Magnetic Anisotropy in NiII–YIII Binuclear Complexes: On the Importance of Both the First Coordination Sphere of the NiII Ion and the YIII Ion Belonging to the Second Coordination Sphere

Antisymmetric Exchange in a Real Copper Triangular Complex

The antisymmetric exchange, also known as the Dzyaloshinskii-Moriya interaction (DMI), is an effective interaction that may be at play in isolated complexes (with transition metals or lanthanides, for instance), nanoparticles, and highly correlated materials with adequate symmetry properties. While many theoretical works have been devoted to the analysis of single-ion zero-field splitting and to a lesser extent to symmetric exchange, only a few ab initio studies deal with the DMI. Actually, it originates from a subtle interplay between weak electronic interactions and spin-orbit couplings. This article aims to highlight the origin of this interaction from theoretical grounds in a real tri-copper(II) complex, capitalizing on previous methodological studies on bi-copper(II) model complexes. By tackling this three-magnetic-center system, we will first show that the multispin model Hamiltonian is appropriate for trinuclear (and likely for higher nuclearity) complexes, then that the correct application of the permutation relationship is necessary to explain the outcomes of the ab initio calculations, and finally, that the model parameters extracted from a binuclear model transfer well to the trinuclear complex. For a more theory-oriented purpose, we will show that the use of a simplified structural model allows one to perform more demanding electronic structure calculations. On this simpler system, we will first check that the previous transferability is still valid, prior to performing more advanced calculations on the derived two-magnetic-center model system. To this end, we will explain in detail the physics of the DMI in the copper triangle of interest, before advocating further theory/experiment efforts.

Magnetic Anisotropy in a Cubane-like Ni4 Complex: An Ab Initio Perspective

Magnetic anisotropy, in the absence of an external magnetic field, relates to the degeneracy lift of energy levels. In the standard case of transition metal complexes, this property is usually modeled by an anisotropic spin Hamiltonian and one speaks of "zero-field splitting" (ZFS) of spin states. While the case of mononuclear complexes has been extensively described by means of ab initio quantum mechanical calculations, the literature on polynuclear complexes studied with these methodologies is rather scarce. In this work, advanced multiconfigurational wave function theory methods are applied to compute the ZFS of the ground S = 4 state of an actual tetranickel(II) complex, displaying a magnet behavior below 0.5 K. First, the isotropic couplings are computed in the absence of the spin-orbit coupling operator, in the full complex and also in clusters with only two active nickel(II) centers, confirming the occurrence of weak ferromagnetic couplings in this system. Second, the single-site magnetic anisotropies are computed on a cluster bearing only one active nickel(II) site, showing that the single-site anisotropy axes are not oriented in an optimal fashion for generating a large uniaxial molecular anisotropy. Furthermore, the possibility for involving only a few local orbital excited states in the calculation is assessed, actually opening the way for a consistent and manageable treatment of the ZFS of the ground S = 4 state. Third, multiconfigurational calculations are performed on the full complex, confirming the weak uniaxial anisotropy occurring for this state and also, interestingly, revealing a significant contribution of the lowest-lying orbitally excited S = 3 states. Overall, by comparison with the experiment, the reported results question the common habit of using only one structure, in particular derived from a crystallography experiment, to compute magnetic anisotropy parameters.

A Design Criteria to Achieve Giant Ising-Type Anisotropy in CoII -Encapsulated Metallofullerenes

Discovery of permanent magnetisation in molecules just like in hard magnets decades ago led to the proposal of utilising these molecules for information storage devices and also as Q-bits in quantum computing. A significant breakthrough with a blocking temperature as high as 80 K has been recently reported for lanthanocene complexes. While enhancing the blocking temperature further remains one of the primary challenges, obtaining molecules that are suitable for the fabrication of the devices sets the bar very high in this area. Encouraged by the fact that our earlier predictions of potential single-molecule magnets (SMMs) in lanthanide-containing endohedral fullerenes have been verified, here we set out to undertake a comprehensive study on Co^II -ion-encapsulated fullerene as potential SMMs. To study this class of molecules, we have utilised an array of theoretical methods ranging from density functional to ab initio CASSCF/NEVPT2 methods for obtaining reliable estimate of zero-field splitting parameters D and E. Additionally, we have also employed, for the first time a combination of molecular dynamics based on DFT methods coupled with CASSCF/NEVPT2 methods to seek the role of conformational isomers in the relaxation of magnetisation. Particularly, we have studied, Co@C₂₈ , Co@C₃₈ and Co@C₄₈ cages and their isomers as potential target molecules that could yield substantial magnetic anisotropy. Our calculations categorically reveal a very large Ising anisotropy in this class of molecules, with Co@C₄₈ cages predicted to yield D values as high as -127 cm^-1 . Our calculations on the smaller cages reveal the free movement of Co^II ion inside the cage, leading to the likely scenario of faster relaxation of magnetisation. However, larger fullerene cages were found to solve this issue. Further models with incorporating units such as {CoOZn}, {CoScZnN} inside larger fullerenes yield axial zero-field splitting values as high as -200 cm^-1 with negligible E/D values. As these units represent a strong axiality coupled with a viable way to obtain air-stable low-coordinate Co^II complexes, this opens up a new paradigm in the search of SMMs in this class of molecules.

