The chimera of 2D- and 1D-graphene magnetization by hydrogenation or fluorination: critically revisiting old schemes and proposing new ones by ab initio methods.

Graphene is an ideal candidate material for spintronics due to its layered structure and peculiar electronic structure. However, in its pristine state, the production of magnetic moments is not trivial. A very appealing approach is the chemical modification of pristine graphene. The main obstacle is the control of the geometrical features and the selectivity of functional groups. The lack of a periodic functionalization pattern of the graphene sheet prevents, therefore, the achievement of long-range magnetic order, thus limiting its use in spintronic devices. In such regards, the stability and the magnitude of the instilled magnetic moment depending on the size and shape of in silico designed graphane islands and ribbons embedded in graphene matrix will be computed and analysed. Our findings thus suggest that a novel and magneto-active graphene derivative nanostructure could become achievable more easily than extended graphone or nanoribbons, with a strong potential for future spintronics applications with a variable spin-current density.

A Heterometallic Porphyrin Dimer as a Potential Quantum Gate: Magneto-Structural Correlations and Spin Coherence Properties.

In the development of two-qubit quantum gates, precise control over the intramolecular spin-spin interaction between molecular spin units plays a pivotal role. A weak but measurable exchange coupling is especially important for achieving selective spin addressability that allows controlled manipulation of the computational basis states |00⟩ |01⟩ |10⟩ |11⟩ by microwave pulses. Here, we report the synthesis and Electron Paramagnetic Resonance (EPR) study of a heterometallic meso-meso (m-m) singly-linked VIV O-CuII porphyrin dimer. X-band continuous wave EPR measurements in frozen solutions suggest a ferromagnetic exchange coupling of ca. 8 ⋅ 10-3  cm-1 . This estimation is supported by Density Functional Theory calculations, which also allow disentangling the ferro- and antiferromagnetic contributions to the exchange. Pulsed EPR experiments show that the dimer maintains relaxation times similar to the monometallic CuII porphyrins. The addressability of the two individual spins is made possible by the different g-tensors of VIV and CuII -ions, in contrast to homometallic dimers where tilting of the porphyrin planes plays a key role. Therefore, single-spin addressability in the heterometallic dimer can be maintained even with small tilting angles, as expected when deposited on surface, unlocking the full potential of molecular quantum gates for practical applications.

Mixed-Sandwich Titanium(III) Qubits on Au(111): Electron Delocalization Ruled by Molecular Packing.

Organometallic sandwich complexes are versatile molecular systems that have been recently employed for single-molecule manipulation and spin sensing experiments. Among related organometallic compounds, the mixed-sandwich S = 1/2 complex (η8-cyclooctatetraene)(η5-cyclopentadienyl)titanium, here [CpTi(cot)], has attracted interest as a spin qubit because of the long coherence time. Here the structural and chemical properties of [CpTi(cot)] on Au(111) are investigated at the monolayer level by experimental and computational methods. Scanning tunneling microscopy suggests that adsorption occurs in two molecular orientations, lying and standing, with a 3:1 ratio. XPS data evidence that a fraction of the molecules undergo partial electron transfer to gold, while our computational analysis suggests that only the standing molecules experience charge delocalization toward the surface. Such a phenomenon depends on intermolecular interactions that stabilize the molecular packing in the monolayer. This orientation-dependent molecule-surface hybridization opens exciting perspectives for selective control of the molecule-substrate spin delocalization in hybrid interfaces.

Quantitative Assessment of Ligand Substituent Effects on σ- and π-Contributions to Fe-N Bonds in Spin Crossover FeII Complexes.

