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UV radiation, desiccation, and starvation induce some cyanobacteria to produce a UVA-absorbing pigment, scytonemin, at extracellular sheaths. Although the accumulation of scytonemin is recognizable as dark sheaths through optical microscopes, it has been nontrivial to identify its redox status and obtain its subcellular distribution in response to physiological conditions. Here, we show that a spontaneous Raman scattering spectral microscopy based on an excitation-laser-line-scanning method unveil 3D subcellular distributions of non-UV-induced scytonemins with distinct redox statuses in a filamentous cyanobacterium with a single nitrogen-fixing cell at the basal end. Cellular differentiations and scytonemin redox conditions were simultaneously visualized with an excitation wavelength at 1064 nm that is virtually free from the optical screening by the dark sheaths. The molecular imaging results give insights into not only secretion mechanisms of the sunscreen pigment but also interdependence between photosynthesis, nitrogen fixation, and redox homeostasis in one of the simplest forms of multicellular organisms.

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.

The matrix product state formulation of the multiconfiguration time-dependent Hartree theory, MPS-MCTDH, reported previously [Kurashige

We propose an efficient ${\cal O}(N^2)$-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 T$_2$ amplitudes of the unitary coupled cluster with generalized singles and doubles, which gives a near full-CI energy, and reproduces it by extending the exponential operator sequence. 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 by a near-term quantum computer. The accuracy of the ansatz was examined for dissociation of a nitrogen dimer, and compared with other existing ${\cal O}(N^2)$-parameter ansatzs. Not only the original ansatzs defined in the second-quantization form but also their Trotterized 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., Comment: 9 pages, 3 figures

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., Though electret materials are attractive for realizing flexible mechanoelectrical devices, these materials are typically solid films. Here, the authors report stretchable ‘liquid-electret’ devices consisting solvent-free liquid porphyrins that show piezoelectric and electroacoustic functionality.

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.

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.

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.

The Complete Active Space Second-Order Perturbation Theory (CASPT2) is well-established as a high-accuracy electronic structure method. It was originally implemented in the early 1990s to an efficient computer code in the molcas program suite, and this implementation has been extensively used as a standard tool. Here, we report a comparison of it against two independent computer-aided implementations of the CASPT2 method, revealing that the CASPT2 energies provided by the original code of molcas (version 8 or earlier) are inconsistent with the predictions of the lately developed computer-aided implementations. It is shown that this error is associated with the projections of the first-order equation onto the fully internally contracted multireference bases which are partially inconsistent between the left- and right-hand sides. The degree of the errors is assessed by performing illustrative CASPT2 calculations. The errors in total CASPT2 energies are demonstrated to be negligible relative to chemical accuracy in many cases, while there is a difficult case where they may substantially alter chemical description. The incorporation of the consistent projections into molcas has been carried out, which is available in the version 8 sp1. (Less)

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.

Metal clusters are effectively stabilized by bridging π-coordination of planar π-conjugated unsaturated hydrocarbons. However, the mechanism of π-envelopment of a metal cluster has been elusive. By employing 1,2-bis(4-aryl-1,3-butadienyl)benzene as the π-conjugated ligand, we found that the π-envelopment of a Pd4 cluster proceeded in a stepwise manner, where the sp(2)-carbon ligands initially envelop the Pd4 cluster through a bent binding mode, and then isomerized to a thermodynamically more stable planar mode under mild heating or visible light irradiation. The involvement of a bent binding mode indicates the kinetically preferred coordination at the axial coordination site trans to a metal-metal bond.

Singlet fission of thienoquinoid compounds in organic photovoltaics is demonstrated. The escalation of the thienoquinoid length of the compounds realizes a suitable packing structure and energy levels for singlet fission. The magnetic-field dependence of the photocurrent and the external quantum efficiency of the devices reveal singlet fission of the compounds and dissociation of triplet excitons into charges.

