Spectroscopic techniques to probe magnetic anisotropy and spin-phonon coupling in metal complexes

Magnetism of molecular quantum materials such as single-molecule magnets (SMMs) has been actively studied for potential applications in the new generation of high-density data storage using SMMs and quantum information science. Magnetic anisotropy and spin-phonon coupling are two key properties of d- and f-metal complexes. Here, phonons refer to both intermolecular and intramolecular vibrations. Direct determination of magnetic anisotropy and experimental studies of spin-phonon coupling are critical to the understanding of molecular magnetism. This article discusses our recent approach in using three complementary techniques, far-IR and Raman magneto-spectroscopies (FIRMS and RaMS, respectively) and inelastic neutron scatterings (INS), to determine magnetic excited states. Spin-phonon couplings are observed in FIRMS and RaMS. DFT phonon calculations give energies and symmetries of phonons as well as calculated INS spectra which help identify magnetic peaks in experimental INS spectra.

Increasing the Magnetic Blocking Temperature of Single-Molecule Magnets

The synthesis of single-molecule magnets (SMMs), magnetic complexes capable of retaining magnetization blocking for a long time at elevated temperatures, has been a major concern for magnetochemists over the last three decades. In this review, we describe basic SMMs and the different approaches that allow high magnetization-blocking temperatures to be reached. We focus on the basic factors affecting magnetization blocking, magnetic axiality and the height of the blocking barrier, which can be used to group different families of complexes in terms of their SMM efficiency. Finally, we discuss several practical routes for the design of mono- and polynuclear complexes that could be applied in memory devices.

Introduction of plumbole to f-element chemistry

Herein, we present the synthesis and characterization of heteroleptic lanthanide complexes bearing a dianionic η5-plumbole ligand in their coordination sphere. The reaction proceeds via a salt elimination reaction between the dilithioplumbole ([Li(thf)]2[1,4-bis-tert-butyl-dimethylsilyl-2,3-bis-phenyl-plumbolyl] = [Li2(thf)2(η5-LPb)]) and specifically designed [Ln(η8-COTTIPS)BH4] precursors (Ln = lanthanide, La, Ce, Sm, Er; COTTIPS = 1,4-bis-triisopropylsilyl-cyclooctatetraenyl), that are capable of stabilizing a planar plumbole moiety in the coordination sphere of different trivalent lanthanide ions. In-depth ab initio calculations show that the aromaticity of the dianionic plumbole is retained upon coordination. Electron delocalization occurs from the plumbole HOMO to an orbital of mainly d-character at the lanthanide ion. The magnetic properties of the erbium congener were investigated in detail, leading to the observation of magnetic hysteresis up to 5 K (200 Oe s-1), an unequivocal proof for single molecule magnet behavior in this system. The magnetic behavior of the erbium species can be modulated by manipulating the position of the lithium cation in the complex, which directly influences the bonding metrics in the central [(η5-LPb)Er(η8-COTTIPS)]- fragment. This allowed us to assess a fundamental magneto-structural correlation in an otherwise identical inner coordination sphere.

Synthesis and structures of fluoride-bridged dysprosium clusters: influence of fluoride ions on magnetic relaxation behaviors

The synthesis of fluoride-bridged 1Dy, 2Dy and hepta-nuclear 3Dy dysprosium complexes is reported here and a hydroxy-bridged dinuclear dysprosium complex 4Dy is synthesized for comparison.

Magnetic behavior of the novel pentagonal-bipyramidal erbium(III) complex (Et3NH)[Er(H2DAPS)Cl2]: high-frequency EPR study and crystal-field analysis

We report the synthesis, crystal structure and magnetic properties of the new heptacoordinated mononuclear erbium(III) complex (Et₃NH)[Er(H₂DAPS)Cl₂] (H₄DAPS = 2,6-diacetylpyridine bis-(salicylhydrazone)) (1). The coordination polyhedron around the Er(III) ion features a slightly distorted pentagonal bipyramid formed by the pentagonal N₃O₂ chelate ring of the H₂DAPS ligand in the equatorial plane and two apical chloride ligands. Detailed high-frequency/high-field electron paramagnetic resonance (HF-EPR) studies of 1 result in the precise determination of the crystal field (CF) splitting energies (0, 290 and 460 GHz) and effective g-values of the three lowest Kramers doublets (KDs) of the Er(III) ion. The obtained HF-EPR data are in good agreement with the results from CF analysis for the Er(III) ion based on the simulation of the dc magnetic data of 1. The results from dynamic susceptibility measurements indicate that there is no slow relaxation of magnetisation behaviour. This observation is discussed in terms of the electronic structure of 1 obtained from experimental and theoretical results.

