Multiple spin–phonon relaxation pathways in a Kramer single-ion magnet

Control of the geometry and anisotropy driven by the combination of steric and anion coordination effects in CoII complexes with N6-tripodal ligands: the impact of the size of the ligand on the magnetization relaxation time

Four mononuclear CoII complexes of formula [Co(L)(SCN)2(CH3OH)0.5(H2O)0.5]·1.5H2O·0.75CH3OH (1), [Co(L1)Cl2]·H2O·2CH3CN (2), [Co(L1)(SCN)2]·1.5H2O·CH3OH (3) and [Co(L1)]ClO4·2CH3OH (4) were prepared from the N6-tripodal Schiff base ligands (S)P[N(Me)NC(H)2-Q]3 (L) and (S)P[N(Me)NC(H)1-ISOQ]3 (L1), where Q and ISOQ represent quinolyl and isoquinolyl moieties, respectively. In 1, the L ligand does not coordinate to the CoII ion in a tripodal manner but using a new N,N,S tridentate mode, which is due to the fact that the N6-tripodal coordination promotes a strong steric hindrance between the quinolyl moieties. However, L1 can coordinate to the CoII ions either in a tripodal manner using CoII salts with poorly coordinating anions to give 4 or in a bisbidentate fashion using CoII salt-containing medium to strongly coordinating anions to afford 2 and 3. In the case of L1, there is no steric hindrance between ISOQ moieties after coordination to the CoII ion. The CoII ion exhibits a distorted octahedral geometry for compounds 1-3, with the anions in cis positions for the former and in trans positions for the two latter compounds. Compound 4 shows an intermediate geometry between an octahedral and trigonal prism but closer to the latter one. DC magnetic properties, HFEPR and FIRMS measurements and ab initio calculations demonstrate that distorted octahedral complexes 1-3 exhibit easy-plane magnetic anisotropy (D > 0), whereas compound 4 shows large easy-axis magnetic anisotropy (D < 0). Comparative analysis of the magneto-structural data underlines the important role that is played not only by the coordination geometry but also the electronic effects in determining the anisotropy of the CoII ions. Compounds 2-3 show a field-induced slow relaxation of magnetization. Despite its large easy-axis magnetic anisotropy, compound 4 does not show significant slow relaxation (SMR) above 2 K under zero applied magnetic fields, but its magnetic dilution with ZnII triggers SMR at zero field. Finally, it is worth remarking that compounds 2-4 show smaller relaxation times than the analogous complexes with the tripodal ligand bearing in its arms pyridine instead of isoquinoline moieties, which is most likely due to the increase of the molecular size in the former one.

Structural, optical and magnetic properties of a new metal-organic CoII-based complex

A mononuclear cobalt(ii) complex [C5H8N3]2[CoCl4(C5H7N3)2] (I) was synthesized and structurally characterized. Single crystal X-ray diffraction analysis indicates that monometallic Co(ii) ions acted as coordination nodes in a distorted octahedral geometry, giving rise to a supramolecular architecture. The latter is made up of a ½ unit form composed of an anionic element [Co0.5Cl2(C5H7N3)]- and one 2-amino-4-methylpyrimidinium cation [C5H8N3]+. The crystalline arrangement of this compound adopts the sandwich form where inorganic parts are sandwiched between the organic sheets following the [100] direction. More information regarding the structure hierarchy has been supplied based on Hirshfeld surface analysis; the X⋯H (X = N, Cl) interactions play a crucial role in stabilizing the self-assembly process of I, complemented by the intervention of π⋯π electrostatic interaction created between organic entities. Thermal analyses were carried out to study the thermal behavior process. Static magnetic measurements and ab initio calculations of compound I revealed the easy-axis anisotropy character of the central Co(ii) ion. Two-channel field-induced slow-magnetic relaxation was observed; the high-frequency channel is characterized by underbarrier relaxation with U eff = 16.5 cm-1, and the low-frequency channel involves a direct relaxation process affected by the phonon-bottleneck effect.

Spin-lattice relaxation with non-linear couplings: Comparison between Fermi's golden rule and extended dissipaton equation of motion

Fermi's golden rule (FGR) offers an empirical framework for understanding the dynamics of spin-lattice relaxation in magnetic molecules, encompassing mechanisms like direct (one-phonon) and Raman (two-phonon) processes. These principles effectively model experimental longitudinal relaxation rates, denoted as T1-1. However, under scenarios of increased coupling strength and nonlinear spin-lattice interactions, FGR's applicability may diminish. This paper numerically evaluates the exact spin-lattice relaxation rate kernels, employing the extended dissipaton equation of motion formalism. Our calculations reveal that when quadratic spin-lattice coupling is considered, the rate kernels exhibit a free induction decay-like feature, and the damping rates depend on the interaction strength. We observe that the temperature dependence predicted by FGR significantly deviates from the exact results since FGR ignores the higher order effects and the non-Markovian nature of spin-lattice relaxation. Our methods can be easily extended to study other systems with nonlinear spin-lattice interactions and provide valuable insights into the temperature dependence of T1 in molecular qubits when the coupling is strong.

Machine Learning-Enhanced Quantum Chemistry-Assisted Refinement of the Active Site Structure of Metalloproteins

Understanding the fine structural details of inhibitor binding at the active site of metalloenzymes can have a profound impact on the rational drug design targeted to this broad class of biomolecules. Structural techniques such as NMR, cryo-EM, and X-ray crystallography can provide bond lengths and angles, but the uncertainties in these measurements can be as large as the range of values that have been observed for these quantities in all the published structures. This uncertainty is far too large to allow for reliable calculations at the quantum chemical (QC) levels for developing precise structure-activity relationships or for improving the energetic considerations in protein-inhibitor studies. Therefore, the need arises to rely upon computational methods to refine the active site structures well beyond the resolution obtained with routine application of structural methods. In a recent paper, we have shown that it is possible to refine the active site of cobalt(II)-substituted MMP12, a metalloprotein that is a relevant drug target, by matching to the experimental pseudocontact shifts (PCS) those calculated using multireference ab initio QC methods. The computational cost of this methodology becomes a significant bottleneck when the starting structure is not sufficiently close to the final one, which is often the case with biomolecular structures. To tackle this problem, we have developed an approach based on a neural network (NN) and a support vector regression (SVR) and applied it to the refinement of the active site structure of oxalate-inhibited human carbonic anhydrase 2 (hCAII), another prototypical metalloprotein target. The refined structure gives a remarkably good agreement between the QC-calculated and the experimental PCS. This study not only contributes to the knowledge of CAII but also demonstrates the utility of combining machine learning (ML) algorithms with QC calculations, offering a promising avenue for investigating other drug targets and complex biological systems in general.

