Spin qubits of Cu(II) doped in Zn(II) metal-organic frameworks above microsecond phase memory time.

With the aim of creating Cu(II) spin qubits in a rigid metal-organic framework (MOF), this work demonstrates a doping of 5 %, 2 %, 1 %, and 0.1 % mol of Cu(II) ions into a perovskite-type MOF [CH6 N3 ][ZnII (HCOO)3 ]. The presence of dopant Cu(II) sites are confirmed with anisotropic g-factors (gx =2.07, gy =2.12, and gz =2.44) in the S=1/2 system by experimentally and theoretically. Magnetic dynamics indicate the occurrence of a slow magnetic relaxation via the direct and Raman processes under an applied field, with a relaxation time (τ) of 3.5 ms (5 % Cu), 9.2 ms (2 % Cu), and 15 ms (1 % Cu) at 1.8 K. Furthermore, pulse-ESR spectroscopy reveals spin qubit properties with a spin-spin relaxation (phase memory) time (T2 ) of 0.21 µs (2 %Cu), 0.39 µs (1 %Cu), and 3.0 µs (0.1 %Cu) at 10 K as well as Rabi oscillation between MS =±1/2 spin sublevels. T2 above microsecond is achieved for the first time in the Cu(II)-doped MOFs. It can be observed at submicrosecond around 50 K. These spin relaxations are very sensitive to the magnetic dipole interactions relating with cross-relaxation between the Cu(II) sites and can be tuned by adjusting the dopant concentration.

Observation of slow magnetic relaxation phenomena in spatially isolated π-radical ions.

The use of molecular spins as quantum bits is fascinating because it offers a wide range of strategies through chemical modifications. In this regard, it is very interesting to search for organic radical ions that have small spin-orbit coupling values. On the other hand, the feature of the magnetic relaxation of π-organic radical ions is rarely exploited due to the difficulty of spin dilution, and π-stacking interaction. In this study, we focus on N,N',N''-tris(2,6-dimethylphenyl)benzenetriimide (BTI-xy), where three xylene moieties connected to the imide groups cover the π-plane of the BTI core. As a result, BTI-xy radical anions without π-stacking interaction were obtained. This led to the slow magnetization relaxation, which is reported for the first time in organic radicals. Furthermore, the relaxation times in a solution state revealed the importance of spin interaction.

A Kinetically Stabilized Nitrogen-Doped Triangulene Cation: Stable and NIR Fluorescent Diradical Cation with Triplet Ground State.

A kinetically-stabilized nitrogen-doped triangulene cation derivative has been synthesized and isolated as the stable diradical with a triplet ground state that exhibits near-infrared emission. As was the case for a triangulene derivative we previously synthesized, the triplet ground state with a large singlet-triplet energy gap was experimentally confirmed by magnetic measurements. In contrast to the triangulene derivative, the nitrogen-doped triangulene cation derivative is highly stable even in solution under air and exhibits near-infrared absorption and emission because the alternancy symmetry of triangulene is broken by the nitrogen cation. Breaking the alternancy symmetry of triplet alternant hydrocarbon diradicals by a nitrogen cation would therefore be an effective strategy to create stable diradicals possessing magnetic properties similar to the parent hydrocarbons but with different electrochemical and photophysical properties.

Bis-periazulene (Cyclohepta[def]fluorene) as a Nonalternant Isomer of Pyrene: Synthesis and Characterization of Its Triaryl Derivatives.

Bis-periazulene (cyclohepta[def]fluorene), which is an unknown pyrene isomer, was synthesized as kinetically protected forms. Its triaryl derivatives 1c-e exhibited the superimposed electronic structures of peripheral, polarized, and open-shell π-conjugated systems. In contrast to previous theoretical predictions, bis-periazulene derivatives were in the singlet ground state. Changing an aryl group controlled the energy gap between the lowest singlet-triplet states.

A Redox-Active Microporous Organosiloxane Containing a Stable Neutral Radical, Trioxotriangulene.

