Relativistic Quantum Chemical Investigation of Actinide Covalency Measured by Electron Paramagnetic Resonance Spectroscopy.

We investigate actinide covalency effects in two [AnCptt3] (An = Th, U) complexes recently studied with pulsed electron paramagnetic resonance spectroscopy, using the Hyperion package to obtain relativistic hyperfine coupling constants from relativistic multiconfigurational wave functions. 1H and 13C HYSCORE simulations using the computed parameters show excellent agreement with the experimental data, highlighting the accuracy of modern relativistic ab initio methods. The extent of covalency indicated from the calculations on [ThCptt3] is in agreement with the original report based on traditional spectral fitting methods, while the covalency in [UCptt3] is found to be previously overestimated. The latter is due to the paramagnetic spin-orbit effect that arises naturally in a relativistic theory of hyperfine coupling and yet was not accounted for in the original study, thus highlighting the necessity of relativistic approaches for the interpretation of magnetic resonance data pertaining to actinides.

Isolation of a Bent Dysprosium Bis(amide) Single-Molecule Magnet.

The isolation of formally two-coordinate lanthanide (Ln) complexes is synthetically challenging, due to predominantly ionic Ln bonding regimes favoring high coordination numbers. In 2015, it was predicted that a near-linear dysprosium bis(amide) cation [Dy{N(SiiPr3)2}2]+ could provide a single-molecule magnet (SMM) with an energy barrier to magnetic reversal (Ueff) of up to 2600 K, a 3-fold increase of the record Ueff for a Dy SMM at the time; this work showed a potential route to SMMs that can provide high-density data storage at higher temperatures. However, synthetic routes to a Dy complex containing only two monodentate ligands have not previously been realized. Here, we report the synthesis of the target bent dysprosium bis(amide) complex, [Dy{N(SiiPr3)2}2][Al{OC(CF3)3}4] (1-Dy), together with the diamagnetic yttrium analogue. We find Ueff = 950 ± 30 K for 1-Dy, which is much lower than the predicted values for idealized linear two-coordinate Dy(III) cations. Ab initio calculations of the static electronic structure disagree with the experimentally determined height of the Ueff barrier, thus magnetic relaxation is faster than expected based on magnetic anisotropy alone. We propose that this is due to enhanced spin-phonon coupling arising from the flexibility of the Dy coordination sphere, in accord with ligand vibrations being of equal importance to magnetic anisotropy in the design of high-temperature SMMs.

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.

Carbene Complexes of Plutonium: Structure, Bonding, and Divergent Reactivity to Lanthanide Analogs.

Organoplutonium chemistry was established in 1965, yet structurally authenticated plutonium-carbon bonds remain rare being limited to π-bonded carbocycle and σ-bonded isonitrile and hydrocarbyl derivatives. Thus, plutonium-carbenes, including alkylidenes and N-heterocyclic carbenes (NHCs), are unknown. Here, we report the preparation and characterization of the diphosphoniomethanide-plutonium complex [Pu(BIPMTMSH)(I)(µ-I)]2 (1Pu, BIPMTMSH = (Me3SiNPPh2)2CH) and the diphosphonioalkylidene-plutonium complexes [Pu(BIPMTMS)(I)(DME)] (2Pu, BIPMTMS = (Me3SiNPPh2)2C) and [Pu(BIPMTMS)(I)(IMe4)2] (3Pu, IMe4 = C(NMeCMe)2), thus disclosing non-actinyl transneptunium multiple bonds and transneptunium NHC complexes. These Pu-C double and dative bonds, along with cerium, praseodymium, samarium, uranium, and neptunium congeners, enable lanthanide-actinide and actinide-actinide comparisons between metals with similar ionic radii and isoelectronic 4f5 vs 5f5 electron-counts within conserved ligand fields over 12 complexes. Quantum chemical calculations reveal that the orbital-energy and spatial-overlap terms increase from uranium to neptunium; however, on moving to plutonium the orbital-energy matching improves but the spatial overlap decreases. The bonding picture that emerges is more complex than the traditional picture of the bonding of lanthanides being ionic and early actinides being more covalent but becoming more ionic left to right. Multiconfigurational calculations on 2M and 3M (M = Pu, Sm) account for the considerably more complex UV/vis/NIR spectra for 5f5 2Pu and 3Pu compared to 4f5 2Sm and 3Sm. Supporting the presence of Pu═C double bonds in 2Pu and 3Pu, 2Pu exhibits metallo-Wittig bond metathesis involving the highest atomic number element to date, reacting with benzaldehyde to produce the alkene PhC(H)═C(PPh2NSiMe3)2 (4) and "PuOI". In contrast, 2Ce and 2Pr do not react with benzaldehyde to produce 4.

