Size-consistency and orbital-invariance issues revealed by VQE-UCCSD calculations with the FMO scheme.

The fragment molecular orbital (FMO) scheme is one of the popular fragmentation-based methods and has the potential advantage of making the circuit shallow for quantum chemical calculations on quantum computers. In this study, we used a GPU-accelerated quantum simulator (cuQuantum) to perform the electron correlation part of the FMO calculation as unitary coupled-cluster singles and doubles (UCCSD) with the variational quantum eigensolver (VQE) for hydrogen-bonded (FH) 3 $$ {}_3 $$ and (FH) 2 $$ {}_2 $$ -H 2 $$ {}_2 $$ O systems with the STO-3G basis set. VQE-UCCSD calculations were performed using both canonical and localized MO sets, and the results were examined from the point of view of size-consistency and orbital-invariance affected by the Trotter error. It was found that the use of localized MO leads to better results, especially for (FH) 2 $$ {}_2 $$ -H 2 $$ {}_2 $$ O. The GPU acceleration was substantial for the simulations with larger numbers of qubits, and was about a factor of 6.7-7.7 for 18 qubit systems.

Predicting the Extent of Damage in the Humphrey Field Analyzer 24-2 Visual Fields Using 10-2 Test Results in Patients With Advanced Glaucoma.

Purpose: To predict Humphrey Field Analyzer 24-2 test (HFA 24-2) results using 10-2 results. Methods: A total of 175 advanced glaucoma eyes (175 patients) with HFA 24-2 mean deviation (MD24-2) of < -20 dB were prospectively followed up for five years using HFA 10-2 and 24-2 (twice and once in a year, respectively). Using all the HFA 24-2 and 10-2 test result pairs measured within three months (350 pairs from 85 eyes, training dataset), a formula to predict HFA 24-2 result using HFA 10-2 results was constructed using least absolute shrinkage and selection operator regression (LASSO). Using 90 different eyes (testing dataset), the absolute differences between the actual and LASSO-predicted MD24-2 and that between the slopes calculated using five actual and LASSO-predicted MD24-2 values, were adopted as the prediction error. Similar analyses were performed for the mean total deviation values (mTD) of the superior (or inferior) hemifield [hemi-mTDsup.24-2(-hemi-mTDinf.24-2)]. Results: The prediction error for the LASSO-predicted MD24-2 and its slope were 2.98 (standard deviation [SD] = 1.90) dB and 0.32 (0.33) dB/yr, respectively. The LASSO-predicted hemi-mTDsup.24-2 (hemi-mTDinf.24-2), and its slope were 3.02 (2.89) and 3.76 (2.72) dB, and 0.37 (0.41) and 0.44 (0.38) dB/year, respectively. These prediction errors were within two times SD of repeatability of the simulated stable HFA 24-2 VF parameter series. Conclusions: HFA 24-2 results could be predicted using the paired HFA 10-2 results with reasonable accuracy using LASSO in patients with advanced glaucoma. Translational Relevance: It is useful to predict HFA24-2 test from HFA10-2 test, when the former is not available, in advanced glaucoma.

Projective Measurement-Based Quantum Phase Difference Estimation Algorithm for the Direct Computation of Eigenenergy Differences on a Quantum Computer.

Quantum computers are capable of calculating the energy difference of two electronic states using the quantum phase difference estimation (QPDE) algorithm. The Bayesian inference-based implementations for the QPDE have been reported so far, but in this approach, the quality of the calculated energy difference depends on the input wave functions being used. Here, we report the inverse quantum Fourier transformation-based QPDE with Na of ancillary qubits, which allows us to compute the difference of eigenenergies based on the single-shot projective measurement. As proof-of-concept demonstrations, we report numerical experiments for the singlet-triplet energy difference of the hydrogen molecule and the vertical excitation energies of halogen-substituted methylenes (CHF, CHCl, CF2, CFCl, and CCl2) and formaldehyde (HCHO).

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.

Identifying central 10° visual subfield associated with future worsening of visual acuity in eyes with advanced glaucoma.

BACKGROUND/AIMS: To determine a cluster of test points: visual subfield (VSF) of Humphrey Field Analyzer 10-2 test (HFA 10-2) of which baseline sensitivities were associated with future worsening of visual acuity (VA) in eyes with advanced glaucoma. METHODS: A total of 175 advanced glaucoma eyes of 175 advanced glaucoma patients with well controlled intraocular pressure (IOP), a mean deviation of the Humphrey Field Analyzer 24-2 (HFA 24-2) test ≤ -20 decibels and best corrected VA ≥20/40, were included. At baseline, HFA 24-2 and HFA 10-2 tests were performed along with VA measurements. All patients underwent prospective follow-up of 5 years, and VA was measured every 6 months. The Cox proportional hazards model was used to identify visual field sensitivities associated with deterioration of VA and also blindness. RESULTS: Deterioration of VA and blindness were observed in 15.4% and 3.4% of the eyes, respectively. More negative total deviation (TD) values in the temporal papillomacular bundle VSF were significantly associated with deterioration in VA. Averages of the TD values in this area of the HFA 10-2 test had the most predictive power of future VA deterioration (OR: 0.92, p<0.001). A very similar tendency was observed for blindness. CONCLUSION: In advanced glaucoma eyes with well-controlled IOP, careful attention is needed when the mean TD values in the temporal papillomacular bundle VSF, measured with a HFA 10-2 test is deteriorated. TD values of this VSF indicate higher risks for future deterioration of VA and also blindness.

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.

Selective Isotope Labeling and LC-Photo-CIDNP Enable NMR Spectroscopy at Low-Nanomolar Concentration.