A new silyl-substituted trioxotriangulene (TOT) neutral radical and corresponding porous organosiloxanes (POSs) were synthesized. The neutral radical exhibited a peculiarly high stability and formed a diamagnetic π-dimer characteristic to TOT neutral radicals stabilized by the strong multiple SOMO-SOMO interaction in both solution and solid states. POSs including TOT units within the organosiloxane-wall were prepared by polycondensation of the silyl groups and formed microporous structures with ∼1 nm-size diameters. Redox ability of TOT units in the POS was demonstrated by the treatment of oxidant/reductant in heterogeneous suspension condition, where the TOT units were reversibly converted between reduced and neutral radical species. Furthermore, the solid-state electrochemical measurements of the POS revealed the reversible multi-stage redox ability of TOT units involving polyanionic species within the organosiloxane-wall.

Double-σ-Bonded Close-Shell Dimers and Peroxy-Linked Open-Shell Dimer Derived from a C3 Symmetric Trioxophenalenyl Neutral Diradical.

A novel neutral diradical of π-extended phenalenyl derivative having three oxo-groups, tri-tert-butyl-1,4,7-trioxophenalenyl, and two types of the corresponding σ-dimers were investigated. Quantum chemical calculations showed that the neutral diradical is in triplet ground state having doubly degenerate singly occupied molecular orbitals. The neutral diradical undergoes a σ-dimerization, generating two types of σ-dimers immediately after the preparation. One of the σ-dimers, which was selectively generated in the crystalline state, was a close-shell dimer linked through double-σ-bonds on the phenalenyl skeleton with a long C-C bond length of 1.66 Å. The other σ-dimer, which existed only in the solution state, was a peroxy-linked open-shell dimer in which one σ-bond was formed between two oxygen atoms. Furthermore, the temperature-dependent 1 H NMR and ESR spectra revealed that these σ-dimers are in equilibrium in the solution state by the reversible σ-bond formation/cleavage via the neutral diradical as a key intermediate.

A Molecule Having 13 Unpaired Electrons: Magnetic Property of a Gadolinium(III) Complex Coordinated with Six Nitronyl Nitroxide Radicals.

A gadolinium(III) complex coordinated with six nitronyl nitroxide radicals showed intriguing temperature-dependent changes in magnetic susceptibilities. The gadolinium(III) ion in the complex is pseudo-eight-coordinated by three singlet-ground-state diradical anion species based on nitronyl nitroxide radicals. The magnetic susceptibility (χpT) of the gadolinium(III) complex at 298 K, whose value corresponded to that of a system with 13 unpaired electrons (seven-spin system), decreased upon a lowering of the temperature to 11 K but increased upon a further lowering of the temperature. Finally, the χpT value at 2 K was found to be higher than that at room temperature. The temperature-dependent magnetic behavior could be explained by a structural change in the diradical anion ligand due to its flexibility.

Synthesis and Isolation of a Kekulé Hydrocarbon with a Triplet Ground State.

Design, synthesis, and isolation of a Kekulé hydrocarbon with a triplet ground state is described. Its triplet ground state was unambiguously confirmed by ESR experiments, and the structure and fundamental physical properties were also revealed. The key feature of the molecular design is the decrease in the bonding interaction in the singlet state by aromatic stabilization of benzene rings and the increase of the exchange interaction of unpaired electrons which are favorable for the triplet state. These results contribute to the development of hydrocarbon-based organic magnetic materials.

Synthesis and Isolation of a Kinetically Stabilized Crystalline Triangulene.

The synthesis and isolation of hydrocarbons with a triplet ground state in crystalline forms have been sought in materials science. Triangulene is one of the most famous triplet-ground-state benzenoid hydrocarbons. Its unique electronic structure and highly symmetric structure have prompted many scientists to synthesize and isolate triangulene and its derivatives, but all attempts so far to isolate them as crystals have been unsuccessful. Herein we report the synthesis and isolation of a kinetically stabilized crystalline triangulene for the first time. The key to success is the introduction of bulky substituents onto the reactive zigzag edges. Its highly symmetric structure was confirmed by X-ray crystallography, and its fundamental properties, including the triplet ground state, were revealed. The achievement here will open the door for the synthesis and isolation of other hydrocarbons with higher spin multiplicity.

