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This paper reviews our historical developments of broken-symmetry (BS) and beyond BS methods that are applicable for theoretical investigations of metalloenzymes such as OEC in PSII. The BS hybrid DFT (HDFT) calculations starting from high-resolution (HR) XRD structure in the most stable S 1 state have been performed to elucidate structure and bonding of whole possible intermediates of the CaMn 4 O x cluster (1) in the S i (i = 0 ~ 4) states of the Kok cycle. The large-scale HDFT/MM computations starting from HR XRD have been performed to elucidate biomolecular system structures which are crucial for examination of possible water inlet and proton release pathways for water oxidation in OEC of PSII. DLPNO CCSD(T 0 ) computations have been performed for elucidation of scope and reliability of relative energies among the intermediates by HDFT. These computations combined with EXAFS, XRD, XFEL, and EPR experimental results have elucidated the structure, bonding, and reactivity of the key intermediates, which are indispensable for understanding and explanation of the mechanism of water oxidation in OEC of PSII. Interplay between theory and experiments have elucidated important roles of four degrees of freedom, spin, charge, orbital, and nuclear motion for understanding and explanation of the chemical reactivity of 1 embedded in protein matrix, indicating the participations of the Ca(H 2 O) n ion and tyrosine(Yz)-O radical as a one-electron acceptor for the O-O bond formation. The Ca-assisted Y z -coupled O-O bond formation mechanisms for water oxidation are consistent with recent XES and very recent time-resolved SFX XFEL and FTIR results., (© 2023. The Author(s).)

Hydrogen-bond (H-bond) interaction energies in α-helices of short alanine peptides were systematically examined by precise density functional theory calculations, followed by a molecular tailoring approach. The contribution of each H-bond interaction in α-helices was estimated in detail from the entire conformation energies, and the results were compared with those in the minimal H-bond models, in which only H-bond donors and acceptors exist with the capping methyl groups. The former interaction energies were always significantly weaker than the latter energies, when the same geometries of the H-bond donors and acceptors were applied. The chemical origin of this phenomenon was investigated by analyzing the differences among the electronic structures of the local peptide backbones of the α-helices and those of the minimal H-bond models. Consequently, we found that the reduced H-bond energy originated from the depolarizations of both the H-bond donor and acceptor groups, due to the repulsive interactions with the neighboring polar peptide groups in the α-helix backbone. The classical force fields provide similar H-bond energies to those in the minimal H-bond models, which ignore the current depolarization effect, and thus they overestimate the actual H-bond energies in α-helices. © 2019 The Authors. Journal of Computational Chemistry published by Wiley Periodicals, Inc., (© 2019 The Authors. Journal of Computational Chemistry published by Wiley Periodicals, Inc.)

The optimized geometries of the CaMn 4 O X (X = 5, 6) cluster in the oxygen evolving complex (OEC) of photosystem II (PSII) by large-scale quantum mechanics (QM) and molecular mechanics (MM) calculations are compared with recent serial femtosecond crystallography (SFX) results for the S i (i = 0-3) states. The valence states of four Mn ions by the QM/MM calculations are also examined in relation to the experimental results by the X-ray emission spectroscopy (XES) for the S i intermediates. Geometrical and valence structures of right-opened Mn-hydroxide, Mn-oxo and Mn-peroxide intermediates in the S 3 state are investigated in detail in relation to recent SFX and XES experiments for the S 3 state. Interplay between theory and experiment indicates that the Mn-oxo intermediate is a new possible candidate for the S 3 state. Implications of the computational results are discussed in relation to possible mechanisms of the oxygenoxygen bond formation for water oxidation in OEC of PSII., (© 2019 Scandinavian Plant Physiology Society.)

We applied our analysis, based on a linear response function of density and spin density, to two typical transition metal complex systems-the reaction centers of P450, and oxygen evolving center in Photosystem II, both of which contain open-shell transition metal ions. We discuss the relationship between LRF of electron density and spin density and the types of units and interactions of the systems. The computational results are discussed in relation to quantum mechanics (QM) cluster and quantum mechanics/molecular mechanics (QM/MM) modeling that are employed to compute the reaction centers of enzymes.

