Proof-of-Concept Quantum Simulator Based on Molecular Spin Qudits.

The use of d-level qudits instead of two-level qubits can largely increase the power of quantum logic for many applications, ranging from quantum simulations to quantum error correction. Magnetic molecules are ideal spin systems to realize these large-dimensional qudits. Indeed, their Hamiltonian can be engineered to an unparalleled extent and can yield a spectrum with many low-energy states. In particular, in the past decade, intense theoretical, experimental, and synthesis efforts have been devoted to develop quantum simulators based on molecular qubits and qudits. However, this remarkable potential is practically unexpressed, because no quantum simulation has ever been experimentally demonstrated with these systems. Here, we show the first prototype quantum simulator based on an ensemble of molecular qudits and a radiofrequency broadband spectrometer. To demonstrate the operativity of the device, we have simulated quantum tunneling of the magnetization and the transverse-field Ising model, representative of two different classes of problems. These results represent an important step toward the actual use of molecular spin qudits in quantum technologies.

Long aliphatic chain derivatives of trigonal lanthanide complexes.

The trigonal lanthanide complexes LnL (H3L = tris(((3-formyl-5-methylsalicylidene)amino)ethyl)amine) contain three pendant aldehyde groups and are known to react with primary amines. Reacting LnL (Ln = Yb, Lu) with 1-octadecylamine yields the novel aliphatic lanthanide complexes LnL18 (H3L18 = tris(((3-(1-octadecylimine)-5-methylsalicylidene)amino)ethyl)amine) where the three aldehyde groups are transformed to 1-octadecylimine groups. Herein the syntheses, structural characterisation and magnetic properties of LnL18 are presented. The crystal structure of YbL18 shows that the reaction of YbL with 1-octadecylamine leads to only very subtle perturbations in the first coordination sphere of Yb(III), with the Yb(III) ion retaining its heptacoordination and similar bond lengths and angles to the ligand. The three octadecyl chains in each complex were found to direct crystal packing into lipophilic arrays of van der Waals interaction-driven hydrocarbon stacking. The static magnetic properties of YbL18 were compared to those of the non-derivatised complex YbL. The energy level splitting of the 2F7/2 ground multiplet was found, by emission spectroscopy, to be very similar between the derivatised and non-derivatised complexes. A.c. magnetic susceptibility measurements on YbL18 and YbL diluted at 4.8% and 4.2% into the diamagnetic hosts LuL18 and LuL, respectively, revealed that the spin-lattice relaxation of both complexes is governed by a low temperature direct process and a high temperature Raman process. In the high temperature regime, the derivatised complex was also found to have faster spin-lattice relaxation, which is likely due to the increased number of phonons in the octadecyl chains.

A bis-calix[4]arene-supported [CuII16] cage.

Reaction of 2,2'-bis-p-tBu-calix[4]arene (H8L) with Cu(NO3)2·3H2O and N-methyldiethanolamine (Me-deaH2) in a basic dmf/MeOH mixture affords [CuII16(L)2(Me-dea)4(µ4-NO3)2(µ-OH)4(dmf)3.5(MeOH)0.5(H2O)2](H6L)·16dmf·4H2O (4), following slow evaporation of the mother liquor. The central core of the metallic skeleton describes a tetracapped square prism, [Cu12], in which the four capping metal ions are the CuII ions housed in the calix[4]arene polyphenolic pockets. The [CuII8] square prism is held together "internally" by a combination of hydroxide and nitrate anions, with the N-methyldiethanolamine co-ligands forming dimeric [CuII2] units which edge-cap above and below the upper and lower square faces of the prism. Charge balance is maintained through the presence of one doubly deprotonated H6L2- ligand per [Cu16] cluster. Magnetic susceptibility measurements reveal the predominance of strong antiferromagnetic exchange interactions and an S = 1 ground state, while EPR is consistent with a large zero-field splitting.

Dipolar-Coupled Entangled Molecular 4f Qubits.

