A 9.2-GHz clock transition in a Lu(II) molecular spin qubit arising from a 3,467-MHz hyperfine interaction

Impact of Zeeman and hyperfine interactions on the magnetic properties of paramagnetic metal Ions: I. Local interactions of the electron spin

The anisotropic Zeeman interaction of an ion, and the strong hyperfine interaction with its own nucleus, can significantly influence its interactions with the local environment. These effects, including the reduction of the effective magnetic moment of the electron spin and the phase memory decay rate, are studied theoretically. Analytical expressions describing the mean magnetic moment of the electron spin are obtained. The results of the theoretical analysis and accompanying numerical computations show that the strong hyperfine interaction of the ion reduces its effective magnetic moment. In particular, a 7% reduction is found for the scandium endofullerene Sc2@C80(CH2Ph) under conditions typical of an X-band EPR experiment.

Impact of Zeeman and hyperfine interactions on the magnetic properties of paramagnetic metal ions: II. Super-hyperfine interactions with surrounding nuclei

The anisotropic Zeeman and strong hyperfine interactions of a Kramers ion can significantly affect its magnetic properties as well as the interactions with the nearby nuclei. The interactions with the local environment are described in the preceding article. In the current work, the change of the spin states of distant nuclei is studied. Analytical expressions describing the depth of the electron spin echo envelope modulation (ESEEM) are obtained for the ions with anisotropic Zeeman and strong hyperfine interactions. Due to the g-tensor anisotropy, the electron Zeeman interaction axis is tilted in respect to the direction of the external magnetic field which makes non-collinear with the Zeeman interaction axes of the ion and the nearby nuclei and significantly modifies the nuclear spin states. Thus, the isotropic hyperfine interaction, and particularly the Fermi contact interaction can directly contribute to the ESEEM. An additional factor, that can significantly modify the ESEEM signal is the mixing of the multiple oscillations arising when several nuclei occur in optimal conditions for the generation of the nuclear coherence. This situation arises when several EPR transitions of the ion covering a wide range of magnetic fields are examined.

Relativistic Douglas-Kroll-Hess calculations of hyperfine interactions within first-principles multireference methods

A relativistic magnetic hyperfine interaction Hamiltonian based on the Douglas-Kroll-Hess (DKH) theory up to the second order is implemented within the ab initio multireference methods, including spin-orbit coupling in the Molcas/OpenMolcas package. This implementation is applied to calculate relativistic hyperfine coupling (HFC) parameters for atomic systems and diatomic radicals with valence s or d orbitals by systematically varying active space size in the restricted active space self-consistent field formalism with restricted active space state interaction for spin-orbit coupling. The DKH relativistic treatment of the hyperfine interaction reduces the Fermi contact contribution to the HFC due to the presence of kinetic factors that regularize the singularity of the Dirac delta function in the nonrelativistic Fermi contact operator. This effect is more prominent for heavier nuclei. As the active space size increases, the relativistic correction of the Fermi contact contribution converges well to the experimental data for light and moderately heavy nuclei. The relativistic correction, however, does not significantly affect the spin-dipole contribution to the hyperfine interaction. In addition to the atomic and molecular systems, the implementation is applied to calculate the relativistic HFC parameters for large trivalent and divalent Tb-based single-molecule magnets (SMMs), such as Tb(III)Pc2 and Tb(II)(CpiPr5)2 without ligand truncation using well-converged basis sets. In particular, for the divalent SMM, which has an unpaired valence 6s/5d hybrid orbital, the relativistic treatment of HFC is crucial for a proper description of the Fermi contact contribution. Even with the relativistic hyperfine Hamiltonian, the divalent SMM is shown to exhibit strong tunability of HFC via an external electric field (i.e., strong hyperfine Stark effect).

