Antisymmetric Magnetic Interactions in Oxo-Bridged Copper(II) Bimetallic Systems

The resolution of the weak-exchange limit made rigorous, simple and general in binuclear complexes

The correct interpretation of magnetic properties in the weak-exchange regime has remained a challenging task for several decades. In this regime, the effective exchange interaction between local spins is quite weak, of the same order of magnitude or smaller than the various anisotropic terms, which generates a complex set of levels characterized by spin mixing. Although the model multispin Hamiltonian in the absence of local orbital momentum, , is considered good enough to map the experimental energies at zero field and in the strong-exchange limit, theoretical works pointed out limitations of this simple model. This work revives the use of ĤMS from a new theoretical perspective, detailing point-by-point a strategy to correctly map the computational energies and wave functions onto ĤMS, thus validating it regardless of the exchange limit. We will distinguish two cases, based on experimentally characterized dicobalt(II) complexes from the literature. If centrosymmetry imposes alignment of the various rank-2 tensors constitutive of ĤMS in the first case, the absence of any symmetry element prevents such alignment in the second case. In such a context, the strategy provided herein becomes a powerful tool to rationalize the experimental magnetic data, since it is capable of fully and rigorously extracting the multispin model without any assumption on the orientation of its constitutive tensors. Furthermore, the strategy allows to question the use of the spin Hamiltonian approach by explicitly controlling the projection norms on the model space, which is showcased in the second complex where local orbital momentum could have occurred (distorted octahedra). Finally, previous theoretical data related to a known dinickel(II) complex is reinterpreted, clarifying initial wanderings regarding the weak exchange limit.

Magnetic exchange and valence delocalization in a mixed valence [Fe2+Fe3+Te2]+ complex: insights from theory and interpretations of magnetic and spectroscopic data

A mixed valence binuclear Fe^2.5+-Fe^2.5+ (Robin-Day Class III) transition metal complex, [Fe^2.5+μTe₂Fe^2.5+]^1-, composed of two FeN₂Te₂ pseudo-tetrahedral units with μ-bridging Te^2- ligands was reported to exist in an unprecedented S = 3/2 ground state (Nature Chemistry, https://doi.org/10.1038/s41557-021-00853-5). For this and the homologous complexes containing Se^2- and S^2-, the Anderson-Hasegawa double exchange spin-Hamiltonian was broadly used to interpret the corresponding structural, spectroscopic and magnetic data. First principles multireference ab initio calculations are used here to simulate magnetic and spectroscopic EPR data; analysis of the results affords a rationale for the stabilization of the S = 3/2 ground state of the Fe₂ pair. Complete Active Space Self-Consistent Field (CASSCF) calculations and dynamical correlation accounted for by means of N-Electron Valence Perturbation Theory to Second Order (NEVPT2) reproduce well the g-factors determined from simulations of X-band EPR spectra. A crucial technical tool to achieve these results is: (i) use of a localized orbital formulation of the many-particle problem at the scalar-relativistic CASSCF step; (ii) choice of state averaging over states of a given spin (at the CASCI/NEVPT2 step); and (iii) accounting for spin-orbit coupling within the non-relativistic Born-Oppenheimer (BO) many-particle basis using Quasi-Degenerate Perturbation Theory (QDPT). The inclusion of the S = 5/2 spin manifold reproduced the observed increase in the magnetic susceptibility (χT) in the high temperature range (T > 100 K), which is explained by thermal population of the S = 5/2 excited state at energy 160 cm^-1 above the S = 3/2 ground state. Theoretical values of χT from experimentally reported data points in the temperature range from 3 to 30 K were further computed and analyzed using a model which takes spin-phonon coupling into account. The model considerations and the computational protocols of this study are generally applicable to any Class I/II mixed valence dimer. The work can potentially stimulate further experimental and theoretical work on bi- and oligonuclear transition metal complexes of importance to bioinorganic chemistry and life sciences.

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.

