A Complete Ab Initio View of Orbach and Raman Spin-Lattice Relaxation in a Dysprosium Coordination Compound

Stable organic radical qubits and their applications in quantum information science

The past century has witnessed the flourishing of organic radical chemistry. Stable organic radicals are highly valuable for quantum technologies thanks to their inherent room temperature quantum coherence, atomic-level designability, and fine tunability. In this comprehensive review, we highlight the potential of stable organic radicals as high-temperature qubits and explore their applications in quantum information science, which remain largely underexplored. Firstly, we summarize known spin dynamic properties of stable organic radicals and examine factors that influence their electron spin relaxation and decoherence times. This examination reveals their design principles and optimal operating conditions. We further discuss their integration in solid-state materials and surface structures, and present their state-of-the-art applications in quantum computing, quantum memory, and quantum sensing. Finally, we analyze the primary challenges associated with stable organic radical qubits and provide tentative insights to future research directions.

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

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

Magnetic behaviour of a spin-canted asymmetric lanthanide quinolate trimer

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

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

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

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

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

Record Quantum Tunneling Time in an Air-Stable Exchange-Bias Dysprosium Macrocycle

In recent years, dysprosium macrocycle single-molecule magnets (SMMs) have received increasing attention due to their excellent air/thermal stability, strong magnetic anisotropy, and rigid molecular skeleton. However, they usually display fast zero-field quantum tunneling of the magnetization (QTM) rate, severely hindering their data storage applications. Herein, we report the design, synthesis, and characterization of an air-stable monodecker didysprosium macrocycle integrating strong single-ion anisotropy, near-perfect local crystal field (CF) symmetry, and efficient exchange bias. These indispensable features enable clear-cut elucidation of the crucial role of very weak antiferromagnetic coupling on magnetization dynamics, creating a prominent SMM with a large effective energy barrier (Ueff) of 670 cm-1, open hysteresis loops at zero field up to 14.9 K, and a record relaxation time of QTM (τQTM), 24281 s, for all known nonradical-bridged lanthanide SMMs.

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

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

Tuning spin dynamics of binuclear Dy complexes using different nitroxide biradical derivatives

By employing nitronyl/imino nitroxide biradicals, three Ln-Zn complexes, namely, [Ln2Zn2(hfac)10(ImPhPyobis)2] (LnIII = Gd 1, Dy 2; hfac = hexafluoroacetylacetonate; ImPhPyobis = 5-(4-oxypyridinium-1-yl)-1,3-bis(1'-oxyl-4',4',5',5'-tetramethyl-4,5-hydro-1H-imidazol-2-yl)benzene) and [Dy2Zn2(hfac)10(NITPhPyobis)2] 3 (NITPhPyobis = 5-(4-oxypyridinium-1-yl)-1,3-bis(1'-oxyl-3'-oxido-4',4',5',5'-tetramethyl-4,5-hydro-1H-imidazol-2-yl)benzene), have been successfully prepared. The three complexes possess {Ln2O2} cores bridged by the oxygen atoms of the 4-oxypyridinium rings of the biradical ligands and one of the imino/nitronyl nitroxide groups of the biradical is coordinated to a ZnII ion, then producing a centrosymmetric tetranuclear six-spin structure. The studies of spin dynamics indicate that complexes 2 and 3 exhibit distinct magnetic relaxation behaviors at zero dc field: complex 2 presents single relaxation with an effective energy barrier (Ueff) of 69.8 K, while complex 3 exhibits double relaxation processes with Ueff values for the fast and slow relaxation being 15.8 K and 50.9 K, respectively. The observed different magnetic relaxation behaviors for the two Dy complexes could be mainly ascribed to the influence of the distinct nitroxide biradical derivatives.

