Coercive Fields Exceeding 30 T in the Mixed-Valence Single-Molecule Magnet (CpiPr5)2Ho2I3.

Mixed-valence dilanthanide complexes of the type (CpiPr5)2Ln2I3 (CpiPr5 = pentaisopropylcyclopentadienyl; Ln = Gd, Tb, Dy) featuring a direct Ln-Ln σ-bonding interaction have been shown to exhibit well-isolated high-spin ground states and, in the case of the Tb and Dy variants, a strong axial magnetic anisotropy that gives rise to a large magnetic coercivity. Here, we report the synthesis and characterization of two new mixed-valence dilanthanide compounds in this series, (CpiPr5)2Ln2I3 (1-Ln; Ln = Ho, Er). Both compounds feature a Ln-Ln bonding interaction, the first such interaction in any molecular compounds of Ho or Er. Like the Tb and Dy congeners, both complexes exhibit high-spin ground states arising from strong spin-spin coupling between the lanthanide 4f electrons and a single σ-type lanthanide-lanthanide bonding electron. Beyond these similarities, however, the magnetic properties of the two compounds diverge. In particular, 1-Er does not exhibit observable magnetic blocking or slow magnetic relaxation, while 1-Ho exhibits magnetic blocking below 28 K, which is the highest temperature among Ho-based single-molecule magnets, and a spin reversal barrier of 556(4) cm-1. Additionally, variable-field magnetization data collected for 1-Ho reveal a coercive field of greater than 32 T below 8 K, more than 6-fold higher than observed for the bulk magnets SmCo5 and Nd2Fe14B, and the highest coercive field reported to date for any single-molecule magnet or molecule-based magnetic material. Multiconfigurational calculations, supported by far-infrared magnetospectroscopy data, reveal that the stark differences in magnetic properties of 1-Ho and 1-Er arise from differences in the local magnetic anisotropy of the lanthanide centers.

Spin-phonon coupling and magnetic relaxation in single-molecule magnets.

Electron-phonon coupling is important in many physical phenomena, e.g. photosynthesis, catalysis and quantum information processing, but its impacts are difficult to grasp on the microscopic level. One area attracting wide interest is that of single-molecule magnets, which is motivated by searching for the ultimate limit in the miniaturisation of binary data storage media. The utility of a molecule to store magnetic information is quantified by the timescale of its magnetic reversal processes, also known as magnetic relaxation, which is limited by spin-phonon coupling. Several recent accomplishments of synthetic organometallic chemistry have led to the observation of molecular magnetic memory effects at temperatures above that of liquid nitrogen. These discoveries have highlighted how far chemical design strategies for maximising magnetic anisotropy have come, but have also highlighted the need to characterise the complex interplay between phonons and molecular spin states. The crucial step is to make a link between magnetic relaxation and chemical motifs, and so be able to produce design criteria to extend molecular magnetic memory. The basic physics associated with spin-phonon coupling and magnetic relaxation was outlined in the early 20th century using perturbation theory, and has more recently been recast in the form of a general open quantum systems formalism and tackled with different levels of approximations. It is the purpose of this Tutorial Review to introduce the topics of phonons, molecular spin-phonon coupling, and magnetic relaxation, and to outline the relevant theories in connection with both the traditional perturbative texts and the more modern open quantum systems methods.

Structural Evolution of Paramagnetic Lanthanide Compounds in Solution Compared to Time- and Ensemble-Average Structures.

