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

Auxiliary Ligands Modulated Bis(imidazolin-2-iminato) Dysprosium Single-Molecule Magnets

A systematic study on the magneto-structural correlation plays an essential role in improving the molecular design of single-molecule magnets (SMMs). Strong axial crystal fields on Dy(III) could help enhance the uniaxial magnetic anisotropy, increasing the relaxation barrier and magnetic blocking temperature, while transverse crystal-field interactions accelerate magnetic relaxation. The imidazolin-2-iminato ligands have been viewed as promising strong-field ligands to construct high-performance Dy(III) SMMs since the large steric hindrance and strong donating capacity make imidazolin-2-iminato ligands possibly impede weak transverse interactions at equatorial positions. Herein, we synthesize a series of bis(imidazolin-2-iminato) Dy(III) SMMs with magneto-structural correlations revealed by combined magnetic and theoretical analyses. The relaxation barriers of these complexes vary over a wide range, indicating that auxiliary ligands at equatorial positions could effectively modulate SMM performance. Additionally, we found that two parameters, the relaxation energy barrier and the Dy-N bond length, follow specific correlation patterns with the N-Dy-N angle, and these correlations exhibit precisely opposite trends. The highest Ueff can be reached when the N-Dy-N angle is approximately 121°, suggesting the greatest potential of this series of complexes.

Role of Electron Correlation beyond the Active Space in Achieving Quantitative Predictions of Spin-Phonon Relaxation

Single-molecule magnets (SMMs) are promising candidates for molecular-scale data storage and processing due to their strong magnetic anisotropy and long spin relaxation times. However, as the temperature rises, interactions between electronic states and lattice vibrations accelerate spin relaxation, significantly limiting their practical applications. Recently, ab initio simulations have made it possible to advance our understanding of phonon-induced magnetic relaxation, but significant deviations from the experiments have often been observed. The description of molecules' electronic structure has been mostly based on complete active space self-consistent field (CASSCF) calculations, and the impact of electron correlation beyond the active space remains largely unexplored. In this study, we provide the first systematic investigation of spin-phonon relaxation in SMMs with post-CASSCF multiconfigurational methods, specifically CAS, followed by second-order perturbation theory and multiconfiguration pair-density functional theory. Taking Co(II)- and Dy(III)-based SMMs as case studies, we analyze how electron correlation influences spin-phonon relaxation rates across a range of temperatures by comparing theoretical predictions with experimental observations. Our findings demonstrate that post-CASSCF treatments make it possible to achieve quantitative predictions for Co(II)-based SMMs. For Dy(III)-based systems, however, accurate predictions require the consideration of additional effects, underscoring the urgent necessity of further advancing the study of the effects of electronic correlation in these complex systems.

Electronic structure of mononuclear and radical-bridged dinuclear cobalt(II) single-molecule magnets

Metal-organic compounds that feature magnetic bistability have been proposed as bits for magnetic storage, but progress has been slow. Four-coordinate cobalt(II) complexes feature high inversion barriers of the magnetic moment, but they lack magnetic bistability. Developing radical-bridged polynuclear systems is a promising strategy to encounter this; however detailed investigations of such species are scarce. We report an air-stable radical-bridged dinuclear cobalt(II) complex, studied by a combination of magnetometry and spectroscopy. Fits of the data give D = -113 cm-1 for the zero-field splitting (ZFS) and J = 390 cm-1 for the metal-radical exchange. Ab initio investigations reveal first-order spin-orbit coupling of the quasi-degenerated x 2 - y 2 and dxy orbitals to be at the heart of the large ZFS. The corresponding transitions are spectroscopically observed, as are transitions related to the exchange coupling. Finally, signatures of spin-phonon coupling are observed and theoretically analyzed. Furthermore, we demonstrate that the spectral features are not predominantly spin excitations, but largely vibrational in character.