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

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

A novel non-adiabatic spin relaxation mechanism in molecular qubits

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

Confining single Er3+ ions in sub-3 nm NaYF4 nanoparticles to induce slow relaxation of the magnetisation

Molecular systems known as single-molecule magnets (SMMs) exhibit magnet-like behaviour of slow relaxation of the magnetisation and magnetic hysteresis and have potential application in high-density memory storage or quantum computing. Often, their intrinsic magnetic properties are plagued by low-energy molecular vibrations that lead to phonon-induced relaxation processes, however, there is no straightforward synthetic approach for molecular systems that would lead to a small amount of low-energy vibrations and low phonon density of states at the spin-resonance energies. In this work, we apply knowledge accumulated over the last decade in molecular magnetism to nanoparticles, incorporating Er3+ ions in an ultrasmall sub-3 nm diamagnetic NaYF4 nanoparticle (NP) and probing the slow relaxation dynamics intrinsic to the Er3+ ion. Furthermore, by increasing the doping concentration, we also investigate the role of intraparticle interactions within the NP. The knowledge gained from this study is anticipated to enable better design of magnetically high-performance molecular and bulk magnets for a wide variety of applications, such as molecular electronics.

Unique Double and Triple Decker Arrangements of Rare-Earth 9,10-Diborataanthracene Complexes Featuring Single-Molecule Magnet Characteristics

Herein, we present the first report on the synthesis of rare-earth complexes featuring a 9,10-diborataanthracene ligand. This 14-π-electron ligand is highly reductive and was previously used in small-molecule activation. Salt elimination reactions between dipotassium 9,10-diethyl-9,10-diborataanthracene [K2(DEDBA)] and [LnIII(η8-CotTIPS)(BH4)(thf)x] (CotTIPS=1,4-(iPr3Si)2C8H6) in a 1 : 1 ratio yielded heteroleptic sandwich complexes [K(η8-CotTIPS)LnIII(η6-DEDBA)] (Ln=Y, Dy, Er). These compounds form Lewis-base-free one-dimensional coordination polymers when crystallised from toluene. In contrast, reaction of [K2(DEDBA)] and [LnIII(η8-CotTIPS)(BH4)(thf)x] in a 1 : 2 ratio led to the formation of heteroleptic triple-decker complexes [(η8-CotTIPS)LnIII(μ-η6:η6-DEDBA)LnIII(η8-CotTIPS)] (Ln=Y, Dy, Er). Notably, these are not only the first lanthanide triple-decker compounds featuring a six-membered ring as a deck but also the first trivalent lanthanide triple-decker featuring a heterocycle in the coordination sphere. Magnetic investigations reveal that [K(η8-CotTIPS)LnIII(η6-DEDBA)] (Ln=Dy, Er) and [(η8-CotTIPS)ErIII(μ-η6:η6-DEDBA)ErIII(η8-CotTIPS)] exhibit Single-Molecule Magnet (SMM) behaviour. In the case of [(η8-CotTIPS)LnIII(μ-η6:η6-DEDBA)LnIII(η8-CotTIPS)] (Ln=Dy, Er), the introduction of a second near lanthanide ion results in strong antiferromagnetic interactions, allowing the enhancement of the magnetic characteristic of the system, compared to the quasi isolated counterpart. This research renews the overlooked coordination chemistry of the DBA ligand and expands it to encompass rare-earth elements.

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.

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

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

Molecular nanomagnets: a viable path toward quantum information processing?

