Polarizing agents beyond pentacene for efficient triplet dynamic nuclear polarization in glass matrices.

Triplet dynamic nuclear polarization (triplet-DNP) is a technique that can obtain high nuclear polarization under moderate conditions. However, in order to obtain practically useful polarization, large single crystals doped with a polarizing agent must be strictly oriented with respect to the magnetic field to sharpen the electron spin resonance (ESR) spectra, which is a fatal problem that prevents its application to truly useful biomolecular targets. Instead of this conventional physical approach of controlling crystal orientation, here, we propose a chemical approach, i.e., molecular design of polarizing agents; pentacene molecules, the most typical triplet-DNP polarizing agent, are modified so as to make the triplet electron distribution wider and more isotropic without loss of the triplet polarization. The thiophene-modified pentacene exhibits a sharper and stronger ESR spectrum than the parent pentacene, and state-of-the-art quantum chemical calculations revealed that the direction of the spin polarization is altered by the modification with thiophene moieties and the size of D and E parameters are reduced from parent pentacene due to the partial delocalization of spin densities on the thiophene moieties. The triplet-DNP with the new polarizing agent successfully exceeds the previous highest 1H polarization of glassy materials by a factor of 5. This demonstrates the feasibility of a polarizing agent that can surpass pentacene, the best polarizing agent for more than 30 y since triplet-DNP was first reported, in the unoriented state. This work provides a pathway toward practically useful high nuclear polarization of various biomolecules by triplet-DNP.

Zero-Field Splitting Tensor of the Triplet Excited States of Aromatic Molecules: A Valence Full-π Complete Active Space Self-Consistent Field Study.

A method to predict the D tensor in the molecular frame with multiconfigurational wave functions in large active space was proposed, and the spin properties of the lowest triplets of aromatic molecules were examined with full-π active space; such calculations were challenging because the size of active space grows exponentially with the number of π electrons. In this method, the exponential growth of complexity is resolved by the density matrix renormalization group (DMRG) algorithm. From the D tensor, we can directly determine the direction of the magnetic axes and the ZFS parameters, D- and E-values, of the phenomenological spin Hamiltonian with their signs, which are not usually obtained in ESR experiments. The method using the DMRG-CASSCF wave function can give correct results even when the sign of D- and E-values is sensitive to the accuracy of the prediction of the D tensor and existing methods fail to predict the correct magnetic axes.

Statistical errors in reduced density matrices sampled from quantum circuit simulation and the impact on multireference perturbation theory.

In this work, we present a detailed analysis of statistical errors in reduced density matrices (RDMs) of active space wavefunctions sampled from quantum circuit simulation and the impact on results obtained by the multireference theories. From the sampling experiments, it is shown that the errors in sampled RDMs have a larger value for higher-order RDMs, and that the errors in sampled RDMs for excited states are larger than those for the ground state. We analytically derive the expected value of the sum of squared errors between the true distribution and sample distribution of weights of the electron configurations based on a multinomial distribution model, with which we present an assessment of the dependency of RDM errors on the number of shots for the observation (Nshot) and on the character of the target electronic state. With the benchmark calculations of short polyenes, C4H6 and C6H8, we report the statistical errors in CASCI and complete active space second-order perturbation theory (CASPT2) energies obtained with the sampled 1,2-RDMs and 1,2,3,4-RDMs, respectively. It was found that the standard deviation (SD) of the sampled CASCI energies is proportional to as predicted. It was also found that the dependence of the SD of the second-order correction energies are somewhat different but the errors in the reference CASCI energies are dominant as compared with the corrections and the SD of the resulting CASPT2 energies are proportional to . This suggests that the required Nshot for 3,4-RDMs used only in the second-order perturbative corrections is smaller than that for 1,2-RDM used to calculate the reference CASCI energies. It was also suggested from the analysis of the errors in the sampled energies that the required Nshot for 3-RDM, which is used to calculate the perturbative correction energies, can be smaller than that for 2-RDM to calculate the CASCI energies. In fact, it was shown that the potential energy curve along the isomerization reaction of the {[Cu(NH3)3]2O2}2+ complex as an archetype of metalloenzyme, in which static and dynamical electron correlations are both important, can be reasonably reproduced with Nshot = 106 for 1,2-RDMs but Nshot = 105 for 3-RDM by the sampling simulation.