We present an extended implementation of the multireference configuration interaction (MRCI) method combined with the quantum-chemical density matrix renormalization group (DMRG). In the previous study, we introduced the combined theory, referred to as DMRGMRCI, as a method to calculate high-level dynamic electron correlation on top of the DMRG wave function that accounts for active-space (or strong) correlation using a large number of active orbitals. The DMRG-MRCI method is built on the full internal-contraction scheme for the compact reference treatment and on the cumulant approximation for the treatment of the four-particle rank reduced density matrix (4-RDM). The previous implementation achieved the MRCI calculations with the active space (24e,24o), which are deemed the record largest, whereas the inherent Nact 8 × N complexity of computation was found a hindrance to using further large active space. In this study, an extended optimization of the tensor contractions is developed by explicitly incorporating the rank reduction of the decomposed form of the cumulant-approximated 4-RDM into the factorization. It reduces the computational scaling (to Nact7 × N) as well as the cache-miss penalty associated with direct evaluation of complex cumulant reconstruction. The present scheme, however, faces the increased complexity of factorization patterns for optimally implementing the tensor contraction terms involving the decomposed 4-RDM objects. We address this complexity using the enhanced symbolic manipulation computer program for deriving and coding programmable equations. The new DMRG-MRCI implementation is applied to the determination of the stability of the iron(IV)-oxo porphyrin relative to the iron(V) electronic isomer (electromer) using the active space (29e,29o) (including four second d-shell orbitals of iron) with triple-ζ-quality atomic orbital basis sets. The DMRG-cu(4)-MRCI+Q model is shown to favor the triradicaloid iron(IV)-oxo state as the lowest energy state and characterize the iron(V) electromer as thermally inaccessible, supporting the earlier experimental and density functional studies. This conflicts with the previous MR calculations using the restricted activespace second-order perturbation theory (RASPT2) with the similar-size active space (29e,28o) reported by Pierloot et al. (Radoń, M.; Broclawik, E.; Pierloot, K. J. Chem. Theory Comput. 2011, 7, 898), showing that the hypothetical iron(V) state indicated by recent laser flash photolysis (LFP) studies is likely thermally accessible because of its underestimated relative energy.

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.

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.

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.

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 (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.

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.

Regulation of electron transfer on organic substances by external stimuli is a fundamental issue in science and technology, which affects organic materials, chemical synthesis, and biological metabolism. Nevertheless, acid/base-responsive organic materials that exhibit reversible electron transfer have not been well studied and developed, owing to the difficulty in inventing a mechanism to associate acid/base stimuli and electron transfer. We discovered a new phenomenon in which N–N linked bicarbazole (BC) and tetramethylbiacridine (TBA) derivatives undergo electron transfer disproportionation by acid stimulus, forming their stable radical cations and reduced species. The reaction occurs through a biradical intermediate generated by the acid-triggered N–N bond cleavage reaction of BC or TBA, which acts as a two electron acceptor to undergo electron transfer reactions with two equivalents of BC or TBA. In addition, in the case of TBA the disproportionation reaction is highly reversible through neutralization with NEt3, which recovers TBA through back electron transfer and N–N bond formation reactions. This highly reversible electron transfer reaction is possible due to the association between the acid stimulus and electron transfer via the acid-regulated N–N bond cleavage/formation reactions which provide an efficient switching mechanism, the ability of the organic molecules to act as multi-electron donors and acceptors, the extraordinary stability of the radical species, the highly selective reactivity, and the balance of the redox potentials. This discovery provides new design concepts for acid/base-regulated organic electron transfer systems, chemical reagents, or organic materials.

We have developed a new computational scheme for high-accuracy prediction of the isotropic hyperfine coupling constant (HFCC) of heavy molecules, accounting for the high-level electron correlation effects, as well as the scalar-relativistic effects. For electron correlation, we employed the ab initio density matrix renormalization group (DMRG) method in conjunction with a complete active space model. The orbital-optimization procedure was employed to obtain the optimized orbitals required for accurately determining the isotropic HFCC. For the scalar-relativistic effects, we initially derived and implemented the Douglas-Kroll-Hess (DKH) hyperfine coupling operators up to the third order (DKH3) by using the direct transformation scheme. A set of 4d transition-metal radicals consisting of Ag atom, PdH, and RhH2 were chosen as test cases. Good agreement between the isotropic HFCC values obtained from DMRG/DKH3 and experiment was archived. Because there are no available gas-phase values for PdH and RhH2 radicals in the literature, the results from the present high-level theory may serve as benchmark data.

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.

The recent advent of the density matrix renormalization group (DMRG) theory has delivered a new capability to compute multireference (MR) wave function with large configuration space, which far exceeds the limitation of conventional approaches. Here, we provide an overview of our recent work on the developments of ab initio DMRG methods in the context of the active space approaches and their applications to MR chemical systems. © 2014 Wiley Periodicals, Inc.

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.

The density matrix renormalization group (DMRG) method is used in conjunction with the complete active space (CAS) procedure, the CAS configuration interaction (CASCI), and the CAS self-consistent field (CASSCF) to evaluate hyperfine coupling constants (HFCCs) for a series of diatomic (2)Σ radicals (BO, CO(+), CN, and AlO) and vinyl (C2H3) radical. The electron correlation effects on the computed HFCC values were systematically investigated using various levels of active space, which were increasingly extended from single valence space to large-size model space entailing double valence and at least single polarization shells. In addition, the core correlation was treated by including the core orbitals in active space. Reasonably accurate results were obtained by the DMRG-CASSCF method involving orbital optimization, while DMRG-CASCI calculations with Hartree-Fock orbitals provided poor agreement of the HFCCs with the experimental values. To achieve further insights into the accuracy of HFCC calculations, the orbital contributions to the total spin density were analyzed at a given nucleus, which is directly related to the FC term and is numerically sensitive to the level of correlation treatment and basis sets. The convergence of calculated HFCCs with an increasing number of renormalized states was also assessed. This work serves as the first study on the performance of the ab initio DMRG method for HFCC prediction.