We demonstrate by use of continuous wave- and pulse-electron paramagnetic resonance spectroscopy on oriented single crystals of magnetically dilute YbIII ions in Yb0.01Lu0.99(trensal) that molecular entangled two-qubit systems can be constructed by exploiting dipolar interactions between neighboring YbIII centers. Furthermore, we show that the phase memory time and Rabi frequencies of these dipolar-interaction-coupled entangled two-qubit systems are comparable to the ones of the corresponding single qubits.

Spin-Lattice Relaxation Decoherence Suppression in Vanishing Orbital Angular Momentum Qubits.

Multifrequency electron paramagnetic resonance spectroscopy on oriented single crystals of magnetically dilute Gd(III) ions in Gd0.004Y0.996(trensal) is used to determine the Hamiltonian parameters of the ground 8S7/2 term and its phase memory time, Tm, characterizing its coherent spin dynamics. The vanishing orbital angular momentum of the 8S7/2 term makes it relatively insensitive to spin-lattice relaxation mediated by magnetoelastic coupling and leads to a Tm of 12 µs at 3 K, which is not limited by spin-lattice relaxation.

Correction: The coordination chemistry of p-tert-butylcalix[4]arene with paramagnetic transition and lanthanide metal ions: an Edinburgh Perspective.

Correction for 'The coordination chemistry of p-tert-butylcalix[4]arene with paramagnetic transition and lanthanide metal ions: an Edinburgh Perspective' by Lucinda R. B. Wilson et al., Dalton Trans., 2022, DOI: 10.1039/d2dt00152g.

The coordination chemistry of p-tert-butylcalix[4]arene with paramagnetic transition and lanthanide metal ions: an Edinburgh Perspective.

The calix[4]arene scaffold is an extremely versatile supramolecular platform that has found widespread use across many research areas due to its synthetic versatility, controllable conformation, and the presence of cavities or clefts for tailorable guest binding. The tetraphenolic lower-rim of p-tert-butylcalix[4]arene in the cone conformation is ideal for binding a variety of paramagnetic transition and lanthanide metals, and in this Perspective we review our endeavours in using such complexes as metalloligands in the synthesis of polymetallic clusters that have fascinating structural and magnetic properties. By varying reactants, stoichiometries and reaction or crystallisation conditions it is possible to access an incredible range of clusters, all of which show consistent trends in coordination preferences and assembly behaviours. p-tert-Butylcalix[4]arene has already given so much, yet it is likely that this remarkable parent calixarene will continue to surprise chemists and deliver even more in terms of novelty and function.

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

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

Magnetic Archimedean Tessellations in Metal-Organic Frameworks.

The self-assembly of lanthanide ions with ditopic organic spacers results in the formation of complex tiling patterns that mimic the structural motifs of quasi-periodic 2D materials. The linking of trans-{LnI2}+ nodes (Ln = Gd, Dy) by both closed-shell and anion radicals of 4,4'-bipyridine affords rare examples of Archimedean tessellations in a metal-organic framework. We furthermore demonstrate the occurrence of sizable magnetic exchange interactions and slow relaxation of magnetization behavior in a complex tessellation pattern. The implementation of Archimedean tessellations in lanthanide(III) coordination solids couriers a strategy to design elusive quasi-periodic metal-organic frameworks with inimitable magnetic properties.

[(VIVO)2MII5] (M = Ni, Co) Anderson wheels.

Heterometallic Anderson wheels of formula [(VIVO)2MII5(hmp)10Cl2](ClO4)2·2MeOH (M = Ni, 1; Co, 2) have been synthesised from the solvothermal reaction of M(ClO4)2·6H2O and VCl3 with hmpH (2-(hydroxymethyl)pyridine). The metallic skeleton describes a centred hexagon, with the two vanadyl ions sitting on opposing sides of the outer ring. Magnetic susceptibility and magnetisation measurements indicate the presence of both ferromagnetic and antiferromagnetic exchange interactions. Theoretical calculations based on density functional methods reproduce both the sign and strength of the exchange interactions found experimentally, and rationalise the parameters extracted.