Antisymmetric Spin Exchange in a μ-1,2-Peroxodicopper(II) Complex with an Orthogonal Cu-O-O-Cu Arrangement and S = 1 Spin Ground State Characterized by THz-EPR

A unique type of Cu₂/O₂ adduct with orthogonal (close to 90°) Cu-O-O-Cu arrangement has been proposed for initial stages of O₂ binding at biological type III dicopper sites, and targeted ligand design has now allowed us to emulate such an adduct in a pyrazolate-based μ-η¹ :η¹-peroxodicopper(II) complex (2) with Cu-O-O-Cu torsion φ of 87°, coined ^⊥ P intermediate. Full characterization of 2, including X-ray diffraction (d _O-O = 1.452 Å) and Raman spectroscopy (ν̃_O-O = 807 cm^-1), completes a series of closely related Cu₂/O₂ intermediates featuring μ-η¹ :η¹-peroxodicopper(II) cores with φ ranging from 55° (A, cis-peroxo ^C P; Brinkmeier A.et al., J. Am. Chem. Soc.2021, 143, 10361) via 87° (2, ^⊥ P type) up to 104° (B, approaching trans-peroxo ^T P; Kindermann N.et al., Angew. Chem., Int. Ed.2015, 54, 1738). SQUID magnetometry revealed ferromagnetic interaction of the Cu^II ions and a triplet (S _t = 1) ground state in 2. Frequency-domain THz-EPR has been employed to quantitatively investigate the spin systems of 2 and B. Magnetic transitions within the triplet ground states confirmed their substantial zero-field splittings (ZFS) suggested by magnetometry. Formally forbidden triplet-to-singlet transitions at 56 (2) and 157 cm^-1 (B), which are in agreement with the exchange coupling strengths J _iso inferred from SQUID data, are reported for the first time for coupled dicopper(II) complexes. Rigorous analysis by spin-Hamiltonian-based simulations attributed the corresponding nonzero transition probabilities and the ZFS to substantial antisymmetric (Dzyaloshinskii-Moriya) exchange d and provided robust values and orientations for the d , J , and g tensors. These interactions can be correlated with the Cu-O-O-Cu geometries, revealing a linear increase of J _iso with the Cu-O-O-Cu torsion and a strong linear decrease with the Cu-O-O angle. Relevance of the ^⊥ P intermediate for O₂ activation at type III dicopper sites and a potential role of antisymmetric exchange in the concomitant intersystem crossing are proposed.

Extraction of giant Dzyaloshinskii-Moriya interaction from ab initio calculations: First-order spin-orbit coupling model and methodological study

The Dzyaloshinskii-Moriya interaction is expected to be at the origin of interesting magnetic properties, such as multiferroicity, skyrmionic states, and exotic spin orders. Despite this, its theoretical determination is far from being established, neither from the point of view of ab initio methodologies nor from that of the extraction technique to be used afterward. Recently, a very efficient way to increase its amplitude has been demonstrated near the first-order spin-orbit coupling regime. Within the first-order regime, the anisotropic spin Hamiltonian involving the Dzyaloshinskii-Moriya operator becomes inappropriate. Nevertheless, in order to approach this regime and identify the spin Hamiltonian limitations, it is necessary to characterize the underlying physics. To this end, we have developed a simple electronic and spin-orbit model describing the first-order regime and used ab initio calculations to conduct a thorough methodological study.

How to create giant Dzyaloshinskii-Moriya interactions? Analytical derivation and ab initio calculations on model dicopper(II) complexes

This paper is a theoretical "proof of concept" on how the on-site first-order spin-orbit coupling (SOC) can generate giant Dzyaloshinskii-Moriya interactions in binuclear transition metal complexes. This effective interaction plays a key role in strongly correlated materials, skyrmions, multiferroics, and molecular magnets of promising use in quantum information science and computing. Despite this, its determination from both theory and experiment is still in its infancy and existing systems usually exhibit very tiny magnitudes. We derive analytical formulas that perfectly reproduce both the nature and the magnitude of the Dzyaloshinskii-Moriya interaction calculated using state-of-the-art ab initio calculations performed on model bicopper(II) complexes. We also study which geometrical structures/ligand-field forces would enable one to control the magnitude and the orientation of the Dzyaloshinskii-Moriya vector in order to guide future synthesis of molecules or materials. This article provides an understanding of its microscopic origin and proposes recipes to increase its magnitude. We show that (i) the on-site mixings of 3d orbitals rule the orientation and magnitude of this interaction, (ii) increased values can be obtained by choosing more covalent complexes, and (iii) huge values (∼1000 cm^-1) and controlled orientations could be reached by approaching structures exhibiting on-site first-order SOC, i.e., displaying an "unquenched orbital momentum."

