Spin coherence and magnetization dynamics of TMA2[KCo1-xFex(CN)6] toward coordination-framework spin qubits.

Metal compounds with S = 1/2 coordination-frameworks have been emerging as new powerful qubit candidates. In this study, we have reported the CN-based coordination framework TMA2[KCo1-xFex(CN)6] to be a qubit. We explored the magnetization dynamics and spin coherence of the magnetic dilution of the S = 1/2 Fe(III) complex TMA2[KFe(CN)6] (TMA = tetramethylammonium) in its Co(III)-based diamagnetic analogue TMA2[KCo(CN)6]. Alternating-current (AC) susceptibility data illustrate a slow magnetic relaxation upon applying a field of 0.1 T, which follows the phonon-bottleneck relaxation mechanism along with the Raman process. A magnetic relaxation time (τ) of 0.3 s (2% Fe) was realized at 1.8 K. Moreover, pulsed EPR data reveal a coherence duration of 1 µs (0.1% Fe) at 4 K with successful observation of Rabi oscillation at 4 K and 13 K (2% Fe) using MW pulses with variable irradiation-field strengths. The overall results indicate that TMA2[KCo1-xFex(CN)6] represents a promising qubit candidate, as it is capable of being placed in any superposition of the two distinct Ms states (Ms = +1/2 and Ms = -1/2).

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.

Synthesis and characterization of a formal 21-electron cobaltocene derivative.

Metallocenes are highly versatile organometallic compounds. The versatility of the metallocenes stems from their ability to stabilize a wide range of formal electron counts. To date, d-block metallocenes with an electron count of up to 20 have been synthesized and utilized in catalysis, sensing, and other fields. However, d-block metallocenes with more than formal 20-electron counts have remained elusive. The synthesis and isolation of such complexes are challenging because the metal-carbon bonds in d-block metallocenes become weaker with increasing deviation from the stable 18-electron configuration. Here, we report the synthesis, isolation, and characterization of a 21-electron cobaltocene derivative. This discovery is based on the ligand design that allows the coordination of an electron pair donor to a 19-electron cobaltocene derivative while maintaining the cobalt-carbon bonds, a previously unexplored synthetic approach. Furthermore, we elucidate the origin of the stability, redox chemistry, and spin state of the 21-electron complex. This study reveals a synthetic method, structure, chemical bonding, and properties of the 21-electron metallocene derivative that expands our conceptual understanding of d-block metallocene chemistry. We expect that this report will open up previously unexplored synthetic possibilities in d-block transition metal chemistry, including the fields of catalysis and materials chemistry.

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.

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.

Quantum Algorithm for Numerical Energy Gradient Calculations at the Full Configuration Interaction Level of Theory.

A Bayesian phase difference estimation (BPDE) algorithm allows us to compute the energy gap of two electronic states of a given Hamiltonian directly by utilizing the quantum superposition of their wave functions. Here we report an extension of the BPDE algorithm to the direct calculation of the energy difference of two molecular geometries. We apply the BPDE algorithm for the calculation of numerical energy gradients based on the two-point finite-difference method, enabling us to execute geometry optimization of one-dimensional molecules at the full-CI level on a quantum computer. Results of numerical quantum circuit simulations of the geometry optimization of the H2 molecule with the STO-3G and 6-31G basis sets, the LiH and BeH2 molecules at the full-CI/STO-3G level, and the N2 molecule at the CASCI(6e,6o)/6-311G* level are given.

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.

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.

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.

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.

Adiabatic state preparation of correlated wave functions with nonlinear scheduling functions and broken-symmetry wave functions.

Adiabatic state preparation (ASP) can generate the correlated wave function by simulating the time evolution of wave function under the time-dependent Hamiltonian that interpolates the Fock operator and the full electronic Hamiltonian. However, ASP is inherently unsuitable for studying strongly correlated systems, and furthermore practical computational conditions for ASP are unknown. In quest for the suitable computational conditions for practical applications of ASP, we performed numerical simulations of ASP in the potential energy curves of N2, BeH2, and in the C2v quasi-reaction pathway of the Be atom insertion to the H2 molecule, examining the effect of nonlinear scheduling functions and the ASP with broken-symmetry wave functions with the S2 operator as the penalty term, contributing to practical applications of quantum computing to quantum chemistry. Eventually, computational guidelines to generate the correlated wave functions having the square overlap with the complete-active space self-consistent field wave function close to unity are discussed.

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.

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.

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.

Quantum Algorithm for Full Configuration Interaction Calculations without Controlled Time Evolutions.

A quantum phase estimation algorithm allows us to perform full configuration interaction (full-CI) calculations on quantum computers with polynomial costs against the system size under study, but it requires quantum simulation of the time evolution of the wave function conditional on an ancillary qubit, which makes the algorithm implementation on real quantum devices difficult. Here, we discuss an application of the Bayesian phase difference estimation algorithm that is free from controlled time evolution operations to the full-CI calculations.

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.

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.

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.

Valence tautomerism in a [2 × 2] Co4 grid complex containing a ditopic arylazo ligand.

We describe the structural and magnetic properties of a tetranuclear [2 × 2] Co4 grid complex containing a ditopic arylazo ligand. At low temperatures and in solution the complex is comprised of Co3+ and singly reduced trianion-radical ligands. In the solid state we demonstrate the presence of valence tautomerization via variable temperature magnetic susceptibility experiments and powder-pattern EPR spectroscopy. Valence tautomerism in polynuclear complexes is very rare and to our knowledge is unprecedented in [2 × 2] grid complexes.

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.