Ab initio calculation of magnetic anisotropy and thermal spin transition in the variable temperature crystal conformations of [Co(terpy)2]2

The structure-property correlation of [Co(terpy)2]2+, which shows a spin crossover at 270 K, has been computationally investigated based on its variable temperature crystal structures. Among the employed DFT functionals, only the re-parametrized hybrid B3LYP* functional could describe the correct spin transition temperature. Explicit consideration of metal-ligand sigma bonding with dynamic electron correlation is found to be necessary for an accurate determination of the SCO temperature with multi-reference calculations. The metal-ligand axial bond distances are found to be the most significant internal coordinates in deciding SCO. A small structural change along the axial distance causes a change in the t2g orbital splitting pattern and a reorientation of the magnetization axes at the SCO temperature. The complex shows an unusual triaxial magnetic anisotropy, with an easy axis of magnetization developing at higher temperatures. The strong coupling of low-frequency wagging motion of the two terpyridine ligands with the spin states of the complex provides an effective pathway for the relaxation of magnetization, resulting in a small magnetic anisotropy barrier.

Unravelling the role of spin-vibrational coupling in designing high-performance pentagonal bipyramidal Dy(iii) single ion magnets

At the cutting edge of high-performance single-molecule magnets (SMMs) lie lanthanide-based complexes, renowned for their potent magnetic anisotropy. SMMs containing one metal centre are defined as single-ion magnets (SIMs). The performance of SMMs is measured generally via the barrier height for magnetisation reversal (Ueff) and blocking temperature (TB), below which the magnetisation is fully frozen. To enhance the Ueff and TB values in lanthanide-based SMMs, the static crystal field splitting of mJ levels has been effectively adjusted through ligand design, leveraging the oblate/prolate ground state 4f electron density shape. However, the maximum fine-tuning achievable through ligand design, known as the axial limit, has already been reached in this class of compounds. This necessitates new design principles to enhance SMM characteristics to better suit end-user applications. Among other avenues that can be explored to improve SMM characteristics, a deeper understanding of spin-phonon coupling is critical to advancing TB values. However, there are only a handful of examples where this has been deciphered. In this work, using a combination of DFT and ab initio CASSCF calculations, we have performed spin-phonon calculations on five classes of pentagonal bipyramidal Dy(iii) SIMs exhibiting TB values in the range of 4.5 K to 36 K ([Dy(bbpen)Br] (1, H2bbpen = N,N'-bis(2-hydroxybenzyl)-N,N'-bis(2-methylpyridyl)ethylenediamine), [Dy(OCMe3)Br(THF)5][BPh4] (2) [Dy(OSiMe3)Br(THF)5] [BPh4] (3), [Dy(LN5)(Ph3SiO)2](BPh4)·CH2Cl2 (4) and [L2Dy(H2O)5][I]3·L2·H2O (5, L = tBuPO(NHiPr)2)). Unlike the method employed elsewhere for the calculation of spin-phonon coupling, in this work, we have employed a set of criteria and intuitively selected vibrational modes to perform the spin-phonon coupling analysis. The approach provided here not only reduces the computational cost significantly but also suggests chemical intuition to improve the performance of this class of compounds. Our calculations reveal that low-energy vibrational modes govern the magnetisation relaxation in these SIMs. A flexible first coordination sphere found on some of the complexes was found to be responsible for low-energy vibrations that flip the magnetisation, reducing the TB values drastically (complexes 2 and 3). On the other hand, a rigid first coordination sphere and a stiff ligand framework move the spin-vibrational coupling that causes the relaxation to lie beyond the secondary coordination sphere, resulting in an increase in TB values. Our calculations also reveal that not only the atoms in the first coordination sphere but also those in the secondary coordination sphere affect the performance of the SMMs. Learning from this exercise, we have undertaken several in silico models based on these vibrations to improve the TB values. Some of these predictions were correlated with literature precedents, offering confidence in the methodology employed. To this end, our comprehensive investigation, involving twenty-three molecules/models and five sets of geometries for pentagonal bipyramidal Dy(iii) single-ion magnets (SIMs), unveils a treasure trove of chemically sound design clues, poised to enhance the TB values in this fascinating molecular realm.

A novel non-adiabatic spin relaxation mechanism in molecular qubits

The interaction of electronic spin and molecular vibrations mediated by spin-orbit coupling governs spin relaxation in molecular qubits. We derive an extended molecular spin Hamiltonian that includes both adiabatic and non-adiabatic spin-dependent interactions, and we implement the computation of its matrix elements using state-of-the-art density functional theory. The new molecular spin Hamiltonian contains a novel spin-vibrational orbit interaction with a non-adiabatic origin, together with the traditional molecular Zeeman and zero-field splitting interactions with an adiabatic origin. The spin-vibrational orbit interaction represents a non-Abelian Berry curvature on the ground-state electronic manifold and corresponds to an effective magnetic field in the electronic spin dynamics. We further develop a spin relaxation rate model that estimates the spin relaxation time via the two-phonon Raman process. An application of the extended molecular spin Hamiltonian together with the spin relaxation rate model to Cu(II) porphyrin, a prototypical S = 1/2 molecular qubit, demonstrates that the spin relaxation time at elevated temperatures is dominated by the non-adiabatic spin-vibrational orbit interaction. The computed spin relaxation rate and its magnetic field orientation dependence are in excellent agreement with experimental measurements.