A pentanuclear iron catalyst designed for water oxidation.

Although the oxidation of water is efficiently catalysed by the oxygen-evolving complex in photosystem II (refs 1 and 2), it remains one of the main bottlenecks when aiming for synthetic chemical fuel production powered by sunlight or electricity. Consequently, the development of active and stable water oxidation catalysts is crucial, with heterogeneous systems considered more suitable for practical use and their homogeneous counterparts more suitable for targeted, molecular-level design guided by mechanistic understanding. Research into the mechanism of water oxidation has resulted in a range of synthetic molecular catalysts, yet there remains much interest in systems that use abundant, inexpensive and environmentally benign metals such as iron (the most abundant transition metal in the Earth's crust and found in natural and synthetic oxidation catalysts). Water oxidation catalysts based on mononuclear iron complexes have been explored, but they often deactivate rapidly and exhibit relatively low activities. Here we report a pentanuclear iron complex that efficiently and robustly catalyses water oxidation with a turnover frequency of 1,900 per second, which is about three orders of magnitude larger than that of other iron-based catalysts. Electrochemical analysis confirms the redox flexibility of the system, characterized by six different oxidation states between Fe(II)5 and Fe(III)5; the Fe(III)5 state is active for oxidizing water. Quantum chemistry calculations indicate that the presence of adjacent active sites facilitates O-O bond formation with a reaction barrier of less than ten kilocalories per mole. Although the need for a high overpotential and the inability to operate in water-rich solutions limit the practicality of the present system, our findings clearly indicate that efficient water oxidation catalysts based on iron complexes can be created by ensuring that the system has redox flexibility and contains adjacent water-activation sites.

Importance of dynamical electron correlation in diabatic couplings of electron-exchange processes.

We demonstrate the importance of the dynamical electron correlation effect in diabatic couplings of electron-exchange processes in molecular aggregates. To perform a multireference perturbation theory with large active space of molecular aggregates, an efficient low-rank approximation is applied to the complete active space self-consistent field reference functions. It is known that kinetic rates of electron-exchange processes, such as singlet fission, triplet-triplet annihilation, and triplet exciton transfer, are not sufficiently explained by the direct term of the diabatic couplings but efficiently mediated by the low-lying charge transfer states if the two molecules are in close proximity. It is presented in this paper, however, that regardless of the distance of the molecules, the direct term is considerably underestimated by up to three orders of magnitude without the dynamical electron correlation, i.e., the diabatic states expressed in the active space are not adequate to quantitatively reproduce the electron-exchange processes.

Prediction models considering psychological factors to identify pain relief in conservative treatment of people with knee osteoarthritis: A multicenter, prospective cohort study.

BACKGROUND: Pain-related affective and/or cognitive characteristics such as depressive symptoms, pain catastrophizing, and self-efficacy are known to exacerbate pain in people with knee osteoarthritis. However, no studies have investigated whether these psychological factors can interfere with pain relief during conservative treatment. The object of this study was to assess the prediction models considering psychological factors to predict pain relief in people with knee osteoarthritis receiving conservative treatment. METHODS: Study design was a multicenter, and prospective cohort study. Data were collected in the department of physical therapy in 1 hospital and 7 orthopedic clinics. Eighty-eight people with knee osteoarthritis participated in this study and were followed for 3 months. The numeric rating scale and the Knee Injury and Osteoarthritis Outcome Score scale were used to evaluate pain relief. Potential predictors for pain relief were depressive symptoms, self-efficacy, and pain catastrophizing. The classification and regression trees methodology was used to develop the model for predicting the presence of pain relief at 1 and 3 months after the start of observation. The prediction accuracy was evaluated using the area under the receiver operating characteristic curves (AUCs). RESULTS: The model at 1 month after the start of observation included pain intensity at baseline, positive affect, and disease duration. The AUC of this model was 0.793 (95% confidential interval, 0.687-0.898). The model at 3 months after the start of observation included pain catastrophizing and self-efficacy. The AUC of this model was 0.808 (95% confidential interval, 0.682-0.934). CONCLUSIONS: The accuracy of prediction model considering pain-related affective and/or cognitive characteristics is moderate for pain relief in people with knee osteoarthritis receiving conservative treatment.