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

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

Structural and vibrational properties of lanthanide Lindqvist polyoxometalate complexes

Molecular spin qubits have demonstrated immense potential in quantum information science research due to the addressability of electron spins using microwave frequencies, and the scalability and tunability of molecular systems. Exemplary in this regard is the holmium polyoxometalate, [Na9Ho(W5O18)2]·35H2O (HoW10), which features an accessible atomic clock transition at 9.4 GHz; however, the coherence time of this molecule is limited by spin-phonon coupling driven decoherence processes. To limit these decoherence pathways, materials need to be designed to reduce energy overlap between spin and phonon states, and this necessitates developing a better understanding on how structural modifications impact the vibrational landscape for classes of complexes. Herein we conducted a full investigation into the fundamental structural and vibrational properties of the lanthanide Lindqvist polyoxometalate series, [Na9Ln(W5O18)2]·xH2O (Ln = La(III)-Lu(III), except Pm(III)) (LnW10), to assess how structural changes effect vibrational characteristics and to elucidate pathways to improve the coherence properties of HoW10. Single crystal X-ray diffraction results revealed four distinct structural polymorphs in complexes 1-14 wherein first coordination spheres were identical, and differences manifested as changes in lattice packing. Interestingly, the subtle changes in packing exhibited by the four polymorphs were found to impact distortions away from ideal D4d symmetry for each of the LnW10 complexes. Raman and far-infrared (FIR) spectra of complexes 1-14 were collected to identify vibrational modes present in low energy regions and peak fitting assignments were made according to literature precedents. Qualitative and Partial least squares (PLS) analysis show correlations between complex structural parameters with the low energy Raman and FIR vibrational modes of interest. Overall, this investigation shows that the second coordination sphere plays an integral role in modulation of the structural and vibrational characteristics of LnW10 complexes, which makes it a viable route for tuning spin and vibrational manifolds of species within this series.

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.

Exploring sulfur donor atom coordination chemistry with La(II), Nd(II), and Tm(II) using a terphenylthiolate ligand

To expand the range of donor atoms known to stabilize 4fn5d1 Ln(II) rare-earth metal (Ln) ions beyond the C, N, and O first row main group donor atoms, the Ln(III) sulfur donor terphenylthiolate iodide complexes, LnIII(SAriPr6)2I (AriPr6 = C6H3-2,6-(C6H2-2,4,6-iPr3)2, Ln = La, Nd) were reduced to form LnII(SAriPr6)2 complexes. These Ln(II) species were structurally characterized, analyzed by density functional theory (DFT) calculations, and compared to Tm(SAriPr6)2, which was synthesized from TmI2(DME)3.

A tetravalent praseodymium complex with field-induced slow magnetic relaxation

Herein the synthesis, structural characterization, and magnetic properties of a Pr(IV) complex [Pr(OSiPh3)4(L)] (1, L = 4,4'-dimethoxy-2,2'-bipyridine) are reported. The stability of the Pr(IV) complex significantly enhanced with the use of the bidentate ligand L. Slow magnetic relaxation was observed at low temperatures, indicating that the complex may be the first single-ion magnet with a tetravalent lanthanide ion being the magnetic center.

Identification of an X-Band Clock Transition in Cp'3Pr- Enabled by a 4f25d1 Configuration

Molecular qubits offer an attractive basis for quantum information processing, but challenges remain with regard to sustained coherence. Qubits based on clock transitions offer a method to improve the coherence times. We propose a general strategy for identifying molecules with high-frequency clock transitions in systems where a d electron is coupled to a crystal-field singlet state of an f configuration, resulting in an MJ = ±1/2 ground state with strong hyperfine coupling. Using this approach, a 9.834 GHz clock transition was identified in a molecular Pr complex, [K(crypt)][Cp'3PrII], leading to 3-fold enhancements in T2 relative to other transitions in the spectrum. This result indicates the promise of the design principles outlined here for the further development of f-element systems for quantum information applications.