NMR spectroscopy is a powerful tool to investigate molecular structure and dynamics. The poor sensitivity of this technique, however, limits its ability to tackle questions requiring dilute samples. Low-concentration photochemically induced dynamic nuclear polarization (LC-photo-CIDNP) is an optically enhanced NMR technology capable of addressing the above challenge by increasing the detection limit of aromatic amino acids in solution up to 1000-fold, either in isolation or within proteins. Here, we show that the absence of NMR-active nuclei close to a magnetically active site of interest (e.g., the structurally diagnostic 1Hα-13Cα pair of amino acids) is expected to significantly increase LC-photo-CIDNP hyperpolarization. Then, we exploit the spin-diluted tryptophan isotopolog Trp-α-13C-ß,ß,2,4,5,6,7-d7 and take advantage of the above prediction to experimentally achieve a ca 4-fold enhancement in NMR sensitivity over regular LC-photo-CIDNP. This advance enables the rapid (within seconds) detection of 20 nM concentrations or the molecule of interest, corresponding to a remarkable 3 ng detection limit. Finally, the above Trp isotopolog is amenable to incorporation within proteins and is readily detectable at a 1 µM concentration in complex cell-like media, including Escherichia coli cell-free extracts.

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.

Variational quantum eigensolver simulations with the multireference unitary coupled cluster ansatz: a case study of the C2v quasi-reaction pathway of beryllium insertion into a H2 molecule.

Variational quantum eigensolver (VQE)-based quantum chemical calculations have been extensively studied as a computational model using noisy intermediate-scale quantum devices. The VQE uses a parametrized quantum circuit defined through an "ansatz" to generate approximated wave functions, and the appropriate choice of an ansatz is the most important step. Because most chemistry problems focus on the energy difference between two electronic states or structures, calculating the total energies in different molecular structures with the same accuracy is essential to correctly understand chemistry and chemical processes. In this context, the development of ansatzes that are capable of describing electronic structures of strongly correlated systems accurately is an important task. Here we applied a conventional unitary coupled cluster (UCC) and a newly developed multireference unitary coupled cluster with partially generalized singles and doubles (MR-UCCpGSD) ansatzes to the quasi-reaction pathway of Be insertion into H2, LiH molecule under covalent bond dissociation, and a rectangular tetra-hydrogen cluster known as a P4 cluster; these are representative systems in which the static electron correlation effect is prominent. Our numerical simulations revealed that the UCCSD ansatz exhibits extremely slow convergence behaviour around the point where an avoided crossing occurs in the Be + H2 → BeH2 reaction pathway, resulting in a large discrepancy of the simulated VQE energy from the full-configuration interaction (full-CI) value. By contrast, the MR-UCCpGSD ansatz can give more reliable results with respect to total energy and the overlap with the full-CI solution, insisting the importance of multiconfigurational treatments in the calculations of strongly correlated systems. The MR-UCCpGSD ansatz allows us to compute the energy with the same accuracy regardless of the strength of multiconfigurational character, which is an essential property to discuss energy differences of various molecular systems.

Factors Threatening Central Visual Function of Patients with Advanced Glaucoma: A Prospective Longitudinal Observational Study.

PURPOSE: To identify risk factors for further deterioration of central visual function in advanced glaucoma eyes. DESIGN: Prospective, observational 5-year study. PARTICIPANTS: Advanced glaucoma patients with well-controlled intraocular pressure (IOP), mean deviation (MD) of the Humphrey Field Analyzer (HFA) 24-2 program ≤-20 dB and best-corrected visual acuity (BCVA) of 20/40. METHODS: The HFA 10-2 test and BCVA examination were performed every 6 months, and the HFA 24-2 test was performed every 12 months for 5 years. The Cox proportional hazards model was used to identify risk factors for deterioration of HFA 10-2 and 24-2 results and BCVA. MAIN OUTCOME MEASURES: Deterioration of HFA 10-2 results was defined by the presence of the same ≥3 points with negative total deviation slope ≤-1 dB/year at P < 0.01 on ≥3 consecutive tests, deterioration of HFA 24-2 results by an increase ≥2 in the Advanced Glaucoma Intervention Study score on ≥2 consecutive tests, and deterioration of BCVA by an increase of ≥0.2 logarithm of the minimum angle of resolution (logMAR) on ≥2 consecutive tests. RESULTS: A total of 175 eyes of 175 patients (mean age, 64.1 years; mean baseline IOP, 13.2 mmHg; mean BCVA, 0.02 logMAR; mean HFA 24-2 and 10-2 MD, -25.9 and -22.9 dB, respectively) were included. The probabilities of deterioration in HFA 10-2 and 24-2 results and BCVA were 0.269 ± 0.043 (standard error), 0.173 ± 0.031, and 0.194 ± 0.033, respectively, at 5 years. Lower BCVA at baseline (P = 0.012) was associated significantly with further deterioration of HFA 10-2 results. Better HFA 24-2 MD (P < 0.001) and use of systemic antihypertensive agents (P = 0.009) were associated significantly with further deterioration of HFA 24-2 results, and a greater ß-peripapillary atrophy area-to-disc area ratio (P < 0.001), use of systemic antihypertensive agents (P = 0.025), and lower BCVA (P = 0.042) were associated significantly with further deterioration of BCVA, respectively. CONCLUSIONS: In advanced glaucoma eyes with well-controlled IOP, BCVA, ß-peripapillary atrophy area-to-disc area ratio, and use of systemic antihypertensive agents were significant prognostic factors for further deterioration of central visual function.

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.

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.

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.

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.

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.