Ligand Effects on the Spin Relaxation Dynamics and Coherent Manipulation of Organometallic La(II) Potential Qudits.

We present pulsed electron paramagnetic resonance (EPR) studies on three La(II) complexes, [K(2.2.2-cryptand)][La(Cp')3] (1), [K(2.2.2-cryptand)][La(Cp″)3] (2), and [K(2.2.2-cryptand)][La(Cptt)3] (3), which feature cyclopentadienyl derivatives as ligands [Cp' = C5H4SiMe3; Cp″ = C5H3(SiMe3)2; Cptt = C5H3(CMe3)2] and display a C3 symmetry. Long spin-lattice relaxation (T1) and phase memory (Tm) times are observed for all three compounds, but with significant variation in T1 among 1-3, with 3 being the slowest relaxing due to higher s-character of the SOMO. The dephasing times can be extended by more than an order of magnitude via dynamical decoupling experiments using a Carr-Purcell-Meiboom-Gill (CPMG) sequence, reaching 161 µs (5 K) for 3. Coherent spin manipulation is performed by the observation of Rabi quantum oscillations up to 80 K in this nuclear spin-rich environment (1H, 13C, and 29Si). The high nuclear spin of 139La (I = 7/2), and the ability to coherently manipulate all eight hyperfine transitions, makes these molecules promising candidates for application as qudits (multilevel quantum systems featuring d quantum states; d >2) for performing quantum operations within a single molecule. Application of HYSCORE techniques allows us to quantify the electron spin density at ligand nuclei and interrogate the role of functional groups to the electron spin relaxation properties.

Halobenzene Adducts of a Dysprosocenium Single-Molecule Magnet.

Dysprosium complexes with strong axial crystal fields are promising candidates for single-molecule magnets (SMMs), which could be used for high-density data storage. Isolated dysprosocenium cations, [Dy(CpR)2]+ (CpR = substituted cyclopentadienyl), have recently shown magnetic hysteresis (a memory effect) above the temperature of liquid nitrogen. Synthetic efforts have focused on reducing strong transverse ligand fields in these systems as they are known to enhance magnetic relaxation by spin-phonon mechanisms. Here we show that equatorial coordination of the halobenzenes PhX (X = F, Cl, Br) and o-C6H4F2 to the cation of a recently reported dysprosocenium complex [Dy(Cpttt)(Cp*)][Al{OC(CF3)3}4] (Cpttt = C5H2tBu3-1,2,4; Cp* = C5Me5) reduces magnetic hysteresis temperatures compared to that of the parent cation. We find that this is due to increased effectiveness of both one- (Orbach) and two-phonon (Raman) relaxation mechanisms, which correlate with the electronegativity and number of interactions with the halide despite κ1-coordination of a single halobenzene having a minimal effect on the metrical parameters of [Dy(Cpttt)(Cp*)(PhX-κ1-X)]+ cations vs the isolated [Dy(Cpttt)(Cp*)]+ cation. We observe unusual divergent behavior of relaxation rates at low temperatures in [Dy(Cpttt)(Cp*)(PhX)][Al{OC(CF3)3}4], which we attribute to a phonon bottleneck effect. We find that, despite the transverse fields introduced by the monohalobenzenes in these cations, the interactions are sufficiently weak that the effective barriers to magnetization reversal remain above 1000 cm-1, being only ca. 100 cm-1 lower than for the parent complex, [Dy(Cpttt)(Cp*)][Al{OC(CF3)3}4].

Synthesis and Magnetic Properties of Bis-Halobenzene Decamethyldysprosocenium Cations.

