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.

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.

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.

Scytonemin redox status in a filamentous cyanobacterium visualized by an excitation-laser-line-scanning spontaneous Raman scattering spectral microscope.

Some cyanobacteria produce a UVA-absorbing pigment, scytonemin, at extracellular sheaths. Although scytonemin-containing dark sheaths are recognizable through optical microscopes and its redox changes have been known for decades, there has been no report to obtain images of both oxidized and reduced scytonemins at subcellular resolution. Here, we show that a spontaneous Raman scattering spectral microscopy based on an excitation-laser-line-scanning method unveil 3D subcellular distributions of both the oxidized and reduced scytonemins in a filamentous cyanobacterium. The redox changes of scytonemin were supported by comparison in the Raman spectra between the cyanobacterial cells, solid-state scytonemin and quantum chemical normal mode analysis. Distributions of carotenoids, phycobilins, and the two redox forms of scytonemin were simultaneously visualized with an excitation wavelength at 1064 nm that is virtually free from the optical screening by the dark sheaths. The redox differentiation of scytonemin will advance our understanding of the redox homeostasis and secretion mechanisms of individual cyanobacteria as well as microscopic chemical environments in various microbial communities. The line-scanning Raman microscopy based on the 1064 nm excitation is thus a promising tool for exploring hitherto unreported Raman spectral features and distribution of nonfluorescent molecules embedded below nontransparent layers for visible light, while avoiding interference by autofluorescence.

Matrix Product State Formulation of the MCTDH Theory in Local Mode Representations for Anharmonic Potentials.

The matrix product state formulation of the multiconfiguration time-dependent Hartree theory, MPS-MCTDH, reported previously [Kurashige, J. Chem. Phys. 2018, 19, 194114] is extended to realistic anharmonic potentials with n-mode representations beyond the linear vibronic coupling model. For realistic vibrational potentials, the local mode representation should give a more compact representation of the potentials, i.e., lowering the dimensionality of the entanglements, than the normal coordinates, and the MPS-MCTDH formulation should work more efficiently and maintain the accuracy with a small bond dimension of the MPS ansatz. In fact, it was confirmed that the use of the local coordinates made the interaction matrices diagonal dominant and the number of terms in the n-body expansion of the potentials was significantly reduced. The method was applied to the IR spectrum of the CH2O molecule, the zero-point energies, and the vibrational energy redistribution dynamics of polyenes C2nH2n+2. The results showed that the efficiency of the MPS-MCTDH method is significantly accelerated by the use of local coordinates even if the long-range interactions are included in the potential.

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.

Jastrow-type Decomposition in Quantum Chemistry for Low-Depth Quantum Circuits.

We propose an efficient O(N2)-parameter ansatz that consists of a sequence of exponential operators, each of which is a unitary variant of Neuscamman's cluster Jastrow operator. The ansatz can also be derived as a decomposition of T2 amplitudes of the unitary coupled cluster with generalized singles and doubles, which gives a near full-CI energy. The proposed ansatz therefore can reproduce the uCCGSD energy, or rather will reach the exact full-CI energy because of the exponential operator product form. Because the cluster Jastrow operators are expressed by a product of number operators and the derived Pauli operator products, namely, the Jordan-Wigner strings, are all commutative, it does not require the Trotter approximation to implement to a quantum circuit and should be a good candidate for the variational quantum eigensolver algorithm of a near-term quantum computer. The accuracy of the ansatz was examined for dissociation of a nitrogen dimer, and compared with other existing O(N2)-parameter ansatzs. Not only the original ansatzs defined in the second-quantization form but also their Trotter-splitting variants, in which the cluster amplitudes are optimized to minimize the energy obtained with a few, typically single, Trotter steps, were examined by quantum circuit simulators.

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.

Soft chromophore featured liquid porphyrins and their utilization toward liquid electret applications.

Optoelectronically active viscous liquids are ideal for fabricating foldable/stretchable electronics owing to their excellent deformability and predictable π-unit-based optoelectronic functions, which are independent of the device shape and geometry. Here we show, unprecedented 'liquid electret' devices that exhibit mechanoelectrical and electroacoustic functions, as well as stretchability, have been prepared using solvent-free liquid porphyrins. The fluidic nature of the free-base alkylated-tetraphenylporphyrins was controlled by attaching flexible and bulky branched alkyl chains at different positions. Furthermore, a subtle porphyrin ring distortion that originated from the bulkiness of alkyl chains was observed. Its consequences on the electronic perturbation of the porphyrin-unit were precisely elucidated by spectroscopic techniques and theoretical modelling. This molecular design allows shielding of the porphyrin unit by insulating alkyl chains, which facilitates its corona-charged state for a long period under ambient conditions.

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.

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.