Anisotropy in the magnetic susceptibility strongly influences the paramagnetic shifts seen in nuclear magnetic resonance (NMR) and magnetic resonance imaging (MRI) experiments. A previous study on a series of C3-symmetric prototype MRI contrast agents showed that their magnetic anisotropy was highly sensitive to changes in molecular geometry and concluded that changes in the average angle between the lanthanide-oxygen (Ln-O) bonds and the molecular C3 axis due to solvent interactions had a significant impact on the magnetic anisotropy and, consequently, the paramagnetic shift. However, this study, like many others, was predicated on an idealized C3-symmetric structural model, which may not be representative of the dynamic structure in solution at the single-molecule level. Here, we address this by using ab initio molecular dynamics simulations to simulate how the molecular geometry, in particular the angles between the Ln-O bonds and the pseudo-C3 axis, evolves over time in the solution, mimicking typical experimental conditions. We observe large-amplitude oscillations in the O-Ln-C̃3 angles, and complete active space self-consistent field spin-orbit calculations show that this leads to similarly large oscillations in the pseudocontact (dipolar) paramagnetic NMR shifts. The time-averaged shifts show good agreement with experimental measurements, while the large fluctuations suggest that an idealized structure provides an incomplete description of the solution dynamics. Our observations have significant implications for modeling the electronic and nuclear relaxation times in this and other systems where the magnetic susceptibility is exquisitely sensitive to the molecular structure.

Accurate and Efficient Spin-Phonon Coupling and Spin Dynamics Calculations for Molecular Solids.

Molecular materials are poised to play a significant role in the development of future optoelectronic and quantum technologies. A crucial aspect of these areas is the role of spin-phonon coupling and how it facilitates energy transfer processes such as intersystem crossing, quantum decoherence, and magnetic relaxation. Thus, it is of significant interest to be able to accurately calculate the molecular spin-phonon coupling and spin dynamics in the condensed phase. Here, we demonstrate the maturity of ab initio methods for calculating spin-phonon coupling by performing a case study on a single-molecule magnet and showing quantitative agreement with the experiment, allowing us to explore the underlying origins of its spin dynamics. This feat is achieved by leveraging our recent developments in analytic spin-phonon coupling calculations in conjunction with a new method for including the infinite electrostatic potential in the calculations. Furthermore, we make the first ab initio determination of phonon lifetimes and line widths for a molecular magnet to prove that the commonplace Born-Markov assumption for the spin dynamics is valid, but such "exact" phonon line widths are not essential to obtain accurate magnetic relaxation rates. Calculations using this approach are facilitated by the open-source packages we have developed, enabling cost-effective and accurate spin-phonon coupling calculations on molecular solids.

A Trinuclear Gadolinium Cluster with a Three-Center One-Electron Bond and an S = 11 Ground State.

The recent discovery of metal-metal bonding and valence delocalization in the dilanthanide complexes (CpiPr5)2Ln2I3 (CpiPr5 = pentaisopropylcyclopentadienyl; Ln = Y, Gd, Tb, Dy) opened up the prospect of harnessing the 4fn5dz21 electron configurations of non-traditional divalent lanthanide ions to access molecules with novel bonding motifs and magnetism. Here, we report the trinuclear mixed-valence clusters (CpiPr5)3Ln3H3I2 (1-Ln, Ln = Y, Gd), which were synthesized via potassium graphite reduction of the trivalent clusters (CpiPr5)3Ln3H3I3. Structural, computational, and spectroscopic analyses support valence delocalization in 1-Ln resulting from a three-center, one-electron σ bond formed from the 4dz2 and 5dz2 orbitals on Y and Gd, respectively. Dc magnetic susceptibility data obtained for 1-Gd reveal that valence delocalization engenders strong parallel alignment of the σ-bonding electron and the 4f electrons of each gadolinium center to afford a high-spin ground state of S = 11. Notably, this represents the first clear instance of metal-metal bonding in a molecular trilanthanide complex, and the large spin-spin exchange constant of J = 168(1) cm-1 determined for 1-Gd is only the second largest coupling constant characterized to date for a molecular lanthanide compound.

AtomAccess: A Predictive Tool for Molecular Design and Its Application to the Targeted Synthesis of Dysprosium Single-Molecule Magnets.