Structural dynamics of the chromo-shadow domain and chromodomain of HP1 bound to histone H3K9 methylated peptide, as measured by site-directed spin-labeling EPR spectroscopy.

The structural dynamics of the chromo-shadow domain (CSD) and chromodomain (CD) of human HP1 proteins essential for heterochromatin formation were investigated at the nanosecond and nanometer scales by site-directed spin labeling electron paramagnetic resonance and pulsed double resonance spectroscopy. Distance measurements showed that the spin-labeled CSD of human HP1α and HP1γ tightly dimerizes. Unlike CD-CD interaction observed in fission yeast HP1 in an inactivated state (Canzio et al., 2013), the two CDs of HP1α and HP1γ were spatially separated from each other, dynamically mobile, and ready for a Brownian search for H3K9-tri-methyl(me3) on histones. Complex formation of the CD with H3K9me3 slowed dynamics of the domain due to a decreased diffusion constant. CSD mobility was significantly (∼1.3-fold) lower in full-length HP1α than in HP1γ, suggesting that the immobilized conformation of human HP1α shows an auto-inactivated state. Differential properties of HP1α and HP1γ to form the inactive conformation could be relevant to its physiological role in the heterochromatin formation in a cell.

Aurophilic Interactions in Multi-Radical Species: Electronic-Spin and Redox Properties of Bis- and Tris-[(Nitronyl Nitroxide)-Gold(I)] Complexes with Phosphine-Ligand Scaffolds.

Multinuclear AuI complexes with two or three nitronyl nitroxide-2-ide radical anion and phosphine-ligand scaffolds, (NN-Au)2 -1 o, (NN-Au)2 -1 m, and (NN-Au)2 -1 p, have been synthesized to investigate the influence of AuI -AuI (aurophilic) interactions on the properties of multispin molecular systems. The desired complexes were successfully prepared in moderate yields in a one-pot synthesis from the corresponding phosphine ligand, AuI source, parent NN, and sodium hydroxide. Among the prepared complexes, (NN-Au)2 -1 o, in which an aurophilic interaction was clearly observed by crystal structure analysis, showed characteristic spin-spin interactions, electrochemical properties, and solvatochromic behavior. The results from theoretical calculations also suggested that the differences in properties between complex (NN-Au)2 -1 o and the other complexes are due to intramolecular aurophilic interactions.

Synthesis and Physical Properties of Trioxotriangulene Having Methoxy and Hydroxy Groups at α-Positions: Electronic and Steric Effects of Substituent Groups and Intramolecular Hydrogen Bonds.

New 4,8,12-trioxotriangulene (TOT) neutral radical derivatives having three methoxy and hydroxy groups at the α-positions were synthesized, and the substituent effects on the electronic spin and redox properties were elucidated in the theoretical and experimental methods. Due to the small SOMO coefficients at the α-positions of TOT, the methoxy groups in the TOT neutral radical had negligible effects on the electronic spin structure and redox ability. On the other hand, methoxy groups greatly increased the LUMO energy having large coefficients at α-positions and, thus, caused a remarkable negative-potential shift of the redox wave of anion species involving the dianion and trianion species. Converting the methoxy groups to hydroxy groups caused a dramatic change in the electronic structure of TOT, where the intramolecular hydrogen bonds between hydroxy groups and oxo groups strongly attracted a minus charge on the TOT skeleton. The HOMO energy of the monoanion species was significantly reduced, causing a blue shift of the HOMO-LUMO transition and an anodic shift of the redox potential. In addition, due to the steric repulsion smaller than that of the methoxy group, the hydroxy derivative showed a more planar molecular structure and a strong π-stacking ability.

Tin(II)-Nitrene Radical Complexes Formed by Electron Transfer from Redox-Active Ligand to Organic Azides and Their Reactivity in C(sp3)-H Activation.