A framework for designing main-group single-molecule magnets

Single-molecule magnets (SMMs) are molecular entities with strongly anisotropic magnetic moment. As a result, SMMs display slow relaxation of magnetization at the macroscopic scale. Up to date all experimentally characterized SMMs are based on either d- or f-block metals with lanthanides proving to be the most successful. In the present work, a framework for constructing SMMs consisting purely of main-group elements will be outlined by computational and theoretical means. The proposed main-group SMMs utilize the strong spin-orbit coupling of a single heavy p-block atom or ion that can lead to strong magnetic anisotropy and pronounced SMM properties. A theoretical crystal-field model is developed to describe the magnetic properties of p-block SMMs with a minimal set of parameters related to the chemical structure of the SMMs. The model is used to establish which p-block elements and oxidation states can lead to SMM behavior. A large number of model structures are studied to establish general features of optimal chemical structures. These include one- and two-coordinate structures involving ligands with different coordination modes and all group 13 to 17 elements in periods 4 to 6. The results show that the most viable structures are based on mono-coordinated complexes of bismuth in oxidation state 0 with σ-donor ligands. Structures with bulkier ligands that sterically protect the bismuth atoms are then proposed as a starting point for the practical realization of main-group SMMs. The calculations show that minimizing the anagostic interactions with the bismuth atom is essential in the ligand design, which along with the low oxidation state of bismuth introduces significant synthetic challenges. The results do, however, show that main-group SMMs are plausible from a practical point of view within a limited set of heavier p-block elements in specific oxidation states. Furthermore, the proposed SMMs display much larger energy barriers for the relaxation of magnetization than even the best lanthanide-based SMMs do. This indicates that it is possible that main-group SMMs can supersede even the best currently known SMMs based on d- or f-block elements.

The role of electronic excited states in the spin-lattice relaxation of spin-1/2 molecules

Magnetic resonance is a prime method for the study of chemical and biological structures and their dynamical processes. The interpretation of many of these experiments relies on understanding how the spin of unpaired electrons exchanges energy with their environment, or lattice, and relaxes to equilibrium. Here, we overcome the common use of effective spin Hamiltonians to describe spin-lattice relaxation in spin-1/2 and apply ab initio open quantum systems theory to their full molecular electronic wavefunction. Simulations for two Cr(V) coordination compounds under this framework show a marked improvement in accuracy and demonstrate that relaxation in spin-1/2 molecules is enabled by virtual transitions to molecular excited states with energy approaching 20,000 cm-1. This work establishes a connection between the original theory of Van Vleck and modern electronic structure methods, ultimately exemplifying the urgency of further advancing an ab initio approach to spin-lattice relaxation.

Phase-dependent polymerization isomerism in the coordination complexes of a flexible bis(β-diketonato) ligand

First prepared in the late 70s, the pro-ligand 1,3-bis(3,5-dioxo-1-hexyl)benzene (H2bdhb) contains two acetoacetyl terminations linked to a central 1,3-phenylene unit through dimethylene bridges. Since each termination can be either in diketonic or keto-enolic form, in organic solution it exists as a mixture of three spectroscopically resolvable tautomers. In the presence of pyridine, Co2+ and the bdhb2- anion form a crystalline dimeric compound with formula [Co2(bdhb)2(py)4] (2) and a Co⋯Co separation of more than 11 Å. Complex 2 contains two pseudo-octahedrally coordinated and non-interacting high-spin cobalt(II) ions (S = 3/2) displaying a large easy-plane anisotropy (D ∼ 70 cm-1), as consistently indicated by magnetic measurements, X-band EPR spectra, and complete active space self-consistent field/N-electron valence state perturbation theory (CASSCF/NEVPT2) calculations. At cryogenic temperatures (T < 7 K) and in an applied static magnetic field, the compound shows detectably slow magnetic relaxation, which occurs through direct and Raman mechanisms. Combined mass spectrometry, UV-Vis, and 1H/2H NMR data, including an isotopic labelling experiment and a determination of molecular weight by diffusion ordered spectroscopy (DOSY), show that 2 rearranges to monomeric high-spin [Co(bdhb)(py)x] species (x = 0, 1, or 2) in organic solution (CH2Cl2, THF) with concomitant partial dissociation of the py ligands. The X-band EPR spectra in a frozen CH2Cl2/toluene matrix concurrently suggest a significant alteration of the coordination environment upon dissolution. These observations are fairly well reproduced by density functional theory (DFT) and CASSCF/NEVPT2 calculations on the lowest Gibbs free energy conformers of each species, as provided by an extensive conformational search based on meta-dynamics simulations and semiempirical tight-binding methods. After the vanadyl analogue, compound 2 provides the second example of polymerization isomerism in the 1 : 1 adducts of bdhb2- with divalent metal ions.