Spectroscopic Analysis of Vibronic Relaxation Pathways in Molecular Spin Qubit [Ho(W5O18)2]9-: Sparse Spectra Are Key

Vibrations play a prominent role in magnetic relaxation processes of molecular spin qubits as they couple to spin states, leading to the loss of quantum information. Direct experimental determination of vibronic coupling is crucial to understand and control the spin dynamics of these nano-objects, which represent the limit of miniaturization for quantum devices. Herein, we measure the magneto-infrared properties of the molecular spin qubit system Na₉[Ho(W₅O₁₈)₂]·35H₂O. Our results place significant constraints on the pattern of crystal field levels and the vibrational excitations allowing us to unravel vibronic decoherence pathways in this system. We observe field-induced spectral changes near 63 and 370 cm^-1 that are modeled in terms of odd-symmetry vibrations mixed with f-manifold crystal field excitations. The overall extent of vibronic coupling in Na₉[Ho(W₅O₁₈)₂]·35H₂O is limited by a modest coupling constant (on the order of 0.25) and a transparency window in the phonon density of states that acts to keep the intramolecular vibrations and M_J levels apart. These findings advance the understanding of vibronic coupling in a molecular magnet with atomic clock transitions and suggest strategies for designing molecular spin qubits with improved coherence lifetimes.

A Complete Ab Initio View of Orbach and Raman Spin-Lattice Relaxation in a Dysprosium Coordination Compound

The unique electronic and magnetic properties of lanthanide molecular complexes place them at the forefront of the race toward high-temperature single-molecule magnets and magnetic quantum bits. The design of compounds of this class has so far being almost exclusively driven by static crystal field considerations, with an emphasis on increasing the magnetic anisotropy barrier. Now that this guideline has reached its maximum potential, a deeper understanding of spin-phonon relaxation mechanisms presents itself as key in order to drive synthetic chemistry beyond simple intuition. In this work, we compute relaxation times fully ab initio and unveil the nature of all spin-phonon relaxation mechanisms, namely Orbach and Raman pathways, in a prototypical Dy single-molecule magnet. Computational predictions are in agreement with the experimental determination of spin relaxation time and crystal field anisotropy, and show that Raman relaxation, dominating at low temperature, is triggered by low-energy phonons and little affected by further engineering of crystal field axiality. A comprehensive analysis of spin-phonon coupling mechanism reveals that molecular vibrations beyond the ion’s first coordination shell can also assume a prominent role in spin relaxation through an electrostatic polarization effect. Therefore, this work shows the way forward in the field by delivering a novel and complete set of chemically sound design rules tackling every aspect of spin relaxation at any temperature.

Azide-Coordination in Homometallic Dinuclear Lanthanide(III) Complexes Containing Nonequivalent Lanthanide Metal Ions: Zero-Field SMM Behavior in the Dysprosium Analogue

A series of homometallic dinuclear lanthanide complexes containing nonequivalent lanthanide metal centers [Ln₂(LH₂)(LH)(CH₃OH)(N₃)]·xMeOH·yH₂O [1, Ln = Dy^III, x = 0, y = 2; 2, Ln = Tb^III, x = 1, y = 1] have been synthesized [LH₄ = 6-((bis(2-hydroxyethyl)amino)-N'-(2-hydroxybenzylidene)picolinohydrazide] and characterized. The dinuclear assembly contains two different types of nine-coordinated lanthanide centers, because the nonequivalent binding of the azide co-ligand as well as the varying coordination of the deprotonated Schiff base ligand. Detailed magnetic studies have been performed on the complexes 1 and 2. Complex 1 and its diluted analogue (1_5%) are zero-field SMMs with effective energy barriers (U_eff) of magnetization reversal equal to 59(3) K and 66(3) K and relaxation times of τ₀ = 10(4) × 10^-6 s and 10(4) × 10^-8 s, respectively. On the other hand, complex 2 shows a field-induced SMM behavior. Combined ab initio and density functional theory calculations were performed to explain the experimental findings and to unravel the nature of the magnetic anisotropy, exchange-coupled spectra, and magnetic exchange interactions between the two lanthanide centers.

