Ab Initio Crystal Field for Lanthanides

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

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

Substituent Positioning Effects on the Magnetic Properties of Sandwich-Type Erbium(III) Complexes with Bis(trimethylsilyl)-Substituted Cyclooctatetraenyl Ligands

Lanthanide complexes with judiciously designed ligands have been extensively studied for their potential applications as single-molecule magnets. With the influence of ligands on their magnetic properties generally established, recent research has unearthed certain effects inherent to site differentiation due to the different types and varying numbers of substituents on the same ligand platform. Using two new sandwich-type Er(III) complexes with cyclooctatetraenyl (COT) ligands featuring two differently positioned trimethylsilyl (TMS) substituents, namely, [Li(DME)Er(COT1,5-TMS2)2]n (Er1) and [Na(DME)3][Er(COT1,3-TMS2)2] (Er2) [COT1,3-TMS2 and COT1,5-TMS2 donate 1,3- and 1,5-bis(trimethylsilyl)-substituted cyclooctatetraenyl ligands, respectively; DME = 1,2-dimethoxyethane], and with reference to previously reported [Li(DME)3][Er(COT1,4-TMS2)2] (A) and [K(DME)2][Er(COT1,4-TMS2)2] (B), any possible substituent position effects have been explored for the first time. The rearrangement of the TMS substituents from the starting COT1,4-TMS2 to COT1,3-TMS2 and COT1,5-TMS2, by way of formal migration of the TMS group, was thermally induced in the case of Er1, while for the formation of Er2, the use of Na+ in the placement of its Li+ and K+ congeners is essential. Both Er1 and Er2 display single-molecule magnetic behaviors with energy barriers of 170(3) and 172(6) K, respectively. Magnetic hysteresis loops, butterfly-shaped for Er1 and wide open for Er2, were observed up to 12 K for Er1 and 13 K for Er2. Studies of magnetic dynamics reveal the different pathways for relaxation of magnetization below 10 K, mainly by the Raman process for Er1 and by quantum tunneling of magnetization for Er2, leading to the order of magnitude difference in magnetic relaxation times and sharply different magnetic hysteresis loops.

Homoleptic Rare-Earth-Metal Sandwiches with Dibenzo[a,e]cyclooctatetraene Dianions

A family of rare-earth complexes [RE(III) = Y, La, Gd, Tb, Dy, and Er] with doubly reduced dibenzo[a,e]cyclooctatetraene (DBCOT) has been synthesized and structurally characterized. X-ray diffraction analysis confirms that all products of the [RE(DBCOT)(THF)4][RE(DBCOT)2] composition consist of the anionic sandwich [RE(DBCOT)2]- and the cationic counterpart [RE(DBCOT)(THF)4]+. Within the sandwich, two elongated π decks are slightly bent toward the metal center (avg. 7.3°) with a rotation angle of 35.9-37.6°. The RE(III) ion is entrapped between the central eight-membered rings of DBCOT2- in a η8 fashion. The trends in the RE-COT bond lengths are consistent with the variations of the ionic radii of RE(III) centers. The 1H NMR spectra of the diamagnetic Y(III) and La(III) analogues illustrate the distinct solution behavior for the cationic and anionic parts in this series. Magnetic measurements for the Dy analogue reveal single-molecule magnetism, which was rationalized by considering the effect of crystal-field splitting for both building units analyzed by electronic structure calculations.

Optical Phenomena in Molecule-Based Magnetic Materials

Since the last century, we have witnessed the development of molecular magnetism which deals with magnetic materials based on molecular species, i.e., organic radicals and metal complexes. Among them, the broadest attention was devoted to molecule-based ferro-/ferrimagnets, spin transition materials, including those exploring electron transfer, molecular nanomagnets, such as single-molecule magnets (SMMs), molecular qubits, and stimuli-responsive magnetic materials. Their physical properties open the application horizons in sensors, data storage, spintronics, and quantum computation. It was found that various optical phenomena, such as thermochromism, photoswitching of magnetic and optical characteristics, luminescence, nonlinear optical and chiroptical effects, as well as optical responsivity to external stimuli, can be implemented into molecule-based magnetic materials. Moreover, the fruitful interactions of these optical effects with magnetism in molecule-based materials can provide new physical cross-effects and multifunctionality, enriching the applications in optical, electronic, and magnetic devices. This Review aims to show the scope of optical phenomena generated in molecule-based magnetic materials, including the recent advances in such areas as high-temperature photomagnetism, optical thermometry utilizing SMMs, optical addressability of molecular qubits, magneto-chiral dichroism, and opto-magneto-electric multifunctionality. These findings are discussed in the context of the types of optical phenomena accessible for various classes of molecule-based magnetic materials.

Engineering Clock Transitions in Molecular Lanthanide Complexes

Molecular lanthanide (Ln) complexes are promising candidates for the development of next-generation quantum technologies. High-symmetry structures incorporating integer spin Ln ions can give rise to well-isolated crystal field quasi-doublet ground states, i.e., quantum two-level systems that may serve as the basis for magnetic qubits. Recent work has shown that symmetry lowering of the coordination environment around the Ln ion can produce an avoided crossing or clock transition within the ground doublet, leading to significantly enhanced coherence. Here, we employ single-crystal high-frequency electron paramagnetic resonance spectroscopy and high-level ab initio calculations to carry out a detailed investigation of the nine-coordinate complexes, [HoIIIL1L2], where L1 = 1,4,7,10-tetrakis(2-pyridylmethyl)-1,4,7,10-tetraaza-cyclododecane and L2 = F- (1) or [MeCN]0 (2). The pseudo-4-fold symmetry imposed by the neutral organic ligand scaffold (L1) and the apical anionic fluoride ion generates a strong axial anisotropy with an mJ = ±8 ground-state quasi-doublet in 1, where mJ denotes the projection of the J = 8 spin-orbital moment onto the ∼C4 axis. Meanwhile, off-diagonal crystal field interactions give rise to a giant 116.4 ± 1.0 GHz clock transition within this doublet. We then demonstrate targeted crystal field engineering of the clock transition by replacing F- with neutral MeCN (2), resulting in an increase in the clock transition frequency by a factor of 2.2. The experimental results are in broad agreement with quantum chemical calculations. This tunability is highly desirable because decoherence caused by second-order sensitivity to magnetic noise scales inversely with the clock transition frequency.