The effect of para-substituent X on the electronic structure of sixteen tridentate 4-X-(2,6-di(pyrazol-1-yl))-pyridine (bppX ) ligands and the corresponding solution spin crossover [FeII (bppX )2 ]2+ complexes is analysed further, to supply quantitative insights into the effect of X on the σ-donor and π-acceptor character of the Fe-NA (pyridine) bonds. EDA-NOCV on the sixteen LS complexes revealed that neither ΔEorb,σ+π (R2 =0.48) nor ΔEorb,π (R2 =0.31) correlated with the experimental solution T1/2 values (which are expected to reflect the ligand field imposed on the iron centre), but that ΔEorb,σ correlates well (R2 =0.82) and implies that as X changes from EDG→EWG (Electron Donating to Withdrawing Group), the ligand becomes a better σ-donor. This counter-intuitive result was further probed by Mulliken analysis of the NA atomic orbitals: NA (px ) involved in the Fe-N σ-bond vs. the perpendicular NA (pz ) employed in the ligand aromatic π-system. As X changes EDG→EWG, the electron population on NA (pz ) decreases, making it a better π-acceptor, whilst that in NA (px ) increases, making it a better σ-bond donor; both increase ligand field, and T1/2 as observed. In 2016, Halcrow, Deeth and co-workers proposed an intuitively reasonable explanation of the effect of the para-X substituents on the T1/2 values in this family of complexes, consistent with the calculated MO energy levels, that M→L π-backdonation dominates in these M-L bonds. Here the quantitative EDA-NOCV analysis of the M-L bond contributions provides a more complete, coherent and detailed picture of the relative impact of M-L σ-versus π-bonding in determining the observed T1/2 , refining the earlier interpretation and revealing the importance of the σ-bonding. Furthermore, our results are in perfect agreement with the ΔE(HS-LS) vs. σp + (X) correlation reported in their work.

An exchange coupled meso-meso linked vanadyl porphyrin dimer for quantum information processing.

We report here the synthesis of a new meso-meso (m-m) singly linked vanadyl-porphyrin dimer that crystallizes in two different pseudo-polymorphs. The single crystal continuous-wave electron paramagnetic resonance investigation evidences a small but crucial isotropic exchange interaction, J, between the two tilted, and thus distinguishable, spin centers of the order of 10-2 cm-1. The experimental and DFT studies evidence a correlation between J values and porphyrin plane tilting angle and distortion. Pulsed EPR analysis shows that the two vanadyl dimers maintain the coherence time of the monomer. With the obtained spin Hamiltonian parameters, we identify suitable transitions that could be used as computational basis states. Our results, coupled with the evaporability of porphyrin systems, establish this class of dimers as extremely promising for quantum information processing applications.

Correction: An exchange coupled meso-meso linked vanadyl porphyrin dimer for quantum information processing.

[This corrects the article DOI: 10.1039/D2SC04969D.].

Hetero-tri-spin systems: an alternative stairway to the single molecule magnet heaven?

The search for molecule-based magnetic materials has stimulated over the years the development of extremely rich coordination chemistry. Various combinations of spin carriers have been investigated and illustrated by a plethora of hetero-spin complexes: 3d-nd, 3d-4f, 2p-3d, and 2p-4f. More recently, two other classes of hetero-spin complexes have grown rapidly: compounds containing three different paramagnetic metal ions, or one radical and two different paramagnetic metal ions (all within the same molecular entity). Such new classes of systems represent a challenge both from a synthetic and theoretical point of view. Indeed, the synthetic control and the understanding of the spin topology effect on the overall magnetic behavior from first-principles is a difficult problem to be solved. The presence of different spin carriers in a single molecule makes such compounds particularly interesting because they offer the possibility of developing new magnetic properties, different from those of hetero-bi-spin or homo-spin systems. A critical overview taking the case of 2p-3d-4f complexes is the focus of this perspective paper. An original organic picture of the state-of-art in this field and new hints about the main directions that should be pursued to achieve hetero-tri-spin systems with large anisotropy barriers, low quantum tunneling of magnetization and, possibly, large blocking temperatures are provided in this article through an analysis based on numerically revisiting already published data and a critical survey of the literature reported so far. The reasons for the limited success obtained for the largely used 3d-2p-4f topology are given along with the ones explaining the failure for the 2p-4f-3d case. The still never synthesized linear 2p-3d-4f spin topology seemed to be the most promising one based on the results obtained for the unique closed hetero-tri-spin closed triangular system synthesized so far.

Temperature Dependence of Spin-Phonon Coupling in [VO(acac)2]: A Computational and Spectroscopic Study.