Influence of the phonon-bottleneck effect and low-energy vibrational modes on the slow spin-phonon relaxation in Kramers-ions-based Cu(II) and Co(II) complexes with 4-amino-3,5-bis-(pyridin-2-yl)-1,2,4-triazole and dicyanamide

Two new complexes, bis-[4-amino-3,5-bis-(pyridin-2-yl)-1,2,4-triazole-κ2N2,N6]bis-(dicyanamide-κN8)copper(II), [Cu(abpt)2(dca)2] (1) and bis-[4-amino-3,5-bis-(pyridin-2-yl)-1,2,4-triazole-κ2N2,N6]bis-(dicyanamide-κN8)cobalt(II), [Co(abpt)2(dca)2] (2), have been prepared and magneto-structurally characterised. Single crystal studies of both complexes have shown that their crystal structures are molecular, in which the central atoms are six-coordinated in the form of a distorted octahedron by two bidentate abpt and two monodentate dca ligands. Even if both complexes have the same composition and crystallize in the same P1̄ space group, they are not isostructural. Both structures contain strong intermolecular N-H⋯N hydrogen bonds and π-π stacking interactions. IR spectra are consistent with the solved structures of both complexes and confirmed the terminal character of the dca ligands and the bidentate coordination of the abpt ligands. The analysis of the magnetic properties showed that both complexes exhibit field-induced slow spin-phonon relaxation. In both complexes, the slow spin-phonon relaxation is influenced by a severe phonon-bottleneck effect that affects the direct process, a dominant relaxation mechanism at low temperatures in both complexes. The phonon-bottleneck effect in 1 was suppressed by simply reducing the crystallite size, and further analysis of the field dependence of the relaxation time yielded the characteristic energy of vibrational modes of 11 cm-1 participating in the Raman process at low magnetic fields. The analysis of magnetic properties and ab initio calculations confirmed that 2 represents a system with a moderate uniaxial anisotropy yielding an average energy barrier of 82 cm-1 (from all four nonequivalent Co(II) sites in the structure of 2).

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.

Spin-Vibronic Dynamics in Open-Shell Systems beyond the Spin Hamiltonian Formalism

Vibronic coupling has a dramatic influence over a large number of molecular processes, ranging from photochemistry to spin relaxation and electronic transport. The simulation of vibronic coupling with multireference wave function methods has been largely applied to organic compounds, and only early efforts are available for open-shell systems such as transition metal and lanthanide complexes. In this work, we derive a numerical strategy to differentiate the molecular electronic Hamiltonian in the context of multireference ab initio methods and inclusive of spin-orbit coupling effects. We then provide a formulation of open quantum system dynamics able to predict the time evolution of the electron density matrix under the influence of a Markovian phonon bath up to fourth-order perturbation theory. We apply our method to Co(II) and Dy(III) molecular complexes exhibiting long spin relaxation times and successfully validate our strategy against the use of an effective spin Hamiltonian. Our study sheds light on the nature of vibronic coupling, the importance of electronic excited states in spin relaxation, and the need for high-level computational chemistry to quantify it.

Zero-Field SMM Behavior Triggered by Magnetic Exchange Interactions and a Collinear Arrangement of Local Anisotropy Axes in a Linear Co3II Complex

A new linear trinuclear Co(II)3 complex with a formula of [{Co(μ-L)}2Co] has been prepared by self-assembly of Co(II) ions and the N3O3-tripodal Schiff base ligand H3L, which is obtained from the condensation of 1,1,1-tris(aminomethyl)ethane and salicylaldehyde. Single X-ray diffraction shows that this compound is centrosymmetric with triple-phenolate bridging groups connecting neighboring Co(II) ions, leading to a paddle-wheel-like structure with a pseudo-C3 axis lying in the Co-Co-Co direction. The Co(II) ions at both ends of the Co(II)3 molecule exhibit distorted trigonal prismatic CoN3O3 geometry, whereas the Co(II) at the middle presents an elongated trigonal antiprismatic CoO6 geometry. The combined analysis of the magnetic data and theoretical calculations reveal strong easy-axis magnetic anisotropy for both types of Co(II) ions (|D| values higher than 115 cm-1) with the local anisotropic axes lying on the pseudo-C3 axis of the molecule. The magnetic exchange interaction between the middle and ends Co(II) ions, extracted by using either a Hamiltonian accounting for the isotropic magnetic coupling and ZFS or the Lines' model, was found to be medium to strong and antiferromagnetic in nature, whereas the interaction between the external Co(II) ions is weak antiferromagnetic. Interestingly, the compound exhibits slow relaxation of magnetization and open hysteresis at zero field and therefore SMM behavior. The significant magnetic exchange coupling found for [{Co(μ-L)}2Co] is mainly responsible for the quenching of QTM, which combined with the easy-axis local anisotropy of the CoII ions and the collinearity of their local anisotropy axes with the pseudo-C3 axis favors the observation of SMM behavior at zero field.

Understanding electrostatics and covalency effects in highly anisotropic organometallic sandwich dysprosium complexes [Dy(CmRm)2] (where R = H, SiH3, CH3 and m = 4 to 9): a computational perspective

In this article, we have thoroughly studied the electronic structure and 4f-ligand covalency of six mononuclear dysprosium organometallic sandwich complexes [Dy(CmRm)2]n+/- (where R = H, SiH3, CH3; m = 4 to 9; n = 1, 3) using both the scalar relativistic density functional and complete active space self-consistent field (CASSCF) and N-electron valence perturbation theory (NEVPT2) method to shed light on the ligand field effects in fine-tuning the magnetic anisotropy of these complexes. Energy decomposition analysis (EDA) and ab initio-based ligand field theory AILFT calculations predict the sizable 4f-ligand covalency in all these complexes. The analysis of CASSCF/NEVPT2 computed spin-Hamiltonian (SH) parameters indicates the stabilization of mJ |±15/2〉 for [Dy(C4(SiH3)4)2]- (1), [Dy(C5(CH3)5)2]+ (2) and [Dy(C6H6)2]3+ (3) complexes with the Ucal value of 1867.5, 1621.5 and 1070.8 cm-1, respectively. On the other hand, we observed mJ |±9/2〉 as the ground state for [Dy(C7H7)2]3- (4) and [Dy(C8H8)2]- (5) complexes with significantly smaller Ucal values of 237.1 and 38.6 cm-1 respectively. For the nine-membered ring [Dy(C9H9)2]+ (6) complex, we observed the stabilization of the mJ |±1/2〉 ground state, with the first excited state being located ∼29 cm-1 higher in energy. AILFT-NEVPT2 ligand field splitting analysis indicates that the presence of π-type 4f-ligand interactions in complexes 1-3 help generate the axial-ligand field, while the δ-type interactions in complexes 4-5 generate the equatorial ligand field despite the ligands approaching from the axial direction. As the ring size increases, φ-type interactions dominate, generating a pure equatorial ligand field stabilising mJ |±1/2〉 as the ground state for 6. Calculations suggest that the nature of the ligand field mainly governs the Ucal values in the following order: 4f-Lσ > 4f-Lπ > 4f-Lδ > 4f-Lφ. Calculations were performed by replacing ligands with CHELPG charges to access the crystal field (CF) effects which suggests the stabilization of pure mJ |±15/2〉 in all the charge-embedded models (1Q-6Q). Our findings point out that the crystal field and ligand field effects complement each other and generate a giant barrier for magnetic relaxation in the small ring complexes 1-3, while a relatively weak crystal field and adverse 4f-Lδ/4f-Lφ interactions diminish the SMM behaviour in the large ring complexes 4-6.