Synergy of Experiment and Broadened Exploration of Ab Initio Calculations for Understanding of Lanthanide-Pentacyanidocobaltate Molecular Nanomagnets and Their Optical Properties

We present a synergistic experimental-theoretical methodology for the investigation of lanthanide-based single-molecule magnets (SMMs), demonstrated using the example of novel heterometallic molecules incorporating Nd3+/Ce3+ ions combined with three different, rarely explored, pentacyanidocobaltate(III) metalloligands, [CoIII(CN)5(azido/nitrito-N/iodido)]3-. The theoretical part of our approach broadens the exploration of ab initio calculations for lanthanide(III) complexes toward the convenient simulations of such physical characteristics as directional dependences of Helmholtz energy, magnetization, susceptibility, and their thermal and field evolution, as well as light absorption and emission bands. This work was conducted using newly designed SlothPy software (https://slothpy.org). It is introduced as an open-source Python library for simulating various physical properties from first-principles based on results of electronic structure calculations obtained within popular quantum chemistry packages. The computational results were confronted with spectroscopic and ac/dc-magnetic data, the latter analyzed using previously designed relACs software. The combination of experimental and computational methods gave insight into phonon-assisted magnetic relaxation mechanisms, disentangling them from the temperature-independent quantum tunneling of magnetization and emphasizing the role of local-mode processes. This study provides an understanding of the changes in lanthanide(III) magnetic anisotropy introduced with pentacyanidocobaltates(III) modifications, theoretically exploring also potential applications of reported compounds as anisotropy switches or optical thermometers.

Magnetic behaviour of a spin-canted asymmetric lanthanide quinolate trimer

An asymmetrical dysprosium trimer with a molecular formula of [Dy3(hq)7(hqH)(NO3)2(H2O)] was obtained through a reflux reaction employing as starting material Dy(NO3)3·nH2O and 8-quinolinoline as ligand. Magnetic susceptibility investigations show the system to be an SMM, which was corroborated by sub-Kelvin μSQUID studies. Upon cooling, the magnetic susceptibility also exhibits a decrease in the χMT product, which was confirmed to be due to intramolecular antiferromagnetic interactions. μSQUID measurements, moreover, reveal a marked magnetic behaviour in the angular dependence of the hysteresis loops. The latter is a direct consequence of the non-colinear spin arrangement of the anisotropy axes of each Dy(III) ion in [Dy3(hq)7(hqH)(NO3)2(H2O)] and the interaction between the ions, as also evidenced by CASSCF calculations. Our results evidence the effect of spin canting along with the intramolecular interactions, which can induce non-trivial magnetic behaviour in SMMs.

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.

Gaining Insights into the Interplay between Optical and Magnetic Properties in Photoexcited Coordination Compounds

We describe early and recent advances in the fascinating field of combined magnetic and optical properties of inorganic coordination compounds and in particular of 3d-4f single molecule magnets. We cover various applied techniques which allow for the correlation of results obtained in the frequency and time domain in order to highlight the specific properties of these compounds and the future challenges towards multidimensional spectroscopic tools. An important point is to understand the details of the interplay of magnetic and optical properties through performing time-resolved studies in the presence of external fields especially magnetic ones. This will enable further exploration of this fundamental interactions i. e. the two components of electromagnetic radiation influencing optical properties.

Dinuclear enantiopure Ln3+ complexes with (S-) and (R-) 2-phenylbutyrate ligands. Luminescence, CPL and magnetic properties