Molecular electronic spins are good candidates as qubits since they are characterized by a large tunability of their electronic and magnetic properties through a rational chemical design. Coordination compounds of light transition metals are promising systems for spin-based quantum information technologies, thanks to their long spin coherence times up to room temperature. Our work aims at presenting an in-depth study on how the spin-phonon coupling in vanadyl-acetylacetonate, [VO(acac)2], can change as a function of temperature using terahertz time-domain spectroscopy and density functional theory (DFT) calculations. Powder THz spectra were recorded between 10 and 300 K. The temperature dependence of vibrational frequencies was then accounted for in the periodic DFT calculations using unit-cell parameters measured at two different temperatures and the optimized ones, as usually reported in the literature. In this way, it was possible to calculate the observed THz anharmonic frequency shift with high accuracy. The overall differences in the spin-phonon coupling magnitudes as a function of temperature were also highlighted showing that the computed trends have to be ascribed to the anisotropic variation of cell parameters.

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

The unique electronic and magnetic properties of lanthanide molecular complexes place them at the forefront of the race toward high-temperature single-molecule magnets and magnetic quantum bits. The design of compounds of this class has so far being almost exclusively driven by static crystal field considerations, with an emphasis on increasing the magnetic anisotropy barrier. Now that this guideline has reached its maximum potential, a deeper understanding of spin-phonon relaxation mechanisms presents itself as key in order to drive synthetic chemistry beyond simple intuition. In this work, we compute relaxation times fully ab initio and unveil the nature of all spin-phonon relaxation mechanisms, namely Orbach and Raman pathways, in a prototypical Dy single-molecule magnet. Computational predictions are in agreement with the experimental determination of spin relaxation time and crystal field anisotropy, and show that Raman relaxation, dominating at low temperature, is triggered by low-energy phonons and little affected by further engineering of crystal field axiality. A comprehensive analysis of spin-phonon coupling mechanism reveals that molecular vibrations beyond the ion's first coordination shell can also assume a prominent role in spin relaxation through an electrostatic polarization effect. Therefore, this work shows the way forward in the field by delivering a novel and complete set of chemically sound design rules tackling every aspect of spin relaxation at any temperature.

Magnetic anisotropy on demand exploiting high-pressure as remote control: an ab initio proof of concept.

Lanthanide based single molecule magnets have recently become very promising systems for creating single molecule devices working at high temperatures (nitrogen boiling temperature). However, the variation of the direction of the anisotropy tensor as a function of the applied pressure still represents a quite unexplored field. Application of external pressure can be a promising method toward neat control of magnetic anisotropy and relaxation processes in the bulk phase. Required criteria for being eligible for such systems are as follows: the presence of first excited energy levels with significantly different orientations of its anisotropy tensor; sufficiently low energies of such levels so that they can mix with the ground state; and the possibility of tuning their energies by small geometrical perturbations. The archetype compound {Na[DyDOTA(H2O)]·4H2O} (1) (H4DOTA = 1,4,7,10-tetraazacyclododecane-1,4,7,10-N,N',N'',N'''-tetraacetic acid) fulfils all such criteria. A state-of-the-art in silico proof of concept study on the possibility of controlling the orientation of the anisotropy tensor as a function of pressure in [DyDOTA(H2O)]- by inducing different apical water molecule (AWM) orientations and/or DOTA-induced crystal field is presented.

Magnetic Anisotropy Trends along a Full 4f-Series: The fn+7 Effect.

The combined experimental and computational study of the 13 magnetic complexes belonging to the Na[LnDOTA(H2O)] (H4DOTA = tetraazacyclododecane-N,N',N″,N‴-tetraacetic acid and Ln = Ce-Yb) family allowed us to identify a new trend: the orientation of the magnetic anisotropy tensors of derivatives differing by seven f electrons practically coincide. We name this trend the fn+7 effect. Experiments and theory fully agree on the match between the magnetic reference frames (e.g., the easy, intermediate, and hard direction). The shape of the magnetic anisotropy of some couples of ions differing by seven f electrons might seem instead different at first look, but our analysis explains a hidden similarity. We thus pave the way toward a reliable predictivity of the magnetic anisotropy of lanthanide complexes with a consequent reduced need of computational and synthetical efforts. We also offer a way to gain information on ions with a relatively small total angular momentum (i.e., Sm3+ and Eu3+) and on the radioactive Pm3+, which are difficult to investigate experimentally.