Metal-carbon bonding in early lanthanide substituted cyclopentadienyl complexes probed by pulsed EPR spectroscopy

We examine lanthanide (Ln)-ligand bonding in a family of early Ln3+ complexes [Ln(Cptt)3] (1-Ln, Ln = La, Ce, Nd, Sm; Cptt = C5H3tBu2-1,3) by pulsed electron paramagnetic resonance (EPR) methods, and provide the first characterization of 1-La and 1-Nd by single crystal XRD, multinuclear NMR, IR and UV/Vis/NIR spectroscopy. We measure electron spin T1 and Tm relaxation times of 12 and 0.2 μs (1-Nd), 89 and 1 μs (1-Ce) and 150 and 1.7 μs (1-Sm), respectively, at 5 K: the T1 relaxation of 1-Nd is more than 102 times faster than its valence isoelectronic uranium analogue. 13C and 1H hyperfine sublevel correlation (HYSCORE) spectroscopy reveals that the extent of covalency is negligible in these Ln compounds, with much smaller hyperfine interactions than observed for equivalent actinide (Th and U) complexes. This is corroborated by ab initio calculations, confirming the predominant electrostatic nature of the metal-ligand bonding in these complexes.

Quantifying the influence of 3d-4s mixing on linearly coordinated metal-ions by L2,3-edge XAS and XMCD

The mixing valence d and s orbitals are predicted to strongly influence the electronic structure of linearly coordinated molecules, including transition metals, lanthanides and actinides. In specific cases, novel magnetic properties, such as single-ion magnetic coercivity or long spin decoherence times, ensue. Inspired by how the local coordination symmetry can engender such novel phenomena, in this study, we focus our attention on dopants (Mn, Fe, Co, Ni, Cu) in lithium nitride to accept innovation from molecular magnetism in a high symmetry P6/mmm solid-state crystal. The linear coordination environment results in strong 3d-4s mixing, proving to be an ideal series to investigate the role of d-s mixing and bonding on electronic structure and magnetism. It is shown that L2,3-edge XAS can be applied to experimentally identify the presence of 3d-4s mixing and the influence this has on the ligand-field splitting. XMCD specifies how spin-orbit coupling is affected. The combined spectroscopies are analysed to determine the effect of 4s mixing with support from ab initio calculations. The results provide new insight of relevance to future applications, including quantum information processing and the sustainable replacement of rare earths in magnets.

A DFT perspective on organometallic lanthanide chemistry

Computational studies of the coordination chemistry and bonding of lanthanides have grown in recent decades as the need for understanding the distinct physical, optical, and magnetic properties of these compounds increased. Density functional theory (DFT) methods offer a favorable balance of computational cost and accuracy in lanthanide chemistry and have helped to advance the discovery of novel oxidation states and electronic configurations. This Frontier article examines the scope and limitations of DFT in interpreting structural and spectroscopic data of low-valent lanthanide complexes, elucidating periodic trends, and predicting their properties and reactivity, presented through selected examples.

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

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

Control and Transferability of Magnetic Interactions in Supramolecular Structures: Trimers of {Cr7 Ni} Antiferromagnetic Rings

A synthetic strategy is demonstrated to prepare two distinct trimers of antiferromagnetically coupled {Cr7 Ni} rings, substantially varying the magnetic interactions between the spin centres. The interactions were studied using multi-frequency cw EPR: in a trimer linked via non-covalent H-bonding interactions no measurable interaction between rings was seen, while in a trimer linked via iso-nicotinate groups isotropic and anisotropic exchange interactions of +0.42 and -0.8 GHz, respectively, were observed. The latter are the same as those for a simpler hetero-dimer system, showing how the spin-spin interactions can be built in a predictable and modular manner in these systems.

Structural distortion by alkali metal cations modulates the redox and electronic properties of Ce3+ imidophosphorane complexes

A series of Ce3+ complexes with counter cations ranging from Li to Cs are presented. Cyclic voltammetry data indicate a significant dependence of the oxidation potential on the alkali metal identity. Analysis of the single-crystal X-ray diffraction data indicates that the degree of structural distortion of the secondary coordination sphere is linearly correlated with the measured oxidation potential. Solution electronic absorption spectroscopy confirms that the structural distortion is reflected in the solution structure. Computational studies further validate this analysis, deciphering the impact of alkali metal cations on the Ce atomic orbital contributions, differences in energies of Ce-dominant molecular orbitals, energy shift of the 4f-5d electronic transitions, and degree of structural distortions. In sum, the structural impact of the alkali metal cation is demonstrated to modulate the redox and electronic properties of the Ce3+ complexes, and provides insight into the rational tuning of the Ce3+ imidophosphorane complex oxidation potential through alkali metal identity.