Exploiting host-guest chemistry to manipulate magnetic interactions in metallosupramolecular M4L6 tetrahedral cages.

Reaction of Ni(OTf)2 with the bisbidentate quaterpyridine ligand L results in the self-assembly of a tetrahedral, paramagnetic cage [NiII 4 L 6]8+. By selectively exchanging the bound triflate from [OTf⊂NiII 4 L 6](OTf)7 (1), we have been able to prepare a series of host-guest complexes that feature an encapsulated paramagnetic tetrahalometallate ion inside this paramagnetic host giving [MIIX4⊂NiII 4 L 6](OTf)6, where MIIX4 2- = MnCl4 2- (2), CoCl4 2- (5), CoBr4 2- (6), NiCl4 2- (7), and CuBr4 2- (8) or [MIIIX4⊂NiII 4 L 6](OTf)7, where MIIIX4 - = FeCl4 - (3) and FeBr4 - (4). Triflate-to-tetrahalometallate exchange occurs in solution and can also be accomplished through single-crystal-to-single-crystal transformations. Host-guest complexes 1-8 all crystallise as homochiral racemates in monoclinic space groups, wherein the four {NiN6} vertexes within a single Ni4L6 unit possess the same Δ or Λ stereochemistry. Magnetic susceptibility and magnetisation data show that the magnetic exchange between metal ions in the host [NiII 4] complex, and between the host and the MX4 n- guest, are of comparable magnitude and antiferromagnetic in nature. Theoretically derived values for the magnetic exchange are in close agreement with experiment, revealing that large spin densities on the electronegative X-atoms of particular MX4 n- guest molecules lead to stronger host-guest magnetic exchange interactions.

Design of pure heterodinuclear lanthanoid cryptate complexes.

Heterolanthanide complexes are difficult to synthesize owing to the similar chemistry of the lanthanide ions. Consequently, very few purely heterolanthanide complexes have been synthesized. This is despite the fact that such complexes hold interesting optical and magnetic properties. To fine-tune these properties, it is important that one can choose complexes with any given combination of lanthanides. Herein we report a synthetic procedure which yields pure heterodinuclear lanthanide cryptates LnLn*LX3 (X = NO3 - or OTf-) based on the cryptand H3L = N[(CH2)2N[double bond, length as m-dash]CH-R-CH[double bond, length as m-dash]N-(CH2)2]3N (R = m-C6H2OH-2-Me-5). In the synthesis the choice of counter ion and solvent proves crucial in controlling the Ln-Ln* composition. Choosing the optimal solvent and counter ion afford pure heterodinuclear complexes with any given combination of Gd(iii)-Lu(iii) including Y(iii). To demonstrate the versatility of the synthesis all dinuclear combinations of Y(iii), Gd(iii), Yb(iii) and Lu(iii) were synthesized resulting in 10 novel complexes of the form LnLn*L(OTf)3 with LnLn* = YbGd 1, YbY 2, YbLu 3, YbYb 4, LuGd 5, LuY 6, LuLu 7, YGd 8, YY 9 and GdGd 10. Through the use of 1H, 13C NMR and mass spectrometry the heterodinuclear nature of YbGd, YbY, YbLu, LuGd, LuY and YGd was confirmed. Crystal structures of LnLn*L(NO3)3 reveal short Ln-Ln distances of ∼3.5 Å. Using SQUID magnetometry the exchange coupling between the lanthanide ions was found to be anti-ferromagnetic for GdGd and YbYb while ferromagnetic for YbGd.

[CrIII8NiII6]n+ Heterometallic Coordination Cubes.