Rank-one basis made from matrix-product states for a low-rank approximation of molecular aggregates.

An efficient low-rank approximation to complete active space (CAS) wavefunctions for molecular aggregates is presented. Molecular aggregates usually involve two different characteristic entanglement structures: strong intramolecular entanglement and weak intermolecular entanglement. In the method, low-lying electronic states of molecular aggregates are efficiently expanded by a small number of rank-one basis states that are direct products of monomolecular wavefunctions, each of which is written as a highly entangled state such as the matrix product state (MPS). The complexities raised by strong intramolecular entanglement are therefore encapsulated by the MPS and eliminated from the degree of freedom of the effective Hamiltonian of molecular aggregates. It is demonstrated that the excitation energies of low-lying excited states of a pair of bacteriochlorophyll units with CAS(52e, 50o) are accurately reproduced by only five rank-one basis states. Because the rank-one basis states naturally have diabatic character and reproduce the low-lying spectrum of the CAS space, off-diagonal elements of the Hamiltonian are expected to give accurate diabatic couplings. It is also demonstrated that the energy splitting and the diabatic couplings in anthracene dimer systems are improved by augmenting with additional rank-one basis states.

Three-Dimensional Sandwich Nanocubes Composed of 13-Atom Palladium Core and Hexakis-Carbocycle Shell.

Coordination of cyclic unsaturated hydrocarbons to transition metal generally gives bis-ligated sandwich complexes, which are a fundamental class of organometallic compounds. This sandwich structure may be extended to a higher-order three-dimensional one when more than two carbocyclic ligands surround an agglomerate of many transition metal atoms. Here, we report synthesis of three-dimensional sandwich nanocube compounds containing a close-packed transition metal cluster core. Reduction of a [Pd3(µ3-C7H7)2]2+ with tetraarylborate under neat conditions afforded [Pd13(µ4-C7H7)6]2+ containing a cuboctahedral Pd13 core with an octahedral ligand-shell.

Experimental and theoretical investigation of fluorescence solvatochromism of dialkoxyphenyl-pyrene molecules.

We investigated the fluorescence properties of dialkoxyphenyl-pyrene molecules experimentally as well as theoretically. Our experiments confirmed fluorescence solvatochromism in 2,5-dimethoxyphenyl-pyrene and, in contrast there was no significant solvent-effect on the emission properties of the isomers, 3,5- and 2,6-dimethoxyphenyl-pyrene. This clear difference in the solvent-dependence would reflect the difference in character of the excited-state between the isomers, which differ only in the substitution positions of the two methoxy groups. The positional effects of the di-substituted molecules are successfully explained theoretically by the topologies of the highest occupied molecular orbital of the phenyl group that are governed by the relative positions of the two substituents, though it is somewhat contradictory to the meta-effect for the mono-substituted molecules. Theoretical calculations were also used to analyze the character of the excited states; 2,5-dimethoxyphenyl-pyrene alone exhibited an intramolecular charge transfer character for the excited state, which was responsible for the solvatochromism effect. The dynamics of the excited states were analyzed using time-resolved fluorescence measurements, in which a characteristic increase of the fluorescence intensity was observed for 2,5-dialkoxyphenyl-pyrene; this observation was supported by the theoretical calculations as well.