Hubbard Trimer with Spin-Orbit Coupling: Hartree-Fock Solutions, (Non)Collinearity, and Anisotropic Spin Hamiltonian

We present unrestricted and generalized Hartree-Fock solutions (UHF and GHF, respectively) for the single-band Hubbard model of an equilateral triangle. Spin-orbit coupling (SOC) is treated self-consistently, and HF stability and properties of different spin structures are studied in detail. The GHF solution switches from noncollinear to collinear when crossing a high-symmetry point in parameter space (spanned by the amplitudes of spin-conserving and spin-dependent hopping, i.e., kinetic energy and SOC, respectively). The collinear GHF solution represents a simple example to disprove the notion that a collinear vector spin density in a Slater determinant necessarily entails a defined spin projection. Spin Hamiltonian parameters for the anisotropic interaction between three spin-1/2 centers are extracted from HF energies and subsequently compared to exact results from effective Hamiltonian theory. This provides an unambiguous benchmark for interpreting broken-symmetry mean-field solutions in terms of spin configurations and puts this semiclassical approach (frequently applied in broken-symmetry density functional theory) on a firmer basis.

Exact Mapping from Many-Spin Hamiltonians to Giant-Spin Hamiltonians

Thermodynamic and spectroscopic data of exchange-coupled molecular spin clusters (e.g. single-molecule magnets) are routinely interpreted in terms of two different models: the many-spin Hamiltonian (MSH) explicitly considers couplings between individual spin centers, while the giant-spin Hamiltonian (GSH) treats the system as a single collective spin. When isotropic exchange coupling is weak, the physical compatibility between both spin Hamiltonian models becomes a serious concern, due to mixing of spin multiplets by local zero-field splitting (ZFS) interactions ('S-mixing'). Until now, this effect, which makes the mapping MSH→GSH ('spin projection') non-trivial, had only been treated perturbationally (up to third order), with obvious limitations. Here, based on exact diagonalization of the MSH, canonical effective Hamiltonian theory is applied to construct a GSH that exactly matches the energies of the relevant (2S+1) states comprising an effective spin multiplet. For comparison, a recently developed strategy for the unique derivation of effective ('pseudospin') Hamiltonians, now routinely employed in ab initio calculations of mononuclear systems, is adapted to the problem of spin projection. Expansion of the zero-field Hamiltonian and the magnetic moment in terms of irreducible tensor operators (or Stevens operators) yields terms of all ranks k (up to k=2S) in the effective spin. Calculations employing published MSH parameters illustrate exact spin projection for the well-investigated [Ni(hmp)(dmb)Cl]₄ ('Ni₄ ') single-molecule magnet, which displays weak isotropic exchange (dmb=3,3-dimethyl-1-butanol, hmp^- is the anion of 2-hydroxymethylpyridine). The performance of the resulting GSH in finite field is assessed in terms of EPR resonances and diabolical points. The large tunnel splitting in the M=± 4 ground doublet of the S=4 multiplet, responsible for fast tunneling in Ni₄ , is attributed to a Stevens operator with eightfold rotational symmetry, marking the first quantification of a k=8 term in a spin cluster. The unique and exact mapping MSH→GSH should be of general importance for weakly-coupled systems; it represents a mandatory ultimate step for comparing theoretical predictions (e.g. from quantum-chemical calculations) to ZFS, hyperfine or g-tensors from spectral fittings.