Field- and Temperature-Dependent Paramagnetic Relaxation Enhancements in Co(II) Trispyrazolylmethanes

A comprehensive field- and temperature-dependent examination of nuclear magnetic resonance paramagnetic relaxation enhancements (PREs) for the constitutive protons of [Co(Tpm)2][BF4]2 is presented. Data for an apically substituted derivative clearly establish that bis-Tpm complexes of Co(II) undergo Jahn-Teller dynamics about the molecular threefold axis. PREs from the parent Tpm complex were used to numerically extract the electron relaxation times (T1e). The Tpm complex showed field-dependent behavior, with an approximately 40% higher activation barrier than the related trispyrazolylborate (Tp) complex, based on fits to the T1e vs T, B0 data. Analysis of the field-dependent line widths revealed a surprisingly large contribution from susceptibility (Curie) relaxation (20-35% at the highest field), and a molecular radius (9.5 Å) that is consistent with a tightly associated counterion slowing rotation in solution. Density functional theory showed a shared vibration that is consistent with the Jahn-Teller and appears proportionately higher in energy in [Co(Tpm)2]2+. Complete active-space self-consistent field calculations support ascribing electron relaxation to enhanced mixing of the two Eg orbital sets that accompanies the tetragonal distortion and the differences in electron correlation times to the higher Jahn-Teller activation barrier in [Co(Tpm)2]2+.

Air-stable four-coordinate cobalt(ii) single-ion magnets: experimental and ab initio ligand field analyses of correlations between dihedral angles and magnetic anisotropy

For single-ion magnets (SIMs), understanding the effects of the local coordination environment and ligand field on magnetic anisotropy is key to controlling their magnetic properties. Here we present a series of tetracoordinate cobalt(ii) complexes of the general formula [FL2Co]X2 (where FL is a bidentate diamido ligand) whose electron-withdrawing -C6F5 substituents confer stability under ambient conditions. Depending on the cations X, these complexes adopt structures with greatly varying dihedral twist angle δ between the N-Co-N' chelate planes in the solid state (48.0 to 89.2°). AC and DC field magnetic susceptibility measurements show this to translate into very different magnetic properties, the axial zero-field splitting (ZFS) parameter D ranging from -69 cm-1 to -143 cm-1 with substantial or negligible rhombic component E, respectively. A close to orthogonal arrangement of the two N,N'-chelating σ- and π-donor ligands at the Co(ii) ion is found to raise the energy barrier for magnetic relaxation to above 400 K. Multireference ab initio methods were employed to describe the complexes' electronic structures, and the results were analyzed within the framework of ab initio ligand field theory to probe the nature of the metal-ligand bonding and spin-orbit coupling. A relationship between the energy gaps of the first few electronic transitions and the ZFS was established, and the ZFS was correlated with the dihedral angle δ as well as with the metal-ligand bonding variations, viz. the two angular overlap parameters eσ and eπs. These findings not only give rise to a Co(ii) SIM showing open hysteresis up to 3.5 K at a sweep rate of 30 Oe s-1, but they also provide design guidelines for Co(ii) complexes with favorable SIM signatures or even switchable magnetic relaxation properties.

The critical role of ultra-low-energy vibrations in the relaxation dynamics of molecular qubits

Improving the performance of molecular qubits is a fundamental milestone towards unleashing the power of molecular magnetism in the second quantum revolution. Taming spin relaxation and decoherence due to vibrations is crucial to reach this milestone, but this is hindered by our lack of understanding on the nature of vibrations and their coupling to spins. Here we propose a synergistic approach to study a prototypical molecular qubit. It combines inelastic X-ray scattering to measure phonon dispersions along the main symmetry directions of the crystal and spin dynamics simulations based on DFT. We show that the canonical Debye picture of lattice dynamics breaks down and that intra-molecular vibrations with very-low energies of 1-2 meV are largely responsible for spin relaxation up to ambient temperature. We identify the origin of these modes, thus providing a rationale for improving spin coherence. The power and flexibility of our approach open new avenues for the investigation of magnetic molecules with the potential of removing roadblocks toward their use in quantum devices.

Strategies to quench quantum tunneling of magnetization in lanthanide single molecule magnets

Enhancing blocking temperature (T_B) is one of the holy grails in Single Molecule Magnets(SMMs), as any future potential application in this class of molecules is directly correlated to this parameter. Among many factors contributing to a reduction of T_B value, Quantum Tunnelling of Magnetisation (QTM), a phenomenon that is a curse or a blessing based on the application sought after, tops the list. Theoretical tools based on density functional and ab initio CASSCF/RASSI-SO methods have played a prominent role in estimating various spin Hamiltonian parameters and establishing the mechanism of magnetization relaxation in this class of molecules. Particularly, various strategies to quench QTM effects go hand-in-hand with experiments, and different methods proposed to quell QTM effects are scattered in the literature. In this perspective, we have explored various approaches that are proposed in the literature to quench QTM effects, and these include the role of (i) local symmetry of lanthanides, (ii) super-exchange interaction in {3d-4f} complexes, (iii) direct-exchange interaction in {radical-4f} and metal-metal bonded complexes to suppress the QTM, (iv) utilizing external stimuli such as an electric field or pressure to modulate the QTM and (v) avoiding QTM effects by stabilising toroidal states in 4f and {3d-4f} clusters. We believe the strategies summarized here will help to design new-generation SMMs.