Molecular nanomagnets (MNMs), molecules containing interacting spins, have been a playground for quantum mechanics. They are characterized by many accessible low-energy levels that can be exploited to store and process quantum information. This naturally opens the possibility of using them as qudits, thus enlarging the tools of quantum logic with respect to qubit-based architectures. These additional degrees of freedom recently prompted the proposal for encoding qubits with embedded quantum error correction (QEC) in single molecules. QEC is the holy grail of quantum computing and this qudit approach could circumvent the large overhead of physical qubits typical of standard multi-qubit codes. Another important strength of the molecular approach is the extremely high degree of control achieved in preparing complex supramolecular structures where individual qudits are linked preserving their individual properties and coherence. This is particularly relevant for building quantum simulators, controllable systems able to mimic the dynamics of other quantum objects. The use of MNMs for quantum information processing is a rapidly evolving field which still requires to be fully experimentally explored. The key issues to be settled are related to scaling up the number of qudits/qubits and their individual addressing. Several promising possibilities are being intensively explored, ranging from the use of single-molecule transistors or superconducting devices to optical readout techniques. Moreover, new tools from chemistry could be also at hand, like the chiral-induced spin selectivity. In this paper, we will review the present status of this interdisciplinary research field, discuss the open challenges and envisioned solution paths which could finally unleash the very large potential of molecular spins for quantum technologies.

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

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

Photochromism and Photomagnetism in Two Ni(II) Complexes Based on a Photoactive 2,4,6-Tris-2-Pyridyl-1,3,5-Triazine Ligand

It is still challenging to construct novel photochromic and photomagnetic materials in the field of molecular materials. Herein, the 2,4,6-tris-2-pyridyl-1,3,5-triazine (TPTz) molecule was found to display photochromic properties under room temperature light irradiation. Two mononuclear structures, [Ni(H2O)(TPTz)(C2O4)]·2H2O (1; C2O42- = oxalate) [Ni(H2O)(TPTz)(C2O4)]·0.5H2O (2), and one chain compound [Ni(TPTz)(H2-HEDP)]·2H2O (3; HEDP = hydroxyethylidene diphosphonate) were obtained by assembling TPTz with polydentate O-ligands (oxalate and phosphonate) and the paramagnetic Ni2+ ions. The electron-transfer (ET)-dominated photochromism was observable in 1 and 2 after light irradiation with the photogeneration of relatively stable radicals, and the resultant photochromism was demonstrated via UV-vis, photoluminescence, X-ray photoelectron spectra, electron paramagnetic resonance spectra, and molecular orbital calculations. Due to the denser stacking interactions between the adjacent organic molecules, 2 exhibited a faster photochromic rate than 1. Compared with 1 and 2, compound 3 did not show photochromic behavior, which was deciphered by the theoretical calculations for all of the compounds. Importantly, the magnetic couplings appeared between photogenerated radicals and paramagnetic Ni2+ ions, resulting in a scarcely photomagnetic phenomenon of 1 and 2 in the Ni-based electron transfer photochromic materials. This work enriches the available kind of ligands for the design of ET photochromic materials, putting forward a method to tune the electron transfer photochromic efficiency in the molecular materials.

Vibronic effects on the quantum tunnelling of magnetisation in Kramers single-molecule magnets

Single-molecule magnets are among the most promising platforms for achieving molecular-scale data storage and processing. Their magnetisation dynamics are determined by the interplay between electronic and vibrational degrees of freedom, which can couple coherently, leading to complex vibronic dynamics. Building on an ab initio description of the electronic and vibrational Hamiltonians, we formulate a non-perturbative vibronic model of the low-energy magnetic degrees of freedom in monometallic single-molecule magnets. Describing their low-temperature magnetism in terms of magnetic polarons, we are able to quantify the vibronic contribution to the quantum tunnelling of the magnetisation, a process that is commonly assumed to be independent of spin-phonon coupling. We find that the formation of magnetic polarons lowers the tunnelling probability in both amorphous and crystalline systems by stabilising the low-lying spin states. This work, thus, shows that spin-phonon coupling subtly influences magnetic relaxation in single-molecule magnets even at extremely low temperatures where no vibrational excitations are present.

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.

