Quantifying Exchange Coupling in f-Ion Pairs Using the Diamagnetic Substitution Method

Ab initio-based determination of lanthanoid-radical exchange as visualised by inelastic neutron scattering

Magnetic exchange coupling can modulate the slow magnetic relaxation in single-molecule magnets. Despite this, elucidation of exchange coupling remains a significant challenge for the lanthanoid(iii) ions, both experimentally and computationally. In this work, the crystal field splitting and 4f-π exchange coupling in the erbium-semiquinonate complex [ErTp2dbsq] (Er-dbsq; Tp- = hydro-tris(1-pyrazolyl)borate, dbsqH2 = 3,5-di-tert-butyl-1,2-semiquinone) have been determined by inelastic neutron scattering (INS), magnetometry, and CASSCF-SO ab initio calculations. A related complex with a diamagnetic ligand, [ErTp2trop] (Er-trop; tropH = tropolone), has been used as a model for the crystal field splitting in the absence of coupling. Magnetic and INS data indicate antiferromagnetic exchange for Er-dbsq with a coupling constant of Jex = -0.23 meV (-1.8 cm-1) (-2Jex formalism) and good agreement is found between theory and experiment, with the low energy magnetic and spectroscopic properties well modelled. Most notable is the ability of the ab initio modelling to reproduce the signature of interference between localised 4f states and delocalised π-radical states that is evident in the Q-dependence of the exchange excitation. This work highlights the power of combining INS with EPR and magnetometry for determination of ground state properties, as well as the enhanced capability of CASSCF-SO ab initio calculations and purposely developed ab initio-based theoretical models. We deliver an unprecedentedly detailed representation of the entangled character of 4f-π exchange states, which is obtained via an accurate image of the spin-orbital transition density between the 4f-π exchange coupled wavefunctions.

Electronic Structure and Magneto-Structural Correlations Study of Cu2UL Trinuclear Schiff Base Complexes: A 3d-5f-3d Case

The magnetic properties of trinuclear Schiff base complexes M₂AnLⁱ (M^II = Zn, Cu; An^IV = Th, U; Lⁱ = Schiff base; i = 1-4, 6, 7, 9), exhibiting the [M(μ-O)₂]₂U core structure with adjacent M1···U and M2···U and next-adjacent M1···M2 interactions, featuring 3d-5f-3d subsystems, have been investigated theoretically using relativistic ZORA/B3LYP computations combined with the broken symmetry (BS) approach. Bond order and natural population analyses reveal that the covalent contribution to the bonding within the Cu-O-U coordination is important thus favoring superexchange coupling between the transition metal and the uranium magnetic centers. The calculated coupling constants J_CuU between the Cu and U atoms, agree with the observed shift from the antiferromagnetic (AF) character of the L^1,2,3,4 complexes to the ferromagnetic (ferro) of the L^6,7,9 ones. The structural parameters, i.e., the Cu···U distances and the Cu-O-U angles, as well as the electronic factors driving the magnetic couplings are discussed. The analyses are supported by the study of the mixed ZnCuULⁱ and Cu₂ThLⁱ systems, where in the first complex the Cu^II (3d⁹) ion is replaced by the diamagnetic Zn^II (3d¹⁰) one, whereas in the second complex the U^IV (5f²) paramagnetic center is replaced by the diamagnetic Th^IV (5f⁰) one.

Magnetic properties of organolanthanide(II) complexes, from the electronic structure and the crystal field effect

The magnetic properties of a series of organometallic complexes [LnCp3]- and Ln(CNT)2, where Cp = cyclopentadienyl and CNT = cyclononatetraenyl, of the lanthanide ions in the 2+ oxidation state, are theoretically studied in terms of the electronic structure obtained via multiconfigurational wave function-based methods. Calculations are performed for two groups of ion complexes selected based on their preferred electronic configuration 4fn+1 or 4fn5d1 (n is the number of f electrons in the 3+ ion). All the properties are discussed in terms of the electron density distribution of the ground state and ligand field effects. This analysis allows giving some molecular design strategies relevant to exploit the magnetic properties in applications like Single-Molecule Magnets (SMMs) for lanthanide ions in the 2+ oxidation state.