Unravelling the Highest Magnetic Anisotropy Among all the n-Shells in 20 Metallocene

Single-molecule magnets (SMMs) with a large magnetization reversal barrier are predominated by the lanthanide systems due to their strong spin-orbit coupling (SOC). However, the transition metals have also emerged as potential contenders and the largest magnetic anisotropy has been identified for a cobalt system among any d-series-based SMMs (Bunting et al. Science 2018, 362, eaat7319). In this work, we have explored the magnetic anisotropy in highly axial ligand field systems of metallocene, having different d-subshell (3d4, 4d4, and 5d4). The wave function-based multireference methods including static and dynamic electron correlations have been employed to investigate the zero-field splitting (ZFS) parameters. Here, we report exceptionally large magnetic anisotropy for a 5d complex of [WCp2]0 with the highest energy barrier that is nearly twice as high as the previous record value for the Co complex. We have also observed that the axial ZFS parameter (D) is increasing down the group in the order of 3d < 4d < 5d, pertaining to a large SOC.

Luminescent Er3+ based single molecule magnets with fluorinated alkoxide or aryloxide ligands

We report the synthesis, structures, and magnetic and luminescence properties of a series of new mono- and dinuclear Er3+ complexes derived from sterically demanding aryloxide and fluorinated alkoxide ligands: [4-tBu-2,6-(Ph2CH)2C6H2O]3Er(THF) (1), [(C6F5)3CO]3Er(Me3SiOH) (2), [(C6F5)3CO]3Er[(Me3Si)2NH] (3), [(C6F5)3CO]3Er(C6H5CH3) (4), [(C6F5)3CO]3Er(o-Me2NC6H4CH3) (5) and {[Ph(CF3)2CO]2Er(μ2-OC(CF3)2Ph)}2 (6). In compounds 1, 2, and 4, the Er3+ ion is four-coordinated and adopts a distorted trigonal pyramidal geometry, while in 3, 5, and 6, the coordination geometry of Er3+ is impacted by the presence of several relatively short Er⋯F distances, making them rather 6-coordinated. All compounds behave as field-induced Single Molecule Magnets (SMMs) and exhibit an Er3+ characteristic near infrared (NIR) emission associated with the 4I13/2 → 4I15/2 transition with a remarkably long lifetime going up to 73 μs, which makes them multifunctional luminescent SMMs. The deconvolution of the NIR emission spectra allowed us to provide a direct probe of the crystal field splitting in these compounds, which was correlated with magnetic data.

Building Molecular Nanomagnets by Encapsulating Lanthanide Ions in Boron Nitride Nanotubes: Ab Initio Investigation

Lanthanide-based single-ion magnets have attracted much interest due to their great potential for information storage at the level of one molecule. Among various strategies to enhance magnetization blocking in such complexes, the synthesis of axially symmetric compounds is regarded as the most promising. Here, we investigate theoretically the magnetization blocking of several lanthanide ions (Tb3+, Dy3+, Ho3+, Er3+, and Tm3+) encapsulated in highly symmetric zigzag boron nitride nanotubes (BNNTs) of different diameters with ab initio methodology. We found that Tb3+@(7,0)BNNT, Dy3+@(7,0)BNNT, and Tm3+@(5,0)BNNT are suitable SIM candidates, while the other investigated complexes from this series show no signs of magnetization blocking owing to a hard competition between contributions to the crystal field of the lanthanide ion from neighboring and more distant atoms of the nanotube.

The resolution of the weak-exchange limit made rigorous, simple and general in binuclear complexes

The correct interpretation of magnetic properties in the weak-exchange regime has remained a challenging task for several decades. In this regime, the effective exchange interaction between local spins is quite weak, of the same order of magnitude or smaller than the various anisotropic terms, which generates a complex set of levels characterized by spin mixing. Although the model multispin Hamiltonian in the absence of local orbital momentum, , is considered good enough to map the experimental energies at zero field and in the strong-exchange limit, theoretical works pointed out limitations of this simple model. This work revives the use of ĤMS from a new theoretical perspective, detailing point-by-point a strategy to correctly map the computational energies and wave functions onto ĤMS, thus validating it regardless of the exchange limit. We will distinguish two cases, based on experimentally characterized dicobalt(II) complexes from the literature. If centrosymmetry imposes alignment of the various rank-2 tensors constitutive of ĤMS in the first case, the absence of any symmetry element prevents such alignment in the second case. In such a context, the strategy provided herein becomes a powerful tool to rationalize the experimental magnetic data, since it is capable of fully and rigorously extracting the multispin model without any assumption on the orientation of its constitutive tensors. Furthermore, the strategy allows to question the use of the spin Hamiltonian approach by explicitly controlling the projection norms on the model space, which is showcased in the second complex where local orbital momentum could have occurred (distorted octahedra). Finally, previous theoretical data related to a known dinickel(II) complex is reinterpreted, clarifying initial wanderings regarding the weak exchange limit.

Covalency versus magnetic axiality in Nd molecular magnets: Nd-photoluminescence, strong ligand-field, and unprecedented nephelauxetic effect in fullerenes NdM2N@C80 (M = Sc, Lu, Y)

Nd-based nitride clusterfullerenes NdM2N@C80 with rare-earth metals of different sizes (M = Sc, Y, Lu) were synthesized to elucidate the influence of the cluster composition, shape and internal strain on the structural and magnetic properties. Single crystal X-ray diffraction revealed a very short Nd-N bond length in NdSc2N@C80. For Lu and Y analogs, the further shortening of the Nd-N bond and pyramidalization of the NdM2N cluster are predicted by DFT calculations as a result of the increased cluster size and a strain caused by the limited size of the fullerene cage. The short distance between Nd and nitride ions leads to a very large ligand-field splitting of Nd3+ of 1100-1200 cm-1, while the variation of the NdM2N cluster composition and concomitant internal strain results in the noticeable modulation of the splitting, which could be directly assessed from the well-resolved fine structure in the Nd-based photoluminescence spectra of NdM2N@C80 clusterfullerenes. Photoluminescence measurements also revealed an unprecedentedly strong nephelauxetic effect, pointing to a high degree of covalency. The latter appears detrimental to the magnetic axiality despite the strong ligand field. As a result, the ground magnetic state has considerable transversal components of the pseudospin g-tensor, and the slow magnetic relaxation of NdSc2N@C80 could be observed by AC magnetometry only in the presence of a magnetic field. A combination of the well-resolved magneto-optical states and slow relaxation of magnetization suggests that Nd clusterfullerenes can be useful building blocks for magneto-photonic quantum technologies.