Analytical nonadiabatic coupling and state-specific energy gradient for the crystal field Hamiltonian describing lanthanide single-ion magnets

Paramagnetic molecules with a metal ion as an electron spin center are promising building blocks for molecular qubits and high-density memory arrays. However, fast spin relaxation and decoherence in these molecules lead to a rapid loss of magnetization and quantum information. Nonadiabatic coupling (NAC), closely related to spin-vibrational coupling, is the main source of spin relaxation and decoherence in paramagnetic molecules at higher temperatures. Predicting these couplings using numerical differentiation requires a large number of computationally intensive ab initio or crystal field electronic structure calculations. To reduce computational cost and improve accuracy, we derive and implement analytical NAC and state-specific energy gradient for the ab initio parametrized crystal field Hamiltonian describing single-ion molecular magnets. Our implementation requires only a single crystal field calculation. In addition, the accurate NACs and state-specific energy gradients can be used to model spin relaxation using sophisticated nonadiabatic molecular dynamics, which avoids the harmonic approximation for molecular vibrations. To test our implementation, we calculate the NAC values for three lanthanide complexes. The predicted values support the relaxation mechanisms reported in previous studies.

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.

Galván I, Alavi A, Aleotti F, Aquilante F, Autschbach J, Avagliano D, Baiardi A, Bao JJ, Battaglia S, Birnoschi L, Blanco-González A, Bokarev SI, Broer R, Cacciari R, Calio PB, Carlson RK, Carvalho Couto R, Cerdán L, Chibotaru LF, Chilton NF, Church JR, Conti I, Coriani S, Cuéllar-Zuquin J, Daoud RE, Dattani N, Decleva P, de Graaf C, Delcey M, De Vico L, Dobrautz W, Dong SS, Feng R, Ferré N, Filatov(Gulak) M, Gagliardi L, Garavelli M, González L, Guan Y, Guo M, Hennefarth MR, Hermes MR, Hoyer CE, Huix-Rotllant M, Jaiswal VK, Kaiser A, Kaliakin DS, Khamesian M, King DS, Kochetov V, Krośnicki M, Kumaar AA, Larsson ED, Lehtola S, Lepetit MB, Lischka H, López Ríos P, Lundberg M, Ma D, Mai S, Marquetand P, Merritt ICD, Montorsi F, Mörchen M, Nenov A, Nguyen VHA, Nishimoto Y, Oakley MS, Olivucci M, Oppel M, Padula D, Pandharkar R, Phung QM, Plasser F, Raggi G, Rebolini E, Reiher M, Rivalta I, Roca-Sanjuán D, Romig T, Safari AA, Sánchez-Mansilla A, Sand AM, Schapiro I, Scott TR, Segarra-Martí J, Segatta F, Sergentu DC, Sharma P, Shepard R, Shu Y, Staab JK, Straatsma TP, Sørensen LK, Tenorio BNC, Truhlar DG, Ungur L, Vacher M, Veryazov V, Voß TA, Weser O, Wu D, Yang X, Yarkony D, Zhou C, Zobel JP, Lindh R. The OpenMolcas Web: A Community-Driven Approach to Advancing Computational Chemistry

The developments of the open-source OpenMolcas chemistry software environment since spring 2020 are described, with a focus on novel functionalities accessible in the stable branch of the package or via interfaces with other packages. These developments span a wide range of topics in computational chemistry and are presented in thematic sections: electronic structure theory, electronic spectroscopy simulations, analytic gradients and molecular structure optimizations, ab initio molecular dynamics, and other new features. This report offers an overview of the chemical phenomena and processes OpenMolcas can address, while showing that OpenMolcas is an attractive platform for state-of-the-art atomistic computer simulations.

Theoretical Magnetic Relaxation and Spin-Phonon Coupling Study in a Series of Molecular Engineering Designed Bridged Dysprosocenium Analogues

A detailed computational study of hypothetical sandwich dysprosium double-decker complexes, bridged by various numbers of aliphatic linkers, was performed to evaluate the effect of the structural modifications on their ground-state magnetic sublevels and assess their potential as candidates for single-molecule magnets (SMMs). The molecular structures of seven complexes were optimized using the TPSSh functional, and the electronic structure and magnetic properties were investigated using the complete active space self-consistent field method (CASSCF). Estimates of the magnetic moment blocking barrier (Ueff) and blocking temperatures (TB) are reported. In addition, a new method based on computed derivatives of effective demagnetization barriers Ueff with respect to vibrational normal modes was introduced and applied to evaluate the impact of spin-phonon coupling on the SMM properties. On the basis of the computed parameters, we have identified promising candidates with properties superior to those of the existing single-molecule magnets.