Isolated dysprosocenium cations, [Dy(CpR)2]+ (CpR = substituted cyclopentadienyl), have recently been shown to exhibit superior single-molecule magnet (SMM) properties over closely related complexes with equatorially bound ligands. However, gauging the crossover point at which the CpR substituents are large enough to prevent equatorial ligand binding, but small enough to approach the metal closely and generate strong crystal field splitting has required laborious synthetic optimization. We therefore created the computer program AtomAccess to predict the accessibility of a metal binding site and its ability to accommodate additional ligands. Here, we apply AtomAccess to identify the crossover point for equatorial coordination in [Dy(CpR)2]+ cations in silico and hence predict a cation that is at the cusp of stability without equatorial interactions, viz., [Dy(Cpttt)(Cp*)]+ (Cpttt = C5H2tBu3-1,2,4, Cp* = C5Me5). Upon synthesizing this cation, we found that it crystallizes as either a contact ion-pair, [Dy(Cpttt)(Cp*){Al[OC(CF3)3]4-κ-F}], or separated ion-pair polymorph, [Dy(Cpttt)(Cp*)][Al{OC(CF3)3}4]·C6H6. Upon characterizing these complexes, together with their precursors, yttrium and yttrium-doped analogues, we find that the contact ion-pair shows inferior SMM properties to the separated ion-pair, as expected, due to faster Raman and quantum tunneling of magnetization relaxation processes, while the Orbach region is relatively unaffected. The experimental verification of the predicted crossover point for equatorial coordination in this work tests the limitations of the use of AtomAccess as a predictive tool and also indicates that the application of this type of program shows considerable potential to boost efficiency in exploratory synthetic chemistry.

Characterisation of magnetic relaxation on extremely long timescales.

The use of magnetisation decay measurements to characterise very slow relaxation of the magnetisation in single-molecule magnets is becoming increasingly prevalent as relaxation times move to longer timescales outside of the AC susceptibility range. However, experimental limitations and a poor understanding of the distribution underlying the stretched exponential function, commonly used to model the data, may be leading to misinterpretation of the results. Herein we develop guidelines on the experimental design, data fitting, and analysis required to accurately interpret magnetisation decay measurements. Various measures of the magnetic relaxation rate extracted from magnetisation decay measurements of [Dy(Dtp)2][Al{OC(CF3)3}4] previously characterised by Evans et al., fitted using combinations of fixing or freely fitting different parameters, are compared to those obtained using the innovative square-wave "waveform" technique of Hilgar et al. The waveform technique is comparable to AC susceptometry for measurement of relaxation rates on long timescales. The most reliable measure of the relaxation time for magnetisation decays is found to be the average logarithmic relaxation time, e〈ln[τ]〉, obtained via a fit of the decay trace using a stretched exponential function, where the initial and equilibrium magnetisation are fixed to first measured point and target values respectively. This new definition causes the largest differences to traditional approaches in the presence of large distributions or relaxation rates, with differences up to 50% with ß = 0.45, and hence could have a significant impact on the chemical interpretation of magnetic relaxation rates. A necessary step in progressing towards chemical control of magnetic relaxation is the accurate determination of relaxation times, and such large variations in experimental measures stress the need for consistency in fitting and interpretation of magnetisation decays.

Ab Initio Prediction of High-Temperature Magnetic Relaxation Rates in Single-Molecule Magnets.

Organometallic molecules based on [Dy(CpR)2]+ cations (where CpR is a substituted cyclopentadienyl anion) have emerged as clear front-runners in the search for high-temperature single-molecule magnets. Within this family of structurally similar molecules, significant variations in their magnetic properties are seen, demonstrating the importance of understanding magneto-structural relationships to develop more efficient design strategies. Here we develop an ab initio spin dynamics methodology and show that it is capable of quantitative prediction of relative relaxation rates in the Orbach region. Applying it to all reported [Dy(CpR)2]+ cations allows us understand differences in their relaxation dynamics, highlighting that the main discriminant is the magnitude of the crystal field splitting, rather than differences in spin-vibrational coupling. We subsequently employ the method to predict relaxation rates for a series of hypothetical organometallic sandwich compounds, revealing an upper limit to the effective barrier to magnetic relaxation of around 2100-2200 K, which has been reached by existing compounds. Our conclusion is that further improvements to monometallic single-molecule magnets require moving vibrational modes off-resonance with electronic excitations.