Matrix product state formulation of the multiconfiguration time-dependent Hartree theory.

A matrix product state formulation of the multiconfiguration time-dependent Hartree (MPS-MCTDH) theory is presented. The Hilbert space that is spanned by the direct products of the phonon degree of freedoms, which is linearly parameterized in the MCTDH ansatz and thus results in an exponential increase in the computational cost, is parametrized by the MPS form. Equations of motion based on the Dirac-Frenkel time-dependent variational principle is derived by using the tangent space projection and the projector-splitting technique for the MPS, which have been recently developed. The mean-field operators, which appear in the equation of motion of the MCTDH single particle functions, are written in terms of the MPS form and efficiently evaluated by a sweep algorithm that is similar to the density-matrix renormalized group sweep. The efficiency and convergence of the MPS approximation to the MCTDH are demonstrated by quantum dynamics simulations of extended excitonic molecular systems.

Synthesis of Molecular Wires Strapped by π-Conjugated Side Chains: Integration of Dehydrobenzo[20]annulene Units.

In this study, π-conjugated molecular wires strapped by cyclic π-conjugated side chains were efficiently synthesized by the integration of dehydrobenzo[20]annulene units by intramolecular Glaser-type cyclization under high dilution conditions.

Aggregation-induced photon upconversion through control of the triplet energy landscapes of the solution and solid states.

Aggregation-induced photon upconversion (iPUC) based on control of the triplet energy landscape is demonstrated for the first time. When a triplet state of a cyano-substituted 1,4-distyrylbenzene derivative is sensitized in solution, no upconverted emission based on triplet-triplet annihilation (TTA) was observed. In stark contrast, crystalline solids obtained by drying the solution revealed clear upconverted emission. Theoretical studies unveiled an underlying switching mechanism: the excited triplets in solution immediately decay back to the ground state through conformational twisting around a CC bond and photoisomerization, whereas this deactivation path is effectively inhibited in the solid state. The finding of iPUC phenomena highlights the importance of controlling excited energy landscapes in condensed molecular systems.

Modulation of benzene or naphthalene binding to palladium cluster sites by the backside-ligand effect.

The backside-ligand modulation strategy to enhance the substrate binding property of Pd clusters is reported. The benzene or naphthalene binding ability of Pd3 or Pd4 clusters is enhanced significantly by the backside cyclooctatetraene ligand, leading to the formation of the first solution-stable benzene- or naphthalene Pd clusters. The present results imply that the ligand design of the metal clusters, especially for the backside ligand of the metal cluster site, is crucial to acquire a desired reactivity of metal clusters.

Reactivity of the binuclear non-heme iron active site of Δ9 desaturase studied by large-scale multireference ab initio calculations.

The results of density matrix renormalization group complete active space self-consistent field (DMRG-CASSCF) and second-order perturbation theory (DMRG-CASPT2) calculations are presented on various structural alternatives for the O-O and first C-H activating step of the catalytic cycle of the binuclear nonheme iron enzyme Δ(9) desaturase. This enzyme is capable of inserting a double bond into an alkyl chain by double hydrogen (H) atom abstraction using molecular O2. The reaction step studied here is presumably associated with the highest activation barrier along the full pathway; therefore, its quantitative assessment is of key importance to the understanding of the catalysis. The DMRG approach allows unprecedentedly large active spaces for the explicit correlation of electrons in the large part of the chemically important valence space, which is apparently conditio sine qua non for obtaining well-converged reaction energetics. The derived reaction mechanism involves protonation of the previously characterized 1,2-µ peroxy Fe(III)Fe(III) (P) intermediate to a 1,1-µ hydroperoxy species, which abstracts an H atom from the C10 site of the substrate. An Fe(IV)-oxo unit is generated concomitantly, supposedly capable of the second H atom abstraction from C9. In addition, several popular DFT functionals were compared to the computed DMRG-CASPT2 data. Notably, many of these show a preference for heterolytic C-H cleavage, erroneously predicting substrate hydroxylation. This study shows that, despite its limitations, DMRG-CASPT2 is a significant methodological advancement toward the accurate computational treatment of complex bioinorganic systems, such as those with the highly open-shell diiron active sites.