Single-Ion Anisotropy and Intramolecular Interactions in CeIII and NdIII Dimers

This article reports the syntheses, characterization, structural description, together with magnetic and spectroscopic properties of two isostructural molecular magnets based on the chiral ligand N,N'-bis((1,2-diphenyl-(pyridine-2-yl)methylene)-(R,R/S,S)-ethane-1,2-diamine), L1, of general formula [Ln2(RR-L1)2(Cl6)]·MeOH·1.5H2O, (Ln = Ce (1) or Nd (2)). Multifrequency electron paramagnetic resonance (EPR), cantilever torque magnetometry (CTM) measurements, and ab initio calculations allowed us to determine single-ion magnetic anisotropy and intramolecular magnetic interactions in both compounds, evidencing a more important role of the anisotropic exchange for the NdIII derivative. The comparison of experimental and theoretical data indicates that, in the case of largely rhombic lanthanide ions, ab initio calculations can fail in determining the orientation of the weakest components, while being reliable in determining their principal values. However, they remain of paramount importance to set the analysis of EPR and CTM on sound basis, thus obtaining a very precise picture of the magnetic interactions in these systems. Finally, the electronic structure of the two complexes, as obtained by this approach, is consistent with the absence of zero-field slow relaxation observed in ac susceptibility.

Applying Unconventional Spectroscopies to the Single-Molecule Magnets, Co(PPh3 )2 X2 (X=Cl, Br, I): Unveiling Magnetic Transitions and Spin-Phonon Coupling

Large separation of magnetic levels and slow relaxation in metal complexes are desirable properties of single-molecule magnets (SMMs). Spin-phonon coupling (interactions of magnetic levels with phonons) is ubiquitous, leading to magnetic relaxation and loss of memory in SMMs and quantum coherence in qubits. Direct observation of magnetic transitions and spin-phonon coupling in molecules is challenging. We have found that far-IR magnetic spectra (FIRMS) of Co(PPh₃ )₂ X₂ (Co-X; X=Cl, Br, I) reveal rarely observed spin-phonon coupling as avoided crossings between magnetic and u-symmetry phonon transitions. Inelastic neutron scattering (INS) gives phonon spectra. Calculations using VASP and phonopy programs gave phonon symmetries and movies. Magnetic transitions among zero-field split (ZFS) levels of the S=3/2 electronic ground state were probed by INS, high-frequency and -field EPR (HFEPR), FIRMS, and frequency-domain FT terahertz EPR (FD-FT THz-EPR), giving magnetic excitation spectra and determining ZFS parameters (D, E) and g values. Ligand-field theory (LFT) was used to analyze earlier electronic absorption spectra and give calculated ZFS parameters matching those from the experiments. DFT calculations also gave spin densities in Co-X, showing that the larger Co(II) spin density in a molecule, the larger its ZFS magnitude. The current work reveals dynamics of magnetic and phonon excitations in SMMs. Studies of such couplings in the future would help to understand how spin-phonon coupling may lead to magnetic relaxation and develop guidance to control such coupling.

Heteroleptic, polynuclear dysprosium(iii)-carbamato complexes through in situ carbon dioxide capture

Amine groups are among the most effective systems for carbon dioxide capture. Reminiscent of the activation of nature's most abundant enzyme RuBisCO, the treatment of amines with CO₂ in the presence of oxophilic metal ions, e.g. Mg²⁺, results in the formation of carbamates. Here we report the synthesis, structure and magnetic properties of three new dysprosium-carbamato complexes. The reaction of gaseous CO₂ with N,N-diisopropylamine and DyCl₃(DME)₂ (DME = Dimethoxyethane) in toluene leads to the formation of the tetrametallic complex [Dy₄(O₂CNⁱPr₂)₁₀(O-C₂H₄-OMe)₂]. The addition of 2-hydroxy-3-methoxybenzaldehyde-N-methylimine yields the hexametallic compound [Dy₆(O₂CNⁱPr₂)₈(O-C₂H₄-OMe)₂(CO₃)₂(C₉O₂NH₁₀)₄] in which the metal sites form a chair-like configuration; The same hexanuclear motif is obtained using N,N-dibenzylamine. We show that by employing CO₂ as a feedstock, we are able to capture up to 2.5 molecules of CO₂ per Dy ion. Magnetic measurements show a decreasing χ_MT at low temperatures. Combining the experimental magnetic data with ab initio calculations reveils tilting of the easy axes and implies the presence of antiferromagnetic interactions between the Dy(iii) metal ions.