The reaction of Ln(NO3)2·6H2O (Ln = Nd, Sm, Eu, Tb, Dy, Tm and Yb) with the respective enantiopure (R)-(-)-2-phenylbutyric or (S)-(+)-2-phenylbutyric acid (R/S-2-HPhBut) and 4,7-diphenyl-1,10-phenanthroline (Bphen) allows the isolation of chiral dinuclear compounds of the formula [Ln2(μ-R/S-2-PhBut)4(R/S-2PhBut)2(Bphen)2] where Ln = Nd3+ (R/S-Nd-a), Sm3+ (R/S-Sm-a), Eu3+ (R/S-Eu-a), Tb3+ (R/S-Tb-a and R/S-Tb-b), Dy3+ (R/S-Dy-a and R/S-Dy-b), Tm3+ (R/S-Tm-b) and Yb3+ (R/S-Yb-b). Single crystal X-ray diffraction was performed for compounds S-Eu-a and S-Tm-b. Powder crystal X-ray diffraction was performed for all complexes. From the crystallographic data two different structural motifs were found which are referred to as structure type a and structure type b. In structure type a, the Ln3+ atoms are bridged through four R or S-2-PhBut ligands with two different kinds of coordination modes whereas in structure type b the two Ln3+ atoms are bridged through four R or S-2-PhBut ligands showing only one kind of coordination mode. For those lanthanide ions exhibiting both structure types, Tb3+ and Dy3+, a difference in the luminescence and magnetism behavior is observed. All compounds (except R/S-Tm-b) exhibit sensitized luminescence, notably the Eu3+ and Tb3+ analogues. Circular Dichroism (CD) and Circular Polarized Luminescence (CPL) in the solid state and in 1 mM dichloromethane (DCM) solutions are reported, leading to improved chiroptical properties for the DCM solutions. The asymmetry factor (glum) in 1 mM DCM is ±0.02 (+ for R-Eu-a) for the magnetically allowed transition 5D0 → 7F1 and ±0.03 (+ for R-Tb-a and R-Tb-b) for the 5D4 → 7F5 transition. Magnetic properties of all compounds were studied and the Dy3+ compound with the structural motif b (R-Dy-b) shows Single Molecular Magnet (SMM) behavior under a 0 T magnetic field. However, R-Dy-a is a field-induced SMM.

Spin-State Control in Dysprosium(III) Metallacrown Magnets via Thioacetal Modification

Integrating controllable spin states into single-molecule magnets (SMMs) enables precise manipulation of magnetic interactions at a molecular level, but remains a synthetic challenge. Herein, we developed a 3d-4f metallacrown (MC) magnet [DyNi5(quinha)5(Clsal)2(py)8](ClO4) ⋅ 4H2O (H2quinha=quinaldichydroxamic acid, HClsal=5-chlorosalicylaldehyde) wherein a square planar NiII is stabilized by chemical stacking. Thioacetal modification was employed via post-synthetic ligand substitutions and yielded [DyNi5(quinha)5(Clsaldt)2(py)8](ClO4) ⋅ 3H2O (HClsaldt=4-chloro-2-(1,3-dithiolan-2-yl)phenol). Thanks to the additional ligations of thioacetal onto the NiII site, coordination-induced spin state switching (CISSS) took place with spin state altering from low-spin S=0 to high-spin S=1. The synergy of CISSS effect and magnetic interactions results in distinct energy splitting and magnetic dynamics. Magnetic studies indicate prominent enhancement of reversal barrier from 57 cm-1 to 423 cm-1, along with hysteresis opening and an over 200-fold increment in coercive field at 2 K. Ab initio calculations provide deeper insights into the exchange models and rationalize the relaxation/tunnelling pathways. These results demonstrate here provide a fire-new perspective in modulating the magnetization relaxation via the incorporation of controllable spin states and magnetic interactions facilitated by the CISSS approach.

Auxiliary Rather Than Dominant. The Role of Direct Dy-S Coordination in Single-Molecule Magnet Unveiled via ab initio Study

The role of Dy-S coordination in a single-molecule magnet (SMM) is investigated via an ab initio study in a group of mononuclear structures. The SMM performance of this group is well interpreted via a concise criterion consisting of long quantum tunneling of magnetization (QTM) time τQTM and high effective barrier for magnetic reversal Ueff. The best SMMs in the selected group, i.e., 1Dy (CCDC refcode: PUKFAF) and 2Dy (CCDC refcode: NIKSEJ), are just those holding the longest τQTM and the highest Ueff simultaneously. Further analysis based on the crystal field model and ab initio magneto-structural exploration indicates that the influence of Dy-S coordination on the SMM performance of 1Dy is weaker than that of axial Dy-O coordination. Thus, Dy-S coordination is more likely to play an auxiliary role rather than a dominant one. However, if placed at the suitable equatorial position, Dy-S coordination could provide important support for good SMM performance. Consequently, starting from 1Dy, we built two new structures where Dy-S coordination only exists at the equatorial position and two axial positions are occupied by strong Dy-O/Dy-F coordination. Compared to 1Dy and 2Dy, these new ones are predicted to have significantly longer τQTM and higher Ueff, as well as a nearly doubled blocking temperature TB. Thus, they are probable candidates of SMM having clearly improved performance.