Molecular Network Approach to Anisotropic Ising Lattices: Parsing Magnetization Dynamics in Er3+ Systems with 0-3-Dimensional Spin Interactivity

We present a wide-ranging interrogation of the border between single-molecule and solid-state magnetism through a study of erbium-based Ising-type magnetic compounds with a fixed magnetic unit, using three different charge-balancing cations as the means to modulate the crystal packing environment. Properties rooted in the isolated spin Hamiltonian remain fixed, yet careful observation of the dynamics reveals the breakdown of this approximation in a number of interesting ways. First, differences in crystal packing lead to a striking 3 orders of magnitude suppression in magnetic relaxation rates, indicating a rich interplay between intermolecular interactions governed by the anisotropic Ising lattice stabilization and localized slow magnetic relaxation driven by the spin-forbidden nature of quantum tunneling of the f-electron-based magnetization. By means of diverse and rigorous physical methods, including temperature-dependent X-ray crystallography, field, temperature, and time-dependent magnetometry, and the application of a new magnetization fitting technique to quantify the magnetic susceptibility peakshape, we are able to construct a more nuanced view of the role nonzero-dimensional interactions can play in what are predominantly considered zero-dimensional magnetic materials. Specifically, we use low field susceptibility and virgin-curve analysis to isolate metamagnetic spin-flip transitions in each system with a field strength corresponding to the expected strength of the internal dipole-dipole lattice. This behavior is vital to a complete interpretation of the dynamics and is likely common for systems with such high anisotropy. This collective interactivity opens a new realm of possibility for molecular magnetic materials, where their unprecedented localized anisotropy is the determining factor in building higher dimensionality.

Peripheral site modification in a family of dinuclear [Dy2(hynad)2-6(NO3)0-6(sol)0-2]0/2- single-molecule magnets bearing a {Dy2(μ-OR)2}4+ diamond-shaped core and exhibiting dissimilar magnetic dynamics

The first use of the organic chelate N-hydroxy-1,8-naphthalimide (hynadH) in DyIII chemistry has unveiled access to a synthetic 'playground' composed of four new dinuclear complexes, all of which possess the same planar {Dy2(μ-OR)2}4+ diamond-shaped core, resulting from the bridging and chelating capacity of the hynad- groups. The structural stability of the central {Dy2} core has allowed for the modulation of the peripheral coordination sites of the metal ions, and specifically the NO3-/hynad- ratio of capping groups, thus affording the compounds [Dy2(hynad)2(NO3)4(DMF)2] (1), (Me4N)2[Dy2(hynad)2(NO3)6] (2), [Dy2(hynad)4(NO3)2(H2O)2] (3), and [Dy2(hynad)6(H2O)2] (4). Because of the chemical and structural modifications in the series 1-4, the DyIII coordination polyhedra are also dissimilar, comprising the muffin (1 and 3), tetradecahedral (2), and spherical tricapped trigonal prismatic (4) geometries. Complexes 1, 2, and 4 exhibit a ferromagnetic response at low temperatures, while 3 is antiferromagnetically coupled. All compounds exhibit out-of-phase (χ''M) ac signals as a function of ac frequency and temperature, thus behaving as single-molecule magnets (SMMs), in the absence or presence of applied dc fields. Interestingly, the hynad--rich and nitrato-free complex 4, demonstrates the largest energy barrier (Ueff = 69.62(1) K) for the magnetization reversal which is attributed to the presence of the two axial triangular faces of the spherical tricapped trigonal prism by the negatively charged O-atoms of the hynad- ligands.