Multi-Technique Experimental Benchmarking of the Local Magnetic Anisotropy of a Cobalt(II) Single-Ion Magnet

A comprehensive understanding of the ligand field and its influence on the degeneracy and population of d-orbitals in a specific coordination environment are crucial for the rational design and enhancement of magnetic anisotropy of single-ion magnets (SIMs). Herein, we report the synthesis and comprehensive magnetic characterization of a highly anisotropic Co^II SIM, [L₂Co](TBA)₂ (L is an N,N'-chelating oxanilido ligand), that is stable under ambient conditions. Dynamic magnetization measurements show that this SIM exhibits a large energy barrier to spin reversal U _eff > 300 K and magnetic blocking up to 3.5 K, and the property is retained in a frozen solution. Low-temperature single-crystal synchrotron X-ray diffraction used to determine the experimental electron density gave access to Co d-orbital populations and a derived U _eff, 261 cm^-1, when the coupling between the d _{x ² - y ²} and d_xy orbitals is taken into account, in very good agreement with ab initio calculations and superconducting quantum interference device results. Powder and single-crystal polarized neutron diffraction (PNPD, PND) have been used to quantify the magnetic anisotropy via the atomic susceptibility tensor, revealing that the easy axis of magnetization is pointing along the N-Co-N' bisectors of the N,N'-chelating ligands (3.4° offset), close to the molecular axis, in good agreement with complete active space self-consistent field/N-electron valence perturbation theory to second order ab initio calculations. This study provides benchmarking for two methods, PNPD and single-crystal PND, on the same 3d SIM, and key benchmarking for current theoretical methods to determine local magnetic anisotropy parameters.

Influence of ligand substitution and the solvent effect on the structures and magnetic properties of dinuclear Dy2 supramolecular architectures constructed with the bis-β-diketonate-Dy2 building block as a metalloligand

Based on the bis-β-diketonate-Dy₂ metalloligand [Dy₂(pbth)₄]·2Et₃N (1, pbth = (3z,3'z)-4,4'-(1,3-phenylene)bis(1,1,1-trifluoro-4-hydroxybut-3-en-2-one)), six dinuclear complexes with eight-coordinated geometries were synthesized solvothermally through different capping N-donor coligands or solvent systems. These complexes are namely [Dy₂(pbth)₃(Phen)₂]·2C₂H₅OH (2), [Dy₂(pbth)₃(BPhen)₂]·2C₂H₅OH (3), [Dy₂(pbth)₃(Dppz)₂]·2C₂H₅OH (4), [Dy₂(pbth)₃(Dppz)₂]·2CH₃OH (4a), [Dy₂(pbth)₃(4-Dmbp)₂]·CH₃OH·C₂H₅OH (5) and [Dy₂(pbth)₃(5-Dmbp)₂]·CH₃OH (6) (Phen = 1,10-phenanthroline, BPhen = 4,7-diphenyl-1,10-phenanthroline, dppz = dipyrido [3,2-a:2',3'-c] phenazine, 4-Dmbp = 4,4'-dimethyl-2,2'-bipyridyl, 5-Dmbp = 5,5'-dimethyl-2,2'-bipyridyl), respectively. In the synthetic processes of 2-6, one of four bis-β-diketonate ligands in the metalloligand is replaced by two capping N-donor coligands. The coordination geometries, metal distances and M-L-M torsion angles of the synthesized complexes are perceptibly fine-tuned by the modification of the capping N-donor coligands or the latticed solvent molecules. Systematic magnetic investigations indicate the different magnetic relaxation dynamics of 1-6. Complex 1 displays no characteristics of single-molecule magnets (SMMs), while complexes 2-6 exhibit SMM behaviours in the absence of a static magnetic field. Complexes 2 and 3 possess effective energy barriers (U_eff) of 110.18 (2) K and 133.21 (4) K, respectively. Theoretical analysis based on ab initio calculation provides some interpretations of experimental observation.

A porous cobalt(II)-organic framework exhibiting high room temperature proton conductivity and field-induced slow magnetic relaxation

A two-dimensional (2D) cobalt(II) metal-organic framework (MOF) constructed by a ditopic organic ligand, formulated as {[Co(Hbic)(H₂O)]·4H₂O}_n (1) (H₂bic = 1H-benzimidazole-5-carboxylic acid), was hydrothermally synthesized and structurally characterized. Single-crystal X-ray diffraction shows that the distorted octahedral Co²⁺ ions, as coordination nodes, are bridged to form 2D honeycomb networks, which are further organized into a 3D supramolecular porous framework through multiple hydrogen bonds and interlayer π-π interactions. Dynamic crystallography experiments reveal the anisotropic thermal expansion behavior of the lattice, suggesting a flexible hydrogen-bonded 3D framework. Interestingly, hydrogen-bonded (H₂O)₄ tetramers were found to be located in porous channels, yielding 1D proton transport pathways. As a result, the compound exhibited a high room-temperature proton conductivity of 1.6 × 10^-4 S cm^-1 under a relative humidity of 95% through a Grotthuss mechanism. Magnetic investigations combined with theoretical calculations reveal giant easy-plane magnetic anisotropy of the distorted octahedral Co²⁺ ions with the experimental and computed D values being 87.1 and 109.3 cm^-1, respectively. In addition, the compound exhibits field-induced slow magnetic relaxation behavior at low temperatures with an effective energy barrier of U_eff = 45.2 cm^-1. Thus, the observed electrical and magnetic properties indicate a rare proton conducting SIM-MOF. The foregoing results provide a unique bifunctional cobalt(II) framework material and suggest a promising way to achieve magnetic and electrical properties using a supramolecular framework platform.

Pushing up the easy-axis magnetic anisotropy and relaxation times in trigonal prismatic CoII mononuclear SMMs by molecular structure design

The replacement of pyridine by 1-methyl-imidazol in the arms of a N₆-tripodal ligand allows preparing two new Co^II complexes with quasi-ideal triangular prismatic geometry, which behave as SIMs (Single Ion Magnets) at zero dc field with enhanced axial magnetic anisotropy, magnetic relaxation times and magnetic hysteresis.

Unraveling the Contributions to Spin-Lattice Relaxation in Kramers Single-Molecule Magnets

The study of how spin interacts with lattice vibrations and relaxes to equilibrium provides unique insights into its chemical environment and the relation between electronic structure and molecular composition. Despite its importance for several disciplines, ranging from magnetic resonance to quantum technologies, a convincing interpretation of spin dynamics in crystals of magnetic molecules is still lacking due to the challenging experimental determination of the correct spin relaxation mechanism. We apply ab initio spin dynamics to a series of 12 coordination complexes of Co2+ and Dy3+ ions selected among ∼240 compounds that largely cover the literature on single-molecule magnets and well represent different regimes of spin relaxation. Simulations reveal that the Orbach spin relaxation rate of known compounds mostly depends on the ions' zero-field splitting and little on the details of molecular vibrations. Raman relaxation is instead found to be also significantly affected by the features of low-energy phonons. These results provide a complete understanding of the factors limiting spin lifetime in single-molecule magnets and revisit years of experimental investigations by making it possible to transparently distinguish Orbach and Raman relaxation mechanisms.