Influence of ancillary ligands and solvents on the nuclearity of Ni-Ln complexes

A Schiff base ligand resulting from the reaction of ovanillin and 2,2-dimethyl-1,3-diaminopropane allows the preparation of hetero-dinuclear [Ni-Ln]³⁺ or -trinuclear [Ni-Ln-Ni]³⁺ complexes. Although empirical parameters for rationalizing the strength of the ferromagnetic Ni-Gd interaction have already been discussed in several papers, no systematic study has been devoted to the control of the nuclearity of such complexes. With the help of structural determinations, we demonstrate the role of solvent and of the nature of ancillary ligands, linked to the Ln ions, in nuclearity. For instance, the presence of one chelating nitrato ligand is already sufficient to impede an increase in the nuclearity, while the replacement of nitrato ligands by chloride anions still yields dinuclear Ni-Ln complexes. This experimental result evidences the role of protic solvents. In contrast, the use of lanthanide salts, soluble in non-protic solvents, allows the isolation of dinuclear [Ni-Ln]³⁺ or trinuclear cationic [LNi-Ln-NiL]³⁺ complexes, depending on the Ni/Ln ratio. A further synthetic step can be overtaken by the reaction of a Ni-Ln complex, soluble in a non-protic solvent, with a LM complex (M = Cu, Zn). By doing so, a heterotrinuclear complex made of three different metal ions, two distinct 3d ions and a 4f one, has been isolated and structurally characterized. Note that the Ni coordination number decreases from 6 to 5 on going from the dinuclear complex to the trinuclear one. Also, the replacement of water molecules by chloride ligands in the hexacoordinate Ni complexes induces a net increase of the positive zero-field splitting parameter D to 20 cm^-1, which is supported by ab initio calculations. Although the Ni-Ln (Ln = Gd, Tb, Dy) magnetic interactions are ferromagnetic, the corresponding trinuclear complexes are devoid of SMM properties in the absence of an applied magnetic field.

Co-crystal structure of a dinuclear (Zn-Y) and a trinuclear (Zn-Y-Zn) complexes derived from a Schiff base ligand

The present investigation describes the synthesis and structural study of a metal-zinc ligand [ZnL.H2O], which was used to generate three dimensional supramolecular complex formulated as [Y{Zn(L)(SCN)}(SCN)2].[Y{Zn(L)(SCN)}2(DMF)2].(NO3). The title compound crystallizes in the triclinic space group P-1 with the following unit cell parameters: a = 14.8987(7) Å, b = 15.6725(8) Å, c = 19.2339(10) Å, a = 94.610(4)°, β = 103.857(4)°, γ = 101.473(4)°, V = 4234.4(4) Å3, Z = 2, R1 = 0.063 and wR2 = 0.96. For this compound, the structure reveals that one heterodinuclear unit [Y{Zn(L)(SCN)}(SCN)2] is co-crystallized with a heterotrinuclear unit [Y{Zn(L)(SCN)}2(DMF)2].(NO3). In the dinuclear moiety, the organic molecule acts as a hexadentate ligand and in the trinuclear unit, it acts as a pentadentate ligand with one of the oxygen methoxy group remaining uncoordinated. In both units the coordination environment of the zinc metal can be described as distorted square pyramidal. In the dinuclear unit the Y(III) is hexacoordinated while it is octacoordinated in the trinuclear unit. The environment of the Y(III) can be described as a distorted octahedral geometry in the dinuclear and as a distorted square antiprism in the trinuclear units respectively.

NiII–LnIII complexes with o-vanillin as the main ligand: syntheses, structures, magnetic and magnetocaloric properties

ortho-Vanillin yields three types of heteronuclear Ni^II–Ln^III complexes, ranging from dinuclear to tetranuclear defect dicubane complexes.