Both direct exchange and super-exchange interactions cooperate to realize inter-spin magnetic interaction in binuclear manganese complex Mn(IV) 2 O 2 (NHCHCO 2 ) 4 with a di-μ-oxo path. We revisited this spin system using DMRG CAS methods and CAS selection procedures. Our results indicate that our previous "dynamically extended spin polarization" (DE-SP) procedure for organic polyradicals and so forth does not work well. Thus, we have examined another selection procedure, the "dynamically extended super-exchange" (DE-SE) procedure. DMRG CASCI [18,18] by UB3LYP(HS)-UNO(DE-SE) can realize antiferromagnetic J values similar to experimental ones (-87 cm -1 ). In addition, all J values between all spin states (HS[septet],IS[quintet],IS[triplet],LS[singlet])were also shown to be correct under sufficiently large M values. © 2018 Wiley Periodicals, Inc., (© 2018 Wiley Periodicals, Inc.)

Au nanoclusters (Au NCs) stabilized by poly(N-vinyl-2-pyrrolidone) and poly(allylamine), abbreviated to Au:PVP and Au:PAA, catalyze the aerobic oxidation of p-hydroxybenzyl alcohols, but the catalytic activity of Au:PVP is much higher than that of Au:PAA. To elucidate the correlations between the catalytic activities and coordination structures of the stabilizing polymer, the substrate accessibility on Au NCs was estimated by density functional theory (DFT) and molecular dynamics (MD) calculations. For MD simulations, we applied a systematic method to optimize the temperature parameters in temperature replica exchange molecular dynamics (T-REMD), and the coordination structures were comprehensively classified by multivariate analysis. The results show that the number of open active sites on the Au NCs is a good index for predicting the catalytic activities. © 2018 Wiley Periodicals, Inc., (© 2018 Wiley Periodicals, Inc.)

The free-energy landscape is an important factor for understanding the conformational equilibria of chemical reactions, and many techniques have been developed to calculate the potential of the mean force. Unfortunately, these methods require a previous knowledge of the system for calculations because the results depend on the reaction coordinates. In this study, we combine the scaled hypersphere search method with the umbrella integration method to obtain the transition states on free-energy landscapes and minimum-free-energy paths (MFEPs). With this approach, the MFEP connections between known and unknown equilibrium points are constructed without the prior knowledge of the free-energy landscape. The problem of reaction coordinates can be solved by using a multidimensional, fully automated interrogation of MFEPs for acquiring the potential of mean force. The efficiency of the proposed method is demonstrated by applying it to alanine dipeptide and alanine tripeptide. © 2018 Wiley Periodicals, Inc., (© 2018 Wiley Periodicals, Inc.)

We present a new approach for automated exploration of free energy landscapes on the basis of the umbrella integration (UI) method. The method to search points in the landscape relies on the normal distributions and gradients of the potential of mean force (PMF) obtained from UI calculations. We applied this approach to the alanine dipeptide in solution and demonstrated that the equilibrium and the transition states were efficiently found in the ascending order of the PMF values., Competing Interests: The authors declare no conflict of interest.

In natural ionic solids, cationic and anionic species are alternately arranged to minimize electrostatic energy. Aggregation of identical ionic species is commonly prohibited due to the repulsive, long-range nature of Coulombic interactions. Recently, we synthesized unique ionic solids, [Au I 4 Co III 2 (dppe) 2 (D-pen) 4 ]X 2 ·nH 2 O (dppe = 1,2-bis(diphenylphosphino)ethane, D-pen = D-penicillaminate), in which complex cations are self-assembled into a cationic supramolecular octahedron, while monovalent or divalent inorganic anions are aggregated into an anomalous anionic cluster accommodating several water molecules. This quite unusual aggregation manner originates from various molecular-level non-Coulombic interactions such as hydrogen bonds and CH-π interactions; thus, this class of ionic solids is referred to as non-Coulombic ionic solids, abbreviated as NCISs. Herein, we report that the NCISs with a peculiar charge-separated (CS) structure in a cubic lattice show a negative, isotropic electrostriction phenomenon that has never been found in any ionic solids, as well as an anomalously large relaxer-like dielectric jump phenomenon reaching to an application level of ε'/ε 0 ~ 10 5 . The appearance of these phenomena was explained by the cooperative dynamics of inorganic anions and dipolar water molecules in the pliable anionic clusters that are surrounded by a rather robust cationic metallosupramolecular framework with a meso-scopic scale.

