EPR Spectroscopy of a Family of CrIII7MII(M = Cd, Zn, Mn, Ni) “Wheels”: Studies of Isostructural Compounds with Different Spin Ground States

Characterizing X-Ray and Solution State Conformations for a Model Qubit System: {Cr7Ni} Ring Rotaxanes on a Mixed Metal Triangle

The synthesis of a series of [4]rotaxanes, each consisting of three [2]rotaxanes joined via a central {CrNi2} triangular linker, is reported. The resultant four [4]rotaxanes were characterized by single crystal X-ray diffraction and electron paramagnetic resonance (EPR) spectroscopy. Orientation-selective 4-pulse double electron-electron resonance (DEER) measurements between the three {Cr7Ni} rings incorporated in each [4]rotaxane reveal that each system is conformationally fluxional in solution, with the most abundant conformations found to differ significantly from the crystal structure geometry for each compound. The degree of similarity between conformations is evaluated using a novel application of the earth mover's distance analysis.

Two- and Three-Spin Hybrid Inorganic-Organic [2]Rotaxanes Containing Metallated Salen Groups

Mono- and bis-salen functionalised [2]rotaxanes have been synthesised from the esterification of [2]rotaxanes containing phenol-terminated threads (salen=N,N'-bis(salicylidene)ethylenediamine). The [2]rotaxanes have general formula [RH][Cr7NiF8(O2CtBu)16], where [RH]+ is a thread with a central secondary ammonium site that templates a [Cr7NiF8(O2CtBu)16]- ring. The threads are terminated at one or both ends by carboxylic acid functionalised salen groups. The {M(salen)} groups can be free-base [M=(H+)2] or metallated [M=Cu2+, Ni2+, (VO)2+]. The [2]rotaxanes have been characterised by single crystal XRD and solid- and solution-state EPR spectroscopy. Where two paramagnetic M ions are involved [M=Cu2+ and/or (VO)2+] the [2]rotaxanes contain three electron spin S=1 / 2 ${{ 1/2 }}$ centres, since the {Cr7Ni} ring has an S=1 / 2 ${{ 1/2 }}$ ground state which is well isolated at low temperatures. These three-spin [2]rotaxanes have been characterised in solution by pulsed dipolar EPR spectroscopies (DEER, also known as PELDOR, and RIDME). The M⋅⋅⋅M and M⋅⋅⋅{Cr7Ni} interactions measured are consistent with dipolar interactions and also with the distances from single crystal XRD. The authors declare no competing financial interest.

One-, two- and three-dimensional interlocked polymers based on hybrid inorganic-organic rotaxanes

We report three new polymers, based on mechanically interlocked inorganic-organic rotaxanes. They are made in very mild conditions and involve pyrimidine head groups binding to copper(ii) linking units. A two-dimensional 6,3 net and a three-dimensional 10,3b net are found depending on the solvent used in the reaction.

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.

Synthesis and characterization of heterometallic rings templated through alkylammonium or imidazolium cations

We report the synthesis and structural characterization of a series of heterometallic rings templated via alkylammonium or imidazolium cations. The template and preference of each metal's coordination geometry can control the structure of heterometallic compounds, leading to octa-, nona-, deca-, dodeca-, and tetradeca-metallic rings. The compounds were characterized by single-crystal X-ray diffraction, elemental analysis, magnetometry, and EPR measurements. Magnetic measurements show that the exchange coupling between metal centres is antiferromagnetic. EPR spectroscopy shows that the spectra of {Cr7Zn} and {Cr9Zn} have S = 3/2 ground states, while the spectra of {Cr12Zn2} and {Cr8Zn} are consistent with S = 1 and 2 excited states. The EPR spectra of {(ImidH)-Cr6Zn2}, {(1-MeImH)-Cr8Zn2}, and {(1,2-diMeImH)-Cr8Zn2} include a combination of linkage isomers. The results on these related compounds allow us to examine the transferability of magnetic parameters between compounds.