Radical O-O coupling reaction in diferrate-mediated water oxidation studied using multireference wave function theory.

The O-O (oxygen-oxygen) bond formation is widely recognized as a key step of the catalytic reaction of dioxygen evolution from water. Recently, the water oxidation catalyzed by potassium ferrate (K2FeO4) was investigated on the basis of experimental kinetic isotope effect analysis assisted by density functional calculations, revealing the intramolecular oxo-coupling mechanism within a di-iron(vi) intermediate, or diferrate [Sarma et al., J. Am. Chem. Soc., 2012, 134, 15371]. Here, we report a detailed examination of this diferrate-mediated O-O bond formation using scalable multireference electronic structure theory. High-dimensional correlated many-electron wave functions beyond the one-electron picture were computed using the ab initio density matrix renormalization group (DMRG) method along the O-O bond formation pathway. The necessity of using large active space arises from the description of complex electronic interactions and varying redox states both associated with two-center antiferromagnetic multivalent iron-oxo coupling. Dynamic correlation effects on top of the active space DMRG wave functions were additively accounted for by complete active space second-order perturbation (CASPT2) and multireference configuration interaction (MRCI) based methods, which were recently introduced by our group. These multireference methods were capable of handling the double shell effects in the extended active space treatment. The calculations with an active space of 36 electrons in 32 orbitals, which is far over conventional limitation, provide a quantitatively reliable prediction of potential energy profiles and confirmed the viability of the direct oxo coupling. The bonding nature of Fe-O and dual bonding character of O-O are discussed using natural orbitals.

Complete active space second-order perturbation theory with cumulant approximation for extended active-space wavefunction from density matrix renormalization group.

We report an extension of our previous development that incorporated quantum-chemical density matrix renormalization group (DMRG) into the complete active space second-order perturbation theory (CASPT2) [Y. Kurashige and T. Yanai, J. Chem. Phys. 135, 094104 (2011)]. In the previous study, the combined theory, referred to as DMRG-CASPT2, was built upon the use of pseudo-canonical molecular orbitals (PCMOs) for one-electron basis. Within the PCMO basis, the construction of the four-particle reduced density matrix (4-RDM) using DMRG can be greatly facilitated because of simplicity in the multiplication of 4-RDM and diagonal Fock matrix in the CASPT2 equation. In this work, we develop an approach to use more suited orbital basis in DMRG-CASPT2 calculations, e.g., localized molecular orbitals, in order to extend the domain of applicability. Because the multiplication of 4-RDM and generalized Fock matrix is no longer simple in general orbitals, an approximation is made to it using the cumulant reconstruction neglecting higher-particle cumulants. Also, we present the details of the algorithm to compute 3-RDM of the DMRG wavefunction as an extension of the 2-RDM algorithm of Zgid et al. [J. Chem. Phys. 128, 144115 (2008)] and Chan et al. [J. Chem. Phys. 128, 144117 (2008)]. The performance of the extended DMRG-CASPT2 approach was examined for large-scale multireference systems, such as low-lying excited states of long-chain polyenes and isomerization potential of {[Cu(NH3)3]2O2}(2+).

Ab initio density matrix renormalization group study of magnetic coupling in dinuclear iron and chromium complexes.