The decamethyldysprosocenium cation, [Dy(Cp*)2]+ (Cp* = {C5Me5}), was a target single-molecule magnet (SMM) prior to the isolation of larger dysprosocenium cations, which have recently shown magnetic memory effects up to 80 K. However, the relatively short Dy···Cp*centroid distances of [Dy(Cp*)2]+, together with the reduced resonance of its vibrational modes with electronic states compared to larger dysprosocenium cations, could lead to more favorable SMM behavior. Here, we report the synthesis and magnetic properties of a series of solvated adducts containing bis-halobenzene decamethyldysprosocenium cations, namely [Dy(Cp*)2(PhX-κ-X)2][Al{OC(CF3)3}4] (X = F or Cl) and [Dy(Cp*)2(C6H4F2-κ2-F,F)(C6H4F2-κ-F)][Al{OC(CF3)3}4]. These complexes were prepared by the sequential reaction of [Dy(Cp*)2(µ-BH4)]∞ with allylmagnesium chloride and [NEt3H][Al{OC(CF3)3}4], followed by recrystallization from parent halobenzenes. The complexes were characterized by powder and single crystal X-ray diffraction, NMR and ATR-IR spectroscopy, elemental analysis, and SQUID magnetometry; experimental data were rationalized by a combination of density functional theory and ab initio calculations. We find that bis-halobenzene adducts of the [Dy(Cp*)2]+ cation exhibit highly bent Cp*···Dy···Cp* angles; these cations are also susceptible to decomposition by C-X (X = F, Cl, Br) activation and displacement of halobenzenes by O-donor ligands. The effective energy barrier to reversal of magnetization measured for [Dy(Cp*)2(PhF-κ-F)2][Al{OC(CF3)3}4] (930(6) cm-1) sets a new record for SMMs containing {Dy(Cp*)2} fragments, though all SMM parameters are lower than would be predicted for an isolated [Dy(Cp*)2]+ cation, as expected due to transverse ligand fields introduced by halobenzenes and the large deviation of the Cp*···Dy···Cp* angle from linearity promoting magnetic relaxation.

Intramolecular bridging strategies to suppress two-phonon Raman spin relaxation in dysprosocenium single-molecule magnets.

Dy(III) bis-cyclopentadienyl (Cp) sandwich compounds exhibit extremely strong single-ion magnetic anisotropy which imbues them with magnetic memory effects such as magnetic hysteresis, and has put them at the forefront of high-performance single-molecule magnets (SMMs). Owing to the great success of design principles focused on maximising the anisotropy barrier, ever higher Ueff values have been reported leading to significant slow down of single-phonon Orbach spin relaxation. However, anisotropy-based SMM design has largely ignored two-phonon Raman spin relaxation, which is still limiting the temperatures at which a memory effect can be observed. In this work, we study the suppression of Raman relaxation through covalent bridging of the Cp ligands by alkyl chains, testing the hypothesis that increasing the rigidity of the ligand framework results in a blue shift of low frequency vibrations in the first coordination sphere of the Dy(III) ion. This reshaping of the vibrational low-energy density of states (DOS) results in lower occupation of pseudo-acoustic phonons available to drive Raman relaxation at low temperatures. We simulate Orbach and Raman spin relaxation in a series of zero-, mono-, di- and tri-bridged [Dy(Cpttt)2]+ analogues fully ab initio, using a quantum mechanics (QM)/molecular mechanics (MM) condensed phase embedding protocol in a periodic solvent matrix as a generic and experimentally testable environment model that can include (pseudo-)acoustic phononic degrees of freedom. We show that this approach can simulate magnetic relaxation dynamics in the condensed phase for the existing non-bridged [Dy(Cpttt)2]+ compound with quantitative experimental accuracy. Subsequently, we find a significant slowing down of Raman relaxation can be achieved for the singly-bridged SMM, while the introduction of further bridges leads to faster relaxation. A key result being that we find the two-phonon Raman rates correlate with the purity of the first-excited Kramers doublet in terms of its mJ = ±13/2 content. Even though the bridging design principle is successful at progressively reshaping the low-energy DOS, the introduction of linker atoms in the equatorial plane successively degrades magnetic anisotropy, suggesting the importance of refined design of the linker chemistry. The accuracy of our results emphasises the value of a generic periodic solvent embedding model, such that it permits the modelling of molecular spin dynamics in the condensed phase without knowledge of a crystal structure. This allows the study of hypothetical molecules or aggregates under real-world conditions, which we expect to have utility beyond the field of molecular magnetism.

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.

Strong Axiality in a Dysprosium(III) Bis(borolide) Complex Leads to Magnetic Blocking at 65 K.