Multireference Ab Initio Investigation on Ground and Low-Lying Excited States: Systematic Evaluation of J-J Mixing in a Eu3+ Luminescent Complex

A theoretical protocol combining density functional theory (DFT) and multireference (CAS) calculations is proposed for a Eu³⁺ complex. In the complex, electronic levels of the central Eu³⁺ ion are correctly calculated at the CASPT2 level of theory, and the effect of introducing different numbers of states in the configuration interaction matrices is highlighted as well as the shortcomings of DFT methods in the treatment of systems with high spin multiplicity and strong spin–orbit coupling effects. For the ⁵D₀ state energy calculation, the inclusion of states with different multiplicity and the number of states considered for each multiplicity are crucial parameters, even if their relative weight is different. Indeed, the addition of triplet and singlets is important, while the number of states is relevant only for the quintets. The herein proposed protocol enables a rigorous, full ab initio treatment of Eu³⁺ complex, which can be easily extended to other Ln³⁺ ions.

A theoretical protocol combining density functional theory and multireference calculations is proposed for a Eu³⁺ complex. For the ⁵D₀ state energy calculation, the inclusion of states with different multiplicity and the number of states considered for each multiplicity are crucial parameters. The herein proposed protocol enables a rigorous, full ab initio treatment of Eu³⁺ complex, which can be easily extended to other Ln³⁺ ions.

Hyperfine and quadrupole interactions for Dy isotopes in DyPc2 molecules

Nuclear spin levels play an important role in understanding magnetization dynamics and implementation and control of quantum bits in lanthanide-based single-molecule magnets. We investigate the hyperfine and nuclear quadrupole interactions for ¹⁶¹Dy and ¹⁶³Dy nuclei in anionic DyPc₂ (Pc  =  phthalocyanine) single-molecule magnets, using multiconfigurational ab initio methods (beyond density-functional theory) including spin-orbit interaction. The two isotopes of Dy are chosen because the others have zero nuclear spin. Both isotopes have the nuclear spin I  =  5/2, although the magnitude and sign of the nuclear magnetic moment differ from each other. The large energy gap between the electronic ground and first-excited Kramers doublets, allows us to map the microscopic hyperfine and quadrupole interaction Hamiltonian onto an effective Hamiltonian with an electronic pseudo-spin [Formula: see text] that corresponds to the ground Kramers doublet. Our ab initio calculations show that the coupling between the nuclear spin and electronic orbital angular momentum contributes the most to the hyperfine interaction and that both the hyperfine and nuclear quadrupole interactions for ¹⁶¹Dy and ¹⁶³Dy nuclei are much smaller than those for the ¹⁵⁹Tb nucleus in TbPc₂ single-molecule magnets. The calculated separations of the electronic-nuclear levels are comparable to experimental data reported for ¹⁶³DyPc₂. We demonstrate that hyperfine interaction for the Dy Kramers ion leads to tunnel splitting (or quantum tunneling of magnetization) at zero field. This effect does not occur for TbPc₂ single-molecule magnets. The magnetic field values of the avoided level crossings for ¹⁶¹DyPc₂ and ¹⁶³DyPc₂ are found to be noticeably different, which can be observed from the experiment.

Inter-Kramers Transitions and Spin-Phonon Couplings in a Lanthanide-Based Single-Molecule Magnet

Spin-phonon coupling plays a critical role in magnetic relaxation in single-molecule magnets (SMMs) and molecular qubits. Yet, few studies of its nature have been conducted. Phonons here refer to both intermolecular and intramolecular vibrations. In the current work, we show spin-phonon couplings between IR-active phonons in a lanthanide molecular complex and Kramers doublets (from the crystal field). For the SMM Er[N(SiMe₃)₂]₃ (1, Me = methyl), the couplings are observed in the far-IR magnetospectroscopy (FIRMS) of crystals with coupling constants ≈ 2-3 cm^-1. In particular, one of the magnetic excitations couples to at least two phonon excitations. The FIRMS reveals at least three magnetic excitations (within the ⁴I_15/2 ground state/manifold; hereafter, manifold) at 0 T at 104, ∼180, and 245 cm^-1, corresponding to transitions from the ground state, M_J = ±15/2, to the first three excited states, M_J = ±13/2, ±11/2, and ±9/2, respectively. The transition between the ground and first excited Kramers doublet in 1 is also observed in inelastic neutron scattering (INS) spectroscopy, moving to a higher energy with an increasing magnetic field. INS also gives complete phonon spectra of 1. Periodic DFT computations provide the energies of all phonon excitations, which compare well with the spectra from INS, supporting the assignment of the inter-Kramers doublet (magnetic) transitions in the spectra. The current studies unveil and measure the spin-phonon couplings in a typical lanthanide complex and throw light on the origin of the spin-phonon entanglement.