Modelling Conformational Flexibility in a Spectrally Addressable Molecular Multi-Qubit Model System

Dipolar coupled multi-spin systems have the potential to be used as molecular qubits. Herein we report the synthesis of a molecular multi-qubit model system with three individually addressable, weakly interacting, spin1 / 2 ${{ 1/2 }}$ centres of differing g-values. We use pulsed Electron Paramagnetic Resonance (EPR) techniques to characterise and separately address the individual electron spin qubits; CuII , Cr7 Ni ring and a nitroxide, to determine the strength of the inter-qubit dipolar interaction. Orientation selective Relaxation-Induced Dipolar Modulation Enhancement (os-RIDME) detecting across the CuII spectrum revealed a strongly correlated CuII -Cr7 Ni ring relationship; detecting on the nitroxide resonance measured both the nitroxide and CuII or nitroxide and Cr7 Ni ring correlations, with switchability of the interaction based on differing relaxation dynamics, indicating a handle for implementing EPR-based quantum information processing (QIP) algorithms.

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.

Decorating polymer beads with 1014 inorganic-organic [2]rotaxanes as shown by spin counting

Polymer beads have been used as the core of magnetic particles for around twenty years. Here we report studies to attach polymetallic complexes to polymer beads for the first time, producing beads of around 115 microns diameter that are attached to 10¹⁴ hybrid inorganic-organic [2]rotaxanes. The bead is then formally a [10¹⁴] rotaxane. The number of complexes attached is counted by EPR spectroscopy after including TEMPO radicals within the thread of the hybrid [2]rotaxanes.

Single Isomer Heterometallic {CrIII6MII2} Rings Templated by Tetramethylammonium

A family of heterometallic rings [Me₄N]₂[Cr^III₆M^II₂F₈(O₂C^tBu)₁₆] is reported using tetramethylammonium hydroxide pentahydrate as the source of a template, where M = Zn, Mn, Ni, and Co. The metal cores are octagons with metal-metal edges bridged by one fluoride and two carboxylate ligands. The divalent metal ions are found ordered at positions 1 and 5 in the octagon. The tetramethylammonium cations are above and below the metal plane of the ring in the crystal structure. Magnetic studies show antiferromagnetic coupling between the paramagnetic metal ions present, leading to paramagnetic ground states in each case. ¹H NMR spectroscopy confirms that the structure of the {Cr^III₆Co^II₂} ring exists in solution, and electron paramagnetic resonance spectroscopy confirms the magnetic structure of the other three rings.

Close Encounters of the Weak Kind: Investigations of Electron-Electron Interactions between Dissimilar Spins in Hybrid Rotaxanes

We report a family of hybrid [2]rotaxanes based on inorganic [Cr7NiF8(O2CtBu)16]- ("{Cr7Ni}") rings templated about organic threads that are terminated at one end with pyridyl groups. These rotaxanes can be coordinated to [Cu(hfac)2] (where Hhfac = 1,1,1,5,5,5-hexafluoroacetylacetone), to give 1:1 or 1:2 Cu:{Cr7Ni} adducts: {[Cu(hfac)2](py-CH2NH2CH2CH2Ph)[Cr7NiF8(O2CtBu)16]}, {[Cu(hfac)2][py-CH2NH2CH2CH3][Cr7NiF8(O2CtBu)16]}, {[Cu(hfac)2]([py-CH2CH2NH2CH2C6H4SCH3][Cr7NiF8(O2CtBu)16])2}, {[Cu(hfac)2]([py-C6H4-CH2NH2(CH2)4Ph][Cr7NiF8(O2CtBu)16])2}, and {[Cu(hfac)2]([3-py-CH2CH2NH2(CH2)3SCH3][Cr7NiF8(O2CtBu)16])2}, the structures of which have been determined by X-ray diffraction. The {Cr7Ni} rings and CuII ions both have electronic spin S = 1/2, but with very different g-values. Continuous-wave EPR spectroscopy reveals the exchange interactions between these dissimilar spins, and hence the communication between the different molecular components that comprise these supramolecular systems. The interactions are weak such that we observe AX or AX2 type spectra. The connectivity between the {Cr7Ni} ring and thread terminus is varied such that the magnitude of the exchange interaction J can be tuned. The coupling is shown to be dominated by through-bond rather than through-space mechanisms.