Design of a Binuclear Ni(II) Complex with Large Ising-type Anisotropy and Weak Anti-Ferromagnetic Coupling

The preparation of a binuclear Ni(II) complex with a pentacoordinate environment using a cryptand organic ligand and the imidazolate bridge is reported. The coordination sphere is close to trigonal bipyramidal (tbp) for one Ni(II) and to square pyramidal (spy) for the other. The use of the imidazolate bridge that undergoes π-π stacking with two benzene rings of the chelating ligand induces steric hindrance that stabilizes the pentacoordinate environment. Magnetic measurements together with theoretical studies of the spin states energy levels allow fitting the data and reveal a large Ising-type anisotropy and a weak anti-ferromagnetic exchange coupling between the metal ions. The magnitude and the nature of the magnetic anisotropy and the difference in anisotropy between the two metal ions are rationalized using wave-function-based calculations. We show that a slight distortion of the coordination sphere of Ni(II) from spy to tbp leads to an Ising-type anisotropy. Broken-symmetry density functional calculations rationalize the weak anti-ferromagnetic exchange coupling through the imidazolate bridge.

Pentagonal Bipyramid FeII Complexes: Robust Ising-Spin Units towards Heteropolynuclear Nanomagnets

Pentagonal bipyramid Fe^II complexes have been investigated to evaluate their potential as Ising-spin building units for the preparation of heteropolynuclear complexes that are likely to behave as single-molecule magnets (SMMs). The considered monometallic complexes were prepared from the association of a divalent metal ion with pentadentate ligands that have a 2,6-diacetylpyridine bis(hydrazone) core (H₂ L^N3O2R ). Their magnetic anisotropy was established by magnetometry to reveal their zero-field splitting (ZFS) parameter D, which ranged between -4 and -13 cm^-1 and was found to be modulated by the apical ligands (ROH versus Cl). The alteration of the D value by N-bound axial CN ligands, upon association with cyanometallates, was also assessed for heptacoordinated Fe^II as well as for related Ni^II and Co^II derivatives. In all cases, N-coordinated cyanide ligands led to large magnetic anisotropy (i.e., -8 to -18 cm^-1 for Fe and Ni, +33 cm^-1 for Co). Ab initio calculations were performed on three Fe^II complexes, which enabled one to rationalize the role of the ligand on the nature and magnitude of the magnetic anisotropy. Starting from the pre-existing heptacoordinated complexes, a series of pentanuclear compounds were obtained by reactions with paramagnetic [W(CN)₈ ]^3- . Magnetic studies revealed the occurrence of ferromagnetic interactions between the spin carriers in all the heterometallic systems. Field-induced slow magnetic relaxation was observed for mononuclear Fe^II complexes (U_eff /k_B up to 53 K (37 cm^-1 ), τ₀ =5×10^-9  s), and SMM behavior was evidenced for a heteronuclear [Fe₃ W₂ ] derivative (U_eff /k_B =35 K and τ₀ =4.6 10^-10  s), which confirmed that the parent complexes were robust Ising-type building units. High-field EPR spectroscopic investigation of the ZFS parameters for a Ni derivative is also reported.

Construction of Giant-Spin Hamiltonians from Many-Spin Hamiltonians by Third-Order Perturbation Theory and Application to an Fe3 Cr Single-Molecule Magnet

A general giant-spin Hamiltonian (GSH) describing an effective spin multiplet of an exchange-coupled metal cluster with dominant Heisenberg interactions was derived from a many-spin Hamiltonian (MSH) by treating anisotropic interactions at the third order of perturbation theory. Going beyond the existing second-order perturbation treatment allows irreducible tensor operators of rank six (or corresponding Stevens operator equivalents) in the GSH to be obtained. Such terms were found to be of crucial importance for the fitting of high-field EPR spectra of a number of single-molecule magnets (SMMs). Also, recent magnetization measurements on trigonal and tetragonal SMMs have found the inclusion of such high-rank axial and transverse terms to be necessary to account for experimental data in terms of giant-spin models. While mixing of spin multiplets by local zero-field splitting interactions was identified as the major origin of these contributions to the GSH, a direct and efficient microscopic explanation had been lacking. The third-order approach developed in this work is used to illustrate the mapping of an MSH onto a GSH for an S=6 trigonal Fe3 Cr complex that was recently investigated by high-field EPR spectroscopy. Comparisons between MSH and GSH consider the simulation of EPR data with both Hamiltonians, as well as locations of diabolical points (conical intersections) in magnetic-field space. The results question the ability of present high-field EPR techniques to determine high-rank zero-field splitting terms uniquely, and lead to a revision of the experimental GSH parameters of the Fe3 Cr SMM. Indeed, a bidirectional mapping between MSH and GSH effectively constrains the number of free parameters in the GSH. This notion may in the future facilitate spectral fitting for highly symmetric SMMs.