Heteroleptic Samarium(III) Chalcogenide Complexes: Opportunities for Giant Exchange Coupling in Bridging σ- and π-Radical Lanthanide Dichalcogenides.

The introduction of (N2)3-• radicals into multinuclear lanthanide molecular magnets raised hysteresis temperatures by stimulating strong exchange coupling between spin centers. Radical ligands with larger donor atoms could promote more efficient magnetic coupling between lanthanides to provide superior magnetic properties. Here, we show that heavy chalcogens (S, Se, Te) are primed to fulfill these criteria. The moderately reducing Sm(II) complex, [Sm(N††)2], where N†† is the bulky bis(triisopropylsilyl)amide ligand, can be oxidized (i) by diphenyldichalcogenides E2Ph2 (E = S, Se, Te) to form the mononuclear series [Sm(N††)2(EPh)] (E = S, 1-S; Se, 1-Se, Te, 1-Te); (ii) S8 or Se8 to give dinuclear [{Sm(N††)2}2(µ-η2:η2-E2)] (E = S, 2-S2; Se, 2-Se2); or (iii) with Te═PEt3 to yield [{Sm(N††)2}(µ-Te)] (3). These complexes have been characterized by single crystal X-ray diffraction, multinuclear NMR, FTIR, and electronic spectroscopy; the steric bulk of N†† dictates the formation of mononuclear complexes with chalcogenate ligands and dinuclear species with the chalcogenides. The Lα1 fluorescence-detected X-ray absorption spectra at the Sm L3-edge yielded resolved pre-edge and white-line peaks for 1-S and 2-E2, which served to calibrate our computational protocol in the successful reproduction of the spectral features. This method was employed to elucidate the ground state electronic structures for proposed oxidized and reduced variants of 2-E2. Reactivity is ligand-based, forming species with bridging superchalcogenide (E2)-• and subchalcogenide (E2)3-• radical ligands. The extraordinarily large exchange couplings provided by these dichalcogenide radicals reveal their suitability as potential successors to the benchmark (N2)3-• complexes in molecular magnets.

Structural Characterization of Lithium and Sodium Bulky Bis(silyl)amide Complexes.

Alkali metal amides are vital reagents in synthetic chemistry and the bis(silyl)amide {N(SiMe3)2} (N'') is one of the most widely-utilized examples. Given that N'' has provided landmark complexes, we have investigated synthetic routes to lithium and sodium bis(silyl)amides with increased steric bulk to analyse the effects of R-group substitution on structural features. To perform this study, the bulky bis(silyl)amines {HN(SitBuMe2)(SiMe3)}, {HN(SiiPr3)(SiMe3)}, {HN(SitBuMe2)2}, {HN(SiiPr3)(SitBuMe2)} and {HN(SiiPr3)2} (1) were prepared by literature procedures as colourless oils; on one occasion crystals of 1 were obtained. These were treated separately with nBuLi to afford the respective lithium bis(silyl)amides [Li{µ-N(SitBuMe2)(SiMe3)}]2 (2), [Li{µ-N(SiiPr3)(SiMe3)}]2 (3), [Li{N(SitBuMe2)2}{µ-N(SitBuMe2)2}Li(THF)] (4), [Li{N(SiiPr3)(SitBuMe2)}(DME)] (6) and [Li{N(SiiPr3)2}(THF)] (7) following workup and recrystallization. On one occasion during the synthesis of 4 several crystals of the 'ate' complex [Li2{µ-N(SitBuMe2)2}(µ-nBu)]2 (5) formed and a trace amount of [Li{N(SiiPr3)2}(THF)2] (8) was identified during the recrystallization of 7. The reaction of {HN(SitBuMe2)2} with NaH in the presence of 2 mol % of NaOtBu gave crystals of [Na{µ-N(SitBuMe2)2}(THF)]2 (9-THF), whilst [Na{N(SiiPr3)2}(C7H8)] (10) was prepared by deprotonation of 1 with nBuNa. The solid-state structures of 1⁻10 were determined by single crystal X-ray crystallography, whilst 2⁻4, 7, 9 and 10 were additionally characterized by NMR and FTIR spectroscopy and elemental microanalysis.