Chemisorption of nitronyl-nitroxide radicals on gold surface: an assessment of morphology, exchange interaction and decoherence time.

A combined Tof-SIMS, XPS and STM characterization has been performed to study the deposition of a sulphur-functionalized nitronyl nitroxide radical on Au(111) clearly demonstrating the chemisorption of intact molecules. Continuous -wave EPR characterization showed that the radical molecules maintain their paramagnetic character. Pulsed EPR measurements allowed to determine the decoherence time of the nanostructure at 80 K, which turned out to be comparable to the one measured in frozen solution and longer than previously reported for many radicals and other paramagnetic molecules at much lower temperatures. Furthermore, we conducted a state-of-the-art ab initio molecular dynamics study, suggesting different possible scenarios for chemisorption geometries and predicting the energetically favoured geometry. Calculation of the magnetic properties indicates a partial non-innocent role of the gold surface in determining the magnetic interactions between radicals in packed structures. This suggests that the observed EPR spectrum is to be attributed to low-density domains of disordered radicals interacting via dipolar interactions.

Exploring the Organometallic Route to Molecular Spin Qubits: The [CpTi(cot)] Case.

The coherence time of the 17-electron, mixed sandwich complex [CpTi(cot)], (η8 -cyclooctatetraene)(η5 -cyclopentadienyl)titanium, reaches 34 µs at 4.5 K in a frozen deuterated toluene solution. This is a remarkable coherence time for a highly protonated molecule. The intramolecular distances between the Ti and H atoms provide a good compromise between instantaneous and spin diffusion sources of decoherence. Ab initio calculations at the molecular and crystal packing levels reveal that the characteristic low-energy ring rotations of the sandwich framework do not yield a too detrimental spin-lattice relaxation because of their small spin-phonon coupling. The volatility of [CpTi(cot)] and the accessibility of the semi-occupied, non-bonding d z 2 orbital make this neutral compound an ideal candidate for single-qubit addressing on surface and quantum sensing in combination with scanning probe microscopy.

Probing Vibrational Symmetry Effects and Nuclear Spin Economy Principles in Molecular Spin Qubits.

The selection of molecular spin qubits with a long coherence time, Tm, is a central task for implementing molecule-based quantum technologies. Even if a sufficiently long Tm can be achieved through an efficient synthetic strategy and ad hoc experimental measurement procedures, many factors contributing to the loss of coherence still need to be thoroughly investigated and understood. Vibrational properties and nuclear spins of hydrogens are two of them. The former plays a paramount role, but a detailed theoretical investigation aimed at studying their effects on the spin dynamics of molecular complexes such as the benchmark phthalocyanine (Pc) is still missing, whereas the effect of the latter deserves to be examined in detail for such a class of compounds. In this work, we adopted a combined theoretical and experimental approach to investigate the relaxation properties of classical [Cu(Pc)] and a CuII complex based on the ligand tetrakis(thiadiazole)porphyrazine (H2TTDPz), characterized by a hydrogen-free molecular structure. Systematic calculations of molecular vibrations exemplify the effect of normal modes on the spin-lattice relaxation process, unveiling a different contribution to T1 depending on the symmetry of normal modes. Moreover, we observed that an appreciable Tm enhancement could be achieved by removing hydrogens from the ligand.

Quantitative and Chemically Intuitive Evaluation of the Nature of M-L Bonds in Paramagnetic Compounds: Application of EDA-NOCV Theory to Spin Crossover Complexes.