Ab initio modelling of magnetic anisotropy in Sr3NiPtO6

First principles calculations in the framework of Density Functional Theory (DFT) and wavefunction-based correlated methods have been performed to investigate in detail the magnetic anisotropy in Sr3NiPtO6. This material is known for the easy-plane anisotropy with a large anisotropy constant of about 7.5-9.3 meV. We find that by properly choosing the onsite Coulomb repulsion and exchange parameters, DFT can correctly explain the easy-plane magnetocrystalline anisotropy of the material, but the magnitude of the anisotropy constant is underestimated. On the other hand, a quantitative agreement with respect to experiments, both in the magnitude and direction of the magnetic anisotropy, can be recovered by using the wavefunction-based approach which is able to fully describe the multiplet physics. We also show that the presence of structural distortions of the local NiO6 coordination is crucial for stabilizing the magnetic anisotropy in this compound.

Magnetic properties of a Kramers doublet. An univocal bridge between experimental results and theoretical predictions

The magnetic response of a Kramers doublet is analyzed in a general case taking into account only the formal properties derived from time reversal operation. It leads to a definition of a matrix G (gyromagnetic matrix) whose expression depends on the chosen reference frame and on the Kramers conjugate basis used to describe the physical system. It is shown that there exists a reference frame and a suitable Kramers conjugate basis that gives a diagonal form for the G-matrix with all non-null elements having the same sign. A detailed procedure for obtaining this canonical expression of G is presented when the electronic structure of the KD is known regardless the level of the used theory. This procedure provides a univocal way to compare the theoretical predictions with the experimental results obtained from a complete set of magnetic experiments. In this way the problems arising from ambiguities in the g-tensor definition are overcome. This procedure is extended to find a spin-Hamiltonian suitable for describing the magnetic behavior of a pair of weakly coupled Kramers systems in the multispin scheme when the interaction between the two moieties as well as the individual Zeeman interaction are small enough as compared with ligand field splitting. Explicit relations between the physical interaction and the parameters of such a spin-Hamiltonian are also obtained.

The ligand field of the azido ligand: insights into bonding parameters and magnetic anisotropy in a Co(II)-azido complex

The azido ligand is one of the most investigated ligands in magnetochemistry. Despite its importance, not much is known about the ligand field of the azido ligand and its influence on magnetic anisotropy. Here we present the electronic structure of a novel five-coordinate Co(II)-azido complex (1), which has been characterized experimentally (magnetically and by electronic d-d absorption spectroscopy) and theoretically (by means of multireference electronic structure methods). Static and dynamic magnetic data on 1 have been collected, and the latter demonstrate slow relaxation of the magnetization in an applied external magnetic field of H = 3000 Oe. The zero-field splitting parameters deduced from static susceptibility and magnetizations (D = -10.7 cm(-1), E/D = 0.22) are in excellent agreement with the value of D inferred from an Arrhenius plot of the magnetic relaxation time versus the temperature. Application of the so-called N-electron valence second-order perturbation theory (NEVPT2) resulted in excellent agreement between experimental and computed energies of low-lying d-d transitions. Calculations were performed on 1 and a related four-coordinate Co(II)-azido complex lacking a fifth axial ligand (2). On the basis of these results and contrary to previous suggestions, the N3(-) ligand is shown to behave as a strong σ and π donor. Magnetostructural correlations show a strong increase in the negative D with increasing Lewis basicity (shortening of the Co-N bond distances) of the axial ligand on the N3(-) site. The effect on the change in sign of D in going from four-coordinate Co(II) (positive D) to five-coordinate Co(II) (negative D) is discussed in the light of the bonding scheme derived from ligand field analysis of the ab initio results.