Analysis of vibronic coupling in a 4f molecular magnet with FIRMS.

Vibronic coupling, the interaction between molecular vibrations and electronic states, is a fundamental effect that profoundly affects chemical processes. In the case of molecular magnetic materials, vibronic, or spin-phonon, coupling leads to magnetic relaxation, which equates to loss of magnetic memory and loss of phase coherence in molecular magnets and qubits, respectively. The study of vibronic coupling is challenging, and most experimental evidence is indirect. Here we employ far-infrared magnetospectroscopy to directly probe vibronic transitions in [Yb(trensal)] (where H3trensal = 2,2,2-tris(salicylideneimino)trimethylamine). We find intense signals near electronic states, which we show arise due to an "envelope effect" in the vibronic coupling Hamiltonian, which we calculate fully ab initio to simulate the spectra. We subsequently show that vibronic coupling is strongest for vibrational modes that simultaneously distort the first coordination sphere and break the C3 symmetry of the molecule. With this knowledge, vibrational modes could be identified and engineered to shift their energy towards or away from particular electronic states to alter their impact. Hence, these findings provide new insights towards developing general guidelines for the control of vibronic coupling in molecules.

Ultrahard magnetism from mixed-valence dilanthanide complexes with metal-metal bonding.

Magnetic effects of lanthanide bonding Lanthanide coordination compounds have attracted attention for their persistent magnetic properties near liquid nitrogen temperature, well above alternative molecular magnets. Gould et al. report that introducing metal-metal bonding can enhance coercivity. Reduction of iodide-bridged terbium or dysprosium dimers resulted in a single electron bond between the metals, which enforced alignment of the other valence electrons. The resultant coercive fields exceeded 14 tesla below 50 and 60 kelvin for the terbium and dysprosium compounds, respectively. ­JSY

Heteroleptic samarium(iii) halide complexes probed by fluorescence-detected L3-edge X-ray absorption spectroscopy.

The addition of various oxidants to the near-linear Sm(ii) complex [Sm(N††)2] (1), where N†† is the bulky bis(triisopropylsilyl)amide ligand {N(SiiPr3)2}, afforded a family of heteroleptic three-coordinate Sm(iii) halide complexes, [Sm(N††)2(X)] (X = F, 2-F; Cl, 2-Cl; Br, 2-Br; I, 2-I). In addition, the trinuclear cluster [{Sm(N††)}3(µ2-I)3(µ3-I)2] (3), which formally contains one Sm(ii) and two Sm(iii) centres, was isolated during the synthesis of 2-I. Complexes 2-X are remarkably stable towards ligand redistribution, which is often a facile process for heteroleptic complexes of smaller monodentate ligands in lanthanide chemistry, including the related bis(trimethylsilyl)amide {N(SiMe3)2} (N''). Complexes 2-X and 3 have been characterised by single crystal X-ray diffraction, elemental analysis, multinuclear NMR, FTIR and electronic spectroscopy. The Lα1 fluorescence-detected X-ray absorption spectra recorded at the Sm L3-edge for 2-X exhibited a resolved pre-edge peak defined as an envelope of quadrupole-allowed 2p → 4f transitions. The X-ray absorption spectral features were successfully reproduced using time-dependent density functional theoretical (TD-DFT) calculations that synergistically support the experimental observations as well as the theoretical model upon which the electronic structure and bonding in these lanthanide complexes is derived.