Insight into ferromagnetic interactions in CuII-LnIII dimers with a compartmental ligand

In the last two decades, efforts have been devoted to obtaining insight into the magnetic interactions between CuII and LnIII utilizing experimental and theoretical means. Experimentally, it has been observed that the exchange coupling (J) in CuII-LnIII systems is often found to be ferromagnetic for ≥4f7 metal ions. However, exchange interactions at sub-Kelvin temperatures between CuII and the anisotropic/isotropic LnIII ions are not often explored. In this report, we have synthesized a series of heterobimetallic [CuLn(HL)(μ-piv)(piv)2] complexes (LnIII = Gd (1), Tb (2), Dy (3) and Er (4)) from a new compartmental Schiff base ligand, N,N'-bis(3-methoxy-5-methylsalicylidene)-1,3-diamino-2-propanol (H3L). X-ray crystallographic analysis reveals that all four complexes are isostructural and isomorphous. Magnetic susceptibility measurements reveal a ferromagnetic coupling between the CuII ion and its respective LnIII ion for all the complexes, as often observed. Moreover, μ-SQUID studies, at sub-Kelvin temperatures, show S-shaped hysteresis loops indicating the presence of antiferromagnetic coupling in complexes 1-3. The antiferromagnetic interaction is explained by considering the shortest Cu⋯Cu distance in the crystal structure. The nearly closed loops for 1-3 highlight their fast relaxation characteristics, while the opened loops for 4 might arise from intermolecular ordering. CASSCF calculations allow the quantitative assessment of the interactions, which are further supported by BS-DFT calculations.

Effects of the tetravanadate [V4O12]4- anion on the structural, magnetic, and biological properties of copper/phenanthroline complexes

The aim to access linked tetravanadate [V4O12]4- anion with mixed copper(II) complexes, using α-amino acids and phenanthroline-derived ligands, resulted in the formation of four copper(II) complexes [Cu(dmb)(Gly)(OH2)]2[Cu(dmb)(Gly)]2[V4O12]·9H2O (1) [Cu(dmb)(Lys)]2[V4O12]·8H2O (2), [Cu(dmp)2][V4O12]·C2H5OH·11H2O (3), and [Cu(dmp)(Gly)Cl]·2H2O (4), where dmb = 4,4'-dimethioxy-2,2'-bipyridine; Gly = glycine; Lys = lysine; and dmp = 2,9-dimethyl-1,10-phenanthroline. The [V4O12]4- anion is functionalized with mixed copper(II) units in 1 and 2; while in 3, it acts as a counterion of two [Cu(dmp)]2+ units. Compound 4 crystallized as a unit that did not incorporate the vanadium cluster. All compounds present magnetic couplings arising from Cu⋯O/Cu⋯Cu bridges. Stability studies of water-soluble 3 and 4 by UV-Vis spectroscopy in cell culture medium confirmed the robustness of 3, while 4 appears to undergo ligand scrambling over time, resulting partially in the stable species [Cu(dmp)2]+ that was also identified by electrospray ionization mass spectrometry at m/z = 479. The in vitro cytotoxicity activity of 3 and 4 was determined in six cancer cell lines; the healthy cell line COS-7 was also included for comparative purposes. MCF-7 cells were more sensitive to compound 3 with an IC50 value of 12 ± 1.2 nmol. The tested compounds did not show lipid peroxidation in the TBARS assay, ruling out a mechanism of action via reactive oxygen species formation. Both compounds inhibited cell migration at 5 µM in wound-healing assays using MCF-7, PC-3, and SKLU-1 cell lines, opening a new window to study the anti-metastatic effect of mixed vanadium-copper(II) systems.

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.

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.

Strengths of covalent bonds in LnO2 determined from O K-edge XANES spectra using a Hubbard model

In LnO2 (Ln = Ce, Pr, and Tb), the amount of Ln 4f mixing with O 2p orbitals was determined by O K-edge X-ray absorption near edge (XANES) spectroscopy and was similar to the amount of mixing between the Ln 5d and O 2p orbitals. This similarity was unexpected since the 4f orbitals are generally perceived to be "core-like" and can only weakly stabilize ligand orbitals through covalent interactions. While the degree of orbital mixing seems incompatible with this view, orbital mixing alone does not determine the degree of stabilization provided by a covalent interaction. We used a Hubbard model to determine this stabilization from the energies of the O 2p to 4f, 5d(eg), and 5d(t2g) excited charge-transfer states and the amount of excited state character mixed into the ground state, which was determined using Ln L3-edge and O K-edge XANES spectroscopy. The largest amount of stabilization due to mixing between the Ln 4f and O 2p orbitals was 1.6(1) eV in CeO2. While this energy is substantial, the stabilization provided by mixing between the Ln 5d and O 2p orbitals was an order of magnitude greater consistent with the perception that covalent bonding in the lanthanides is largely driven by the 5d orbitals rather than the 4f orbitals.

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.

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.

Bonding and Magnetic Trends in the [AnIII(DPA)3]3- Series Compared to the Ln(III) and An(IV) Analogues

The crystal field parameters are determined from first-principles calculations in the [AnIII(DPA)3]3- series, completing previous work on the [LnIII(DPA)3]3- and [AnIV(DPA)3]2- series. The crystal field strength parameter follows the Ln(III) < An(III) < An(IV) trend. The parameters deduced at the orbital level decrease along the series, while J-mixing strongly impacts the many-electron parameters, especially for the Pu(III) complex. We further compile the available data for the three series. In some aspects, An(III) complexes are closer to Ln(III) than to An(IV) complexes with regard to the geometrical structure and bonding descriptors. At the beginning of the series, up to Pu(III), there is a quantitative departure from the free ion, especially for the Pa(III) complex. The magnetic properties of the actinides keep the trends of the lanthanides; in particular, the axial magnetic susceptibility follows Bleaney's theory qualitatively.

Eu3+ ions as a crystal-field probe for low-symmetry sites in doped phosphors - a case study: Eu3+ at triclinic sites in Li6RE(BO3)3 (RE = Y, Gd), YBO3 and ZnO and at trigonal sites in YAl3(BO3)4

We present crystal-field (CF) calculations of energy levels (Ei) of Eu3+ ions doped in various hosts aimed at exploring the low-symmetry properties of CF parameters (CFPs) and reliability of CFP modelling with decreasing site symmetry. The hosts studied are: Li6Y(BO3)3, Li6Gd(BO3)3, YBO3, and ZnO with Eu3+ at triclinic sites; YAl3(BO3)4 with Eu3+ ions at trigonal D3 symmetry. Two independent CFP modelling approaches utilizing the hosts' structural data are employed: the exchange charge model (ECM) and the superposition model (SPM). We adopt the Eu3+ actual site symmetry and not the approximated one. The Ei values calculated using CFPs modelled by the ECM and SPM mutually agree with the observed ones. For triclinic symmetry, the ECM/CFPs and SPM/CFPs were numerically distinct, yet turned out to be physically equivalent yielding identical rotational invariants, Sk (k = 2, 4, 6) and Ei. For trigonal symmetry, both CFP sets agree numerically, thus Sk and Ei are identical. This disparity poses a dilemma, since the modified crystallographic axis system was used in both approaches. The standardization of the triclinic CFPs using the 3DD package was performed to solve this dilemma. It has enabled discussing standardization aspects in experimental and computed CFP sets and elucidating intricate low-symmetry aspects inherent in CFP sets. Understanding of low-symmetry aspects in CF studies may bring about a better interpretation of the spectroscopic and magnetic properties of rare-earth ion doped host crystals. Thus, our study could provide more deep insights into the importance of clear definitions of axis systems and adequate treatment of actual site symmetry in the modelling of CFPs for low-symmetry cases which is essential for technological applications and engineering of rare-earth activated phosphor materials.