We present the linear response function of bond-orders (LRF-BO) based on a real space integration scheme for molecular systems. As in the case of the LRF of density, the LRF-BO is defined as the response of the bond order of the molecule for the virtual perturbation. Our calculations show that the LRF-BO enables us not only to detect inductive and resonating effects of conjugating systems, but also to predict p K a values on substitution groups via linear relationships between the Hammett constants and the LRF-BO values for meta- and para-substituted benzoic acids. More importantly, the LRF-BO values for the O-H bonds strongly depend on the sites to which the virtual perturbation is applied, implying that the LRF-BO values include essential information about reaction mechanism of the acid-dissociation of substituted benzoic acids., Competing Interests: The authors declare no conflict of interest.

We present a quantum mechanics/molecular mechanics (QM/MM) and QM-only study on the oxidative ring-cleaving reaction of quercetin catalyzed by quercetin 2,4-dioxygenase (2,4-QD). 2,4-QD has a mononuclear type 2 copper center and incorporates two oxygen atoms at C2 and C4 positions of the substrate. It has not been clear whether dioxygen reacts with a copper ion or a substrate radical as the first step. We have found that dioxygen is more likely to bind to a Cu(2+) ion, involving the dissociation of the substrate from the copper ion. Then a Cu(2+)-alkylperoxo complex can be generated. Comparison of geometry and stability between QM-only and QM/MM results strongly indicates that steric effects of the protein environment contribute to maintain the orientation of the substrate dissociated from the copper center. The present QM/MM results also highlight that a prior rearrangement of the Cu(2+)-alkylperoxo complex and a subsequent hydrogen bond switching assisted by the movement of Glu73 can facilitate formation of an endoperoxide intermediate selectively.

We examined nearsightedness of electronic matter (NEM) of finite systems on the basis of linear response function (LRF). From the computational results of a square-well model system, the behavior of responses obviously depends on the number of electrons (N): as N increases, LRF, δρ(r)/δv(r'), decays rapidly for the distance, |r-r'|. This exemplifies that the principle suggested by Kohn and Prodan holds even for finite systems: the cause of NEM is destructive interference among electron density amplitudes. In addition, we examined double-well model systems, which have low-lying degenerate levels. In this case, there are two types of LRF: the cases of the half-filled and of full-filled in low-lying degenerate levels. The response for the former is delocalized, while that of the later is localized. These behaviors of model systems are discussed in relation to the molecular systems' counterparts, H2, He22+, and He2 systems. We also see that NEM holds for the dissociated limit of H2, of which the mechanism is similar to that of the insulating state of solids as suggested by Kohn. We also examined LRF of alanine tripeptide system as well as butane and butadiene molecules, showing that NEM of the polypeptide system is caused by sp3 junctions at Cα atoms that prevent propagation of amplitudes of LRF, which is critically different from that of NEM for finite and infinite homogeneous systems.

The nature of chemical bonds of ruthenium(Ru)-quinine(Q) complexes, mononuclear [Ru(trpy)(3,5-t-Bu(2)Q)(OH(2))](ClO(4))(2) (trpy = 2,2':6',2''-terpyridine, 3,5-di-tert-butyl-1,2-benzoquinone) (1), and binuclear [Ru(2)(btpyan)(3,6-di-Bu(2)Q)(2)(OH(2))](2+) (btpyan = 1,8-bis(2,2':6',2''-terpyrid-4'-yl)anthracene, 3,6-t-Bu(2)Q = 3,6-di-tert-butyl-1,2-benzoquinone) (2), has been investigated by broken-symmetry (BS) hybrid density functional (DFT) methods. BS DFT computations for the Ru complexes have elucidated that the closed-shell structure (2b) Ru(II)-Q complex is less stable than the open-shell structure (2bb) consisting of Ru(III) and semiquinone (SQ) radical fragments. These computations have also elucidated eight different electronic and spin structures of tetraradical intermediates that may be generated in the course of water splitting reaction. The Heisenberg spin Hamiltonian model for these species has been derived to elucidate six different effective exchange interactions (J) for four spin systems. Six J values have been determined using total energies of the eight (or seven) BS solutions for different spin configurations. The natural orbital analyses of these BS DFT solutions have also been performed in order to obtain natural orbitals and their occupation numbers, which are useful for the lucid understanding of the nature of chemical bonds of the Ru complexes. Implications of the computational results are discussed in relation to the proposed reaction mechanisms of water splitting reaction in artificial photosynthesis systems and the similarity between artificial and native water splitting systems.