An ab initio MO study of heavy atom effects on the zero-field splitting tensors of high-spin nitrenes: how the spin–orbit contributions are affected

The CASSCF and hybrid CASSCF–MRMP2 methods reproduce the ZFS tensors of spin-septet 2,4,6-trinitrenopyridines, focusing on the heavy atom effects on the spin–orbit terms of the tensors.

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.

Origin of the magnetic anisotropy in heptacoordinate Ni(II) and Co(II) complexes

The nature and magnitude of the magnetic anisotropy of heptacoordinate mononuclear Ni(II) and Co(II) complexes were investigated by a combination of experiment and ab initio calculations. The zero-field splitting (ZFS) parameters D of [Ni(H(2)DAPBH)(H(2)O)(2)](NO(3))(2)⋅2 H(2)O (1) and [Co(H(2)DAPBH)(H(2)O)(NO(3))](NO(3)) [2; H(2)DAPBH = 2,6-diacetylpyridine bis- (benzoyl hydrazone)] were determined by means of magnetization measurements and high-field high-frequency EPR spectroscopy. The negative D value, and hence an easy axis of magnetization, found for the Ni(II) complex indicates stabilization of the highest M(S) value of the S = 1 ground spin state, while a large and positive D value, and hence an easy plane of magnetization, found for Co(II) indicates stabilization of the M(S) = ±1/2 sublevels of the S = 3/2 spin state. Ab initio calculations were performed to rationalize the magnitude and the sign of D, by elucidating the chemical parameters that govern the magnitude of the anisotropy in these complexes. The negative D value for the Ni(II) complex is due largely to a first excited triplet state that is close in energy to the ground state. This relatively small energy gap between the ground and the first excited state is the result of a small energy difference between the d(xy) and d(x(2)-y(2)) orbitals owing to the pseudo-pentagonal-bipyramidal symmetry of the complex. For Co(II), all of the excited states contribute to a positive D value, which accounts for the large magnitude of the anisotropy for this complex.

Rationalization of the behavior of M2(CH3CS2)4I (M = Ni, Pt) chains at room temperature from periodic density functional theory and ab initio cluster calculations

The electrical conductivities and plausible charge-ordering states in the room temperature (r.t.) phase for MMX chains [Ni(2)(dta)(4)I](∞) and [Pt(2)(dta)(4)I](∞) (dta = CH(3)CS(2)(-)) have been analyzed with periodic density functional theory (DFT) and correlated ab initio calculations combined with the effective Hamiltonian theory. Periodic DFT calculations show a more delocalized nature of the ground state in [Pt(2)(dta)(4)I](∞) compared to [Ni(2)(dta)(4)I](∞), which features a rather large energy gap between the occupied and empty bands, and charge polarized dimer units. A larger electrical conductivity for the Pt chain can be expected, especially because the Fermi level lies within a band with contributions from Pt and I orbitals. Electronic structure parameters extracted from ab initio cluster calculations show that the large difference between the observed conductivities at 300 K for Ni and Pt compounds, of 3 orders of magnitude, cannot be explained from the parameters extracted from an embedded M(2)(dta)(4)I(2) dimer fragment alone. When tetramer fragments are considered, we observe that the interdimer transfer integral (t) between neighboring M(2) units connected by an iodine atom at correlated level is comparable in both chains. On the other hand, the energy to transfer an electron from a dimer to the neighboring one (Coulomb repulsion U) is three times larger in the Ni compound with respect to the Pt chain, in line with the poor conductivity of the former. The electronic structure of the M(4)(dta)(8)I(3) fragment points to an alternate charge-polarization state for Ni and an average valence state for Pt when the r.t. X-ray structure is considered.