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.

Single-Molecule Magnet Properties in 3d4f Heterobimetallic Iron and Dysprosium Complexes Involving Hydrazone Ligand

The reaction between the ((E)-N'-(2-hydroxy-3-methoxybenzylidene)pyrazine-2-carbohydrazide) (H2opch) ligand and the metallo-precursor [Dy(hfac)3]·2H2O led to the formation of an homometallic coordination complex with the formula [Dy2(hfac)3(H2O)(Hopch)2][Dy(hfac)4] (1). In presence of both [Dy(hfac)3] 2H2O and the Fe(II) salt, the heterobimetallic tetranuclear [FeDy3(hfac)8(H2O)2(opch)2] (2) was isolated, while the addition of the co-ligand 1,2-Bis(2-hydroxy-3-methoxybenzylidene) hydrazine (H2bmh) led to the formation of two heterobimetallic tetranuclear complexes with the formula [Fe3Dy(hfac)6(opch)2(H2bmh)] C6H14 (3) C6H14 and [Fe2Dy2(hfac)7(opch)2(H2bmh)] 0.5C7H16 (4) 0.5C7H16. Single crystal X-ray diffraction and dc magnetic investigation demonstrated that 3 and 4 involved the iron center in the +II and +III oxidation states. Dynamic magnetic measurements highlighted the single-molecule magnet behavior of 1 and 2 in a zero applied dc field primarily due to the ferromagnetic interactions taking place in these compounds.

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

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

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.

Desolvation-Induced Highly Symmetrical Terbium(III) Single-Molecule Magnet Exhibiting Luminescent Self-Monitoring of Temperature

A conjunction of Single-Molecule Magnet (SMM) behavior and luminescence thermometry is an emerging research line aiming at contactless read-out of temperature in future SMM-based devices. The shared working range between slow magnetic relaxation and the thermometric response is typically narrow or absent. We report TbIII -based emissive SMMs formed in a cyanido-bridged framework whose properties are governed by the reversible structural transformation from [TbIII (H2 O)2 ][CoIII (CN)6 ] ⋅ 2.7H2 O (1) to its dehydrated phase, TbIII [CoIII (CN)6 ] (2). The 8-coordinated complexes in 1 show the moderate SMM effect but it is enhanced for trigonal-prismatic TbIII complexes in 2, showing the SMM features up to 42 K. They are governed by the combination of QTM, Raman, and Orbach relaxation with the energy barrier of 594(18) cm-1 (854(26) K), one of the highest among the TbIII -based molecular nanomagnets. Both systems exhibit emission related to the f-f electronic transitions, with the temperature variations resulting in the optical thermometry below 100 K. The dehydration leads to a wide temperature overlap between the SMM behavior and thermometry, from 6 K to 42 K. These functionalities are further enriched after the magnetic dilution. The role of post-synthetic formation of high-symmetry TbIII complexes in achieving the SMM effect and hot-bands-based optical thermometry is discussed.

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.

A Combined Synthetic, Magnetic, and Theoretical Study on Enhancing Ligand-Field Axiality for Dy(III) Single-Molecule Magnets Supported by Ferrocene Diamide Ligands