The spin-unrestricted Hartree-Fock (UHF)-based coupled cluster singles and doubles (UHF-CCSD) and Mukherjee's state-specific multireference CCSD (MkCCSD) methods are applied to four ring-opening reactions. The spin-restricted Hartree-Fock (RHF)-based CCSD (RHF-CCSD) calculations are also performed for comparison. In the case of the UHF-CCSD method, an approximate spin-projection (AP) method is applied to the broken-symmetry (BS) singlet solution to remove the spin contamination effect. For potential energy curves (PECs) of all reactions presented in this study, the results of RHF-CCSD and UHF-CCSD are substantially different from those of MkCCSD, while the results after the AP method (AP-UCCSD) reproduce the MkCCSD results well. It strongly suggests that the spin contamination effect should be removed by the AP correction even at the UHF-CCSD level to predict reliable energetics of these reactions.

In the present study, the concerted and stepwise reaction mechanisms for 1,3-dipole cycloaddition of ozone with ethylene (1) and acrylonitrile (2) are investigated. The stationary points are optimized by using four hybrid R(U)DFT methods. A geometry optimization method based on an approximate spin projection (AP-opt method) is applied to eliminate a spin contamination from the broken-symmetry (BS) solution. The AP-opt method reveals that a diradical intermediate for the stepwise pathway is spurious due to the spin contamination. The revised reaction profile with no diradical intermediate supports the stereospecificity. On the basis of the experimental data, the RCCSD(T) method outperforms AP-UCCSD(T), AP-UBD(T), and MkMRCCSD(4e,4o) for the systems, indicating that the RCCSD(T) method can describe the diradical character of ozone within a framework of single reference wave function. The subsequent single point energy calculations show that the highly synchronous transition state is much more favorable than the asynchronous one for 1. In the case of 2, there is not much difference between two transition states because of its asymmetric structure and charge separations in the transition states.

We quantify a spin contamination error caused by a broken-symmetry (BS) method on the geometry at the stationary points and barrier heights of the [2 + 2] reaction between singlet oxygen and ethylene, which goes through a diradical intermediate. Several hybrid GGA, hybrid meta-GGA, and long-range corrected hybrid functionals, O3LYP, B3LYP, PBE0, MPW1B95, BHandHLYP, and omegaB97X, are examined to elucidate their original nature without the spin contamination error. For that purpose, the geometry of each reaction step for the BS state as well as its total energy is corrected by using an approximate spin projection method. The CCSD and CCSD(T) single-point calculations are also carried out at optimized geometries at the DFT level to confirm the results of the DFT methods. The single-point calculations by means of Mukherjee's multireference coupled cluster with single and double excitations at CASSCF(10e,8o)-optimized geometries are also presented to assess the DFT methods. After the energy and geometry corrections, the barrier height of each functional is consistent with conventional closed-shell-type reactions even in the reaction involving singlet diradical species. We also find that the spin contamination error on the geometric change is not negligible especially at the early stage of the reaction ( approximately 3 kcal/mol), where the triplet state is the ground state.

On the basis of density-functional theory (DFT) calculations, a theoretical analysis of the exchange interactions in Ni9L2(O2CMe)8{(2-py)2CO2}4, was performed, where L is a bridging ligand, OH- (1) or N3- (2). Each magnetic interaction between the Ni spin centers is analyzed for 1 and 2 in terms of exchange integrals (J values), orbital overlap integrals (T values) and natural orbitals. It was found that a J3 interaction, which is a magnetic interaction via the bridging ligand orbitals, mainly controls the whole magnetic properties, and the dominant interaction is a sigma-type orbital interaction between Ni dz2 orbitals. Further investigations on the magnetostructural correlations are performed on the J3 interactions using simplest Ni-L-Ni models. These models reproduced the magnetic interactions qualitatively well not only for the Ni9 complexes but also for other inorganic complexes. Strong correlations have been found between the magnetic orbital overlaps (T values) and the Ni-L-Ni angle. These results revealed that the difference of the magnetic properties between OH- and N3- is caused by the orbital overlap integral (T values) of the sigma-type J3 interaction pathway. The magnetic interactions are also discussed from a Hubbard model by evaluating the transfer integral (t) and on-site Coulomb integrals (U), in relation to the Heisenberg picture.