Computational design of magnetic molecules and their environment using quantum chemistry, machine learning and multiscale simulations

Having served as a playground for fundamental studies on the physics of d and f electrons for almost a century, magnetic molecules are now becoming increasingly important for technological applications, such as magnetic resonance, data storage, spintronics and quantum information. All of these applications require the preservation and control of spins in time, an ability hampered by the interaction with the environment, namely with other spins, conduction electrons, molecular vibrations and electromagnetic fields. Thus, the design of a novel magnetic molecule with tailored properties is a formidable task, which does not only concern its electronic structures but also calls for a deep understanding of the interaction among all the degrees of freedom at play. This Review describes how state-of-the-art ab initio computational methods, combined with data-driven approaches to materials modelling, can be integrated into a fully multiscale strategy capable of defining design rules for magnetic molecules.

Toward exact predictions of spin-phonon relaxation times: An ab initio implementation of open quantum systems theory

Spin-phonon coupling is the main driver of spin relaxation and decoherence in solid-state semiconductors at finite temperature. Controlling this interaction is a central problem for many disciplines, ranging from magnetic resonance to quantum technologies. Spin relaxation theories have been developed for almost a century but often use a phenomenological description of phonons and their coupling to spin, resulting in a nonpredictive tool and hindering our detailed understanding of spin dynamics. Here, we combine time-local master equations up to the fourth order with advanced electronic structure methods and perform predictions of spin-phonon relaxation time for a series of solid-state coordination compounds based on both transition metals and lanthanide Kramers ions. The agreement between experiments and simulations demonstrates that an accurate, universal, and fully ab initio implementation of spin relaxation theory is possible, thus paving the way to a systematic study of spin-phonon relaxation in solid-state materials.

Ligand Fluorination to Mitigate the Raman Relaxation of DyIII Single-Molecule Magnets: A Combined Terahertz, Far-IR and Vibronic Barrier Model Study

The fast Raman relaxation process via a virtual energy level has become a puzzle for how to chemically engineer single-molecule magnets (SMMs) with better performance. Here, we use the trifluoromethyl group to systematically substitute the methyl groups in the axial position of the parent bis-butoxide pentapyridyl dysprosium(III) SMM. The resulting complexes-[Dy(OL^A )₂ py₅ ][BPh₄ ] (L^A =CH(CF₃ )₂ ^- 1, CH₂ CF₃ ^- 2, CMe₂ CF₃ ^- 3)-show progressively enhanced T_B ^hys (@100 Oe s^-1 ) from 17 K (for 3), 20 K (for 2) to 23 K (for 1). By experimentally identifying the varied under barrier relaxation energy in the 5-500 cm^-1 regime, we are able to identify that the C-F bond related vibration energy of the axial ligand ranging from 200 to 350 cm^-1 is the key variant for this improvement. Thus, this finding not only reveals a correlation between the structure and the Raman process but also provides a paradigm for how to apply the vibronic barrier model to analyze multi-phonon relaxation processes in lanthanide SMMs.

A dysprosium single molecule magnet outperforming current pseudocontact shift agents

A common criterion for designing performant single molecule magnets and pseudocontact shift tags is a large magnetic anisotropy. In this article we present a dysprosium complex chemically designed to exhibit strong easy-axis type magnetic anisotropy that is preserved in dichloromethane solution at room temperature. Our detailed theoretical and experimental studies on the magnetic properties allowed explaining several features typical of highly performant SMMs. Moreover, the NMR characterization shows remarkably large chemical shifts, outperforming the current state-of-the art PCS tags.

Phonon-induced relaxation mechanisms are changed by a chelating effect in a CoII single-ion magnet

It is well known that phonon-induced relaxation processes play a significant role in accelerating magnetization relaxation in the low-temperature regime. Unfortunately, many SIMs (single-ion magnets) suffer from being quenched by these mechanisms such that neither out-of-phase signals nor magnetization hysteresis can be readily observed. Nevertheless, because it involves molecular motions at low-frequency (low-energy) levels, methods for synthetically controlling this factor have not yet been addressed by chemists. In this study, we prepared a series of three compounds in which one contains a rigid chelating ligand, and the other two contain analogous ligands that can coordinate more liberally. To our surprise, compound 1, with a rigid chelating ligand, displayed promising SIM behavior with out-of-phase signals up to 11 K in a zero d.c. magnetic field at an a.c. frequency of 1000 Hz. The other two (2 and 3) with dangling ligands failed to show significant out-of-phase signals until an extra d.c. field was applied. The results of magnetization relaxation studies suggest that the phonon-induced relaxation processes play an essential role in 2 and 3, even at very low temperatures. Nevertheless, the rigid chelating ligand in 1 prevents the molecule from being involved in phonon-induced relaxation processes that seriously interfere with the magnetization relaxation up to 5.6 K. Therefore, we concluded that the presence of a rigid chelating ligand can efficiently change the phonon-induced relaxation processes at low temperatures.

Hydrogen-Bonded Framework of a Cobalt(II) Complex Showing Superior Stability and Field-Induced Slow Magnetic Relaxation

A unique hydrogen-bonded organic-inorganic framework (HOIF) constructed from a mononuclear cobalt(II) complex, [Co(MCA)₂·(H₂O)₂] (HMCA = 4-imidazolecarboxylic acid), via multiple hydrogen-bonding interactions was synthesized and structurally characterized. The Co(II) center in the HOIF features a highly distorted octahedral coordination environment. Remarkably, the Co^II HOIF showed permanent porosity with superior stability as established by combined thermogravimetric analysis (TGA), variable-temperature infrared spectra (IR), variable-temperature powder X-ray diffraction data (PXRD), and a CO₂ isotherm. Structural studies reveal that short multiple hydrogen bonds should be responsible for the superior thermal and chemical stability of a HIOF. Magnetic investigations reveal the large easy-plane magnetic anisotropy of the Co²⁺ ions with the fitted D values being 22.1 (magnetic susceptibility and magnetization data) and 29.1 cm^-1 (reduced magnetization data). In addition, the HOIF exhibits field-induced slow magnetic relaxation at low temperature with an effective energy barrier of U_eff = 45.2 cm^-1, indicative of a hydrogen-bonded framework single-ion magnet of the compound. The origin of the significant magnetic anisotropy of the complex was also understood from computational studies. In addition, BS-DFT calculations indicate that the superexchange interactions between the neighboring Co^II ions are non-negligible antiferromagnetism with J_Co-Co = -0.5 cm^-1. The foregoing results provide not only a carboxylate-imidazole ligand approach toward a stable HOIF but also a promising way to build a robust single-ion magnet via hydrogen-bond interactions.