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.

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.

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).

Bimetallic Synergy Enables Silole Insertion into THF and the Synthesis of Erbium Single-Molecule Magnets

The potassium silole K2 [SiC4 -2,5-(SiMe3 )2 -3,4-Ph2 ] reacts with [M(η8 -COT)(THF)4 ][BPh4 ] (M=Er, Y; COT=cyclo-octatetraenyl) in THF to give products that feature unprecedented insertion of the nucleophilic silicon centre into a carbon-oxygen bond of THF. The structure of the major product, [(μ-η8  : η8 -COT)M(μ-L1 )K]∞ (1M ), consists of polymeric chains of sandwich complexes, where the spiro-bicyclic silapyran ligand [C4 H8 OSiC4 (SiMe3 )2 Ph2 ]2- (L1 ) coordinates to potassium via the oxygen. The minor product [(μ-η8  : η8 -COT)M(μ-L1 )K(THF)]2 (2M ) features coordination of the silapyran to the rare-earth metal. In forming 1M and 2M , silole insertion into THF only occurs in the presence of potassium and the rare-earth metal, highlighting the importance of bimetallic synergy. The lower nucleophilicity of germanium(II) leads to contrasting reactivity of the potassium germole K2 [GeC4 -2,5-(SiMe3 )2 -3,4-Me2 ] towards [M(η8 -COT)(THF)4 ][BPh4 ], with intact transfer of the germole occurring to give the coordination polymers [{η5 -GeC4 (SiMe3 )2 Me2 }M(η8 -COT)K]∞ (3M ). Despite the differences in reactivity induced by the group 14 heteroatom, the single-molecule magnet properties of 1Er , 2Er and 3Er are similar, with thermally activated relaxation occurring via the first-excited Kramers doublet, subject to effective energy barriers of 122, 80 and 91 cm-1 , respectively. Compound 1Er is also analysed by high-frequency dynamic magnetic susceptibility measurements up to 106  Hz.

Understanding Single-Molecule Magnet properties of lanthanide complexes from 4f orbital splitting

We present an approach for connecting the magnetic anisotropy of lanthanide mononuclear complexes with their f-orbital splitting for both idealized and real coordination environments. Our proposal is straightforward to apply and provides sensible estimations of the energy spacing of the ground multiplet for axial magnetic systems. This energy splitting controls Single-Molecule Magnet properties of lanthanide complexes, determining key parameters such as the demagnetization energy barrier (Ueff). Importantly, this approach is consistent with the current paradigm of oblate and prolate preferences for the distribution of the f-electron density, but delivers a finer description for ions belonging to the same group (e.g. the oblates TbIII and DyIII). The model provides simple explanations for some general trends observed experimentally (e.g. the low barriers for ErIII complexes in comparison to DyIII or the large barriers observed for cyclopentadienyl DyIII complexes in comparison with other ligands based on organometallic rings), contributing as a valuable tool to expand our description of ligand field effects in lanthanide-based SMMs.

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.

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.

LnDOTA puppeteering: removing the water molecule and imposing tetragonal symmetry

Complexes of lanthanide(iii) ions (Ln) with tetraazacyclododecane-N,N',N'',N'''-tetraacetate (DOTA) are a benchmark in the field of magnetism due to their well-investigated and sometimes surprising features. Ab initio calculations suggest that the ninth ligand, an axial water molecule, is key in defining the magnetic properties because it breaks the potential C4 symmetry of the resulting complexes. In this paper, we experimentally isolate the role of the water molecule by excluding it from the metal coordination sphere without altering the chemical structure of the ligand. Our complexes are therefore designed to be geometrically tetragonal and strict crystallographic symmetry is achieved by exploiting a combination of solution ionic strength and solid state packing effects. A thorough multitechnique approach has been used to unravel the electronic structure and magnetic anisotropy of the complexes. Moreover, the geometry enhancement allows us to predict, using only one angle obtained from the crystal structure, the ground state composition of all the studied derivatives (Ln = Tb to Yb). Therefore, these systems also provide an excellent platform to test the validity and limitations of the ab initio methods. Our combined experimental and theoretical investigation proves that the water molecule is indeed key in defining the magnetic anisotropy and the slow relaxation of these complexes.