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.

Luminescent Single-Molecule Magnets as Dual Magneto-Optical Molecular Thermometers

Luminescent thermometry allows the remote detection of the temperature and holds great potential in future technological applications in which conventional systems could not operate. Complementary approaches to measuring the temperature aiming to enhance the thermal sensitivity would however represent a decisive step forward. For the first time, we demonstrate the proof-of-concept that luminescence thermometry could be associated with a complementary temperature readout related to a different property. Namely, we propose to take advantage of the temperature dependence of both magnetic (canonical susceptibility and relaxation time) and luminescence features (emission intensity) found in Single-Molecule Magnets (SMM) to develop original dual magneto-optical molecular thermometers to conciliate high-performance SMM and Boltzmann-type luminescence thermometry. We highlight this integrative approach to concurrent luminescent and magnetic thermometry using an air-stable benchmark SMM [Dy(bbpen)Cl] (H2 bbpen=N,N'-bis(2-hydroxybenzyl)-N,N'-bis(2-methylpyridyl)ethyl-enediamine)) exhibiting Dy3+ luminescence. The synergy between multiparametric magneto-optical readouts and multiple linear regression makes possible a 10-fold improvement in the relative thermal sensitivity of the thermometer over the whole temperature range, compared with the values obtained with the single optical or magnetic devices.

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.

Ab initio prediction of key parameters and magneto-structural correlation of tetracoordinated lanthanide single-ion magnets

Single-molecule magnets (SMMs) have great potential in becoming revolutionary materials for micro-electronic devices. As one type of SMM and holding the performance record, lanthanide single-ion magnets (Ln-SIMs) stand at the forefront of the family. Lowering the coordination number (CN) is an important strategy to improve the performance of Ln-SIMs. Here, we report a theoretical study on a typical group of low-CN Ln-SIMs, i.e., tetracoordinated structures. Our results are consistent with those of experiments and they identify the same three best Ln-SIMs via a concise criterion, i.e., the co-existence of long τ_QTM and high U_eff. Compared to the record-holding dysprosocenium systems, the best SIMs here possess τ_QTM values that are shorter by several orders of magnitude and U_eff values that are lower by ∼1000 Kelvin (K). These are important reasons for the fact that the tetracoordinated Ln-SIMs are clearly inferior to dysprosocenium. A simple but intuitive crystal-field analysis leads to several routes to improve the performance of a given Ln-SIM, including compression of the axial bond length, widening the axial bond angle, elongation of the equatorial bond length and usage of weaker equatorial donor ligands. Although these routes are not brand-new, the most efficient option and the degree of improvement resulting from it are not known in advance. Consequently, a theoretical magneto-structural study, covering various routes, is carried out for the best Ln-SIM here and the most efficient route is shown to be widening the axial ∠O-Dy-O angle. The most optimistic case, having a ∠O-Dy-O of 180°, could have a τ_QTM (up to 10³ s) and U_eff (∼2400 K) close to those of the record-holders. Subsequently, a blocking temperature (T_B) of 64 K is predicted to be possible for it. A more practical case, with ∠O-Dy-O being 160°, could have a τ_QTM of up to 400 s, U_eff of around 2200 K and the possibility of a T_B of 57 K. Although having an inherent precision limit, these predictions provide a guide to performance improvement, starting from an existing system.

Structural and Magnetization Dynamics of Borohydride-Bridged Rare-Earth Metallocenium Cations

The structure and magnetic properties of the bimetallic borohydride-bridged dysprosocenium compound [{(η⁵-Cp^ttt)(η⁵-Cp^Me4t)Dy}₂(μ:κ²:κ²-BH₄)]⁺[B(C₆F₅)₄]^- ([3_Dy][B(C₆F₅)₄]) are reported along with the solution-phase dynamics of the isostructural yttrium and lutetium analogues (Cp^ttt is 1,2,4-tri(tert-butyl)cyclopentadienyl, Cp^Me4t is tetramethyl(tert-butyl)cyclopentadienyl). The synthesis of [3_M][B(C₆F₅)₄] was accomplished in the 2:1 stoichiometric reactions of [(η⁵-Cp^ttt)(η⁵-Cp^Me4t)Dy(BH₄)] (2_M) with [CPh₃][B(C₆F₅)₄], with the metallocenes 2_M obtained from reactions of the half-sandwich complexes [(η⁵-Cp^ttt)M(BH₄)₂(THF)] (1_M) (M = Y, Dy, Lu) with NaCp^Me4t. Crystallographic studies show significant lengthening of the M···B distance on moving through the series 1_M, 2_M, and 3_M, with essentially linear {M···B···M} bridges in 3_M. Multinuclear NMR spectroscopy indicates restricted rotation of the Cp^ttt ligands in 3_Y and 3_Lu in solution. The single-molecule magnet (SMM) properties of [3_M][B(C₆F₅)₄] are characterized by Raman and Orbach processes, with an effective barrier of 533(18) cm^-1 and relaxation via the second-excited Kramers doublet. Although quantum tunneling of the magnetization (QTM) was not observed for [3_M][B(C₆F₅)₄], it was, surprisingly, found in its magnetically dilute version, which has a very similar barrier of U_eff = 499(21) cm^-1. Consistent with this observation, slightly wider openings of the magnetic hysteresis loop at 2 K are found for [3_M][B(C₆F₅)₄] but not for the diluted analogue. The dynamic magnetic properties of the dysprosium SMMs and the role of exchange interactions in 3_Dy are interpreted with the aid of multireference ab initio calculations.