To improve understanding of M-L bonds in 3d transition metal complexes, analysis by energy decomposition analysis and natural orbital for chemical valence model (EDA-NOCV) is desirable as it provides a full, quantitative and chemically intuitive ab initio description of the M-L interactions. In this study, a generally applicable fragmentation and computational protocol was established and validated by using octahedral spin crossover (SCO) complexes, as the transition temperature (T1/2 ) is sensitive to subtle changes in M-L bonding. Specifically, EDA-NOCV analysis of Fe-N bonds in five [FeII (Lazine )2 (NCBH3 )2 ], in both low-spin (LS) and paramagnetic high-spin (HS) states led to: 1) development of a general, widely applicable, corrected M+L6 fragmentation, tested against a family of five LS [FeII (Lazine )3 ](BF4 )2 complexes; this confirmed that three Lazine are stronger ligands (ΔEorb,σ+π =-370 kcal mol-1 ) than 2 Lazine +2 NCBH3 (=-335 kcal mol-1 ), as observed. 2) Analysis of Fe-L bonding on LS→HS, reveals more ionic (ΔEelstat ) and less covalent (ΔEorb ) character (ΔEelstat :ΔEorb 55:45 LS→64:36 HS), mostly due to a big drop in σ (ΔEorb,σ ↓50 %; -310→-145 kcal mol-1 ), and a drop in π contributions (ΔEorb,π ↓90 %; -30→-3 kcal mol-1 ). 3) Strong correlation of observed T1/2 and ΔEorb,σ+π , for both LS and HS families (R2 =0.99 LS, R2 =0.95 HS), but no correlation of T1/2 and ΔΔEorb,σ+π (LS-HS) (R2 =0.11). Overall, this study has established and validated an EDA-NOCV protocol for M-L bonding analysis of any diamagnetic or paramagnetic, homoleptic or heteroleptic, octahedral transition metal complex. This new and widely applicable EDA-NOCV protocol holds great promise as a predictive tool.

An Oxalate-Bridged Copper(II) Complex Combining Monodentate Benzoate, 2,2'-bipyridine and Aqua Ligands: Synthesis, Crystal Structure and Investigation of Magnetic Properties.

A dinuclear copper(II) complex of formula [{Cu(bipy)(bzt)(OH2)}2(µ-ox)] (1) (where bipy = 2,2'-bipyridine, bzt = benzoate and ox = oxalate) was synthesised and characterised by diffractometric (powder and single-crystal XRD) and thermogravimetric (TG/DTG) analyses, spectroscopic techniques (IR, Raman, electron paramagnetic resonance spectroscopy (EPR) and electronic spectroscopy), magnetic measurements and density functional theory (DFT) calculations. The analysis of the crystal structure revealed that the oxalate ligand is in bis(bidentate) coordination mode between two copper(II) centres. The other four positions of the coordination environment of the copper(II) ion are occupied by one water molecule, a bidentate bipy and a monodentate bzt ligand. An inversion centre located on the ox ligand generates the other half of the dinuclear complex. Intermolecular hydrogen bonds and π-π interactions are responsible for the organisation of the molecules in the solid state. Molar magnetic susceptibility and field dependence magnetisation studies evidenced a weak intramolecular-ferromagnetic interaction (J = +2.9 cm-1) between the metal ions. The sign and magnitude of the calculated J value by density functional theory (DFT) are in agreement with the experimental data.

Quantum dynamics of a single molecule magnet on superconducting Pb(111).

Magnetic materials interfaced with superconductors may reveal new physical phenomena with potential for quantum technologies. The use of molecules as magnetic components has already shown great promise, but the diversity of properties offered by the molecular realm remains largely unexplored. Here we investigate a submonolayer of tetrairon(III) propeller-shaped single molecule magnets deposited on a superconducting lead surface. This material combination reveals a strong influence of the superconductor on the spin dynamics of the single molecule magnet. It is shown that the superconducting transition to the condensate state switches the single molecule magnet from a blocked magnetization state to a resonant quantum tunnelling regime. Our results open perspectives to control single molecule magnetism via superconductors and to use single molecule magnets as local probes of the superconducting state.

The Origin of Magnetic Anisotropy and Single-Molecule Magnet Behavior in Chromium(II)-Based Extended Metal Atom Chains.