Recent advances in quantum chemical density matrix renormalisation group (DMRG) theory are presented. The DMRG, originally devised as an alternative to the exact diagonalisation in condensed matter physics, has become a powerful quantum chemical method for molecular systems that exhibit a multireference character, e.g., excited states, π-conjugated systems, transition metal complexes, and in particular for large systems by combining it with conventional multireference electron correlation methods. The capability of the current quantum chemical DMRG is demonstrated for an application involving the potential energy curve of the chromium dimer, which is one of the most demanding multireference systems and thus requires the best electronic structure treatment for non-dynamical and dynamical correlation as well as large basis sets.

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 of 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 appears 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 DMRG sweep. The efficiency and convergence of the MPS formulation to the MCTDH are demonstrated by quantum dynamics simulations of extended excitonic molecular systems., 9 pages, 1figure

The energy levels of low-lying π → π* excited states of oligoacenes, anthracene to hexacene, were studied by using the DMRG-CASPT2 method with a full π-valence complete active space. The effects of...

The photochromic ring-opening reaction of spiropyran has been revisited at the multireference CASSCF and CASPT2 level with a CAS(22e,20o) active space, in combination with density matrix renormalization group (DMRG) methods. The accuracy of the DMRG-CASSCF and DMRG-CASPT2 calculations, with respect to the number of renormalized states, the number of roots in state-averaged wave functions, and the number basis functions, was examined. For the current system, chemically accurate results can be obtained with a relatively small number of renormalized states. The nature and vertical excitation energies of the excited (S1 and S2) states are consistent with conventional CAS(or RAS)PT2 with medium active spaces. The capability of the DMRG-CASSCF method in the optimization of molecular geometry is demonstrated for the first time. The computation costs (several hours per optimization cycle) are comparable with that of the conventional CASSCF geometry optimization with small active space. Finally, the DMRG-PT2 computed S1-MEP for the C-O and C-N bond-cleavage processes show good agreement with our previous calculations with a CAS(12e,10o) active space [Liu, F.; Morokuma, K. J. Am. Chem. Soc. 2013, 135, 10693-10702]. Especially, the role of the HOOP valleys in the S1 → S0 nonadiabatic decay has been confirmed.

It is a long-standing goal to understand the reaction mechanisms of catalytic metalloenzymes at an entangled many-electron level, but this is hampered by the exponential complexity of quantum mechanics. Here, by exploiting the special structure of physical quantum states and using the density matrix renormalization group, we compute near-exact many-electron wavefunctions of the Mn_4CaO_5 cluster of photosystem II, with more than 1 × 10^(18) quantum degrees of freedom. This is the first treatment of photosystem II beyond the single-electron picture of density functional theory. Our calculations support recent modifications to the structure determined by X-ray crystallography. We further identify multiple low-lying energy surfaces associated with the structural distortion seen using X-ray crystallography, highlighting multistate reactivity in the chemistry of the cluster. Direct determination of Mn spin-projections from our wavefunctions suggests that current candidates that have been recently distinguished using parameterized spin models should be reassessed. Through entanglement maps, we reveal rich information contained in the wavefunctions on bonding changes in the cycle.

Graphene nanoribbons (GNRs), also seen as rectangular polycyclic aromatic hydrocarbons, have been intensively studied to explore their potential applicability as superior organic semiconductors with high mobility. The difficulty arises in the synthesis or isolation of GNRs with increased conjugate length, GNRs being known to have radical electrons on their zigzag edges. Here, we use a most advanced ab initio theory based on density matrix renormalization group (DMRG) theory to show the emerging process of how GNRs develop electronic states from nonradical to radical characters with increasing ribbon length. We show the mesoscopic size effect that comes into play in quantum many-body interactions of π electrons, which is responsible for the polyradical nature. An analytic form is presented to model the size dependence of the number of radicals for arbitrary-length GNRs. These results and associated insights deepen the understanding of carbon-based chemistry and offer useful information for the synthesis and design of stable and functional GNRs.

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.

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.