Field-induced slow magnetic relaxation behaviours in binuclear cobalt(II) metallocycle and exchange-coupled cluster

Precise control of structures and magnetic properties of a molecular material constitutes an important challenge to realize the tailor-made magnetic function. Herein, we reported that the ligand-directed coordination self-assembly of...

The interpretation and prediction of lanthanide single-ion magnet from ab initio electronic structure calculation: The capability and limit

Single-molecule magnet (SMM) is a fascinating system holding the potential of being revolutionary micro-electronic device in information technology. However current SMMs are still far away from real-life application due to...

Tuning chain topologies and magnetic anisotropy in one-dimensional cobalt(II) coordination polymers via distinct dicarboxylates

Based on a terpyridine derivative and two different dicarboxylate ligands, two new cobalt(II) coordination polymers, namely [Co(pytpy)(DClbdc)]n (1) and [Co(pytpy)(ndc)]n (2) (pytpy = 4'-(4-Pyridyl)-2,2':6',2''-terpyridine, H2DClbc = 2,5-Dichloroterephthalic acid, and H2ndc...

Large easy-axis magnetic anisotropy in a series of trigonal prismatic mononuclear cobalt (II) complexes with zero-field hidden single-molecule magnet behaviour: The important role of the distortion of the coordination sphere and intermolecular interactions on the slow relaxation

The complexes [Co(L)]X·S (X = CoCl42- , S = CH3CN (1); X = ZnCl42- , S = CH3OH (2)), [Co(L)]X2·S (X = ClO4-, S = 2CH3OH (3) and X =...

Significantly Enhancing the Single-Molecule-Magnet Performance of a Dinuclear Dy(III) Complex by Utilizing an Asymmetric Auxiliary Organic Ligand

In this work, we employed an asymmetric auxiliary organic ligand (1,1,1-trifluoroacetylacetone, Htfac) to further regulate the magnetic relaxation behavior of series of Dy₂ single-molecule magnets (SMMs) with a N1,N3-bis(3-methoxysalicylidene)diethylenetriamine (H₂L) ligand. Fortunately, an air-stable Dy₂ complex, [Dy₂(L)₂(tfac)₂] (1; Htfac = 1,1,1-trifluoroacetylacetone) was obtained at room temperature. A structural analysis indicated that some Dy-O or Dy-N bond lengths for 1 are not in the range of those for the complexes [Dy^III₂(L)₂(acac)₂]·2CH₂Cl₂ (Dy₂-acac; Hacac = acetylacetone) and [Dy^III₂(L)₂(hfac)₂] (Dy₂-hfac; Hhfac = hexafluoroacetylacetone), although the electron-withdrawing ability of tfac^- is stronger than that of acac^- but weaker than that of hfac^-. Additionally, the Dy-O3/O3a (the two O atoms bridged to Dy^III ions) bond lengths are also affected by the asymmetrical Htfc ligand. This indicated that the charge distribution of the coordination atoms around Dy^III has been modified in 1, which leads to the fine-tuning of the magnetic relaxation behavior of 1. Magnetic studies indicated that the values of effective energy barrier (U_eff) for 1 and its diluted sample (2) are 234.8(3) and 188.0(6) K, respectively, which are both higher than the reported value of 110 K for the complex Dy₂-hfac. More interestingly, 1 exhibits a magnetic hysteresis opening when T < 2.5 K at zero field, while the hysteresis loops of 2 are closed at a zero dc field. This discrepancy is due to the weak intramolecular exchange coupling in 2, which cannot overcome the QTM of the single Dy^III ion. Ab initio calculations for 1 revealed that the charge distributions of the coordination atoms around Dy^III ions were regulated and the intramolecular exchange coupling was indeed improved when the asymmetrical Htfc was employed as a ligand for the synthesis of this kind of Dy₂ SMM.

Effect of Spin-Orbit Coupling on Phonon-Mediated Magnetic Relaxation in a Series of Zero-Valent Vanadium, Niobium, and Tantalum Isocyanide Complexes

Spin-vibronic coupling leads to spin relaxation in paramagnetic molecules, and an understanding of factors that contribute to this phenomenon is essential for designing next-generation spintronics technology, including single-molecule magnets and spin-based qubits, wherein long-lifetime magnetic ground states are desired. We report spectroscopic and magnetic characterization of the isoelectronic and isostructural series of homoleptic zerovalent transition metal triad M(CNDipp)₆ (M = V, Nb, Ta; CNDipp = 2,6-diisopropylphenyl isocyanide) and show experimentally the significant increase in spin relaxation rate upon going from V to Nb to Ta. Correlated electronic calculations and first principle spin-phonon computations support the role of spin-orbit coupling in modulating spin-phonon relaxation. Our results provide experimental evidence that increasing magnetic anisotropy through spin-orbit coupling interactions leads to increased spin-vibronic relaxation, which is detrimental to long spin lifetime in paramagnetic molecules.

Hetero-tri-spin systems: an alternative stairway to the single molecule magnet heaven?

The search for molecule-based magnetic materials has stimulated over the years the development of extremely rich coordination chemistry. Various combinations of spin carriers have been investigated and illustrated by a plethora of hetero-spin complexes: 3d-nd, 3d-4f, 2p-3d, and 2p-4f. More recently, two other classes of hetero-spin complexes have grown rapidly: compounds containing three different paramagnetic metal ions, or one radical and two different paramagnetic metal ions (all within the same molecular entity). Such new classes of systems represent a challenge both from a synthetic and theoretical point of view. Indeed, the synthetic control and the understanding of the spin topology effect on the overall magnetic behavior from first-principles is a difficult problem to be solved. The presence of different spin carriers in a single molecule makes such compounds particularly interesting because they offer the possibility of developing new magnetic properties, different from those of hetero-bi-spin or homo-spin systems. A critical overview taking the case of 2p-3d-4f complexes is the focus of this perspective paper. An original organic picture of the state-of-art in this field and new hints about the main directions that should be pursued to achieve hetero-tri-spin systems with large anisotropy barriers, low quantum tunneling of magnetization and, possibly, large blocking temperatures are provided in this article through an analysis based on numerically revisiting already published data and a critical survey of the literature reported so far. The reasons for the limited success obtained for the largely used 3d-2p-4f topology are given along with the ones explaining the failure for the 2p-4f-3d case. The still never synthesized linear 2p-3d-4f spin topology seemed to be the most promising one based on the results obtained for the unique closed hetero-tri-spin closed triangular system synthesized so far.