Accurate Magnetic Couplings in Chromium-Based Molecular Rings from Broken-Symmetry Calculations within Density Functional Theory

We present a comprehensive analysis of magnetic coupling in a group of three popular chromium-based molecular rings, the homometallic Cr₈ ring and the heterometallic Cr₇Ni and Cr₇Zn molecules. We show conclusively that the broken symmetry approach within density functional theory (DFT), based on suitable conventional or range-separated hybrid functionals, provides a quantitatively reliable tool to extract magnetic exchange coupling parameters in all rings considered, which opens a window for additional applications in molecular magnetism. We further show that a nonempirical model spin Hamiltonian, based on the parameters extracted from DFT, leads to excellent agreement with experimental susceptibility data and energy spectra. Moreover, based on an optimally tuned range-separated hybrid functional approach, we find that gas-phase gaps of the studied molecular rings are much larger than previously calculated and discuss the implications of the revised electronic structure to potential applications in molecular spintronics.

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

Simultaneous retention of SMM behaviour and of optical activity is demonstrated upon surface deposition for a chiral SMM.

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 [Mn^III₉] core originates from the directional bridging of the Me-sao^2– ligands via the –N–O– oximate moieties, which define a clockwise (1ΔΔ) or counter-clockwise (1ΛΛ) rotation in both the upper [Mn^III₃] and lower [Mn^III₆] 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.

A Clock Transition in the Cr7Mn Molecular Nanomagnet

A viable qubit must have a long coherence time T 2 . In molecular nanomagnets, T 2 is often limited at low temperatures by the presence of dipole and hyperfine interactions, which are often mitigated through sample dilution, chemical engineering and isotope substitution in synthesis. Atomic-clock transitions offer another route to reducing decoherence from environmental fields by reducing the effective susceptibility of the working transition to field fluctuations. The Cr7Mn molecular nanomagnet, a heterometallic ring, features a clock transition at zero field. Both continuous-wave and spin-echo electron-spin resonance experiments on Cr7Mn samples, diluted via co-crystallization, show evidence of the effects of the clock transition with a maximum T 2 ∼ 390 ns at 1.8 K. We discuss improvements to the experiment that may increase T 2 further.

Hybrid Organic-Inorganic Rotaxanes, Including a Hetero-Hybrid [3]Rotaxane Featuring Two Distinct Heterometallic Rings and a Molecular Shuttle

[2] and [3] hybrid rotaxanes are reported based on {Ti₇ M} rings (M is a trivalent metal such as Fe^III or Ga^III ). NMR studies show that [2]rotaxanes can act as molecular shuttles, while EPR studies of [3]rotaxanes show weak interactions between the paramagnetic components of the supramolecular assemblies.

A simple methodology for constructing ferromagnetically coupled Cr(iii) compounds

A large family of chromium(iii) dimers has been synthesised and magneto-structurally characterised using a combination of carboxylate and diethanolamine type ligands. The compounds have the general formula [Cr2(R1-deaH)2(O2CR2)Cl2]Cl where R1 = Me and R2 = H (1), Me (2), CMe3 (3), Ph (4), 3,5-(Cl)2Ph (5), (Me)5Ph (6), R1 = Et and R2 = H (7), Ph (8). The compound [Cr2(Me-deaH)2Cl4] (9) was synthesised in order to study the effect of removing/adding the carboxylate bridge on the observed magnetic behaviour. Direct current (DC) magnetic susceptibility measurements showed ferromagnetic (FM) exchange interactions between the Cr(iii) centres in the carboxylate bridged family with coupling constants in the range +0.37 < J < +8.02 cm-1. Removal of the carboxylate to produce the dialkoxide-bridged compound 9 resulted in antiferromagnetic (AFM) exchange between the Cr(iii) ions. DFT calculations reveal the ferromagnetic exchange is the result of an orbital counter-complementarity effect occuring upon introduction of the bridging carboxylate.

Chromium chains as polydentate fluoride ligands for actinides and group IV metals

New heterometallic rings containing Cr(iii) and tetravalent metals are reported, including a {Cr₆Th₂} cage.

Measuring Spin⋅⋅⋅Spin Interactions between Heterospins in a Hybrid [2]Rotaxane

Use of molecular electron spins as qubits for quantum computing will depend on the ability to produce molecules with weak but measurable interactions between the qubits. Here we demonstrate use of pulsed EPR spectroscopy to measure the interaction between two inequivalent spins in a hybrid rotaxane molecule.