Three new heterometallic [CrIII8NiII6] coordination cubes of formulae [CrIII8NiII6L24(H2O)12](NO3)12 (1), [CrIII8NiII6L24(MeCN)7(H2O)5](ClO4)12 (2), and [CrIII8NiII6L24Cl12] (3) (where HL = 1-(4-pyridyl)butane-1,3-dione), were synthesised using the paramagnetic metalloligand [CrIIIL3] and the corresponding NiII salt. The magnetic skeleton of each capsule describes a face-centred cube in which the eight CrIII and six NiII ions occupy the eight vertices and six faces of the structure, respectively. Direct current magnetic susceptibility measurements on (1) reveal weak ferromagnetic interactions between the CrIII and NiII ions, with JCr-Ni = + 0.045 cm-1. EPR spectra are consistent with weak exchange, being dominated by the zero-field splitting of the CrIII ions. Excluding wheel-like structures, examples of large heterometallic clusters containing both CrIII and NiII ions are rather rare, and we demonstrate that the use of metalloligands with predictable bonding modes allows for a modular approach to building families of related polymetallic complexes. Compounds (1)-(3) join the previously published, structurally related family of [MIII8MII6] cubes, where MIII = Cr, Fe and MII = Cu, Co, Mn, Pd.

Functionalized Trigonal Lanthanide Complexes: A New Family of 4f Single-Ion Magnets.

We report the synthesis, characterization, and magnetic properties of eight neutral functionalized trigonal lanthanide coordination complexes LnL with Ln = Gd (1), Tb (2), Dy (3), Ho (4), Er (5), Tm (6), Yb (7), Lu (8). These were prepared through a one-pot synthesis where, first, the ligand H3L was synthesized in situ through a Schiff base reaction of tris(2-aminoethyl)amine with 2,6-diformyl-p-cresol. Following addition of Ln(OTf)3·xH2O and base, LnL was obtained. Powder X-ray diffraction confirms that all complexes are isostructural. LnL contain pendant, noncoordinating carbonyl functions that are reactive and represent direct anchoring points to appropriately functionalized surfaces. Furthermore, these reactive carbonyl functions can be used to postfunctionalize LnL: for example, with aromatic π systems. We present herein the Schiff base condensation of 7 with benzylamine to yield 9 as well as the characterization and magnetic properties of 9. Our study establishes LnL as a truly versatile module for the surface deposition of Ln-based single-ion magnets.

Lanthanide cryptate monometallic coordination complexes.

We report the synthesis, characterisation and magnetic properties of six novel neutral lanthanide cryptate coordination complexes. Reaction of 2,6-diformyl-4-methylphenol, tris(2-aminoethyl)amine and Ln(OTf)3·9H2O in the ratio 3 : 2 : 1, respectively, and in the presence of base affords the isolation of the six complexes LnL·4H2O (Ln = Tb (1), Dy (2), Ho (3), Er (4), Tm (5) and Yb (6)), with H3L being the cryptand N[(CH2)2N[double bond, length as m-dash]CH-R-CH[double bond, length as m-dash]N-(CH2)2]3N (R = m-C6H2OH-2-Me-5). Powder X-ray diffraction confirms that the six complexes are isostructural. The crystal structure of 6 reveals that the Ln(iii) centre is heptacoordinated, in a geometry close to a monocapped distorted octahedron and lies on a pseudo (non-crystallographically imposed) C3 axis. This coordination sphere is similar to the one found in the previously studied Ln(trensal) complexes (H3trensal = 2,2',2''-tris(salicylideneimino)triethylamine). The static and dynamic magnetic properties of these complexes were investigated by SQUID magnetometry. Crystal field parameters were determined for all complexes by modelling of the direct current magnetic susceptibility and variable-temperature-variable-field magnetisation data. As for Ln(trensal), only complexes containing the Kramers ions Dy, Er and Yb displayed out-of-phase susceptibility signals in SQUID measurements in an applied magnetic field. Investigation of the dynamic susceptibility of the Yb complex revealed that the magnetic relaxation is governed by a direct process at low temperatures and a Raman process at higher temperatures, similar to Yb(trensal).

Hard X-ray magnetochiral dichroism in a paramagnetic molecular 4f complex.