TURBOMOLE: Today and Tomorrow

TURBOMOLE is a highly optimized software suite for large-scale quantum-chemical and materials science simulations of molecules, clusters, extended systems, and periodic solids. TURBOMOLE uses Gaussian basis sets and has been designed with robust and fast quantum-chemical applications in mind, ranging from homogeneous and heterogeneous catalysis to inorganic and organic chemistry and various types of spectroscopy, light-matter interactions, and biochemistry. This Perspective briefly surveys TURBOMOLE's functionality and highlights recent developments that have taken place between 2020 and 2023, comprising new electronic structure methods for molecules and solids, previously unavailable molecular properties, embedding, and molecular dynamics approaches. Select features under development are reviewed to illustrate the continuous growth of the program suite, including nuclear electronic orbital methods, Hartree-Fock-based adiabatic connection models, simplified time-dependent density functional theory, relativistic effects and magnetic properties, and multiscale modeling of optical properties.

Hilbert Space in Isotopologue Dy(III) SMM Dimers: Dipole Interaction Limit in [163/164Dy2(tmhd)6(tape)]0 Complexes

Single-molecule magnets are molecular complexes proposed to be useful for information storage and quantum information processing applications. In the quest for multilevel systems that can act as Qudits, two dysprosium-based isotopologues were synthesized and characterized. The isotopologues are [164Dy2(tmhd)6(tape)] (1(I=0)) and [163Dy2(tmhd)6(tape)] (2(I=5/2)), where tmhd = 2,2,6,6-tetramethylheptandionate and tape = 1,6,7,12-tetraazaperylene. Both complexes showed slow relaxation at a zero applied magnetic field with dominant Orbach and Raman relaxation mechanisms. μSQUID studies at milli-Kelvin temperatures reveal quasi-single ion loops, in contrast with the expected S-shape (near zero field) butterfly loops, characteristic of antiferromagnetically coupled dimeric complexes. Through analysis of the low-temperature data, we find that the interaction operating between Dy(III) is small, leading to a small exchange biasing from the zero-field transition. The resulting indirectly coupled nuclear states are degenerate or possess a small energy difference between them. We, therefore, conclude that for the creation of Qudits with enlarged Hilbert spaces, shorter Dy(III)···Dy(III) distances are deemed essential.

Increased Crystal Field Drives Intermediate Coupling and Minimizes Decoherence in Tetravalent Praseodymium Qubits

Crystal field (CF) control of rare-earth (RE) ions has been employed to minimize decoherence in qubits and to enhance the effective barrier of single-molecule magnets. The CF approach has been focused on the effects of symmetry on dynamic magnetic properties. Herein, the magnitude of the CF is increased via control of the RE oxidation state. The enhanced 4f metal-ligand covalency in Pr4+ gives rise to CF energy scales that compete with the spin-orbit coupling of Pr4+ and thereby shifts the paradigm from the ionic ζSOC ≫ VCF limit, used to describe trivalent RE-ion, to an intermediate coupling (IC) regime. We examine Pr4+-doped perovskite oxide lattices (BaSnO3 and BaZrO3). These systems are defined by IC which quenches orbital angular momentum. Therefore, the single-ion spin-orbit coupled states in Pr4+ can be chemically tuned. We demonstrate a relatively large hyperfine interaction of Aiso = 1800 MHz for Pr4+, coherent manipulation of the spin with QM = 2ΩRTm, reaching up to ∼400 for 0.1Pr:BSO at T = 5 K, and significant improvement of the temperature at which Tm is limited by T1 (T* = 60 K) compared to other RE ion qubits.