Heterodimers of heterometallic rings

Nine new complexes are reported involving linked heterometallic rings; one ring is designed as a ligand for the second, and the compounds produced can be regarded as molecular prototypes for implementing quantum gates featuring two subtly different qubits.

Electronic Structure of a Mixed-Metal Fluoride-Centered Triangle Complex: A Potential Qubit Component

A novel fluoride-centered triangular-bridged carboxylate complex, [Ni2Cr(μ3-F)(O2C(t)Bu)6(HO2C(t)Bu)3] (1), is reported. Simple postsynthetic substitution of the terminal pivalic acids in 1 with pyridine and 4-methylpyridine led to the isolation of [Ni2Cr(μ3-F)(O2C(t)Bu)6(C5H5N)3] (2) and [Ni2Cr(μ3-F)(O2C(t)Bu)6((4-CH3)C5H4N)3] (3). Structural and magnetic characterizations carried out on the series reveal a dominating antiferromagnetic interaction between the nickel and chromium centers leading to an S = (1)/2 ground state with a very unusual value of geff = 2.48.

Heterometallic Rings: Their Physics and use as Supramolecular Building Blocks

An enormous family of heterometallic rings has been made. The first were Cr7 M rings where M = Ni(II), Zn(II), Mn(II), and rings have been made with as many as fourteen metal centers in the cyclic structure. They are bridged externally by carboxylates, and internally by fluorides or a penta-deprotonated polyol. The size of the rings is controlled through templates which have included a range of ammonium or imidazolium ions, alkali metals and coordination compounds. The rings can be functionalized to act as ligands, and incorporated into hybrid organic-inorganic rotaxanes and into molecules containing up to 200 metal centers. Physical studies reported include: magnetic measurements, inelastic neutron scattering (including single crystal measurements), electron paramagnetic resonance spectroscopy (including measurements of phase memory times), NMR spectroscopy (both solution and solid state), and polarized neutron diffraction. The rings are hence ideal for understanding magnetism in elegant exchange-coupled systems.

CW-EPR Spectral Simulations: Solid State

This chapter summarizes the core concepts underlying the simulation of EPR spectra from biological samples in the solid state, from a user perspective. The key choices and decisions that have to be made by a user when simulating an experimental EPR spectrum are outlined. These include: the choice of the simulation model (the network of spins and the associated spin Hamiltonian), the dynamic regime (solid, liquid, slow motion), the level of theory used in the simulation (matrix diagonalization, perturbation theory, etc.), the treatment of orientational order and disorder (powder, crystal, partial ordering), the inclusion of the effects of structural disorder (strains), the effects of other line broadening mechanisms (unresolved hyperfine couplings, relaxation), and the inclusion of experimental distortions (field modulation, power saturation, filtering). Additionally, the salient aspects of utilizing least-squares fitting algorithms to aid the analysis of experimental spectra with the help of simulations are outlined. Although drawing from the experience gained from implementing EasySpin and from interacting with EasySpin's user base, this chapter applies to any EPR simulation software.

g-Engineering in Hybrid Rotaxanes To Create AB and AB2 Electron Spin Systems: EPR Spectroscopic Studies of Weak Interactions between Dissimilar Electron Spin Qubits

Hybrid [2]rotaxanes and pseudorotaxanes are reported where the magnetic interaction between dissimilar spins is controlled to create AB and AB2 electron spin systems, allowing independent control of weakly interacting S=${{ 1/2 }}$ centers.

Inducing magnetic communication in caged dinuclear Co(ii) systems

Magnetic interactions were probed for a series of mono and tri atomic bridged dinuclear Co(ii) azacryptand complexes. Magneto-structural correlations were established usingab initiocalculations.

A hybrid organic–inorganic molecular daisy chain

A hybrid daisy-chain has been made, involving an organic thread for an inorganic ring, where the organic thread for the ring also acts as a ligand for a second ring. The ring contains six chromium(iii) and two zinc(ii) ions, and two isomers of the rings are found in the daisy-chain.