Substituted dysprosocenium complexes of the type [Dy(CpR)2]+ exhibit slow magnetic relaxation at cryogenic temperatures and have emerged as top-performing single-molecule magnets. The remarkable properties of these compounds derive in part from the strong axial ligand field afforded by the cyclopentadiene anions, and the design of analogous compounds with even stronger ligand fields is one promising route toward identifying new single-molecule magnets that retain a magnetic memory at even higher temperatures. Here, we report the synthesis and characterization of a dysprosium bis(borolide) compound, [K(18-crown-6)][Dy(BC4Ph5)2] (1), featuring the dysprosocenate anion [Dy(BC4Ph5)2]- with a pseudoaxial coordination environment afforded by two dianionic pentaphenyl borolide ligands. Variable-field magnetization data reveal open magnetic hysteresis up to 66 K, establishing 1 as a top-performing single-molecule magnet among its dysprosocenium analogues. Ac magnetic susceptibility data indicate that 1 relaxes via an Orbach mechanism above ∼80 K with Ueff = 1500(100) cm-1 and τ0 = 10-12.0(9) s, whereas Raman relaxation and quantum tunneling of the magnetization dominate at lower temperatures. Compound 1 exhibits a 100 s blocking temperature of 65 K, among the highest reported for dysprosium-based single-molecule magnets. Ab initio spin dynamics calculations support the experimental Ueff and τ0 values and enable a quantitative comparison of the relaxation dynamics of 1 and two representative dysprosocenium cations, yielding additional insights into the impact of the crystal field splitting and vibronic coupling on the observed relaxation behavior. Importantly, compound 1 represents a step toward the development of alternatives to substituted dysprosocenium single-molecule magnets with increased axiality.

Taming Super-Reduced Bi23- Radicals with Rare Earth Cations.

Here, we report the synthesis of two new sets of dibismuth-bridged rare earth molecules. The first series contains a bridging diamagnetic Bi22- anion, (Cp*2RE)2(µ-η2:η2-Bi2), 1-RE (where Cp* = pentamethylcyclopentadienyl; RE = Gd (1-Gd), Tb (1-Tb), Dy (1-Dy), Y (1-Y)), while the second series comprises the first Bi23- radical-containing complexes for any d- or f-block metal ions, [K(crypt-222)][(Cp*2RE)2(µ-η2:η2-Bi2•)]·2THF (2-RE, RE = Gd (2-Gd), Tb (2-Tb), Dy (2-Dy), Y (2-Y); crypt-222 = 2.2.2-cryptand), which were obtained from one-electron reduction of 1-RE with KC8. The Bi23- radical-bridged terbium and dysprosium congeners, 2-Tb and 2-Dy, are single-molecule magnets with magnetic hysteresis. We investigate the nature of the unprecedented lanthanide-bismuth and bismuth-bismuth bonding and their roles in magnetic communication between paramagnetic metal centers, through single-crystal X-ray diffraction, ultraviolet-visible/near-infrared (UV-vis/NIR) spectroscopy, SQUID magnetometry, DFT and multiconfigurational ab initio calculations. We find a πz* ground SOMO for Bi23-, which has isotropic spin-spin exchange coupling with neighboring metal ions of ca. -20 cm-1; however, the exchange coupling is strongly augmented by orbitally dependent terms in the anisotropic cases of 2-Tb and 2-Dy. As the first examples of p-block radicals beneath the second row bridging any metal ions, these studies have important ramifications for single-molecule magnetism, main group element, rare earth metal, and coordination chemistry at large.

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.

Thermally Stable Terbium(II) and Dysprosium(II) Bis-amidinate Complexes.

The thermostable four-coordinate divalent lanthanide (Ln) bis-amidinate complexes [Ln(Piso)2] (Ln = Tb, Dy; Piso = {(NDipp)2CtBu}, Dipp = C6H3iPr2-2,6) were prepared by the reduction of parent five-coordinate Ln(III) precursors [Ln(Piso)2I] (Ln = Tb, Dy) with KC8; halide abstraction of [Ln(Piso)2I] with [H(SiEt3)2][B(C6F5)] gave the respective Ln(III) complexes [Ln(Piso)2][B(C6F5)]. All complexes were characterized by X-ray diffraction, ICP-MS, elemental analysis, SQUID magnetometry, UV-vis-NIR, ATR-IR, NMR, and EPR spectroscopy and ab initio CASSCF-SO calculations. These data consistently show that [Ln(Piso)2] formally exhibit Ln(II) centers with 4fn5dz21 (Ln = Tb, n = 8; Dy, n = 9) valence electron configurations. We show that simple assignments of the f-d coupling to either L-S or J-s schemes are an oversimplification, especially in the presence of significant crystal field splitting. The coordination geometry of [Ln(Piso)2] is intermediate between square planar and tetrahedral. Projecting from the quaternary carbon atoms of the CN2 ligand backbones shows near-linear C···Ln···C arrangements. This results in strong axial ligand fields to give effective energy barriers to magnetic reversal of 1920(91) K for the Tb(II) analogue and 1964(48) K for Dy(II), the highest values observed for mononuclear Ln(II) single-molecule magnets, eclipsing 1738 K for [Tb(C5iPr5)2]. We tentatively attribute the fast zero-field magnetic relaxation for these complexes at low temperatures to transverse fields, resulting in considerable mixing of mJ states.