Slow Magnetic Relaxation in Silver(II) Macrocyclic Systems

The spin-lattice relaxation time has been studied trough alternating-current susceptometry and ultralow-frequency Raman spectroscopy in a family of silver(II)-derived molecular systems with spin 1/2 and formulas [AgII(m-CTH)(NO3)2] (1) and [AgII(m-CTH)(ClO4)2] (2), where CTH = meso-5,5,7,12,12,14-hexamethyl-1,4,8,11-tetraazacyclotetradecane. The combination of both techniques demonstrates the occurrence of slow spin magnetic relaxation induced by spin-phonon interaction. The magnetic behavior of these silver(II)-derived systems opens the door to a new cation in the scarce family of S = 1/2 systems with slow relaxation of magnetization.

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.

Trityl-Based Lanthanide-Supramolecular Assemblies Exhibiting Slow Magnetic Relaxation

The triphenylmethane (trityl) group has been recognized as a supramolecular synthon in crystal engineering, molecular machine rotors and stereochemical chirality inductors in materials science. Herein we demonstrate for the first time how it can be utilized in the domain of molecular magnetic materials through shaping of single molecule magnet (SMM) properties within the lanthanide complexes in tandem with other non-covalent interactions. Trityl-appended mono- (HL1 ) and bis-compartmental (HL2 ) hydrazone ligands were synthesized and complexated with Dy(III) and Er(III) triflate and nitrate salts to generate four monometallic (1-4) and two bimetallic (5, 6) complexes. The static and dynamic magnetic properties of 1-6 were investigated, revealing that only ligand HL1 induces assemblies (1-4) capable of showing SMM behaviour, with Dy(III) congeners (1, 2) able to exhibit the phenomenon also under zero field conditions. Theoretical ab initio studies helped in determination of Dy(III) energetic levels, magnetic anisotropic axes and corroborated magnetic relaxation mechanisms to be a combination of Raman and quantum tunnelling in zero dc field, the latter being cancelled in the optimum non-zero dc field. Our work represents the first study of magneto-structural correlations within the trityl Ln-SMMs, leading to generation of slowly relaxing zero-field dysprosium complexes within the hydrogen-bonded assemblies.

Layered lanthanide phosphonates Ln(2-qpH)(SO4)(H2O)2 (Ln = La, Ce, Pr, Nd, Sm): polymorphism and magnetic properties

Polymorphic layered lanthanide coordination polymers provide opportunities to study the effect of intralayer and interlayer interactions on their magnetic dynamics. Herein we report a series of layered lanthanide phosphonates, namely, α-Ln(2-qpH)(SO4)(H2O)2 (Ln = Sm) (α-Ln), β-Ln(2-qpH)(SO4)(H2O)2 (Ln = Pr, Nd, Sm) (β-Ln) and γ-Ln(2-qpH)(SO4)(H2O)2 (Ln = La, Ce, Pr, Nd, Sm) (γ-Ln) (2-qpH2 = 2-quinolinephosphonic acid), which crystallize in monoclinic P21/c (α-Ln), triclinic P1̄ (β-Ln) and orthorhombic Pbca (γ-Ln) space groups, respectively. The structural differences between the β- and γ-phases lie not only in the intralayer but also in the interlayer. Within the layers, the Ln2O2 dimers are aligned parallel in the β-phase, but are non-parallel in the γ-phase. In the interlayer, there are π-π interactions between the quinoline groups in the α- and β-phases but not in the γ-phase. Magnetic studies reveal a field-induced slow relaxation of the magnetisation at low temperatures for compounds γ-Ce, β-Nd, and γ-Nd, and the impact of polymorphism on the magnetic dynamics of Nd(III) compounds is discussed.

Synthesis, X-ray structure and magnetic properties of the apically functionalized monocapped cobalt(II) tris-pyridineoximates possessing SMM behaviour

The title cobalt(II) pseudoclathrochelate complexes possess an intermediate trigonal prismatic-trigonal antiprismatic geometry. As follows from PPMS data, they exhibit an SMM behaviour with Orbach relaxation barriers of approximately 90 K. Paramagnetic NMR experiments confirmed a persistence of these magnetic characteristics in solution. Therefore, a straightforward apical functionalization of this 3D molecular platform for its targeted delivery to a given biosystem can be performed without substantial changes.