Synthesis and Crystallographic Characterization of a Reduced Bimetallic Yttrium ansa-Metallocene Hydride Complex, [K(crypt)][(μ-CpAn)Y(μ-H)]2 (CpAn = Me2Si[C5H3(SiMe3)-3]2), with a 3.4 Å Yttrium-Yttrium Distance

The reduction of a bimetallic yttrium ansa-metallocene hydride was examined to explore the possible formation of Y-Y bonds with 4d¹ Y(II) ions. The precursor [Cp^AnY(μ-H)(THF)]₂ (Cp^An = Me₂Si[C₅H₃(SiMe₃)-3]₂) was synthesized by hydrogenolysis of the allyl complex Cp^AnY(η³-C₃H₅)(THF), which was prepared from (C₃H₅)MgCl and [Cp^AnY(μ-Cl)]₂. Treatment of [Cp^AnY(μ-H)(THF)]₂ with excess KC₈ in the presence of one equivalent of 2.2.2-cryptand (crypt) generates an intensely colored red-brown product crystallographically identified as [K(crypt)][(μ-Cp^An)Y(μ-H)]₂. The two rings of each Cp^An ligand in the reduced anion [(μ-Cp^An)Y(μ-H)]₂^1- are attached to two yttrium centers in a "flyover" configuration. The 3.3992(6) and 3.4022(7) Å Y···Y distances between the equivalent metal centers within two crystallographically independent complexes are the shortest Y···Y distances observed to date. Ultraviolet-visible (UV-visible)/near infrared (IR) and electron paramagnetic resonance (EPR) spectroscopy support the presence of Y(II), and theoretical analysis describes the singly occupied molecular orbital (SOMO) as an Y-Y bonding orbital composed of metal 4d orbitals mixed with metallocene ligand orbitals. A dysprosium analogue, [K(18-crown-6)(THF)₂][(μ-Cp^An)Dy(μ-H)]₂, was also synthesized, crystallographically characterized, and studied by variable temperature magnetic susceptibility. The magnetic data are best modeled with the presence of one 4f⁹ Dy(III) center and one 4f⁹(5d_z²)¹ Dy(II) center with no coupling between them. CASSCF calculations are consistent with magnetic measurements supporting the absence of coupling between the Dy centers.

Tris(carbene)borates; alternatives to cyclopentadienyls in organolanthanide chemistry

The chemistry of the tris-carbene anion phenyltris(3-alkyl-imidazoline-2-yliden-1-yl)borate, [C3Me]- ligand, is initiated for f-block metal cations. Neutral, molecular complexes of the form Ln(C3)2I are formed for cerium(III), while a separated ion pair [Ln(C3)2]I forms for ytterbium(III). DFT/QTAIM computational analyses of the complexes and related tridentate tris(pyrazolyl)borate (Tp) - supported analogs demonstrates the anticipated strength of the σ donation and confirms greater covalency in the metal-carbon bonds of the [C3Me]- complexes in comparison with those in the TpMe,Me complexes. The DFT calculations demonstrate the crucial role of THF solvent in accurately reproducing the contrasting molecular and ion-pair geometries observed experimentally for the Ce and Yb complexes.

Synthesis, Isolation, and Characterization of Two Cationic Organobismuth(II) Pincer Complexes Relevant in Radical Redox Chemistry

Herein, we report the synthesis, isolation, and characterization of two cationic organobismuth(II) compounds bearing N,C,N pincer frameworks, which model crucial intermediates in bismuth radical processes. X-ray crystallography uncovered a monomeric Bi(II) structure, while SQUID magnetometry in combination with NMR and EPR spectroscopy provides evidence for a paramagnetic S = 1/2 state. High-resolution multifrequency EPR at the X-, Q-, and W-band enable the precise assignment of the full g- and ²⁰⁹Bi A-tensors. Experimental data and DFT calculations reveal both complexes are metal-centered radicals with little delocalization onto the ligands.