Molecular design is crucial for improving the performance of single-molecule magnets (SMMs). For dysprosium(III) SMMs, enhancing ligand-field axiality is a well-suited strategy to achieve high-performance SMMs. We synthesized a series of dysprosium(III) complexes, (NN^TIPS)DyBr(THF)₂ (1, NN^TIPS = fc(NSiⁱPr₃)₂; fc = 1,1'-ferrocenediyl, THF = tetrahydrofuran), [(NN^TIPS)Dy(THF)₃][BPh₄] (2), (NN^TIPS)DyI(THF)₂ (3), and [(NN^TBS)Dy(THF)₃][BPh₄] (4, NN^TBS = fc(NSi^tBuMe₂)₂), supported by ferrocene diamide ligands. X-ray crystallography shows that the rigid ferrocene backbone enforces a nearly axial ligand field with weakly coordinating equatorial ligands. Dysprosium(III) complexes 1-4 all exhibit slow magnetic relaxation under zero fields and possess high effective barriers (U_eff) around 1000 K, comparable to previously reported (NN^TBS)DyI(THF)₂ (5). We probed the influences of structural variations on SMM behaviors by theoretical calculations and found that the distribution of negative charges defined by r_q, i.e., the ratio of the charges on the axial ligands to the charges on the equatorial ligands, plays a decisive role. Moreover, theoretical calculations on a series of model complexes 1'-5' without equatorial ligands unveil that the axial crystal-field parameters B₂⁰ are directly proportional to the N-Dy-N angles and support the hypothesis that enhancing the ligand-field axiality could improve SMM performance.

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

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

Magnetic and optical studies of a new family of multidimensional and multiproperty PO-lanthanide(III) derived systems

A new family of lanthanide compounds has been synthesized using 1,2-bis(diphenylphosphino)ethane dioxide (dppeO₂) as an O-donor ligand through the phosphoryl group to lanthanide(III) cations and structurally, magnetically and optically studied. Depending on the lanthanide, two different topologies appear: the two-dimensional structure [Ln^III(dppeO₂)_1.5(NO₃)₃(H₂O)_0.5]_n (Ln = Ce (1), Sm (2) and Dy (6)) and the one-dimensional structure [Ln(dppeO₂)(NO₃)₃DMF]_n (Ln = Eu (3), Gd (4) and Tb (5)). Some of the Ln-derived complexes have been used as structural probes, while others have been synthesized to use the specific characteristics of each cation to take advantage of their magnetic/luminescence properties. Complex 6 presents slow relaxation of the magnetization while 2, 3 and 5 present emitting properties in the visible range.

Photocontrollable Magnetism and Photoluminescence in a Binuclear Dysprosium Anthracene Complex

By incorporating photoreactive anthracene moieties into binuclear Dy₂O₂ motifs, we obtain two new compounds with the formulas [Dy₂(SCN)₄(L)₂(dmpma)₄] (1) and [Dy₂(SCN)₄(L)₂(dmpma)₂(CH₃CN)₂] (2), where HL is 4-methyl-2,6-dimethoxyphenol and dmpma is dimethylphosphonomethylanthracene. Compound 1 contains face-to-face π-π interacted anthracene groups that meet the Schmidt rule for a [4 + 4] photocycloaddition reaction, while stacking of the anthracene groups in compound 2 does not meet the Schmidt rule. Compound 1 undergoes a reversible single-crystal-to-single-crystal structural transformation upon UV-light irradiation and thermal annealing, forming a one-dimensional coordination polymer of [Dy₂(SCN)₄(L)₂(dmpma)₂(dmpma₂)]_n (1UV). The process is concomitant with changes in the magnetic dynamics and photoluminescent properties. The spin-reversal energy barrier is significantly increased from 1 (55.9 K) to 1UV (116 K), and the emission color is changed from bright yellow for 1 to weak blue for 1UV. This is the first binuclear lanthanide complex that exhibits synergistic photocontrollable magnetic dynamics and photoluminescence. Ab initio calculations are conducted to understand the magnetostructural relationships of compounds 1, 1UV, and 2.