New members of the polynuclear manganese family: MnMn single-molecule magnets and MnMn antiferromagnetic complexes. Synthesis and magnetostructural correlations

The synthesis, crystal structures and magnetic properties are reported for three novel mixed-valence tetranuclear [MnII2MnIII2(HBuDea)2(BuDea)2(EBA)4] (1), [MnII2MnIII2(HBuDea)2(BuDea)2(DMBA)4] (2) and undecanuclear [MnII3MnIII8O4(OH)2(BuDea)6(DMBA)8] (3) clusters, where H2BuDea is N-butyldiethanolamine, HEBA is 2-ethylbutyric acid and HDMBA is 2,2-dimethylbutyric acid. The compounds have been prepared through self-assembly reactions of manganese(ii) chloride with H2BuDea and respective carboxylic acid in methanol solution in air, affording 1 with HEBA, and 2 or 3 with HDMBA, depending on the experimental conditions. The single crystal X-ray analysis reveals that 1 and 2 have similar centrosymmetric structures based on the {M4(μ3-O)2(μ-O)4} core, while 3 discloses the unprecedented {M11(μ-O)4(μ3-O)12} one. The Mn4 complexes display single-molecule magnet (SMM) behavior with a S = 9 spin ground state and a high energy barrier Ueff/kB of up to 51 K. The magnetic properties of 2 are successfully modeled with JMnIII-MnIII/hc = 25.7 cm-1 and two JMnIII-MnII/hc constants of 3.1 and -0.93 cm-1 (data correspond to the Ĥ = -Jŝ1·ŝ2 formalism). The Mn11 cluster exhibits a paramagnetic behavior with dominant antiferromagnetic coupling. A possible influence of intermolecular effects and of different peripheries of the magnetic cores designed by using 2-ethylbutyrate (in 1) or 2,2-dimethylbutyrate (in 2) on the magnetic properties of 1 and 2 is discussed. The experimental magnetostructural correlations for the {MnII2MnIII2(μ3-O)2(μ-O)4} cores, supported by broken symmetry DFT calculations, disclose the X-MnIIIMnIII angle and MnIII-O distance (where MnIII-X and MnIII-O are axial Jahn-Teller bonds) as the structural factors having the strongest influence on JMnIII-MnIII exchange coupling. It is shown that two JMnIII-MnII constants are necessary for the correct description of magnetic exchange couplings in the {MnII2MnIII2(μ3-O)2(μ-O)4} tetranuclear unit.

Reactive Heterobimetallic Complex Combining Divalent Ytterbium and Dimethyl Nickel Fragments

This article presented the synthesis and characterization of original heterobimetallic species combining a divalent lanthanide fragment and a divalent nickel center bridged by the bipyrimidine ligand, a redox-active ligand. X-ray crystal structures were obtained for the Ni monomer (bipym)NiMe₂, 1, as well as the heterobimetallic dimer compounds, Cp*₂Yb(bipym)NiMe₂, 2, along with ¹H solution NMR, solid-state magnetic data, and DFT calculations only for 1. The reactivity with CO was investigated on both compounds and the stoichiometric acetone formation is discussed based on kinetic and mechanistic studies. The key role of the lanthanide fragment was demonstrated by the relatively slow CO migratory insertion step, which indicated the stability of the intermediate.

Theoretical Investigation of the Electronic Structure and Magnetic Properties of Oxo-Bridged Uranyl(V) Dinuclear and Trinuclear Complexes

The uranyl(V) complexes [UO₂(dbm)₂K(18C6)]₂ (dbm = dibenzoylmethanate) and [UO₂(L)]₃(L = 2-(4-tolyl)-1,3-bis(quinolyl)malondiiminate), exhibiting diamond-shaped U₂O₂ and triangular-shaped U₃O₃ cores respectively with 5f¹-5f¹ and 5f¹-5f¹-5f¹ configurations, have been investigated using relativistic density functional theory (DFT). The bond order and QTAIM analyses reveal that the covalent contribution to the bonding within the oxo cores is slightly more important for U₃O₃ than for U₂O₂, in line with the shorter U-O distances existing in the trinuclear complex in comparison to those in the binuclear complex. Using the broken symmetry (BS) approach combined with the B3LYP functional for the calculation of the magnetic exchange coupling constants (J) between the magnetic centers, the antiferromagnetic (AF) character of these complexes was confirmed, the estimated J values being respectively equal to -24.1 and -7.2 cm^-1 for the dioxo and trioxo species. It was found that the magnetic exchange is more sensitive to small variations of the core geometry of the dioxo species in comparison to the trioxo species. Although the robust AF exchange coupling within the U_xO_x cores is generally maintained when small variations of the UOU angle are applied, a weak ferromagnetic character appears in the dioxo species when this angle is higher than 114°, its value for the actual structure being equal to 105.9°. The electronic factors driving the magnetic coupling are discussed.