Electronic Structure and Photoluminescence Properties of Eu(η9-C9H9)2

The electronic structure of Eu²⁺ compounds results from a complex combination of strongly correlated electrons and relativistic effects as well as weak ligand-field interaction. There is tremendous interest in calculating the electronic structure as nowadays the Eu²⁺ ion is becoming more and more crucial, for instance, in lighting technologies. Recently, interest in semiempirical methods to qualitatively evaluate the electronic structure and to model the optical spectra has gained popularity, although the theoretical methods strongly rely upon empirical inputs, hindering their prediction capabilities. Besides, ab initio multireference models are computationally heavy and demand very elaborative theoretical background. Herein, application of the ligand-field density functional theory (LFDFT) method that is recently available in the Amsterdam Modeling Suite is shown: (i) to elucidate the electronic structure properties on the basis of the multiplet energy levels of Eu configurations 4f⁷ and 4f⁶5d¹ and (ii) to model the optical spectra quite accurately if compared to the conventional time-dependent density functional theory tool. We present a theoretical study of the molecular Eu(η⁹-C₉H₉)₂ complex and its underlying photoluminescence properties with respect to the Eu 4f-5d electron transitions. We model the excitation and emission spectra with good agreement with the experiments, opening up the possibility of modeling lanthanides in complex environment like nanomaterials by means of LFDFT at much-reduced computational resources and cost.

Importance of Axial Symmetry in Elucidating Lanthanide-Transition Metal Interactions

In this paper, we experimentally study and model the electron donating character of an axial diamagnetic Pd²⁺ ion in four metalloligated lanthanide complexes of formula [PPh₄][Ln{Pd(SAc)₄}₂] (SAc^- = thioacetate, Ln = Tb, Dy, Ho, and Er). A global model encompassing inelastic neutron scattering, torque magnetometry, and dc magnetometry allows to precisely determine the energy level structure of the complexes. Solid state nuclear magnetic resonance reveals a less donating character of Pd²⁺ compared to the previously reported isostructural Pt²⁺-based complexes. Consequently, all complexes invariably show a lower crystal field strength compared to their Pt²⁺-analogues. The dynamic properties show an enhanced single molecule magnet behavior due to the suppression of quantum tunneling, in agreement with our model.

Weak exchange coupling effects leading to fast magnetic relaxations in a trinuclear dysprosium single-molecule magnet

In this work, we investigated the magnetic anisotropy and the influence of weak exchange interactions on the magnetic relaxations of a triangular type dysprosium single-molecule magnet.

Role of Ab Initio Calculations in the Design and Development of Organometallic Lanthanide-Based Single-Molecule Magnets

Single-molecule magnets based on lanthanides are very attractive due to their potential applications proposed in the area of microelectronic devices. Very recent advances in this area are due to the blend of conventional lanthanide chemistry with organometallic ligands, and several breakthrough achievements are attained with this combination. Ab initio methods based on multi-reference CASSCF calculations are playing a vital role in the design and development of such molecules. In this minireview, we aim to appraise various contributions in the area of organometallic lanthanide complexes (those containing lanthanide-carbon bonds) and describe how these robust wavefunction-based methods have played a constructive role not only in rationalizing the observed magnetic properties but also proven to be a potential predictive tool with some selected examples.

Comparison of two field-induced ErIII single ion magnets

We present the synthesis, magnetic and photophysical properties of four mononuclear Ln^III complexes in two isostructural lattices containing Gd^III and Er^III. A heptadentate Schiff base ligand and acetate versus trifluoroacetate were used to synthesise complexes 1-4, among which the two Er^III complexes 2 and 4 exhibit field-induced SIM behaviour with almost similar U_eff values (31.6 K for 2 and 32.7 K for 4). Ab initio calculations show the structure of the low-lying energy states and highlight that there is already significant tunnelling in the ground doublet state, but the application of a weak magnetic field of 0.05 T is sufficient for ac magnetic measurements to suppress tunnelling in the ground state. The calculated main magnetic axes (g_Z) of the ground Kramers doublets show small differences between the two Er^III compounds 2 and 4 due to their different ligand fields.