Direct determination of high-order transverse ligand field parameters via µSQUID-EPR in a Et4N[160GdPc2] SMM

The development of quantum technologies requires a thorough understanding of systems possessing quantum effects that can ultimately be manipulated. In the field of molecular magnetism, one of the main challenges is to measure high-order ligand field parameters, which play an essential role in the relaxation properties of SMMs. The development of highly advanced theoretical calculations has allowed the ab-initio determination of such parameters; however, currently, there is a lack of quantitative assessment of how good the ab-initio parameters are. In our quest for technologies that can allow the extraction of such elusive parameters, we develop an experimental technique that combines the EPR spectroscopy and µSQUID magnetometry. We demonstrate the power of the technique by performing EPR-µSQUID measurement of a magnetically diluted single crystal of Et₄N[GdPc₂], by sweeping the magnetic field and applying a range of multifrequency microwave pulses. As a result, we were able to directly determine the high-order ligand field parameters of the system, enabling us to test theoretical predictions made by state-of-the-art ab-initio methods.

Slow Magnetic Relaxation and Modulated Photoluminescent Emission of Coordination Polymer Based on 3-Amino-4-hydroxybenzoate Zn and Co Metal Ions

As a starting point, a new 3D porous framework with the {[CoL]·0.5DMF·H₂O}_n chemical formula (where L = 3-amino-4-hydroxybenzoate) is described. Its performance as a single molecule magnet was explored. The study of magnetic properties reveals that Co-MOF shows no frequency-fdependant alternating current (ac) signals under zero direct current (dc) magnetic field, whereas single-molecule magnet behaviour is achieved when Co^II ions are diluted in a Zn^II based matrix. Interestingly, this strategy renders a bifunctional [Co_xZn_1-xL]_n material that is also characterized by a strong photoluminescent emitting capacity.

Inelastic Neutron Scattering Measurement of the Ground State Tunneling Gap in Tb and Ho Analogues of a Dy Field-Induced Single-Molecule Magnet

Recent advances in single-molecule magnet (SMM) research have placed great value on interpretation of inelastic neutron scattering (INS) data for rare earth (RE)-containing SMMs. Here, we present the synthesis of several rare earth complexes where combined magnetic and INS studies have been performed, supported by ab initio calculations. The reaction of rare earth nitrate salts with 2,2'-bipyridine (2,2'-bpy) and tetrahalocatecholate (X₄Cat^2-, X = Br, Cl) ligands in methanol (MeOH) afforded two new families of compounds [RE(2,2'-bpy)₂(X₄Cat)(X₄CatH)(MeOH)] (X = Br and RE = Y, Eu, Gd, Tb, Dy, Ho, Yb for 1-RE; X = Cl and RE = Y, Tb, Dy, Ho, and Yb for 2-RE). Addition of triethylamine (Et₃N) to the reaction mixture delivered Et₃NH[RE(2,2'-bpy)₂(Br₄Cat)₂] (3-RE, RE = Er and Yb). Interestingly, cerium behaves differently to the rest of the series, generating (2,2'-bpyH)₂[Ce(Br₄Cat)₃(2,2'-bpy)] (4-Ce) with tetravalent Ce(IV) in contrast to the trivalent metal ions in 1-3. The static magnetic properties of 1-RE (RE = Gd, Tb, Dy and Ho) were investigated in conjunction with INS measurements on 1-Y, 1-Tb, and 1-Ho to probe their ground state properties and any crystal field excitations. To facilitate interpretation of the INS spectra and provide insight into the magnetic behavior, ab initio calculations were performed using the single-crystal X-ray diffraction structural data of 1-RE (RE = Tb, Dy and Ho). The ab initio calculations indicate ground doublets dominated by the maximal angular momentum projection states of Kramers type for 1-Dy and Ising type for 1-Tb and 1-Ho. Dynamic magnetic susceptibility measurements indicate that 1-Dy exhibits slow magnetic relaxation in the presence of a small applied magnetic field mainly through Raman pathways. Inelastic neutron scattering spectra exhibit distinct transitions corresponding to crystal field-induced tunneling gaps between the pseudo-doublet ground state components for 1-Tb and 1-Ho, which is one of the first direct experimental measurements with INS of such tunneling transitions in a molecular nanomagnet. The power of high-resolution INS is demonstrated with evidence of two distinct tunneling gaps measurable for the two crystallographically unique Tb coordination environments observed in the single crystal X-ray structure.

Theoretical Investigation of Single-Molecule-Magnet Behavior in Mononuclear Dysprosium and Californium Complexes

Early-actinide-based (U, Np, and Pu) single-molecule magnets (SMMs) have yet to show magnetic properties similar to those of highly anisotropic lanthanide-based ones. However, there are not many studies exploring the late-actinides (more than half-filled f shells) as potential candidates for SMM applications. We computationally explored the electronic structure and magnetic properties of a hypothetical Cf(III) complex isostructural to the experimentally synthesized Dy(dbm)₃(bpy) complex (bpy = 2,2'-bipyridine; dbm = dibenzoylmethanoate) via multireference methods and compared them to those of the Dy(III) analogue. This study shows that the Cf(III) complex can behave as a SMM and has a greater magnetic susceptibility compared to other experimentally and computationally studied early-actinide-based (U, Np, and Pu) magnetic complexes. However, Cf spontaneously undergoes α-decay and converts to Cm. Thus, we also explored the isostructural Cm(III)-based complex. The computed magnetic susceptibility and g-tensor values show that the Cm(III) complex has poor SMM behavior in comparison to both the Dy(III) and Cf(III) complexes, suggesting that the performance of Cf(III)-based magnets may be affected by α-decay and can explain the poor performance of experimentally studied Cf(III)-based molecular magnets in the literature. Further, this study suggests that the ligand field is dominant in Cf(III), which helps to increase the magnetization blocking barrier by nearly 3 times that of its 4f congener.

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

Substituted dysprosocenium complexes of the type [Dy(Cp^R)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 U_eff = 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 U_eff 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.

Analytic Linear Vibronic Coupling Method for First-Principles Spin-Dynamics Calculations in Single-Molecule Magnets

Accurate modeling of vibronically driven magnetic relaxation from ab initio calculations is of paramount importance to the design of next-generation single-molecule magnets (SMMs). Previous theoretical studies have been relying on numerical differentiation to obtain spin-phonon couplings in the form of derivatives of spin Hamiltonian parameters. In this work, we introduce a novel approach to obtain these derivatives fully analytically by combining the linear vibronic coupling (LVC) approach with analytic complete active space self-consistent field derivatives and nonadiabatic couplings computed at the equilibrium geometry with a single electronic structure calculation. We apply our analytic approach to the computation of Orbach and Raman relaxation rates for a bis-cyclobutadienyl Dy(III) sandwich complex in the frozen-solution phase, where the solution environment is modeled by electrostatic multipole expansions, and benchmark our findings against results obtained using conventional numerical derivatives and a fully electronic description of the whole system. We demonstrate that our LVC approach exhibits high accuracy over a wide range of coupling strengths and enables significant computational savings due to its analytic, "single-shot" nature. Evidently, this offers great potential for advancing the simulation of a wide range of vibronic coupling phenomena in magnetism and spectroscopy, ultimately aiding the design of high-performance SMMs. Considering different environmental representations, we find that a point charge model shows the best agreement with the reference calculation, including the full electronic environment, but note that the main source of discrepancies observed in the magnetic relaxation rates originates from the approximate equilibrium electronic structure computed using the electrostatic environment models rather than from the couplings.