Chromium(II)-based extended metal atom chains have been the focus of considerable discussion regarding their symmetric versus unsymmetric structure and magnetism. We have now investigated four complexes of this class, namely, [Cr3(dpa)4X2] and [Cr5(tpda)4X2] with X = Cl- and SCN- [Hdpa = dipyridin-2-yl-amine; H2tpda = N2,N6-di(pyridin-2-yl)pyridine-2,6-diamine]. By dc/ac magnetic techniques and EPR spectroscopy, we found that all these complexes have easy-axis anisotropies of comparable magnitude in their S = 2 ground state (|D| = 1.5-1.8 cm-1) and behave as single-molecule magnets at low T. Ligand-field and DFT/CASSCF calculations were used to explain the similar magnetic properties of tri- versus pentachromium(II) strings, in spite of their different geometrical preferences and electronic structure. For both X ligands, the ground structure is unsymmetric in the pentachromium(II) species (i.e., with an alternation of long and short Cr-Cr distances) but is symmetric in their shorter congeners. Analysis of the electronic structure using quasi-restricted molecular orbitals (QROs) showed that the four unpaired electrons in Cr5 species are largely localized in four 3d-like QROs centered on the terminal, "isolated" Cr2+ ion. In Cr3 complexes, they occupy four nonbonding combinations of 3d-like orbitals centered only on the two terminal metals. In both cases, then, QRO eigenvalues closely mirror the 3d-level pattern of the terminal ions, whose coordination environment remains quite similar irrespective of chain length. We conclude that the extent of unpaired-electron delocalization has little impact on the magnetic anisotropy of these wire-like molecular species.

Surface effects on a photochromic spin-crossover iron(ii) molecular switch adsorbed on highly oriented pyrolytic graphite.

Thin films of an iron(ii) complex with a photochromic diarylethene-based ligand and featuring a spin-crossover behaviour have been grown by sublimation in ultra-high vacuum on highly oriented pyrolytic graphite and spectroscopically characterized through high-resolution X-ray and ultraviolet photoemission, as well as via X-ray absorption. Temperature-dependent studies demonstrated that the thermally induced spin-crossover is preserved at a sub-monolayer (0.7 ML) coverage. Although the photochromic ligand ad hoc integrated into the complex allows the photo-switching of the spin state of the complex at room temperature both in bulk and for a thick film on highly oriented pyrolytic graphite, this photomagnetic effect is not observed in sub-monolayer deposits. Ab initio calculations justify this behaviour as the result of specific adsorbate-substrate interactions leading to the stabilization of the photoinactive form of the diarylethene ligand over photoactive one on the surface.

Covalency and magnetic anisotropy in lanthanide single molecule magnets: the DyDOTA archetype.

Lanthanide ions when complexed by polyamino-polycarboxylate chelators form a class of compounds of paramount importance in several research and technological areas, particularly in the fields of magnetic resonance and molecular magnetism. Indeed, the gadolinium derivative is one of the most employed contrast agents for magnetic resonance imaging while the dysprosium one belongs to a new generation of contrast agents for T2-weighted MRI. In molecular magnetism, Single Molecule Magnets (SMMs) containing lanthanide ions have become readily popular in the chemistry and physics communities since record energy barriers to the reversal of magnetization were reported. The success of lanthanide complexes lies in their large anisotropy due to the contribution of the unquenched orbital angular momentum. However, only a few efforts have been made so far to understand how the f-orbitals can be influenced by the surrounding ligands. The outcomes have been rationalized using mere electrostatic perturbation models. In the archetype compound [Na{Dy(DOTA) (H2O)}]·4H2O (Na{DyDOTA}·4H2O) an unexpected easy axis of magnetization perpendicular to the pseudo-tetragonal axis of the molecule was found. Interestingly, a dependency of the orientation of the principal magnetization axis on the simple rotation of the coordinating apical water molecule (AWM) - highly relevant for MRI contrast - around the Dy-OAWM bond was predicted by ab initio calculations, too. However, such a behaviour has been contested in a subsequent paper justifying their conclusions on pure electrostatic assumptions. In this paper, we want to shed some light on the nature of the subtle effects induced by the water molecule on the magnetic properties of the DyDOTA archetype complex. Therefore, we have critically reviewed the structural models already published in the literature along with new ones, showing how the easy axis orientation can dangerously depend on the chosen model. The different computed behaviors of the orientation of the easy axis of magnetization have been rationalized as a function of the energy gap between the ground and the first excited doublet. Magneto-structural correlations together with a mapping of the electrostatic potential generated by the ligands around the Dy(iii) ion through a multipolar expansion have also been used to evidence and quantify the covalent contribution of the AWM orbitals.