Multimodeling Approach to Ferromagnetic Spin-Wave Excitations in the High-Spin Cluster Mn18Sr Observed by Inelastic Neutron Scattering

The magnetism of the mixed-valence high-spin cluster [Mn₁₈SrO₈(N₃)₇Cl(MedhmpH)₁₂(MeCN)₆]Cl₂ (1) exhibiting intramolecular ferromagnetic interactions was studied using inelastic neutron scattering (INS), and reliable values for the exchange coupling constants were determined based on the quality of simultaneous fits to the INS and magnetic data. The challenge of the huge size of the Hilbert space (3 375 000) and many exchange coupling constants (7 assuming a C₃ symmetry) generally encountered in large spin clusters was resolved as follows: (a) The results of the restricted Hilbert space ferromagnetic cluster spin wave theory were compared to the experimental spectroscopic data. The observed INS transitions were thus assigned to spin wave excitations in a bounded ferromagnetic spin cluster and moreover could be visualized in a straightforward way based on this theory. (b) Simultaneously, Quantum Monte Carlo (QMC) calculations of the temperature-dependent magnetic susceptibility with the same parameter set were compared to the experimental data. Application of state-of-the-art QMC algorithms, as available in the open source ALPS package, in ferromagnetic clusters avoids the full Hamiltonian diagonalization without sacrificing calculation accuracy of the magnetic susceptibility down to the lowest temperatures, which was crucial for the successful analysis. The combined fits revealed two exchange-coupling models with equally good overall agreement to the data. Our preferred model was inspired by magnetostructural correlations and is consistent with them. The model involves three different exchange interactions, one describing the interaction between the core Mn^III spins J_a = 14.3(1.0) K and two interactions linking the core and the peripheral Mn^II spins: J_b = 8.3(4) K and J₆ = 3.6(4) K. The use of open-source QMC software and our systematic approach to fitting multiple sets of data obtained by different experimental techniques are described in detail and are generally applicable for understanding large ferromagnetically coupled clusters.

Covalency and magnetic anisotropy in lanthanide single molecule magnets: the DyDOTA archetype

The unexpected covalent contribution in the DOTADy-OH₂ bond revealed by ab initio calculations of the easy axis of magnetization through simple H₂O rotations.

Lanthanide ions when complexed by polyamino-polycarboxylate chelators form a class of compounds of paramount importance in several research and technological areas, particularly in the fields of magnetic resonance and molecular magnetism. Indeed, the gadolinium derivative is one of the most employed contrast agents for magnetic resonance imaging while the dysprosium one belongs to a new generation of contrast agents for T₂-weighted MRI. In molecular magnetism, Single Molecule Magnets (SMMs) containing lanthanide ions have become readily popular in the chemistry and physics communities since record energy barriers to the reversal of magnetization were reported. The success of lanthanide complexes lies in their large anisotropy due to the contribution of the unquenched orbital angular momentum. However, only a few efforts have been made so far to understand how the f-orbitals can be influenced by the surrounding ligands. The outcomes have been rationalized using mere electrostatic perturbation models. In the archetype compound [Na{Dy(DOTA) (H₂O)}]·4H₂O (Na{DyDOTA}·4H₂O) an unexpected easy axis of magnetization perpendicular to the pseudo-tetragonal axis of the molecule was found. Interestingly, a dependency of the orientation of the principal magnetization axis on the simple rotation of the coordinating apical water molecule (AWM) – highly relevant for MRI contrast – around the Dy-O_AWM bond was predicted by ab initio calculations, too. However, such a behaviour has been contested in a subsequent paper justifying their conclusions on pure electrostatic assumptions. In this paper, we want to shed some light on the nature of the subtle effects induced by the water molecule on the magnetic properties of the DyDOTA archetype complex. Therefore, we have critically reviewed the structural models already published in the literature along with new ones, showing how the easy axis orientation can dangerously depend on the chosen model. The different computed behaviors of the orientation of the easy axis of magnetization have been rationalized as a function of the energy gap between the ground and the first excited doublet. Magneto-structural correlations together with a mapping of the electrostatic potential generated by the ligands around the Dy(iii) ion through a multipolar expansion have also been used to evidence and quantify the covalent contribution of the AWM orbitals.

