental results. Negative sign of the zero-field splitting parameter D in two binuclear complexes, [Cu(CF(3)COO)(2) x CH(3)CN](2) and [Cu(CF(3)COO)(2) x (quin)](2), was found from single-crystal high-field EPR spectra, confirming recent results for nonhalogenated dimeric copper carboxylates.