A tin(II) complex coordinated by a sterically demanding o-phenylenediamido ligand is synthesized. The ligand is redox-active to reach a tin(II) complex with the diiminobenzosemiquinone radial anion in the oxidation by AgPF6. The tin(II) complex reacts with a series of nosylazides (x-NO2C6H4-SO2-N3; x = o, m, or p) at -30 °C to yield the corresponding nitrene radical bound tin(II) complexes. The nitrene radical complexes exhibit C(sp3)-H activation and amination reactivity.

Bayesian phase difference estimation: a general quantum algorithm for the direct calculation of energy gaps.

Quantum computers can perform full configuration interaction (full-CI) calculations by utilising the quantum phase estimation (QPE) algorithms including Bayesian phase estimation (BPE) and iterative quantum phase estimation (IQPE). In these quantum algorithms, the time evolution of wave functions for atoms and molecules is simulated conditionally with an ancillary qubit as the control, which make implementation to real quantum devices difficult. Also, most of the problems in chemistry discuss energy differences between two electronic states rather than total energies themselves, and thus direct calculations of energy gaps are promising for future applications of quantum computers to real chemistry problems. In the race of finding efficient quantum algorithms to solve quantum chemistry problems, we test a Bayesian phase difference estimation (BPDE) algorithm, which is a general algorithm to calculate the difference of two eigenphases of unitary operators in the several cases of the direct calculations of energy gaps between two electronic states on quantum computers, including vertical ionisation energies, singlet-triplet energy gaps, and vertical excitation energies. In the BPDE algorithm, state preparation is carried out conditionally on the ancillary qubit, and the time evolution of the wave functions in superposition of two electronic states are executed unconditionally. Based on our test, we conclude that BPDE is capable of computing the energy gap with an accuracy similar to BPE without controlled-time evolution simulations and with the smaller number of iterations in Bayesian optimisations.

Redox-Induced Modulation of Exchange Interaction in a High-Spin Ground-State Diradical/Triradical System.

A triplet ground-state diradical molecule, bis(nitronyl nitroxide)-substituted diphenyldihydrophenazine (1.. ), that can be converted into a one-electron oxidized species, 1…+ , in the quartet ground state has been developed. Surprisingly, these species, 1.. and 1…+ , can be used under ambient conditions because they are reasonably stable under aerobic conditions, even in solution. The temperature-dependent magnetic susceptibilities reveal that 1.. and 1…+ are in the triplet state, with a weak exchange interaction (J1 /kB = +3.1 K) and quartet ground state with a strong exchange interaction (J2 /kB = +160 K), respectively. The interconversion between the neutral and one-electron oxidized species can be realized through electrochemical reactions. Significantly different absorption bands in the near-IR region newly appeared in the electronic spectra acquired during electrochemical oxidation/reduction.

A probabilistic spin annihilation method for quantum chemical calculations on quantum computers.

A probabilistic spin annihilation method based on the quantum phase estimation algorithm is presented for quantum chemical calculations on quantum computers. This approach can eliminate more than one spin component from the spin contaminated wave functions by single operation. Comparison with the spin annihilation operation on classical computers is given.

Magnetic Properties of π-Conjugated Hybrid Phenoxyl-Nitroxide Radicals with Extended π-Spin Delocalization.