Modular Approach to Creating Functionalized Surface Arrays of Molecular Qubits

The quest for developing quantum technologies is driven by the promise of exponentially faster computations, ultrahigh performance sensing, and achieving thorough understanding of many-particle quantum systems. Molecular spins are excellent qubit candidates because they feature long coherence times, are widely tunable through chemical synthesis, and can be interfaced with other quantum platforms such as superconducting qubits. A present challenge for molecular spin qubits is their integration in quantum devices, which requires arranging them in thin films or monolayers on surfaces. However, clear proof of the survival of quantum properties of molecular qubits on surfaces has not been reported so far. Furthermore, little is known about the change in spin dynamics of molecular qubits going from the bulk to monolayers. Here, a versatile bottom-up method is reported to arrange molecular qubits as functional groups of self-assembled monolayers (SAMs) on surfaces, combining molecular self-organization and click chemistry. Coherence times of up to 13 µs demonstrate that qubit properties are maintained or even enhanced in the monolayer.

Quantum Mimicry With Inorganic Chemistry

Quantum objects, such as atoms, spins, and subatomic particles, have important properties due to their unique physical properties that could be useful for many different applications, ranging from quantum information processing to magnetic resonance imaging. Molecular species also exhibit quantum properties, and these properties are fundamentally tunable by synthetic design, unlike ions isolated in a quadrupolar trap, for example. In this comment, we collect multiple, distinct, scientific efforts into an emergent field that is devoted to designing molecules that mimic the quantum properties of objects like trapped atoms or defects in solids. Mimicry is endemic in inorganic chemistry and featured heavily in the research interests of groups across the world. We describe a new field of using inorganic chemistry to design molecules that mimic the quantum properties (e.g. the lifetime of spin superpositions, or the resonant frequencies thereof) of other quantum objects, "quantum mimicry." In this comment, we describe the philosophical design strategies and recent exciting results from application of these strategies.

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.

Back to the future of organolanthanide chemistry

At the dawn of the development of structural organometallic chemistry, soon after the discovery of ferrocene, the description of the LnCp₃ complexes, featuring large and mostly trivalent lanthanide ions, was rather original and sparked curiosity. Yet, the interest in these new architectures rapidly dwindled due to the electrostatic nature of the bonding between π-aromatic ligands and 4f-elements. Almost 70 years later, it is interesting to focus on how the discipline has evolved in various directions with the reports of multiple catalytic reactivities, remarkable potential in small molecule activation, and the development of rich redox chemistry. Aside from chemical reactivity, a better understanding of their singular electronic nature - not precisely as simplistic as anticipated - has been crucial for developing tailored compounds with adapted magnetic anisotropy or high fluorescence properties that have witnessed significant popularity in recent years. Future developments shall greatly benefit from the detailed reactivity, structural and physical chemistry studies, particularly in photochemistry, electro- or photoelectrocatalysis of inert small molecules, and manipulating the spins' coherence in quantum technology.

Room-Temperature Stable Ln(II) Complexes Supported by 2,6-Diadamantyl Aryloxide Ligands

The sterically bulky aryloxide ligand OAr* (OAr* = ^-OC₆H₂-Ad₂-2,6^tBu-4; Ad = 1-adamantyl) has been used to generate Ln(II) complexes across the lanthanide series that are more thermally stable than complexes of any other ligand system reported to date for 4fⁿd¹ Ln(II) ions. The Ln(III) precursors Ln(OAr*)₃ (1-Ln) were synthesized by reacting 1.2 equiv of Ln(NR₂)₃ (R = SiMe₃) with 3 equiv of HOAr* for Ln = La, Ce, Nd, Gd, Dy, Yb, and Lu. 1-Ce, 1-Nd, 1-Gd, 1-Dy, and 1-Lu were identified by single-crystal X-ray diffraction studies. Reductions of 1-Ln with potassium graphite (KC₈) in tetrahydrofuran in the presence of 2.2.2-cryptand (crypt) yielded the Ln(II) complexes [K(crypt)][Ln(OAr*)₃] (2-Ln). The 2-Ln complexes for Ln = Nd, Gd, Dy, and Lu were characterized by X-ray crystallography and found to have Ln-O bond distances 0.038-0.087 Å longer than those of their 1-Ln analogues; this is consistent with 4fⁿ5d¹ electron configurations. The structure of 2-Yb has Yb-O distances 0.167 Å longer than those predicted for 1-Yb, which is consistent with a 4f¹⁴ electron configuration. Although 2-La and 2-Ce proved to be challenging to isolate, with 18-crown-6 (18-c-6) as the potassium chelator, La(II) and Ce(II) complexes with OAr* could be isolated and crystallographically characterized: [K(18-c-6)][Ln(OAr*)₃] (3-Ln). The Ln(II) complexes decompose at room temperature more slowly than other previously reported 4fⁿ5d¹ Ln(II) complexes. For example, only 30% decomposition of 2-Dy was observed after 30 h at room temperature compared to complete decomposition of [Dy(OAr')₃]^- and [DyCp'₃]^- under similar conditions (OAr' = OC₆H₂-2,6-^tBu₂-4-Me; Cp' = C₅H₄SiMe₃).