DFT Investigations of the Magnetic Properties of Actinide Complexes

Over the past 25 years, magnetic actinide complexes have been the object of considerable attention, not only at the experimental level, but also at the theoretical one. Such systems are of great interest, owing to the well-known larger spin–orbit coupling for actinide ions, and could exhibit slow relaxation of the magnetization, arising from a large anisotropy barrier, and magnetic hysteresis of purely molecular origin below a given blocking temperature. Furthermore, more diffuse 5f orbitals than lanthanide 4f ones (more covalency) could lead to stronger magnetic super-exchange. On the other hand, the extraordinary experimental challenges of actinide complexes chemistry, because of their rarity and toxicity, afford computational chemistry a particularly valuable role. However, for such a purpose, the use of a multiconfigurational post-Hartree-Fock approach is required, but such an approach is computationally demanding for polymetallic systems—notably for actinide ones—and usually simplified models are considered instead of the actual systems. Thus, Density Functional Theory (DFT) appears as an alternative tool to compute magnetic exchange coupling and to explore the electronic structure and magnetic properties of actinide-containing molecules, especially when the considered systems are very large. In this paper, relevant achievements regarding DFT investigations of the magnetic properties of actinide complexes are surveyed, with particular emphasis on some representative examples that illustrate the subject, including actinides in Single Molecular Magnets (SMMs) and systems featuring metal-metal super-exchange coupling interactions. Examples are drawn from studies that are either entirely computational or are combined experimental/computational investigations in which the latter play a significant role.

Magnetic Coupling in the Ce(III) Dimer Ce2(COT)3

The monomer [Ce(COT)₂]^- and the dimer [Ce₂(COT)₃], with Ce(III) and COT = 1,3,5,7-cyclooctatetraenide, are studied by quantum chemistry calculations. Due to the large spin-orbit coupling, the ground state of the monomer is a strong mixing of σ and π states. The experimental isotropic coupling in the dimer was evaluated by Walter et al. to be J = -7 cm^-1 (with a Heisenberg Hamiltonian [Formula: see text]) with a small anisotropic coupling of 0.02 cm^-1. The coupling between the two Ce(III) in the dimer is calculated using CI methods. The low energy part of the spectra are modeled by spin Hamiltonians. All spin Hamiltonians parameters are deduced from ab initio calculations. g factors are calculated for both the pseudodoublet of the monomer and the pseudotriplet of the dimer and their sign have been determined. The magnetic coupling in the dimer is rationalized by a model based on crystal field theory. The kinetic and exchange contributions arising from the different configurations to the isotropic and anisotropic couplings are evaluated. It is shown that the main contribution to isotropic coupling is kinetic and originates from the f_σ-f_σ interaction due to the large transfer integral between those orbitals. However, the f_π-f_π interaction plays a non-negligible role. The anisotropic coupling originates from the difference of exchange energy of states arising from the f_σf_π configuration and is, in no matter, related to the anisotropy of the local magnetic moments as already pointed by van Vleck for a fictitious s-p system. The analysis of the natural orbitals evidences a superexchange mechanism through a σ_CH^* orbital of the bridging cycle favored by a local 4f_σ/5d_σ hybridization and that the δ type orbitals, both the HOMOs of the ligands and the virtual f_δ orbitals of the cerium atoms play an important polarization role, and to a less extend the π type orbitals, the HOMOs-1 of the ligands, and the metal f_π orbitals.

Element specific determination of the magnetic properties of two macrocyclic tetranuclear 3d-4f complexes with a Cu3Tb core by means of X-ray magnetic circular dichroism (XMCD)

We apply X-ray magnetic circular dichroism to study the internal magnetic structure of two very promising star shaped macrocyclic complexes with a CuII3TbIII core. These complexes are rare examples prepared with a macrocyclic ligand that show indications of SMM (Single Molecule Magnet) behavior, and they differ only in ring size: one has a propylene linked macrocycle, [CuII3TbIII(LPr)(NO3)2(MeOH)(H2O)2](NO3)·3H2O (nickname: Cu3Tb(LPr)), and the other has the butylene linked analogue, [CuII3TbIII(LBu)(NO3)2(MeOH)(H2O)](NO3)·3H2O (nickname: Cu3Tb(LBu)). We analyze the orbital and spin contributions to the Cu and Tb ions quantitatively by applying the spin and orbital sum rules concerning the L2 (M4)/L3 (M5) edges. In combination with appropriate ligand field simulations, we demonstrate that the Tb(iii) ions contribute with high orbital magnetic moments to the magnetic anisotropy, whereas the ligand field determines the easy axis of magnetization. Furthermore, we confirm that the Cu(ii) ions in both molecules are in a divalent valence state, the magnetic moments of the three Cu ions appear to be canted due to 3d-3d intramolecular magnetic interactions. For Cu3Tb(LPr), the corresponding element specific magnetization loops reflect that the Cu(ii) contribution to the overall magnetic picture becomes more important as the temperature is lowered. This implies a low value for the 3d-4f coupling.