A series of stable and genuinely organic open-shell systems, π-conjugated phenoxyl-nitroxide free radicals (hybrid phenoxyl-nitroxide radicals), have been synthesized and their magnetic properties in the crystalline state investigated, revealing their usefulness as new building blocks for molecular magnetic materials. The salient electronic structure of the hybrid phenoxyl-nitroxide radicals is extended π-spin delocalization from the nitroxide moiety, mediating the localization effect intrinsic to nitroxide radicals. Five representative hybrid radicals containing an aliphatic, aromatic, and heteroaromatic substituent in the side part of the compact hybrid radical centers were synthesized, and their molecular/crystal structures in the crystalline state were determined by X-ray diffraction analyses. CW X-band ESR, 1H-ENDOR spectroscopy, and DFT calculations for the hybrid radicals confirmed that an unpaired spin delocalizes over the whole molecular frame including the nonconjugated fragments, suggesting the possibility of tuning their electronic properties through substituent effects in the crystalline state. Significant influence of the phenoxyl moiety on the electronic structure was analyzed in terms of the g-tensor calculations. The SQUID magnetization measurements revealed that the nitroxides bearing alkyl or aromatic substituents behave as 3D Curie-Weiss paramagnets with weak antiferromagnetic (AFM) (Θ = -1 to -2.6 K) or ferromagnetic (FM) (Θ = +0.33 K) spin-spin exchange interactions. On the other hand, heteroaromatically substituted hybrid phenoxyl-nitroxide showed significant AFM interactions with J/kB = -25.6 K. The analysis of the bulk magnetic properties based on the crystallographic data and DFT calculations revealed competition between the intermolecular AFM and FM interactions which originate from the C-O(phenoxyl)···Me(nitroxide) or (N)O-C(arom) infinite 1D head-to-tail chains and the C(arom)-C(arom) head-over-tail dimers forming 3D networks in their crystal lattices.

Open-Shell and Antiaromatic Character Induced by the Highly Symmetric Geometry of the Planar Heptalene Structure: Synthesis and Characterization of a Nonalternant Isomer of Bisanthene.

A nonbenzenoid hydrocarbon, difluoreno[1,9,8- alkj:1',9',8'- gfed]heptalene 1, is synthesized. Experimental and theoretical investigations demonstrate that the planar and symmetric heptalene core within 1 effectively induces the antiaromatic and open-shell character. These properties are not shared by bisanthene 2, a benzenoid isomer of 1.

Triplet Diradical-Cation Salts Consisting of the Phenothiazine Radical Cation and a Nitronyl Nitroxide.

The spin-spin and magnetic properties of two (nitronyl nitroxide)-(di-p-anisylamine-phenothiazine) diradical cation salts, (DAA-PTZ)+ -NN⋅MBr4 - (M=Ga, Fe), have been investigated. These diradical-cation species were prepared by the cross-coupling of iodophenothiazine DAA-PTZ-I with NN-AuPPh3 followed by oxidation with the thianthrenium radical cation (TA+ ⋅MBr4 - ). These salts were found to be highly stable under aerobic conditions. For the GaBr4 salt, large ferromagnetic intramolecular and small antiferromagnetic intermolecular interactions (J1 /kB =+320 K and J2 /kB =-2 K, respectively) were observed. The magnetic property of the Fe3+ salt was analyzed by using a six-spin model assuming identical intramolecular exchange interaction (J3 /kB =+320 K) and the other exchange interactions (J4 /kB =-7 K and J5 /kB =-4 K). A significant color change was observed in the UV/Vis/NIR absorption spectra upon electrochemical oxidation of the doublet DAA-PTZ-NN to the triplet (DAA-PTZ)+ -NN.

Quantum chemistry on quantum computers: quantum simulations of the time evolution of wave functions under the S2 operator and determination of the spin quantum number S.

Quantum computers have an enormous impact on quantum chemical calculations. Approaches to calculate the energies of atoms and molecules on quantum computers by utilizing quantum phase estimation (QPE) and the variational quantum eigensolver (VQE) have been well documented, and dozens of methodological improvements to decrease computational costs and to mitigate errors have been reported until recently. However, the possible methodological implementation of observables on quantum computers such as calculating the spin quantum numbers of arbitrary wave functions, which is a crucial issue in quantum chemistry, has been discussed less. Here, we propose a quantum circuit to simulate the time evolution of wave functions under an S2 operator, exp(-iS2t)|Ψ, and integrate it into the QPE circuit enabling us to determine the spin quantum number of the arbitrary wave functions. We demonstrate that the spin quantum numbers of up to three spins can be determined by only one qubit measurement in QPE.