Multiprocessing Quantum Computing through Hyperfine Couplings in Endohedral Fullerene Derivatives

Magnetic molecules have shown great potential in quantum information processing due to the chemical tunablity of their quantum behaviors. Chemical derivatives of endohedral nitrogen fullerenes with long coherence time and rich energy levels were synthesized and studied to demonstrate the ability of multiprocessing in quantum information using electron magnetic resonance. After initialization of the 12-levelled spin system, subgroups of spin energy levels coursed by the hyperfine couplings can be selectively manipulated. The cooperatively combining of the parallel calculations enabled quantum error correction, increasing the correct rate by up to 17.82 %. Also, different subgroups of transitions divided by hyperfine coupling can be treated as independent qubits, and multi-task quantum computing were realized by performing Z-gate and X-gate simultaneously, which accelerates the overall gating speed.

Five-Spin Supramolecule for Simulating Quantum Decoherence of Bell States

We report a supramolecule that contains five spins of two different types and with, crucially, two different and predictable interaction energies between the spins. The supramolecule is characterized, and the interaction energies are demonstrated by electron paramagnetic resonance (EPR) spectroscopy. Based on the measured parameters, we propose experiments that would allow this designed supramolecule to be used to simulate quantum decoherence in maximally entangled Bell states that could be used in quantum teleportation.

Paramagnetic NMR Shielding Tensors Based on Scalar Exact Two-Component and Spin-Orbit Perturbation Theory

The temperature-dependent Fermi-contact and pseudocontact terms are important contributions to the paramagnetic NMR shielding tensor. Herein, we augment the scalar-relativistic (local) exact two-component (X2C) framework with spin-orbit perturbation theory including the screened nuclear spin-orbit correction for the EPR hyperfine coupling and g tensor to compute these temperature-dependent terms. The accuracy of this perturbative ansatz is assessed with the self-consistent spin-orbit two-component and four-component treatments serving as reference. This shows that the Fermi-contact and pseudocontact interaction is sufficiently described for paramagnetic NMR shifts; however, larger deviations are found for the EPR spectra and the principle components of the EPR properties of heavy elements. The impact of the perturbative treatment is further compared to that of the density functional approximation and the basis set. Large-scale calculations are routinely possible with the multipole-accelerated resolution of the identity approximation and the seminumerical exchange approximation, as shown for [CeTi₆O₃(OiPr)₉(salicylate)₆].

X-Band Parallel-Mode and Multifrequency Electron Paramagnetic Resonance Spectroscopy of S = 1/2 Bismuth Centers

The recent successes in the isolation and characterization of several bismuth radicals inspire the development of new spectroscopic approaches for the in-depth analysis of their electronic structure. Electron paramagnetic resonance (EPR) spectroscopy is a powerful tool for the characterization of main group radicals. However, the large electron-nuclear hyperfine interactions of Bi (²⁰⁹Bi, I = 9/2) have presented difficult challenges to fully interpret the spectral properties for some of these radicals. Parallel-mode EPR (B₁∥B₀) is almost exclusively employed for the study of S > 1/2 systems but becomes feasible for S = 1/2 systems with large hyperfine couplings, offering a distinct EPR spectroscopic approach. Herein, we demonstrate the application of conventional X-band parallel-mode EPR for S = 1/2, I = 9/2 spin systems: Bi-doped crystalline silicon (Si:Bi) and the molecular Bi radicals [L(X)Ga]₂Bi^• (X = Cl or I) and [L(Cl)GaBi(^MecAAC)]^•+ (L = HC[MeCN(2,6-iPr₂C₆H₃)]₂). In combination with multifrequency perpendicular-mode EPR (X-, Q-, and W-band frequencies), we were able to fully refine both the anisotropic g- and A-tensors of these molecular radicals. The parallel-mode EPR experiments demonstrated and discussed here have the potential to enable the characterization of other S = 1/2 systems with large hyperfine couplings, which is often challenging by conventional perpendicular-mode EPR techniques. Considerations pertaining to the choice of microwave frequency are discussed for relevant spin-systems.