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

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

Single-Molecule Magnetism in Linear Fe(I) Complexes with Aufbau and Non-Aufbau Ground States

With the ongoing efforts on synthesizing mononuclear single-ion magnets (SIMs) with promising applications in high-density data storage and spintronics devices, the linear or quasi-linear Fe(I) complexes emerge as the enticing candidates possessing large unquenched angular momentum. Herein, we have studied five experimentally synthesized linear Fe(I) complexes to uncover the origin of single-molecule magnetic behavior of these complexes. To begin with, we benchmarked the methodology on the experimentally and theoretically well-studied complex [Fe(C(SiMe₃)₃)₂]^-1 (1) (SiMe₃ = trimethylsilyl), which is characterized with a large spin-reversal barrier of 226 cm^-1. Subsequently, the spin-phonon coupling coefficients are calculated for the low-frequency vibrational modes to understand the relaxation mechanism of the complex. Furthermore, the two Fe(I) complexes, that is, [Fe(cyIDep)₂]⁺¹ (2) (cyIDep = 1,3-bis(2',6'-diethylphenyl)-4,5-(CH₂)₄-imidazole-2-ylidene) and [Fe(sIDep)₂]⁺¹ (3) (sIDep = 1,3-bis(2',6'-diethylphenyl)-imidazolin-2-ylidene), are studied that are experimentally reported with no SIM behavior under ac or dc magnetic fields; however, they exhibit large opposite axial zero field splitting (-62.4 and +34.0 cm^-1, respectively) from ab initio calculations. We have unwrapped the origin of this contrasting observation between experiment and theory by probing their magnetic relaxation pathways and the pattern of d orbital splitting. Additionally, the two experimentally synthesized Fe(I) complexes, that is, [(η⁶-C₆H₆)FeAr*-3,5-Pr₂ⁱ] (4) (Ar*-3,5-Pr₂ⁱ = C₆H-2,6-(C₆H₂-2,4,6-Pr₃ⁱ)₂-3,5-Pr₂ⁱ) and [(CAAC)₂Fe]⁺¹ (5) (CAAC = cyclic (alkyl) (amino)carbene), are investigated for SIM behavior, since there is no report on their magnetic anisotropy. To this end, complex 4 presents itself as the possible candidate for SIM.

Long story short: donor set symmetry in [Eu(DOTA)(H2O)]- crystals determines the electronic structure

Lanthanide complexes of 1,4,7,10-tetraazacyclododecane-1,4,7,10-tetraacetic acid DOTA have been studied in great detail due to their use as MRI contrast agents. Since the first report from Desreux in 1980, the Ln[DOTA]^- complexes of gadolinium(III) in particular have been thoroughly investigated. The forms of the nine-coordinated [Ln(DOTA)(H₂O)]^- complexes are well known, and the ligand backbone has been used extensively to create functional MRI contrast agents, luminescent probes, and as a model system for studying the properties of lanthanide(III) ions. In solution, the photophysical properties have been mapped, but as the structures are not known, direct structure-property relationships have not been created. Here, the electronic properties of two Eu[DOTA] compounds (1 and 2) and a Eu[DOTA]-like compound (3) were studied using single-crystal luminescence spectroscopy. The donor set in the three compounds is identical (4N 4O 1O), and using the symmetry deviation value σ_ideal it was shown that the coordination geometry is close to identical. Nevertheless, the electronic properties evaluated using the luminescence spectrum were found to differ significantly between the three compounds. The magnitude of the crystal field splitting was found not to scale with the symmetry of the coordination geometry. It was concluded that the donor set dictates the splitting, yet the structure-property relationships governing the electronic properties of europium(III) ions still elude us.

Elucidation of LMCT Excited States for Lanthanoid Complexes: A Theoretical and Solid-State Experimental Framework

Photophysical and magnetic properties arising from both ground and excited states of lanthanoid ions are relevant for numerous applications. These properties can be substantially affected, both adversely and beneficially, by ligand-to-metal charge-transfer (LMCT) states. However, probing LMCT states remains a significant challenge in f-block chemistry, particularly in the solid state. Intriguingly, the europium compounds [Eu^III(18-c-6)(X₄Cat)(NO₃)]·MeCN (18-c-6 = 18-crown-6; X = Cl (tetrachlorocatecholate, 1-Eu) or Br (tetrabromocatecholate, 2-Eu) are distinctly darkly-colored, in marked contrast to the analogues with other lanthanoid ions in the 1-Ln and 2-Ln series (Ln = La, Ce, Nd, Gd, Tb, and Dy). Herein, we report a multi-technique investigation of these compounds that has allowed elucidation of the LMCT character of the relevant absorption bands using magnetometry, absorption and emission spectroscopies, and solid-state electrochemistry. To support experimental observations, we present a semi-quantitative multireference ab initio model that (i) captures the anomalously low-lying LMCT excited state observed in the visible spectrum of 1-Eu (and its absence in the other 1-Ln analogues); (ii) elucidates the contribution of the LMCT excitation to the crystal field split ⁷F_J ground-state wave functions; and (iii) identifies the crucial role played by radial dynamical correlation of the Eu^III 4f electrons in the description of the LMCT excited state, modeled by the inclusion of 4f → 5f excitations in the optimized wave function. By providing a set of experimental and theoretical tools, this work establishes a framework for the elucidation of LMCT excited states in lanthanoid compounds in the solid state.