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

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

Luminescence, CPL and magnetic properties of 1D enantiopure Ln3+ complexes with (S-) and (R-) α-methoxyphenylacetate ligand

The reaction of Ln(NO₃)₂·6H₂O (Ln = Eu, Tb, Dy and Sm) with (R)-(-)-α-methoxyphenylacetic acid (R-HMPA) and 1,10-phenanthroline (phen) in EtOH/H₂O allows the isolation of 1D chiral compounds of formula [Ln(μ-R-MPA)(R-MPA)₂(phen)]_n in which Ln = Eu (R-Eu), Tb (R-Tb), Dy (R-Dy) and Sm (R-Sm). The same synthesis by using (S)-(+)-α-methoxyphenylacetic acid (S-HMPA) instead of (R)-(-)-α-methoxyphenylacetic acid allows the isolation of the enantiomeric compounds with formula [Ln(μ-S-MPA)(S-MPA)₂(phen)]_n where Ln = Eu (S-Eu), Tb (S-Tb), Dy (S-Dy) and Sm (S-Sm). Single crystal X-Ray diffraction measurements were performed for compounds R/S-Eu, R/S-Tb, S-Dy and S-Sm. The luminescence and the circular dichroism measured in the solid state are reported. All compounds show sensitized luminescence, notably the Eu³⁺ and Tb³⁺ ones, whose emission color can be perceived by the naked eye. For the Eu³⁺ and Tb³⁺ derivatives the quantum yield and the circular polarized luminescence have been measured. For the magnetic allowed transition ⁵D₀ → ⁷F₁ of the Eu³⁺ compound, the anisotropy factor g_lum is ±0.013 (+for S-Eu). Also, magnetic properties of all compounds were studied with the Dy³⁺ analogue showing slow relaxation of the magnetization under a direct current magnetic field of 1000 Oe.

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

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

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.

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

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

Data-driven design of molecular nanomagnets

Three decades of research in molecular nanomagnets have raised their magnetic memories from liquid helium to liquid nitrogen temperature thanks to a wise choice of the magnetic ion and coordination environment. Still, serendipity and chemical intuition played a main role. In order to establish a powerful framework for statistically driven chemical design, here we collected chemical and physical data for lanthanide-based nanomagnets, catalogued over 1400 published experiments, developed an interactive dashboard (SIMDAVIS) to visualise the dataset, and applied inferential statistical analysis. Our analysis shows that the Arrhenius energy barrier correlates unexpectedly well with the magnetic memory. Furthermore, as both Orbach and Raman processes can be affected by vibronic coupling, chemical design of the coordination scheme may be used to reduce the relaxation rates. Indeed, only bis-phthalocyaninato sandwiches and metallocenes, with rigid ligands, consistently present magnetic memory up to high temperature. Analysing magnetostructural correlations, we offer promising strategies for improvement, in particular for the preparation of pentagonal bipyramids, where even softer complexes are protected against molecular vibrations.

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.

Lanthanide single-molecule magnets with high anisotropy barrier: where to from here?

High-temperature lanthanide single-molecule magnets with large coercive fields are being pursued.

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.

Understanding the effect of structural changes on slow magnetic relaxation in mononuclear octahedral copper(II) complexes

Current advances in molecular magnetism are aimed at the construction of molecular nanomagnets and spin qubits for their utilization as high-density data storage materials and quantum computers. Mononuclear coordination compounds with low spin values of S = ½ are excellent candidates for this endeavour, but knowledge of their construction via rational design is limited. This particularly applies to the single copper(II) spin center, having been only recently demonstrated to exhibit slow relaxation of magnetisation in the appropriate octahedral environment. We have thus prepared a unique organic scaffold that would allow one to gain in-depth insight into how purposeful structural differences affect the slow magnetic relaxation in monometallic, transition metal complexes. As a proof-of-principle, we demonstrate how one can construct two, structurally very similar complexes with isolated Cu(II) ions in an octahedral ligand environment, the magnetic properties of which differ significantly. The differences in structural symmetry effects and in magnetic relaxation are corroborated with a series of experimental techniques and theoretical approaches, showing how symmetry distortions and crystal packing affect the relaxation behaviour in these isolated Cu(II) systems. Our unique organic platform can be efficiently utilized for the construction of various transition-metal ion systems in the future, effectively providing a model system for investigation of magnetic relaxation via targeted structural distortions.