Contrasting behaviour under pressure reveals the reasons for pyramidalization in tris(amido)uranium(III) and tris(arylthiolate) uranium(III) molecules

A range of reasons has been suggested for why many low-coordinate complexes across the periodic table exhibit a geometry that is bent, rather a higher symmetry that would best separate the ligands. The dominating reason or reasons are still debated. Here we show that two pyramidal UX₃ molecules, in which X is a bulky anionic ligand, show opposite behaviour upon pressurisation in the solid state. UN″₃ (UN3, N″ = N(SiMe₃)₂) increases in pyramidalization between ambient pressure and 4.08 GPa, while U(SAr)₃ (US3, SAr = S-C₆H₂-^tBu₃−2,4,6) undergoes pressure-induced planarization. This capacity for planarization enables the use of X-ray structural and computational analyses to explore the four hypotheses normally put forward for this pyramidalization. The pyramidality of UN3, which increases with pressure, is favoured by increased dipole and reduction in molecular volume, the two factors outweighing the slight increase in metal-ligand agostic interactions that would be formed if it was planar. The ambient pressure pyramidal geometry of US3 is favoured by the induced dipole moment and agostic bond formation but these are weaker drivers than in UN3; the pressure-induced planarization of US3 is promoted by the lower molecular volume of US3 when it is planar compared to when it is pyramidal.

The reasons for which many low-coordinate complexes exhibit bent geometry, rather than a higher symmetry, are still under debate. Here, the authors use high-pressure crystallography to examine whether low-coordinate f-block molecules become more planar or pyramidal under pressure; which happens is dictated by the dipole moment of the complex and the volume of the planar form.

Quasi-Relativistic Calculation of EPR g Tensors with Derivatives of the Decoupling Transformation, Gauge-Including Atomic Orbitals, and Magnetic Balance

We present an exact two-component (X2C) ansatz for the EPR g tensor using gauge-including atomic orbitals (GIAOs) and a magnetically balanced basis set expansion. In contrast to previous X2C and four-component relativistic ansätze for the g tensor, this implementation results in a gauge-origin-invariant formalism. Furthermore, the derivatives of the relativistic decoupling matrix are incorporated to form the complete analytical derivative of the X2C Hamiltonian. To reduce the associated computational costs, we apply the diagonal local approximation to the unitary decoupling transformation (DLU). The quasi-relativistic X2C and DLU-X2C Hamiltonians accurately reproduce the results of the parent four-component relativistic theory when accounting for two-electron picture-change effects with the modified screened nuclear spin-orbit approximation in the respective one-electron integrals and integral derivatives. According to our benchmark studies, the uncontracted Dyall and segmented-contracted Karlsruhe x2c-type basis sets perform well when compared to large even-tempered basis sets. Moreover, (range-separated) hybrid density functional approximations such as LC-ωPBE and ωB97X-D are needed to match the experimental findings. The impact of the GIAOs depends on the distribution of the spin density, and their use may change the Δg shifts by 10-50% as shown for [(C₅Me₅)₂Y(μ-S)₂Mo(μ-S)₂Y(C₅Me₅)₂]^-. Routine calculations of large molecules are possible with widely available and comparably low-cost hardware as demonstrated for [Pt(C₆Cl₅)₄]^- with 3003 basis functions and three spin-(1/2) La(II) and Lu(II) compounds, for which we observe good agreement with the experimental findings.