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

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

Ab initio non-covalent crystal field theory for lanthanide complexes: a multiconfigurational non-orthogonal group function approach

We present a multiconfigurational ab initio methodology based on non-orthogonal fragments for the calculation of crystal field energy levels and magnetic properties of lanthanide complexes, implementing a systematic description of non-covalent contributions to metal-ligand bonding. The approach consists of two steps. In the first step, appropriate ab initio wave functions for the various ionic fragments (lanthanide ions and coordinating ligands) are optimized separately, accounting for the influence of the surrounding environment within various approximations. In the second and final step, the scalar relativistic (DKH2) electrostatic Hamiltonian of the whole molecule is represented on the basis of the optimized metal-ligand multiconfigurational non-orthogonal group functions (MC-NOGFs), and reduced to an effective (2J + 1)-dimensional non-orthogonal configuration interaction (CI) problem via Löwdin-partitioning. Within the proposed formalism, the projected non-orthogonal CI Hamiltonian can be expanded to any desired order of perturbation theory in the fragment-localised excitations out of the degenerate space, and its eigenvalues and eigenfunctions provide systematic approximations to the crystal field energies and wave functions. We present here a preliminary implementation of the proposed MC-NOGF method developed for first-order degenerate perturbation theory within our own ab initio code CERES, and compare its performance both with the simpler non-covalent orthogonal ab initio approach, Fragment Ab Initio Model Potential (FAIMP) approximation, and the full CAHF/CASCI-SO method, accounting for metal-ligand covalency in a mean-field manner. We found that the energies and magnetic properties of 44 complexes obtained via an iteratively optimized version of our MC-NOGF first-order non-covalent method compare remarkably well with those obtained using the full CAHF/CASCI-SO method including metal-ligand covalency, thus exposing the predominantly electrostatic character of the metal-ligand interactions, and are superior to those obtained using the FAIMP approach, which in its iteratively optimised variant was believed to date to be the best ab initio description of non-covalent metal-ligand interactions.

Strong Relativistic Effects in Lanthanide-Based Single-Molecule Magnets

Lanthanide-based single-molecule magnets (SMMs) are promising building blocks for quantum memory and spintronic devices. Designing lanthanide-based SMMs with long spin relaxation time requires a detailed understanding of their electronic structure, including the crucial role of the spin-orbit coupling (SOC). While traditional calculations of SOC using the perturbation theory applied to a solution of the nonrelativistic Schrödinger equation are valid for light atoms, this approach is questionable for systems containing heavy elements such as lanthanides. We investigate the accuracy of the perturbation estimates of SOC by variationally solving the Dirac equation for the [DyO]+ molecule, a prototype of a lanthanide-based SMM. We show that the energy splittings between the M J states involved in spin relaxation depend on the interplay between strong SOC and dynamic electron correlation. We demonstrate that this interplay affects the resonances between the spin and vibrational transitions and, therefore, the spin relaxation time.

Combined experimental and theoretical investigation on the magnetic properties derived from the coordination of 6-methyl-2-oxonicotinate to 3d-metal ions

Five new compounds are reported herein starting from 2-hydroxy-6-methylnicotinic acid (H2h6mnic) and first-row transition metal ions, although H2h6mnic shows a prototropy in solution to lead to the 6-methyl-2-oxonicotinate (6m2onic) ligand that is the molecule eventually present in the compounds. The structural and chemical characterization reveals the following chemical formulae: {[MnNa(μ₃-6m2onic)₂(μ-6m2onic)(MeOH)]·H₂O·MeOH}_n (1Mn), {[M₂Na₂(μ₃-6m2onic)₂(μ-6m2onic)₂(μ-H₂O)(H₂O)₆](NO₃)₂}_n [M^II = Co (2Co) and Ni (3Ni)], 2[Cu₂(6m2onic)₃(μ-6m2onic)(MeOH)]·[Cu₂(6m2onic)₂(μ-6m2onic)₂]·2[Cu(6m2onic)₂(MeOH)]·32H₂O (4Cu) and {[Cu(μ-6m2onic)₂]·6H₂O}_n (5Cu) (where 6m2onic = 6-methyl-2-oxonicotinate). An unusual structural diversity is observed for the compounds, ranging from isolated complexes (in 4Cu), 1D arrays (in 1Mn and 5Cu) and 3D frameworks (in 2Co and 3Ni). Magnetic properties have been studied for all compounds. Analysis of the magnetic dc susceptibility and magnetization data for 4Cu and 5Cu suggests the occurrence of ferromagnetic exchange, which is well explained by broken-symmetry and CASSCF calculations. The sizeable easy-plane magnetic anisotropy present in compound 2Co allows for a field-induced magnet behaviour with an experimental effective energy barrier of 16.2 cm^-1, although the slow relaxation seems to be best described through Raman and direct processes in agreement with the results of ab initio calculations.

Dipolar and Contact Paramagnetic NMR Chemical Shifts in AnIV Complexes with Dipicolinic Acid Derivatives

Actinide +IV complexes (An^IV = Th^IV, U^IV, Np^IV, and Pu^IV) with two dipicolinic acid derivatives (DPA and Et-DPA) have been studied by ¹H and ¹³C NMR spectroscopies and first-principles calculations. The Fermi contact and dipolar contributions to the actinide-induced shifts (AIS) are evaluated from a temperature dependence analysis, combined with ab initio results. It allows an experimental estimation of the axial anisotropy of the magnetic susceptibility Δχ_ax and of the hyperfine coupling constants of the NMR-active nuclei. Due to the compactness of the coordination sphere, the magnetic anisotropy of the paramagnetic center is small, and this makes the contact contribution to be the dominant one, even on the remote atoms. The sign of the hyperfine coupling constants and related spin densities is alternating on the nuclei of the ligand cycle, denoting a preponderant spin polarization mechanism. This is well reproduced by unrestricted density functional theory (DFT) calculations. Those values are furthermore slightly decreasing in the actinide series, which indicates a small decrease of the covalency from U^IV to Pu^IV.

We are never ever getting (back to) ideal symmetry: structure and luminescence in a ten-coordinated europium(III) sulfate crystal

Our theoretical treatment of electronic structures in coordination complexes often rests on assumptions of symmetry. Experiments rarely provide fully symmetric systems to study. In solutions, fluctuations in solvation, variations in conformations, and even changes in constitution occur and complicate the picture. In crystals, lattice distortion, energy transfer, and phonon quenching play a role, but we are able to identify distinct symmetries. Yet the question remains: How is the real symmetry in a crystal compared to ideal symmetries?