Cerium Tetrakis(tropolonate) and Cerium Tetrakis(acetylacetonate) Are Not Diamagnetic but Temperature-Independent Paramagnets

A new synthesis of cerium tetrakis(tropolonate), Ce(trop)₄, where trop is deprotonated 2-hydroxy-2,4,6-cycloheptatrienone) or Ce(O₂C₇H₅)₄, is developed that results in dark-purple crystals whose X-ray crystal structure shows that the geometry of the eight-coordinate compound closely resembles a D_{2 d} dodecahedron, based on shape parameters. The magnetic susceptibility as a function of the temperature (4-300 K) shows that it is a temperature-independent paramagnet, χ = 1.2(3) × 10^-4 emu/mol, and the L_III-edge X-ray absorption near-edge structure spectrum shows that the molecule is multiconfigurational, comprised of a f¹:f⁰ configuration mixture in a 50:50 ratio. Ce(acac)₄ and Ce(tmtaa)₂ (where acac is acetylacetonate and tmtaaH₂ is tetramethyldibenzotetraaza[14]annulene) have similar physical properties, as does the solid-state compound CeO₂. The concept is advanced that trop^-, acac^-, tmtaa^2-, cot^2-, and O^2- are redox-active ligands that function as electron donors, rendering the classification of these compounds according to their oxidation numbers misleading because their magnetic susceptibilities, χ, are positive and their effective magnetic moments, μ_eff, lie in the range of 0.1-0.7 μ_B at 300 K.

Electronic Structure and Magnetic Properties of Dioxo-Bridged Diuranium Complexes with Diamond-Core Structural Motifs: A Relativistic DFT Study

Electronic structures and magnetic properties of the binuclear bis(μ-oxo) U(IV)/U(IV) K2[{(((nP,Me)ArO)3tacn)U(IV)}2(μ-O)2] and U(V)/U(V) [{(((nP,Me)ArO)3tacn)U(V)}2(μ-O)2] (tacn = triazacyclononane, nP = neopentyl) complexes, exhibiting [U(μ-O)2U] diamond-core structural motifs, have been investigated computationally using scalar relativistic Density Functional Theory (DFT) combined with the Broken Symmetry (BS) approach for their magnetic properties. Using the B3LYP hybrid functional, the BS ground state of the pentavalent [U(V)(μ-O)2U(V)] 5f(1)-5f(1) complex has been found of lower energy than the high spin (HS) triplet state, thus confirming the antiferromagnetic character in agreement with experimental magnetic susceptibility measurements. The nonmagnetic character observed for the tetravalent K2[U(IV)(μ-O)2U(IV)] 5f(2)-5f(2) species is also predicted by our DFT calculations, which led practically to the same energy for the HS and BS states. As reported for related dioxo diuranium(V) systems, superexchange is likely to be responsible for the antiferromagnetic coupling through the π-network orbital pathway within the (μ-O)2 bridge, the dissymmetrical structure of the U2O2 core playing a determining role. In the case of the U(IV) species, our computations indicate that the K(+) counterions are likely to play a role for the observed magnetic property. Finally, the MO analysis, in conjunction with NPA and QTAIM analyses, clarify the electronic structures of the studied complexes. In particular, the fact that the experimentally attempted chemical oxidation of the U(V) species does not lead straightforwardly to binuclear complexes U(VI) is clarified by the MO analysis.

Actinide-based single-molecule magnets

Actinide single-molecule magnets compose a small yet complex consortium, presenting new design and characterization challenges for magnetochemists and physicists.

Reversible sigma C-C bond formation between phenanthroline ligands activated by (C5Me5)2Yb