An algorithm that accelerates the convergence of the iterative optimization of the complete active space self-consistent field (CASSCF) wavefunction so as to find a optimum solution in fewer macroiterations is described. The algorithm is oriented to large-scale CASSCF problems that are to be solved with a combination of density matrix renormalization group (DMRG) method for the configuration interaction (CI) process. The algorithm is based on the alternating (or two-step) CASSCF optimization in which the CI and molecular orbital (MO) parameters are optimized separately. Convergence ratio is improved by finding further optimized MOs from a linear extrapolation of the MO sets of the iteration history. The acceleration results in fewer diagonalizations in a total CASSCF calculation to save a considerable computational cost. The convergence performance is examined in a couple of realistic applications on SiC3 and poly(phenyl)carbenes. For poly(phenyl)carbenes, the large-size CASSCF calculations with CAS(30e,30o) that entails full π valence space as well as sp2 orbital space of carbenes are performed by using the practical implementation of DMRG-CASSCF in conjunction with the acceleration technique.

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.

Carotenes are naturally abundant unsaturated hydrocarbon pigments, and their fascinating physical and chemical properties have been studied intensively not only for better understanding of the roles in biological processes but also for the use in artificial chemical systems. However, their metal-binding ability has been virtually unexplored. Here we report that β-carotene has the ability to assemble and align ten metal atoms to afford decanuclear homo- and heterometal chain complexes. The metallo–carotenoid framework shows reversible metalation–demetalation reactivity with multiple metals, which allows us to control the size of metal chains as well as the heterobimetallic composition and arrangement of the carotene-supported metal chains., Carotenes are naturally abundant, widely studied unsaturated hydrocarbon pigments but their metal-binding ability has been virtually unexplored. Here, the authors demonstrate that they can be used to reversibly assemble and align homo- and hetero-metallic decanuclear chain complexes.

We have developed the adaptive density partitioning technique (ADPT) in the auxiliary plane wave method, in which a part of the density is expanded to plane waves, for the fast evaluation of Coulomb matrix. Our partitioning is based on the error estimations and allows us to control the accuracy and efficiency. Moreover, we can drastically reduce the core Gaussian products that are left in Gaussian representation (its analytical integrals is the bottleneck in this method). For the taxol molecule with 6-31G** basis, the core Gaussian products accounted only for 5% in submicrohartree error.

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.

Multireference Moller–Plesset perturbation theory with complete active space configuration interaction (CASCI-MRMP) is applied to the study of the valence π → π* excited states of all-trans linear polyenes C2nH2n+2 (n = 3–14). Our focus was to determine the nature of the four lowest-lying singlet excited states, 2 1 A g - , 1 1 B u + , 1 1 B u - and 3 1 A g - and their ordering. The ionic 1 1 B u + state is the lowest optically allowed excited state, while the covalent 2 1 A g - , 1 1 B u - and 3 1 A g - states are the optically forbidden states. Theory predicts that the 1 1 B u - state becomes lower than the 1 1 B u + state at n ⩾ 7 and that the 3 1 A g - state also becomes lower than the 1 1 B u + state at n ⩾ 11.

The most stable structure of the SiC 3 molecule has been investigated using second-order perturbation theory with general multiconfiguration self-consistent field reference functions (GMC-PT) and Dunning's augmented correlation-consistent polarized valence quadruple-ζ (aug-cc-pVQZ) basis set. The results showed that a closed-shell rhomboidal C 2 v isomer with a C-C transannular bond (2s) was most stable. Another closed-shell rhomboidal C 2 v isomer with a Si-C transannular bond (3s) and a linear triplet Si-C-C-C isomer (1t) was less stable by 5.3 and 6.7 kcal/mol, respectively, at the geometries optimized by the coupled cluster singles, doubles, and perturbative triples (CCSD(T)) method and the correlation-consistent polarized core-valence quadruple-ζ (cc-pCVQZ) basis set, and by 9.0 and 9.9 kcal/mol, respectively, at the geometries optimized by the fully optimized reaction space self-consistent field (FORS-SCF) method and the 6-31G(d) basis set.

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.

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.

It is a long-standing goal to understand the reaction mechanisms of catalytic metalloenzymes at an entangled many-electron level, but this is hampered by the exponential complexity of quantum mechanics. Here, by exploiting the special structure of physical quantum states and using the density matrix renormalization group, we compute near-exact many-electron wavefunctions of the Mn4CaO5 cluster of photosystem II, with more than 1 × 10(18) quantum degrees of freedom. This is the first treatment of photosystem II beyond the single-electron picture of density functional theory. Our calculations support recent modifications to the structure determined by X-ray crystallography. We further identify multiple low-lying energy surfaces associated with the structural distortion seen using X-ray crystallography, highlighting multistate reactivity in the chemistry of the cluster. Direct determination of Mn spin-projections from our wavefunctions suggests that current candidates that have been recently distinguished using parameterized spin models should be reassessed. Through entanglement maps, we reveal rich information contained in the wavefunctions on bonding changes in the cycle.