How Do Heavier Halide Ligands Affect the Signs and Magnitudes of the Zero-Field Splittings in Halogenonickel(II) Scorpionate Complexes? A Theoretical Investigation Coupled to Ligand-Field Analysis

This work presents a detailed analysis of the physical origin of the zero-field splittings (ZFSs) in a series of high-spin (S = 1) nickel(II) scorpionate complexes Tp*NiX (Tp* = hydrotris(3,5-dimethylpyrazole)borate, X = Cl, Br, I) using quantum chemical approaches. High-frequency and -field electron paramagnetic resonance studies have shown that the complexes with heavier halide ligands (Br, I) have greater magnitudes but opposite signs of the ZFSs compared with the chloro congener (Desrochers, P. J.; Telser, J.; Zvyagin, S. A.; Ozarowski, A.; Krzystek, J.; Vicic, D. A. Inorg. Chem.2006, 45, 8930-8941). To rationalize the experimental findings, quantum chemical calculations of the ZFSs in this Ni(II) halide series have been conducted. The computed ZFS using wave-function-based ab initio methods (state-averaged CASSCF, NEVPT2, and SORCI) are in good agreement with the experiment. For comparison, density functional theory was only marginally successful. The ligand-field analysis demonstrates that the signs and magnitudes of the ZFSs are subtly determined by the trade-off between the negative contributions from the (1,3)A1(1e→2e) transitions relative to the positive contributions from the remaining d-d excited states. The term from (1,3)A1(1e→2e) stems from the structural feature that the metal center displaces out of the equatorial plane, and gains the importance when heavier halide ligand is involved.

Detailed ab initio first-principles study of the magnetic anisotropy in a family of trigonal pyramidal iron(II) pyrrolide complexes

A theoretical, computational, and conceptual framework for the interpretation and prediction of the magnetic anisotropy of transition metal complexes with orbitally degenerate or orbitally nearly degenerate ground states is explored. The treatment is based on complete active space self-consistent field (CASSCF) wave functions in conjunction with N-electron valence perturbation theory (NEVPT2) and quasidegenerate perturbation theory (QDPT) for treatment of magnetic field- and spin-dependent relativistic effects. The methodology is applied to a series of Fe(II) complexes in ligand fields of almost trigonal pyramidal symmetry as provided by several variants of the tris-pyrrolylmethyl amine ligand (tpa). These systems have recently attracted much attention as mononuclear single-molecule magnet (SMM) complexes. This study aims to establish how the ligand field can be fine tuned in order to maximize the magnetic anisotropy barrier. In trigonal ligand fields high-spin Fe(II) complexes adopt an orbitally degenerate (5)E ground state with strong in-state spin-orbit coupling (SOC). We study the competing effects of SOC and the (5)E⊗ε multimode Jahn-Teller effect as a function of the peripheral substituents on the tpa ligand. These subtle distortions were found to have a significant effect on the magnetic anisotropy. Using a rigorous treatment of all spin multiplets arising from the triplet and quintet states in the d(6) configuration the parameters of the effective spin-Hamiltonian (SH) approach were predicted from first principles. Being based on a nonperturbative approach we investigate under which conditions the SH approach is valid and what terms need to be retained. It is demonstrated that already tiny geometric distortions observed in the crystal structures of four structurally and magnetically well-documented systems, reported recently, i.e., [Fe(tpa(R))](-) (R = tert-butyl, Tbu (1), mesityl, Mes (2), phenyl, Ph (3), and 2,6-difluorophenyl, Dfp (4), are enough to lead to five lowest and thermally accessible spin sublevels described sufficiently well by S = 2 SH provided that it is extended with one fourth order anisotropy term. Using this most elementary parametrization that is consistent with the actual physics, the reported magnetization data for the target systems were reinterpreted and found to be in good agreement with the ab initio results. The multiplet energies from the ab initio calculations have been fitted with remarkable consistency using a ligand field (angular overlap) model (ab initio ligand field, AILFT). This allows for determination of bonding parameters and quantitatively demonstrates the correlation between increasingly negative D values and changes in the σ-bond strength induced by the peripheral ligands. In fact, the sigma-bonding capacity (and hence the Lewis basicity) of the ligand decreases along the series 1 > 2 > 3 > 4.