Magnetochiral dichroism (MΧD) originates in the coupling of local electric fields and magnetic moments in systems where a simultaneous break of space parity and time-reversal symmetries occurs. This magnetoelectric coupling, displayed by chiral magnetic materials, can be exploited to manipulate the magnetic moment of molecular materials at the single molecule level. We demonstrate herein the first experimental observation of X-ray magnetochiral dichroism in enantiopure chiral trigonal single crystals of a chiral mononuclear paramagnetic lanthanide coordination complex, namely, holmium oxydiacetate, at the Ho L3-edge. The observed magnetochiral effect is opposite for the two enantiomers and is rationalised on the basis of a multipolar expansion of the matter-radiation interaction. These results demonstrate that 4f-5d hybridization in chiral lanthanoid coordination complexes is at the origin of magnetochiral dichroism, an effect that could be exploited for addressing of their magnetic moment at the single molecule level.

Molecular multifunctionality preservation upon surface deposition for a chiral single-molecule magnet.

The synthesis and characterization of a chiral, enneanuclear Mn(iii)-based, Single-Molecule Magnet, [Mn9O4(Me-sao)6(L)3(MeO)3(MeOH)3]Cl (1; Me-saoH2 = methylsalicylaldoxime, HL = lipoic acid) is reported. Compound 1 crystallizes in the orthorhombic P212121 space group and consists of a metallic skeleton describing a defect super-tetrahedron missing one vertex. The chirality of the [MnIII 9] core originates from the directional bridging of the Me-sao2- ligands via the -N-O- oximate moieties, which define a clockwise (1ΔΔ) or counter-clockwise (1ΛΛ) rotation in both the upper [MnIII 3] and lower [MnIII 6] subunits. Structural integrity and retention of chirality upon dissolution and upon deposition on (a) gold nanoparticles, 1@AuNPs, (b) transparent Au(111) surfaces, 1ΛΛ@t-Au(111); 1ΔΔ@t-Au(111), and (c) epitaxial Au(111) on mica surfaces, 1@e-Au(111), was confirmed by CD and IR spectroscopies, mass spectrometry, TEM, XPS, XAS, and AFM. Magnetic susceptibility and magnetization measurements demonstrate the simultaneous retention of SMM behaviour and optical activity, from the solid state, via dissolution, to the surface deposited species.

Correction: Determination of the electronic structure of a dinuclear dysprosium single molecule magnet without symmetry idealization.

[This corrects the article DOI: 10.1039/C8SC03170C.].

Determination of the electronic structure of a dinuclear dysprosium single molecule magnet without symmetry idealization.

We present the in-depth determination of the magnetic properties and electronic structure of the luminescent and volatile dysprosium-based single molecule magnet [Dy2(bpm)(fod)6] (Hfod = 6,6,7,7,8,8,8-heptafluoro-2,2-dimethyl-3,5-octanedione, bpm = 2,2'-bipyrimidine). Ab initio calculations were used to obtain a global picture of the electronic structure and to predict possible single molecule magnet behaviour, confirmed by experiments. The orientation of the susceptibility tensor was determined by means of cantilever torque magnetometry. An experimental determination of the electronic structure of the lanthanide ion was obtained combining Luminescence, Far Infrared and Magnetic Circular Dichroism spectroscopies. Fitting these energies to the full single ion plus crystal field Hamiltonian allowed determination of the eigenstates and crystal field parameters of a lanthanide complex without symmetry idealization. We then discuss the impact of a stepwise symmetry idealization on the modelling of the experimental data. This result is particularly important in view of the misleading outcomes that are often obtained when the symmetry of lanthanide complexes is idealized.

Coherent Manipulation of a Molecular Ln-Based Nuclear Qudit Coupled to an Electron Qubit.

We demonstrate that the [Yb(trensal)] molecule is a prototypical coupled electronic qubit-nuclear qudit system. The combination of noise-resilient nuclear degrees of freedom and large reduction of nutation time induced by electron-nuclear mixing enables coherent manipulation of this qudit by radio frequency pulses. Moreover, the multilevel structure of the qudit is exploited to encode and operate a qubit with embedded basic quantum error correction.