Determination of the electronic structure of a dinuclear dysprosium single molecule magnet without symmetry idealization

We present the in-depth determination of the magnetic properties and electronic structure of the luminescent and volatile dysprosium-based single molecule magnet [Dy2(bpm)(fod)6] (Hfod = 6,6,7,7,8,8,8-heptafluoro-2,2-dimethyl-3,5-octanedione, bpm = 2,2'-bipyrimidine). Ab initio calculations were used to obtain a global picture of the electronic structure and to predict possible single molecule magnet behaviour, confirmed by experiments. The orientation of the susceptibility tensor was determined by means of cantilever torque magnetometry. An experimental determination of the electronic structure of the lanthanide ion was obtained combining Luminescence, Far Infrared and Magnetic Circular Dichroism spectroscopies. Fitting these energies to the full single ion plus crystal field Hamiltonian allowed determination of the eigenstates and crystal field parameters of a lanthanide complex without symmetry idealization. We then discuss the impact of a stepwise symmetry idealization on the modelling of the experimental data. This result is particularly important in view of the misleading outcomes that are often obtained when the symmetry of lanthanide complexes is idealized.

Spectroscopic Determination of the Electronic Structure of a Uranium Single-Ion Magnet

Early actinide ions have large spin-orbit couplings and crystal field interactions, leading to large anisotropies. The success in using actinides as single-molecule magnets has so far been modest, underlining the need for rational strategies. Indeed, the electronic structure of actinide single-molecule magnets and its relation to their magnetic properties remains largely unexplored. A uranium(III) single-molecule magnet, [U^III {SiMe₂ NPh}₃ -tacn)(OPPh₃ )] (tacn=1,4,7-triazacyclononane), has been investigated by means of a combination of magnetic, spectroscopic and theoretical methods to elucidate the origin of its static and dynamic magnetic properties.

Field-induced slow magnetic relaxation in the first Dy(iii)-centered 12-metallacrown-4 double-decker

The first double-decker Ga(iii)/Dy(iii) 12-MC-4 complex has been isolated and magnetic studies revealed its SMM properties.

A large barrier single-molecule magnet without magnetic memory

We report a six coordinate Dy^III single-molecule magnet (SMM) with an energy barrier of 1110 K for thermal relaxation of magnetization, but no magnetic hysteresis above 2 K.

A linear cobalt(II) complex with maximal orbital angular momentum from a non-Aufbau ground state

Orbital angular momentum is a prerequisite for magnetic anisotropy, although in transition metal complexes it is typically quenched by the ligand field. By reducing the basicity of the carbon donor atoms in a pair of alkyl ligands, we synthesized a cobalt(II) dialkyl complex, Co(C(SiMe2ONaph)3)2 (where Me is methyl and Naph is a naphthyl group), wherein the ligand field is sufficiently weak that interelectron repulsion and spin-orbit coupling play a dominant role in determining the electronic ground state. Assignment of a non-Aufbau (dx2–y2, dxy)3(dxz, dyz)3(dz2)1 electron configuration is supported by dc magnetic susceptibility data, experimental charge density maps, and ab initio calculations. Variable-field far-infrared spectroscopy and ac magnetic susceptibility measurements further reveal slow magnetic relaxation via a 450–wave number magnetic excited state.

Closing the Circle of the Lanthanide-Murexide Series: Single-Molecule Magnet Behavior and Near-Infrared Emission of the NdIII Derivative

Up to now, even if murexide-based complexometric studies are performed with all 3d or 4f ions, the crystal structures of the light-lanthanide derivatives of the lanthanide-murexide series are unknown. In this work, we report the crystal structure of the NdIII derivative named NdMurex. Contrary to all known complexes of the 3d or 4f series, a dimeric compound was obtained. As for its already reported DyIII and YbIII parents, the NdIII complex responsible for the color-change behaves as a single-molecule magnet (SMM). This behavior was observed on both the crystalline (NdMurex: Ueff = 6.20(0.80) K, 4.31 cm−1; τ0 = 2.20(0.92) × 10−5 s, Hdc = 1200 Oe) and anhydrous form (NdMurexAnhy: Ueff = 6.25(0.90) K, 4.34 cm−1; τ0 = 4.85(0.40) × 10−5 s, Hdc = 1200 Oe). The SMM behavior is reported also for the anhydrous CeIII derivative (CeMurexAnhy: Ueff = 5.40(0.75) K, 3.75 cm−1; τ0 = 3.02(1.10) × 10−5 s, Hdc = 400 Oe). The Near-Infrared Emission NIR emission was observed for NdMurexAnhy and highlights its bifunctionality.