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.

Determinative Effect of Axial Linearity on Single-Molecule Magnet Performance in Dinuclear Dysprosium Complexes.

Two dichloride-bridged dinuclear dysprosium(III) complexes based on salen ligands, namely, [Dy(L1 )(µ-Cl)(thf)]2 (1; H2 L1 =N,N'-bis(3,5-di-tert-butylsalicylidene)phenylenediamine) and [Dy2 (L2 )2 (µ-Cl)2 (thf)2 ]2 (2; H2 L2 =N,N'-bis(3,5-di-tert-butylsalicylidene)ethylenediamine) are reported. These two complexes have two short Dy-O(PhO) bonds that exhibit angles of ∼90° for 1 and ∼143° for 2, leading to clear slow relaxation of the magnetization for 2 and not for 1. Compound 2 has a near-identical core to the recently reported compound [Dy2 (L3 )2 (µ-Cl)2 (thf)2 ] (3; H2 L3 =N-(2-pyridylmethyl)-N,N-bis(2'-hydroxy-3',5'-di-tert-butylbenzyl)amine). The only substantial difference is the relative angle of the two O(PhO) -Dy-O(PhO) vectors, which is collinear in 2 owing to inversion symmetry and ∼68° in 3 due to a molecular C2 axis. It is shown that this subtle structural difference leads to large differences in the dipolar ground states, giving rise to open magnetic hysteresis for 3 and not for 2.

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.

Molecular magnetic hysteresis at 60 kelvin in dysprosocenium.

Lanthanides have been investigated extensively for potential applications in quantum information processing and high-density data storage at the molecular and atomic scale. Experimental achievements include reading and manipulating single nuclear spins, exploiting atomic clock transitions for robust qubits and, most recently, magnetic data storage in single atoms. Single-molecule magnets exhibit magnetic hysteresis of molecular origin-a magnetic memory effect and a prerequisite of data storage-and so far lanthanide examples have exhibited this phenomenon at the highest temperatures. However, in the nearly 25 years since the discovery of single-molecule magnets, hysteresis temperatures have increased from 4 kelvin to only about 14 kelvin using a consistent magnetic field sweep rate of about 20 oersted per second, although higher temperatures have been achieved by using very fast sweep rates (for example, 30 kelvin with 200 oersted per second). Here we report a hexa-tert-butyldysprosocenium complex-[Dy(Cpttt)2][B(C6F5)4], with Cpttt = {C5H2tBu3-1,2,4} and tBu = C(CH3)3-which exhibits magnetic hysteresis at temperatures of up to 60 kelvin at a sweep rate of 22 oersted per second. We observe a clear change in the relaxation dynamics at this temperature, which persists in magnetically diluted samples, suggesting that the origin of the hysteresis is the localized metal-ligand vibrational modes that are unique to dysprosocenium. Ab initio calculations of spin dynamics demonstrate that magnetic relaxation at high temperatures is due to local molecular vibrations. These results indicate that, with judicious molecular design, magnetic data storage in single molecules at temperatures above liquid nitrogen should be possible.

Studies of the Temperature Dependence of the Structure and Magnetism of a Hexagonal-Bipyramidal Dysprosium(III) Single-Molecule Magnet.

The hexagonal-bipyramidal lanthanide(III) complex [Dy(OtBu)Cl(18-C-6)][BPh4] (1; 18-C-6 = 1,4,7,10,13,16-hexaoxacyclooctadecane ether) displays an energy barrier for magnetization reversal (Ueff) of ca. 1000 K in a zero direct-current field. Temperature-dependent X-ray diffraction studies of 1 down to 30 K reveal bending of the Cl-Ln-OtBu angle at low temperature. Using ab initio calculations, we show that significant bending of the O-Dy-Cl angle upon cooling from 273 to 100 K leads to a ca. 10% decrease in the energy of the excited electronic states. A thorough exploration of the temperature and field dependencies of the magnetic relaxation rate reveals that magnetic relaxation is dictated by five mechanisms in different regimes: Orbach, Raman-I, quantum tunnelling of magnetization, and Raman-II, in addition to the observation of a phonon bottleneck effect.