Reactions of a series of ZnL, CuL and NiL Schiff base and non-Schiff base complexes with MCl2 salts (M = Cu, Ni, Mn): syntheses, structures, magnetic properties and DFT calculations

DFT calculations demonstrate that the weak antiferromagnetic interaction in the highly non-symmetric diphenoxo Cu–Cu bridge results from two antagonistic bridging pathways

On The Density Functional Theory Treatment of Lanthanide Coordination Compounds: A Comparative Study in a Series of Cu-Ln (Ln = Gd, Tb, Lu) Binuclear Complexes

The nontrivial aspects of electron structure in lanthanide complexes, considering ligand field (LF) and exchange coupling effects, have been investigated by means of density functional theory (DFT) calculations, taking as a prototypic case study a series of binuclear complexes [LCu(O₂COMe)Ln(thd)₂], where L^2- = N,N'-2,2-dimethyl-propylene-di(3-methoxy-salicylidene-iminato) and Ln = Tb, Lu, and Gd. Particular attention has been devoted to the Cu-Tb complex, which shows a quasi-degenerate nonrelativistic ground state. Challenging the limits of density functional theory (DFT), we devised a practical route to obtain different convergent solutions, permuting the starting guess orbitals in a manner resembling the run of the β electron formally originating from the f⁸ configuration of the Tb(III) over seven molecular orbitals (MOs) with predominant f-type character. Although the obtained states cannot be claimed as the DFT computed split of the ⁷F multiplet, the results are yet interesting numeric experiments, relevant for the ligand field effects. We also performed broken symmetry (BS) DFT estimation of exchange coupling in the Cu-Gd system, using different settings, with Gaussian-type and plane-wave bases, finding a good match with the coupling parameter from experimental data. We also caught BS-type states for each of the mentioned series of different states emulated for the Cu-Tb complex, finding almost equal exchange coupling parameters throughout the seven LF-like configurations, the magnitude of the J parameter being comparable with those of the Cu-Gd system.

Exploration of unconventional π–hole and C–H⋯H–C types of supramolecular interactions in a trinuclear Cd(ii) and a heteronuclear Cd(ii)–Ni(ii) complex and experimental evidence for preferential site selection of the ligand by 3d and 4d metal ions

We report the synthesis of a trinuclear cadmium(ii) (1) and a di(phenoxido)-bridged dinuclear cadmium(ii)–nickel(ii) (2) complex derived from a bicompartmental (N₂O₄) Schiff base ligand.

Inducing magnetic communication in caged dinuclear Co(ii) systems

Magnetic interactions were probed for a series of mono and tri atomic bridged dinuclear Co(ii) azacryptand complexes. Magneto-structural correlations were established usingab initiocalculations.

Magnetic anisotropy of mononuclear Ni(II) complexes: on the importance of structural diversity and the structural distortions

Mononuclear Ni(II) complexes are particularly attractive in the area of single-molecule magnets as the axial zero-field splitting (D) for the Ni(II) complexes is in the range of -200 to +200 cm(-1) . Despite this advantage, very little is known on the origin of anisotropy across various coordination ligands, coordination numbers, and particularly what factors influence the D parameter in these complexes. To answer some of these questions, herein we have undertaken a detailed study of a series of mononuclear Ni(II) complexes with ab initio calculations. Our results demonstrate that three prominent spin-conserved low-lying d-d transitions contribute significantly to the D value. Variation in the sign and the magnitude of D values are found to correlate to the specific structural distortions. Apart from the metal-ligand bond lengths, two different parameters, namely, Δα and Δβ, which are correlated to the cis angles present in the coordination environment, are found to significantly influence the axial D values. Developed magneto-structural D correlations suggest that the D values can be enhanced significantly by fine tuning the structural distortion in the coordination environment. Calculations performed on a series of Ni(II) models with coordination numbers two to six unfold an interesting observation-the D parameter increases significantly upon a reduction in coordination number compared with a reference octahedral coordination. Besides, if high symmetry is maintained, even larger coordination numbers yield large D values.

Magnetic state of pyrochlore Cd(2)Os(2)O(7) emerging from strong competition of ligand distortions and longer-range crystalline anisotropy

By many-body quantum-chemical calculations, we investigate the role of two structural effects--local ligand distortions and the anisotropic Cd-ion coordination--on the magnetic state of Cd(2)Os(2)O(7), a spin S = 3/2 pyrochlore. We find that these effects strongly compete, rendering the magnetic interactions and ordering crucially dependent on these geometrical features. Without trigonal distortions, a large easy-plane magnetic anisotropy develops. Their presence, however, reverses the sign of the zero-field splitting and causes a large easy-axis anisotropy (D ≃ -6.8 meV), which in conjunction with the antiferromagnetic exchange interaction (J ≃ 6.4 meV) stabilizes an all-in-all-out magnetic order. The competition uncovered here is a generic feature of pyrochlore magnets.