Crystal Field Splittings in Lanthanide Complexes: Inclusion of Correlation Effects beyond Second Order Perturbation Theory

State-averaged complete active space self-consistent field (CASSCF) calculations and a subsequent spin-orbit calculation mixing the CASSCF wave functions (CASSCF/state-interaction with spin-orbit coupling) is the conventional approach used for ab initio calculations of crystal-field splittings and magnetic properties of lanthanide complexes. However, this approach neglects dynamical correlation. Complete active space second-order perturbation theory (CASPT2) can be used to account for dynamical correlation but suffers from the well-known problems of multireference perturbation theory, e.g., intruder state problems. Variational multireference configuration interaction (MRCI) calculations do not show these problems but are usually not feasible due to the large size of real lanthanide complexes. Here, we present a quasi-local projected internally contracted MRCI approach which makes MRCI calculations of lanthanide complexes feasible and allows assessing the influence of dynamical correlation beyond second-order perturbation theory. We apply the method to two well-studied molecules, namely, [Er{N(SiMe₃)₂}₃] and {C(NH₂)₃}₅[Er(CO₃)₄]·11H₂O.

Chemical tunnel-splitting-engineering in a dysprosium-based molecular nanomagnet

Total control over the electronic spin relaxation in molecular nanomagnets is the ultimate goal in the design of new molecules with evermore realizable applications in spin-based devices. For single-ion lanthanide systems, with strong spin-orbit coupling, the potential applications are linked to the energetic structure of the crystal field levels and quantum tunneling within the ground state. Structural engineering of the timescale of these tunneling events via appropriate design of crystal fields represents a fundamental challenge for the synthetic chemist, since tunnel splittings are expected to be suppressed by crystal field environments with sufficiently high-order symmetry. Here, we report the long missing study of the effect of a non-linear (C₄) to pseudo-linear (D_4d) change in crystal field symmetry in an otherwise chemically unaltered dysprosium complex. From a purely experimental study of crystal field levels and electronic spin dynamics at milliKelvin temperatures, we demonstrate the ensuing threefold reduction of the tunnel splitting.

Modelling spin Hamiltonian parameters of molecular nanomagnets

Molecular nanomagnets encompass a wide range of coordination complexes possessing several potential applications. A formidable challenge in realizing these potential applications lies in controlling the magnetic properties of these clusters. Microscopic spin Hamiltonian (SH) parameters describe the magnetic properties of these clusters, and viable ways to control these SH parameters are highly desirable. Computational tools play a proactive role in this area, where SH parameters such as isotropic exchange interaction (J), anisotropic exchange interaction (Jx, Jy, Jz), double exchange interaction (B), zero-field splitting parameters (D, E) and g-tensors can be computed reliably using X-ray structures. In this feature article, we have attempted to provide a holistic view of the modelling of these SH parameters of molecular magnets. The determination of J includes various class of molecules, from di- and polynuclear Mn complexes to the {3d-Gd}, {Gd-Gd} and {Gd-2p} class of complexes. The estimation of anisotropic exchange coupling includes the exchange between an isotropic metal ion and an orbitally degenerate 3d/4d/5d metal ion. The double-exchange section contains some illustrative examples of mixed valance systems, and the section on the estimation of zfs parameters covers some mononuclear transition metal complexes possessing very large axial zfs parameters. The section on the computation of g-anisotropy exclusively covers studies on mononuclear Dy(III) and Er(III) single-ion magnets. The examples depicted in this article clearly illustrate that computational tools not only aid in interpreting and rationalizing the observed magnetic properties but possess the potential to predict new generation MNMs.

CERES: An ab initio code dedicated to the calculation of the electronic structure and magnetic properties of lanthanide complexes

We have developed and implemented a new ab initio code, Ceres (Computational Emulator of Rare Earth Systems), completely written in C++11, which is dedicated to the efficient calculation of the electronic structure and magnetic properties of the crystal field states arising from the splitting of the ground state spin-orbit multiplet in lanthanide complexes. The new code gains efficiency via an optimized implementation of a direct configurational averaged Hartree-Fock (CAHF) algorithm for the determination of 4f quasi-atomic active orbitals common to all multi-electron spin manifolds contributing to the ground spin-orbit multiplet of the lanthanide ion. The new CAHF implementation is based on quasi-Newton convergence acceleration techniques coupled to an efficient library for the direct evaluation of molecular integrals, and problem-specific density matrix guess strategies. After describing the main features of the new code, we compare its efficiency with the current state-of-the-art ab initio strategy to determine crystal field levels and properties, and show that our methodology, as implemented in Ceres, represents a more time-efficient computational strategy for the evaluation of the magnetic properties of lanthanide complexes, also allowing a full representation of non-perturbative spin-orbit coupling effects. © 2017 Wiley Periodicals, Inc.