Terminal Ligand and Packing Effects on Slow Relaxation in an Isostructural Set of [Dy(H2 dapp)X2 ]+ Single Molecule Magnets*

We report three structurally related single ion Dy compounds using the pentadentate ligand 2,6-bis((E)-1-(2-(pyridin-2-yl)-hydrazineylidene)ethyl)pyridine (H2 dapp) [Dy(H2 dapp)(NO3 )2 ]NO3 (1), [Dy(H2 dapp)(OAc)2 ]Cl (2) and [Dy(H2 dapp)(NO3 )2 ]Cl0.92 (NO3 )0.08 (3). The (H2 dapp) occupies a helical twisted pentagonal equatorial arrangement with two anionic ligands in the axial positions. Further influence on the electronic and magnetic structure is provided by a closely associated counterion interacting with the central N-H group of the (H2 dapp). The slow relaxation of the magnetisation shows that the anionic acetates give the greatest slowing down of the magnetisation reversal. Further influence on the relaxation properties of compounds1 and 2 is the presence of short nitrate-nitrate intermolecular ligand contact opening further lattice relaxation pathways.

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.

Deconvolving Contributions to Decoherence in Molecular Electron Spin Qubits: A Dynamic Ligand Field Approach

In the past decade, transition metal complexes have gained momentum as electron spin-based quantum bit (qubit) candidates due to their synthetic tunability and long achievable coherence times. The decoherence of magnetic quantum states imposes a limit on the use of these qubits for quantum information technologies, such as quantum computing, sensing, and communication. With rapid recent development in the field of molecular quantum information science, a variety of chemical design principles for prolonging coherence in molecular transition metal qubits have been proposed. Here the spin-spin, motional, and spin-phonon regimes of decoherence are delineated, outlining design principles for each. It is shown how dynamic ligand field models can provide insights into the intramolecular vibrational contributions in the spin-phonon decoherence regime. This minireview aims to inform the development of molecular quantum technologies tailored for different environments and conditions.

Iron(II), Cobalt(II), and Nickel(II) Complexes of Bis(sulfonamido)benzenes: Redox Properties, Large Zero-Field Splittings, and Single-Ion Magnets

Metal complexes of 1,2-diamidobenzenes have been long studied because of their intriguing redox properties and electronic structures. We present here a series of such complexes with 1,2-bis(sulfonamido)benzene ligands to probe the utility of these ligands for generating a large zero-field splitting (ZFS, D) in metal complexes that possibly act as single-ion magnets. To this end, we have synthesized a series of homoleptic ate complexes of the form (X)_n[M{bis(sulfonamido)benzene}₂] (n equals 4 minus the oxidation state of the metal), where M (Fe/Co/Ni), X [K⁺/(K-18-c-6)⁺/(HNEt₃)⁺, with 18-c-6 = 18-crown ether 6], and the substituents (methyl and tolyl) on the ligand [bmsab = 1,2-bis(methanesulfonamido)benzene; btsab = 1,2-bis(toluenesulfonamido)benzene] were varied to analyze their effect on the ZFS, possible single-ion-magnet properties, and redox behavior of these metal complexes. A combination of X-ray crystallography, (spectro)electrochemistry, superconducting quantum interference device magnetometry, high-frequency electron paramagnetic resonance spectroscopy, and Mössbauer spectroscopy was used to investigate the electronic/geometric structures of these complexes and the aforementioned properties. These investigations show that the cobalt(II) complexes display very high negative D values in the range of -100 to -130 cm^-1, and the nickel(II) complexes display very high positive D values of 76 and 58 cm^-1. In addition, the cobalt(II) complexes shows barriers of 200-260 cm^-1 and slow relaxation of the magnetization in the absence of an external magnetic field, underscoring the robustness of this class of complexes. The iron(II) complex exhibits a D value of -3.29 cm^-1 and can be chemically oxidized to an iron(III) complex that has D = -1.96 cm^-1. These findings clearly show that bis(sulfonamido)benzenes are ideally suited to stabilize ate complexes, to generate very high ZFSs at the metal centers with single-ion-magnet properties, and to induce exclusive oxidation at the metal center (for iron) despite the presence of ligands that are potentially noninnocent. Our results therefore substantially enhance the scope for this class of redox-active ligands.

A Quantum Chemistry View on Two Archetypical Paramagnetic Pentacoordinate Nickel(II) Complexes Offers a Fresh Look on Their NMR Spectra

Quantum chemical methods for calculating paramagnetic NMR observables are becoming increasingly accessible and are being included in the inorganic chemistry practice. Here, we test the performance of these methods in the prediction of proton hyperfine shifts of two archetypical high-spin pentacoordinate nickel(II) complexes (NiSAL-MeDPT and NiSAL-HDPT), which, for a variety of reasons, turned out to be perfectly suited to challenge the predictions to the finest level of detail. For NiSAL-MeDPT, new NMR experiments yield an assignment that perfectly matches the calculations. The slightly different hyperfine shifts from the two “halves” of the molecules related by a pseudo-C₂ axis, which are experimentally divided into two well-defined spin systems, are also straightforwardly distinguished by the calculations. In the case of NiSAL-HDPT, for which no X-ray structure is available, the quality of the calculations allowed us to refine its structure using as a starting template the structure of NiSAL-MeDPT.

State-of-the-art quantum chemical methods and paramagnetism-tailored NMR experiments provide a deep insight on the relation between the spectra and the electronic structure for two paramagnetic pentacoordinate nickel(II) complexes.

Syntheses, structures and magnetic properties of two isostructural dicyanamide-bridged 2D polymers

Complexes [Co(biq)(μ_1,5-dca)₂]_n (1) and [Ni(biq)(μ_1,5-dca)₂]_n (2) (biq is 2,2′-biquinoline, dca is dicyanamide anion, N(CN)₂⁻) have been characterized by crystal structure analysis, and spectral and magnetic measurements.