Investigating magnetostructural correlations in the pseudooctahedral trans-[Ni(II){(OPPh2)(EPPh2)N}2(sol)2] complexes (E = S, Se; sol = DMF, THF) by magnetometry, HFEPR, and ab initio quantum chemistry

In this work, magnetometry and high-frequency and -field electron paramagnetic resonance spectroscopy (HFEPR) have been employed in order to determine the spin Hamiltonian (SH) parameters of the non-Kramers, S = 1, pseudooctahedral trans-[Ni(II){(OPPh(2))(EPPh(2))N}(2)(sol)(2)] (E = S, Se; sol = DMF, THF) complexes. X-ray crystallographic studies on these compounds revealed a highly anisotropic NiO(4)E(2) coordination environment, as well as subtle structural differences, owing to the nature of the Ni(II)-coordinated solvent molecule or ligand E atoms. The effects of these structural characteristics on the magnetic properties of the complexes were investigated. The accurately HFEPR-determined SH zero-field-splitting (zfs) D and E parameters, along with the structural data, provided the basis for a systematic density functional theory (DFT) and multiconfigurational ab initio computational analysis, aimed at further elucidating the electronic structure of the complexes. DFT methods yielded only qualitatively useful data. However, already entry level ab initio methods yielded good results for the investigated magnetic properties, provided that the property calculations are taken beyond a second-order treatment of the spin-orbit coupling (SOC) interaction. This was achieved by quasi-degenerate perturbation theory, in conjunction with state-averaged complete active space self-consistent-field calculations. The accuracy in the calculated D parameters improves upon recovering dynamic correlation with multiconfigurational ab initio methods, such as the second-order N-electron valence perturbation theory NEVPT2, the difference dedicated configuration interaction, and the spectroscopy-oriented configuration interaction. The calculations showed that the magnitude of D (∼3-7 cm(-1)) in these complexes is mainly dominated by multiple SOC contributions, the origin of which was analyzed in detail. In addition, the observed largely rhombic regime (E/D = 0.16-0.33) is attributed to the highly distorted metal coordination sphere. Of special importance is the insight by this work on the zfs effects of Se coordination to Ni(II). Overall, a combined experimental and theoretical methodology is provided, as a means to probe the electronic structure of octahedral Ni(II) complexes.

Chiral crystallization of a heterodinuclear Ni-Ln series: comprehensive analysis of the magnetic properties

Four heterodinuclear (H(2)O)(2)NiL-Ln(NO(3))(3) complexes (Ln = Tb, Dy, Er, Yb) with a double phenoxo bridge coming from the dideprotonated Schiff-base ligand are synthesized and characterized by crystal and powder X-ray diffraction studies. This series of compounds devoid of any chiral center, crystallizes in a noncentrosymmetric space group P2(1), as the previously described (H(2)O)(2)NiL-Gd(NO(3))(3) equivalent. All four complexes are ferromagnetically coupled. If this behavior is clearly shown by the χ(M)T increase at low temperature in the case of the Ni-Tb and Ni-Dy complexes, it necessitates the preparation of the Zn-Er and Zn-Yb equivalent entities to be evidenced in the case of the Ni-Er and Ni-Yb complexes. Out-of-phase susceptibility signals are found in the four cases, but the SMM behavior is neither confirmed, nor completely studied because of the presence of fast quantum tunnelling at zero field. Thorough ab initio multiconfiguration calculations are carried out, achieving a realistic account of ligand field effects, exchange coupling and magnetic anisotropy in the discussed systems. The calculations reveal the ferromagnetic intercenter exchange coupling, the interplay with spin-orbit effects leading to a Ising-like scheme of the lowest levels. The ab initio simulation of the magnetic susceptibility is in semiquantitative agreement with experimental data, certifying the reasonableness of the theoretical treatments in obtaining valuable information for the interacting mechanisms. The anisotropy is accounted for by drawing polar diagrams of state-specific magnetization functions, obtained by handling of the data resulting from ab initio calculations including the spin-orbit effects. Supplementary, Density Functional Theory (DFT) calculations are carried out, presenting new methodological clues and assessments. The DFT is not perfectly adequate for lanthanide systems because of orbital pseudodegeneracy issues. However, we show that in particular circumstances the DFT can be partly used, succeeding here in mimicking different orbital configurations of the Ni-Tb system. The DFT seems to offer reasonable estimations of exchange coupling parameters, while it remains problematic in the complete account of Ligand Field splitting. The Paper presents unprecedented methodological advances and correlations with phenomenological and heuristic interpretation of experimental data, taking into focus relevant d-f systems constructed with a prototypical binucleating ligand.