Electronically Excited Solute Described by RISM Approach Coupled with Multireference Perturbation Theory: Vertical Excitation Energies of Bioimaging Probes.

For theoretically studying molecules with fluorescence in the near-infrared region, high-accuracy determination of state energy level is required for meaningful analyses since the spectra of interest are of very narrow energy range. In particular, these molecules are in many cases handled in solution; therefore, consideration of the solvation effect is essential upon calculation together with the electronic structure of the excited state. Earlier studies showed that they cannot be described with conventional methods such as PCM-TD-DFT, yielding results far from experimental data. Here, we have developed a new method by combining a solvation theory based on statistical mechanics (RISM) and a multireference perturbation theory (CASPT2) with the extension of the density matrix renormalization group reference states for calculating the photochemical properties of near-infrared molecules and have obtained higher-accuracy prediction.

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.

Phosphorescence Resulting from Interaction between Two Non-equivalent Metals on a Helical π-Conjugated Surface.

A [7]helicene bis-ruthenium complex, with one ruthenium atom bound to the cyclopentadienyl (Cp) ring and the other coordinated to the arene ring at the edge of the helicene, was synthesized. This complex showed phosphorescence both in butyronitrile (Φ=31 %, 77 K) and in the solid state (Φ=18 %, 77 K). The two non-equivalent ruthenium metal atoms, attached to the helicene ligand, interact with each other upon photoabsorption and emission.

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.

Multistate Complete-Active-Space Second-Order Perturbation Theory Based on Density Matrix Renormalization Group Reference States.

We present the development of the multistate multireference second-order perturbation theory (CASPT2) with multiroot references, which are described using the density matrix renormalization group (DMRG) method to handle a large active space. The multistate first-order wave functions are expanded into the internally contracted (IC) basis of the single-state single-reference (SS-SR) scheme, which is shown to be the most feasible variant to use DMRG references. The feasibility of the SS-SR scheme comes from two factors: first, it formally does not require the fourth-order transition reduced density matrix (TRDM) and second, the computational complexity scales linearly with the number of the reference states. The extended multistate (XMS) treatment is further incorporated, giving suited treatment of the zeroth-order Hamiltonian despite the fact that the SS-SR based IC basis is not invariant with respect to the XMS rotation. In addition, the state-specific fourth-order reduced density matrix (RDM) is eliminated in an approximate fashion using the cumulant reconstruction formula, as also done in the previous state-specific DMRG-cu(4)-CASPT2 approach. The resultant method, referred to as DMRG-cu(4)-XMS-CASPT2, uses the RDMs and TRDMs of up to third-order provided by the DMRG calculation. The multistate potential energy curves of the photoisomerization of diarylethene derivatives with CAS(26e,24o) are presented to illustrate the applicability of our theoretical approach.

Coherent singlet fission activated by symmetry breaking.

Singlet fission, in which a singlet exciton is converted to two triplet excitons, is a process that could be beneficial in photovoltaic applications. A full understanding of the dynamics of singlet fission in molecular systems requires detailed knowledge of the relevant potential energy surfaces and their (conical) intersections. However, obtaining such information is a nontrivial task, particularly for molecular aggregates. Here we investigate singlet fission in rubrene crystals using transient absorption spectroscopy and state-of-the-art quantum chemical calculations. We observe a coherent and ultrafast singlet-fission channel as well as the well-known and conventional thermally assisted incoherent channel. This coherent channel is accessible because the conical intersection for singlet fission on the excited-state potential energy surface is located very close to the equilibrium position of the ground-state potential energy surface and also because of the excitation of an intermolecular symmetry-breaking mode, which activates the electronic coupling necessary for singlet fission.

Computational Evidence of Inversion of (1)La and (1)Lb-Derived Excited States in Naphthalene Excimer Formation from ab Initio Multireference Theory with Large Active Space: DMRG-CASPT2 Study.

The naphthalene molecule has two important lowest-lying singlet excited states, denoted (1)La and (1)Lb. Association of the excited and ground state monomers yields a metastable excited dimer (excimer), which emits characteristic fluorescence. Here, we report a first computational result based on ab initio theory to corroborate that the naphthalene excimer fluorescence is (1)La parentage, resulting from inversion of (1)La and (1)Lb-derived dimer states. This inversion was hypothesized by earlier experimental studies; however, it has not been confirmed rigorously. In this study, the advanced multireference (MR) theory based on the density matrix renormalization group that enables using unprecedented large-size active space for describing significant electron correlation effects is used to provide accurate potential energy curves (PECs) of the excited states. The results evidenced the inversion of the PECs and accurately predicted transition energies for excimer fluorescence and monomer absorption. Traditional MR calculations with smaller active spaces and single-reference theory calculations exhibit serious inconsistencies with experimental observations.