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.

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.

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.

Quantum Algorithm for the Direct Calculations of Vertical Ionization Energies.

Recently, a quantum algorithm that is capable of directly calculating the energy gap between two electronic states having different spin quantum numbers without inspecting the total energy of the individual electronic states was proposed. This quantum algorithm guarantees an exponential speedup, like quantum phase estimation (QPE)-based full-CI, with much lower costs. In this work, we propose a modified quantum circuit for the direct calculations of spin state energy gaps to reduce the number of qubits and quantum gates, extending the quantum algorithm to the direct calculation of vertical ionization energies. Numerical quantum circuit simulations for the ionization of light atoms (He, Li, Be, B, C, and N) and small molecules (HF, BF, CF, CO, O2, NO, CN, F2, H2O, and NH3) revealed that the proposed quantum algorithm affords the vertical ionization energies within 0.1 eV of precision.

Syntheses and Properties of (Nitronyl nitroxide)-substituted Tri-phenylamine ortho-Bridged by Two Oxygen and Sulfur Atoms.

A nitronyl nitroxide unit (NN) was linked with a triphenylamine-based condensed polycyclic skeleton DOTT to form a radical substituted donor NN-DOTT. X-ray crystal structure analysis demonstrated a flat bowl shape of the DOTT unit. EPR spectra showed the localization of electron spin on the NN unit. Chemical oxidation of the DOTT unit produced radical-substituted radical cation salts NN-DOTT+ ⋅ SbF6 - and NN-DOTT+ ⋅ FeBr4 - that are stable under ambient conditions. The magnetic behavior of NN-DOTT+ ⋅ SbF6 - is characterized by the strong intramolecular ferromagnetic interaction between NN and DOTT+ . The X-ray structural analysis of NN-DOTT+ ⋅ FeBr4 - shows planar structure of DOTT and 1D mixed-stack column of NN-DOTT+ and FeBr4 - . Magnetic measurements established that NN-DOTT+ ⋅ FeBr4 - undergoes magnetic phase transition into a weak ferromagnet at 7 K.

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.

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 quantum algorithm for spin chemistry: a Bayesian exchange coupling parameter calculator with broken-symmetry wave functions.

The Heisenberg exchange coupling parameter J (H = -2J S i · S j ) characterises the isotropic magnetic interaction between unpaired electrons, and it is one of the most important spin Hamiltonian parameters of multi-spin open shell systems. The J value is related to the energy difference between high-spin and low-spin states, and thus computing the energies of individual spin states are necessary to obtain the J values from quantum chemical calculations. Here, we propose a quantum algorithm, B̲ayesian ex̲change coupling parameter calculator with b̲roken-symmetry wave functions (BxB), which is capable of computing the J value directly, without calculating the energies of individual spin states. The BxB algorithm is composed of the quantum simulations of the time evolution of a broken-symmetry wave function under the Hamiltonian with an additional term j S 2, the wave function overlap estimation with the SWAP test, and Bayesian optimisation of the parameter j. Numerical quantum circuit simulations for H2 under a covalent bond dissociation, C, O, Si, NH, OH+, CH2, NF, O2, and triple bond dissociated N2 molecule revealed that the BxB can compute the J value within 1 kcal mol-1 of errors with less computational costs than conventional quantum phase estimation-based approaches.