The electronic structure and associated magnetic properties of the 1,10-phenanthroline adducts of Cp*2Yb are dramatically different from those of the 2,2'-bipyridine adducts. The monomeric phenanthroline adducts are ground state triplets that are based upon trivalent Yb(III), f(13), and (phen(•-) ) that are only weakly exchange coupled, which is in contrast to the bipyridine adducts whose ground states are multiconfigurational, open-shell singlets in which ytterbium is intermediate valent ( J. Am. Chem. Soc 2009 , 131 , 6480 ; J. Am. Chem. Soc 2010 , 132 , 17537 ). The origin of these different physical properties is traced to the number and symmetry of the LUMO and LUMO+1 of the heterocyclic diimine ligands. The bipy(•-) has only one π*1 orbital of b1 symmetry of accessible energy, but phen(•-) has two π* orbitals of b1 and a2 symmetry that are energetically accessible. The carbon pπ-orbitals have different nodal properties and coefficients and their energies, and therefore their populations change depending on the position and number of methyl substitutions on the ring. A chemical ramification of the change in electronic structure is that Cp*2Yb(phen) is a dimer when crystallized from toluene solution, but a monomer when sublimed at 180-190 °C. When 3,8-Me2phenanthroline is used, the adduct Cp*2Yb(3,8-Me2phen) exists in the solution in a dimer-monomer equilibrium in which ΔG is near zero. The adducts with 3-Me, 4-Me, 5-Me, 3,8-Me2, and 5,6-Me2-phenanthroline are isolated and characterized by solid state X-ray crystallography, magnetic susceptibility and LIII-edge XANES spectroscopy as a function of temperature and variable-temperature (1)H NMR spectroscopy.

Oxo-functionalization and reduction of the uranyl ion through lanthanide-element bond homolysis: synthetic, structural, and bonding analysis of a series of singly reduced uranyl-rare earth 5f1-4f(n) complexes

The heterobimetallic complexes [{UO2Ln(py)2(L)}2], combining a singly reduced uranyl cation and a rare-earth trication in a binucleating polypyrrole Schiff-base macrocycle (Pacman) and bridged through a uranyl oxo-group, have been prepared for Ln = Sc, Y, Ce, Sm, Eu, Gd, Dy, Er, Yb, and Lu. These compounds are formed by the single-electron reduction of the Pacman uranyl complex [UO2(py)(H2L)] by the rare-earth complexes Ln(III)(A)3 (A = N(SiMe3)2, OC6H3Bu(t)2-2,6) via homolysis of a Ln-A bond. The complexes are dimeric through mutual uranyl exo-oxo coordination but can be cleaved to form the trimetallic, monouranyl "ate" complexes [(py)3LiOUO(μ-X)Ln(py)(L)] by the addition of lithium halides. X-ray crystallographic structural characterization of many examples reveals very similar features for monomeric and dimeric series, the dimers containing an asymmetric U2O2 diamond core with shorter uranyl U═O distances than in the monomeric complexes. The synthesis by Ln(III)-A homolysis allows [5f(1)-4f(n)]2 and Li[5f(1)-4f(n)] complexes with oxo-bridged metal cations to be made for all possible 4f(n) configurations. Variable-temperature SQUID magnetometry and IR, NIR, and EPR spectroscopies on the complexes are utilized to provide a basis for the better understanding of the electronic structure of f-block complexes and their f-electron exchange interactions. Furthermore, the structures, calculated by restricted-core or all-electron methods, are compared along with the proposed mechanism of formation of the complexes. A strong antiferromagnetic coupling between the metal centers, mediated by the oxo groups, exists in the U(V)Sm(III) monomer, whereas the dimeric U(V)Dy(III) complex was found to show magnetic bistability at 3 K, a property required for the development of single-molecule magnets.

Application of the Hubbard model to Cp*(2)Yb(bipy), a model system for strong exchange coupling in lanthanide systems

Exchange coupling is quantified in lanthanide (Ln) single-molecule magnets (SMMs) containing a bridging N(2)(3-) radical ligand and between [Cp*(2)Yb](+) and bipy(•-) in Cp*(2)Yb(bipy), where Cp* is pentamethylcyclopentadienyl and bipy is 2,2'-bipyridyl. In the case of these lanthanide SMMs, the magnitude of exchange coupling between the Ln ion and the bridging N(2)(3-), 2J, is very similar to the barrier to magnetic relaxation, U(eff). A molecular version of the Hubbard model is applied to systems in which unpaired electrons on magnetic metal ions have direct overlap with unpaired electrons residing on ligands. The Hubbard model explicitly addresses electron correlation, which is essential for understanding the magnetic behavior of these complexes. This model is applied quantitatively to Cp*(2)Yb(bipy) to explain its very strong exchange coupling, 2J = -0.11 eV (-920 cm(-1)). The model is also used to explain the presence of strong exchange coupling in Ln SMMs in which the lanthanide spins are coupled via bridging N(2)(3-) radical ligands. The results suggest that increasing the magnetic coupling in lanthanide clusters could lead to an increase in the blocking temperatures of exchange-coupled lanthanide SMMs, suggesting routes to rational design of future lanthanide SMMs.