Development of Nd (III)-Based Terahertz Absorbers Revealing Temperature Dependent Near-Infrared Luminescence

Molecular vibrations in the solid-state, detectable in the terahertz (THz) region, are the subject of research to further develop THz technologies. To observe such vibrations in terahertz time-domain spectroscopy (THz-TDS) and low-frequency (LF) Raman spectroscopy, two supramolecular assemblies with the formula [Nd^III (phen)₃ (NCX)₃] 0.3EtOH (X = S, 1-S; Se, 1-Se) were designed and prepared. Both compounds show several THz-TDS and LF-Raman peaks in the sub-THz range, with the lowest frequencies of 0.65 and 0.59 THz for 1-S and 1-Se, and 0.75 and 0.61 THz for 1-S and 1-Se, respectively. The peak redshift was observed due to the substitution of SCN⁻ by SeCN⁻. Additionally, temperature-dependent TDS-THz studies showed a thermal blueshift phenomenon, as the peak position shifted to 0.68 THz for 1-S and 0.62 THz for 1-Se at 10 K. Based on ab initio calculations, sub-THz vibrations were ascribed to the swaying of the three thiocyanate/selenocyanate. Moreover, both samples exhibited near-infrared (NIR) emission from Nd (III), and very good thermometric properties in the 300–150 K range, comparable to neodymium (III) oxide-based thermometers and higher than previously reported complexes. Moreover, the temperature dependence of fluorescence and THz spectroscopy analysis showed that the reduction in anharmonic thermal vibrations leads to a significant increase in the intensity and a reduction in the width of the emission and LF absorption peaks. These studies provide the basis for developing new routes to adjust the LF vibrational absorption.

The coexistence of long τQTM and high Ueff as a concise criterion for a good single-molecule magnet: a theoretical case study of square antiprism dysprosium single-ion magnets

A systematic theoretical study is performed on a group of 16 square antiprism dysprosium single-ion magnets. Based on ab initio calculations, the quantum tunneling of magnetization (QTM) time, i.e., τ_QTM, and effective barrier of magnetic reversal, U_eff, are theoretically predicted. The theoretical τ_QTM is able to identify the ones with the longest QTM time with small numerical deviations. Similar results occur with respect to U_eff too. The systems possessing the best single-molecule magnet (SMM) properties here are just the ones having both the longest τ_QTM and the highest U_eff, from either experiment or theory. Thus, our results suggest the coexistence of long τ_QTM and high U_eff to be a criterion for high-performance SMMs. Although having its own limits, this criterion is easy to be applied in a large number of systems since both τ_QTM and U_eff could be predicted by theory with satisfactory efficiency and reliability. Therefore, this concise criterion could provide screened candidates for high-performance SMMs quickly and, hence, ease the burden of further exploration aiming for a higher degree of precision. This screening is important since the further exploration could easily demand tens or even hundreds of ab initio calculations for a single SMM. A semi-quantitative crystal field (CF) analysis is performed and shown here to be capable of indicating the general trends in a more chemically intuitive way. This analysis could help to identify the most important coordinating atoms for both diagonal and non-diagonal CF components. Thus, it could give some direct clues for improving the SMM properties: reducing the distance of the axial atom to the central ion, rotating the axial atom closer to the easy axis or increasing the amount of its negative charge. Correspondingly, opposite operations on the equatorial atom could give the same result.

Dominance of Cyclobutadienyl Over Cyclopentadienyl in the Crystal Field Splitting in Dysprosium Single-Molecule Magnets

Replacing a monoanionic cyclopentadienyl (Cp) ligand in dysprosium single‐molecule magnets (SMMs) with a dianionic cyclobutadienyl (Cb) ligand in the sandwich complexes [(η⁴‐Cb′′′′)Dy(η⁵‐C₅Me₄^tBu)(BH₄)]⁻ (1), [(η⁴‐Cb′′′′)Dy(η⁸‐Pn^†)K(THF)] (2) and [(η⁴‐Cb′′′′)Dy(η⁸‐Pn^†)]⁻ (3) leads to larger energy barriers to magnetization reversal (Cb′′′′=C₄(SiMe₃)₄, Pn^†=1,4‐di(tri‐isopropylsilyl)pentalenyl). Short distances to the Cb′′′′ ligands and longer distances to the Cp ligands in 1–3 are consistent with the crystal field splitting being dominated by the former. Theoretical analysis shows that the magnetic axes in the ground Kramers doublets of 1–3 are oriented towards the Cb′′′′ ligands. The theoretical axiality parameter and the relative axiality parameter Z and Z_rel are introduced to facilitate comparisons of the SMM performance of 1–3 with a benchmark SMM. Increases in Z and Z_rel when Cb′′′ replaces Cp signposts a route to SMMs with properties that could surpass leading systems.

Mechanisms of Luminescence in Lanthanide Complexes: A Crucial Role of Metal-Ligand Covalency

A current understanding of the luminescence of lanthanide complexes is based on the phenomenological Judd-Ofelt (JO) theory. However, the mechanisms of electric-dipole transitions lying at its basis were never subjected to a rigorous analysis. Here, we investigate the contributions to the electric-dipole transitions in the Er^{3+ 4}S_3/2 → ⁴I_15/2 band of an erbium trensal complex using state-of-the-art ab initio calculations. We find that the conventional JO mechanism based on the electrostatic crystal field yields only a quarter of the integral intensity of this band. Accordingly, three quarters of it is contributed by covalent binding of erbium and ligand orbitals via three major mechanisms, the 4f ligand and ligand-ligand electric-dipole transitions and covalent enhancement of the hybridization of 4f and even empty orbitals of erbium. We expect that these findings will inspire the design of efficient rare-earth luminescent materials.

Discovery of a Dysprosium Metallocene Single-Molecule Magnet with Two High-Temperature Orbach Processes

Magnetic bistability in single-molecule magnets (SMMs) is a potential basis for new types of nanoscale information storage material. The standard model for thermally activated relaxation of the magnetization in SMMs is based on the occurrence of a single Orbach process. Here, we show that incorporating a phosphorus atom into the framework of the dysprosium metallocene [(Cp^iPr5)Dy(Cp^PEt4)]⁺[B(C₆F₅)₄]⁻ (Cp^iPr5 is penta-isopropylcyclopentadienyl, Cp^PEt4 is tetraethylphospholyl) leads to the occurrence of two distinct high-temperature Orbach processes, with energy barriers of 1410(10) and 747(7) cm^–1, respectively. These barriers provide experimental evidence for two different spin–phonon coupling regimes, which we explain with the aid of ab initio calculations. The strong and highly axial crystal field in this SMM also allows magnetic hysteresis to be observed up to 70 K, using a scan rate of 25 Oe s^–1. In characterizing this SMM, we show that a conventional Debye model and consideration of rotational contributions to the spin–phonon interaction are insufficient to explain the observed phenomena.

A phospholyl-ligated dysprosium metallocene single-molecule magnet shows two high-temperature Orbach relaxation processes with effective energy barriers of 1410(10) and 747(7) cm⁻¹, and magnetic hysteresis up to 70 K when using a scan rate of 25 Oe s⁻¹.