Magnetic anisotropy of mononuclear Ni(II) complexes: on the importance of structural diversity and the structural distortions

Mononuclear Ni(II) complexes are particularly attractive in the area of single-molecule magnets as the axial zero-field splitting (D) for the Ni(II) complexes is in the range of -200 to +200 cm(-1) . Despite this advantage, very little is known on the origin of anisotropy across various coordination ligands, coordination numbers, and particularly what factors influence the D parameter in these complexes. To answer some of these questions, herein we have undertaken a detailed study of a series of mononuclear Ni(II) complexes with ab initio calculations. Our results demonstrate that three prominent spin-conserved low-lying d-d transitions contribute significantly to the D value. Variation in the sign and the magnitude of D values are found to correlate to the specific structural distortions. Apart from the metal-ligand bond lengths, two different parameters, namely, Δα and Δβ, which are correlated to the cis angles present in the coordination environment, are found to significantly influence the axial D values. Developed magneto-structural D correlations suggest that the D values can be enhanced significantly by fine tuning the structural distortion in the coordination environment. Calculations performed on a series of Ni(II) models with coordination numbers two to six unfold an interesting observation-the D parameter increases significantly upon a reduction in coordination number compared with a reference octahedral coordination. Besides, if high symmetry is maintained, even larger coordination numbers yield large D values.

Large zero-field splittings of the ground spin state arising from antisymmetric exchange effects in heterometallic triangles

[Ru2Mn(O)(O2CtBu)6(py)3] has an S=5/2 ground state with a very large zero-field splitting (ZFS) of D=2.9 cm(-1), as characterized by EPR spectroscopy at 4-330 GHz. This is far too large to be due to the Mn(II) ion (D <0.2 cm(-1)), as shown from the {Fe2Mn} analogue, but can be modeled by antisymmetric exchange effects.

A classification of spin frustration in molecular magnets from a physical study of large odd-numbered-metal, odd electron rings

The term "frustration" in the context of magnetism was originally used by P. W. Anderson and quickly adopted for application to the description of spin glasses and later to very special lattice types, such as the kagomé. The original use of the term was to describe systems with competing antiferromagnetic interactions and is important in current condensed matter physics in areas such as the description of emergent magnetic monopoles in spin ice. Within molecular magnetism, at least two very different definitions of frustration are used. Here we report the synthesis and characterization of unusual nine-metal rings, using magnetic measurements and inelastic neutron scattering, supported by density functional theory calculations. These compounds show different electronic/magnetic structures caused by frustration, and the findings lead us to propose a classification for frustration within molecular magnets that encompasses and clarifies all previous definitions.

Physical studies of heterometallic rings: an ideal system for studying magnetically-coupled systems

Heterometallic rings of general formula [Cat][M(7)M'F(8)(O(2)C(t)Bu)(8)] (M = a trivalent metal, M' = a divalent metal, cat = a secondary ammonium cation, caesium or rubidium) contain an octagon of metal centres with each metal-metal edge bridged by a fluoride and two carboxylates. The rings when M = Cr(III) give remarkably beautiful EPR and INS spectra, and allow us to examine new techniques. Use of these techniques allows us to study the models used to describe magnetic behaviour in exchange coupled systems. In this tutorial review we discuss the two main approaches to modelling magnetic data - the strong exchange limit and the microscopic Hamiltonian approaches, aiming to explain the major differences between the two approaches. We also describe some more esoteric measurements and theories.

Chemical engineering of molecular qubits

We show that the electron spin phase memory time, the most important property of a molecular nanomagnet from the perspective of quantum information processing, can be improved dramatically by chemically engineering the molecular structure to optimize the environment of the spin. We vary systematically each structural component of the class of antiferromagnetic Cr(7)Ni rings to identify the sources of decoherence. The optimal structure exhibits a phase memory time exceeding 15  μs.

Linking heterometallic rings for quantum information processing and amusement

Linking polymetallic cages can be a method for creating new structures and new properties. In this tutorial review we use heterometallic anti-ferromagnetically coupled rings (AF-rings) as exemplars for three approaches that can be used to link cage compounds. The first of three routes involves an ion-pair interaction supported by hydrogen-bonding interactions, which allows the synthesis of hybrid rotaxanes among other materials. The second route involves functionalising the exterior of the AF-ring so that it will act as a Lewis base; complexes involving coordination of pyridine to bridging monometallic and dimetallic fragments are discussed. The third route involves creating a vacancy on one site of the AF-ring, and then using the ring as a Lewis acid. Di-imine ligands can then be used to link the AF-rings into dimers. A brief discussion of the physical properties of these systems is also included.