The applicability of ab initio multireference wavefunction-based methods to the study of magnetic complexes has been restricted by the quickly rising active-space requirements of oligonuclear systems and dinuclear complexes with S > 1 spin centers. Ab initio density matrix renormalization group (DMRG) methods built upon an efficient parameterization of the correlation network enable the use of much larger active spaces, and therefore may offer a way forward. Here, we apply DMRG-CASSCF to the dinuclear complexes [Fe2OCl6](2-) and [Cr2O(NH3)10](4+). After developing the methodology through systematic basis set and DMRG M testing, we explore the effects of extended active spaces that are beyond the limit of conventional methods. We find that DMRG-CASSCF with active spaces including the metal d orbitals, occupied bridging-ligand orbitals, and their virtual double shells already capture a major portion of the dynamic correlation effects, accurately reproducing the experimental magnetic coupling constant (J) of [Fe2OCl6](2-) with (16e,26o), and considerably improving the smaller active space results for [Cr2O(NH3)10](4+) with (12e,32o). For comparison, we perform conventional MRCI+Q calculations and find the J values to be consistent with those from DMRG-CASSCF. In contrast to previous studies, the higher spin states of the two systems show similar deviations from the Heisenberg spectrum, regardless of the computational method.

Encoding a Many-Body Potential Energy Surface into a Grid-Based Matrix Product Operator.

An efficient algorithm for compressing a given many-body potential energy surface (PES) of molecular systems into a grid-based matrix product operator (MPO) is proposed. The PES is once represented by a full-dimensional or truncated many-body expansion form, which is obtained by ab initio calculations at each grid mesh point, and then all terms in the expansion are compressed and merged into a single MPO while maintaining the bond dimension of the MPO as small as possible. It was shown that the ab initio PES of the H2CO was compressed by more than 2 orders of magnitude in the size of the site operators without loss of accuracy. By the use of grid basis, the tensor rank of the site operators of the MPO is reduced from four to three due to the diagonal nature of the position-dependent operators on grid basis, which significantly reduces the computational cost of the tensor contractions required in the real and imaginary time evolution of the matrix product state (MPS) wave functions with the grid-based MPO (Grid-MPO) Hamiltonian. Similar to other grid-based methods, Grid-MPO is easily applicable to any kinds of potentials of molecular systems, such as analytical empirical model potentials expressed by position operators and ab initio potentials, if the values at the grid points are available. Using the Grid-MPO combined with the MPS, we calculated the time correlation function of the Eigen cation H3O+(H2O)3 to predict the infrared spectrum and compared with the experimental and the previous theoretical studies. The actual scaling with the size of systems was examined for the multidimensional Henon-Heiles Hamiltonian. It was shown that the method is considerably accelerated by the graphic processing unit (GPU) because the sizes of site operators were kept small and all tensors were able to be stored on the VRAM of a GPU.

Multireference configuration interaction theory using cumulant reconstruction with internal contraction of density matrix renormalization group wave function.

We report development of the multireference configuration interaction (MRCI) method that can use active space scalable to much larger size references than has previously been possible. The recent development of the density matrix renormalization group (DMRG) method in multireference quantum chemistry offers the ability to describe static correlation in a large active space. The present MRCI method provides a critical correction to the DMRG reference by including high-level dynamic correlation through the CI treatment. When the DMRG and MRCI theories are combined (DMRG-MRCI), the full internal contraction of the reference in the MRCI ansatz, including contraction of semi-internal states, plays a central role. However, it is thought to involve formidable complexity because of the presence of the five-particle rank reduced-density matrix (RDM) in the Hamiltonian matrix elements. To address this complexity, we express the Hamiltonian matrix using commutators, which allows the five-particle rank RDM to be canceled out without any approximation. Then we introduce an approximation to the four-particle rank RDM by using a cumulant reconstruction from lower-particle rank RDMs. A computer-aided approach is employed to derive the exceedingly complex equations of the MRCI in tensor-contracted form and to implement them into an efficient parallel computer code. This approach extends to the size-consistency-corrected variants of MRCI, such as the MRCI+Q, MR-ACPF, and MR-AQCC methods. We demonstrate the capability of the DMRG-MRCI method in several benchmark applications, including the evaluation of single-triplet gap of free-base porphyrin using 24 active orbitals.