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Possible mechanisms for water cleavage in oxygen evolving complex (OEC) of photosystem II (PSII) have been investigated based on broken-symmetry (BS) hybrid DFT (HDFT)/def2 TZVP calculations in combination with available XRD, XFEL, EXAFS, XES and EPR results. The BS HDFT and the experimental results have provided basic concepts for understanding of chemical bonds of the CaMn4O5 cluster in the catalytic site of OEC of PSII for elucidation of the mechanism of photosynthetic water cleavage. Scope and applicability of the hybrid DFT (HDFT) methods have been examined in relation to relative stabilities of possible nine intermediates such as Mn-hydroxide, Mn-oxo, Mn-peroxo, Mn-superoxo, etc., in order to understand the O–O (O–OH) bond formation in the S3 and/or S4 states of OEC of PSII. The relative stabilities among these intermediates are variable, depending on the weight of the Hartree–Fock exchange term of HDFT. The Mn-hydroxide, Mn-oxo and Mn-superoxo intermediates are found to be preferable in the weak, intermediate and strong electron correlation regimes, respectively. Recent different serial femtosecond X-ray (SFX) results in the S3 state are investigated based on the proposed basic concepts under the assumption of different water-insertion steps for water cleavage in the Kok cycle. The observation of water insertion in the S3 state is compatible with previous large-scale QM/MM results and previous theoretical proposal for the chemical equilibrium mechanism in the S3 state . On the other hand, the no detection of water insertion in the S3 state based on other SFX results is consistent with previous proposal of the O–OH (or O–O) bond formation in the S4 state . Radical coupling and non-adiabatic one-electron transfer (NA-OET) mechanisms for the OO-bond formation are examined using the energy diagrams by QM calculations and by QM(UB3LYP)/MM calculations . Possible reaction pathways for the O–O and O–OH bond formations are also investigated based on two water-inlet pathways for oxygen evolution in OEC of PSII. Future perspectives are discussed in relation to post HDFT calculations of the energy diagrams for elucidation of the mechanism of water oxidation in OEC of PSII.

In this work, we show that the natural orbitals of unrestricted hybrid density functional theory (UHDFT) can be used as the active space orbitals to perform multireference (MR) calculations, for example, the density matrix renormalisation group (DMRG) and Mukherjee-type (Mk) MR coupled-cluster (CC) method. By including a sufficiently large number of these natural orbitals, full-valence (FV) active space can be identified without recourse of the expensive self-consistent procedures for DMRG-SCF. Several useful chemical indices are derived based on the occupation numbers of the natural orbitals for seamless continuation from broken-symmetry (BS) to symmetry-adapted (SA) methods. These procedures are used on 1,3-didehydrobenzene (meta-benzyne) to calculate its singlet (S)-triplet (T) gap. We compare our results to available experiments and computational results obtained by several other groups. We see our procedures as a seamless bridge between single-reference BS methods, such as UHDFT, and the SA MR methods, such as FV DMRG and MkMRCC.

Theoretical examinations of the ferromagnetic coupling in the m-phenylene-bis-methylene molecule and its oligomer were carried out. These systems are good candidates for exchange-coupled systems to investigate strong electronic correlations. We studied effective exchange integrals (J), which indicated magnetic coupling between interacting spins in these species. First, theoretical calculations based on a broken-symmetry single-reference procedure, i.e. the UHF, UMP2, UMP4, UCCSD(T) and UB3LYP methods, were carried out with a GAUSSIAN program code under an SR wave function. From these results, the J value by the UHF method was largely positive because of the strong ferromagnetic spin polarisation effect. The J value by the UCCSD(T) and UB3LYP methods improved an overestimation problem by correcting the dynamical electronic correlation. Next, magnetic coupling among these spins was studied using the CAS-based method of the symmetry-adapted multireference methods procedure. Thus, the UNO DMRG CASCI (...

Fundamental principles for theoretical understanding and elucidation of structure and reactivity of iron-sulfur (Fe-S) FenSm (n, m=2∼8) clusters are investigated and elucidated on the theoretical and experimental grounds. To this end, the nature of chemical bonds of these clusters is investigated by three methods; (1) the spin Hamiltonian model for analysis of EPR results, (2) broken-symmetry (BS) hybrid density functional theory (HDFT) methods for full geometry optimisations and elucidations of complete active spaces (CAS) for one-electron transfers reactions and (3) beyond HDFT methods such as CAS configuration interaction (CI) and MR CI for high precision energy calculations on classical and quantum computers. Theoretical concepts revealed are applied for elucidation of the mechanism of nitrogen fixation with FeMoco (Fe7MoS9C) cluster, indicating an important role of proton-coupled (PC) one electron spin transfer (OEST) processes instead of radical reaction mechanisms.

We have investigated nearsightedness of electronic matter (NEM) of finite systems on the basis of linear response function to examine theoretical foundation of contemporary computational chemistry such as quantum mechanics/molecular mechanics methods. In this study, we introduce several nearsightedness-related indices to assess the magnitude of localisability of responses for one-dimensional finite model systems. We started from two electrons' systems, which are beyond the scope of the original concept of NEM, and increased the number of electrons (N) to a hundred electrons to analyse dependency of such indices on N. In the process of construction of the indices, we analysed the factors, because of which the magnitude of nonlocal parts of linear response functions becomes small, into several ones, and extracted purely the magnitude of propagation of responses.

Quantum mechanical (QM)/molecular mechanics (MM) calculations by the use of a large-scale QM model (QM Model V) have been performed to elucidate hydrogen-bonding networks and proton wires for proton release pathways (PRP) of water oxidation reaction in the oxygen evolving complex (OEC) of photosystem II (PSII). Full geometry optimisations of PRP by the QM/MM model have been carried out starting from the geometry of heavy atoms determined by the recent high-resolution X-ray diffraction (XRD) experiment of PSII refined to 1.9 A resolution. Computational results by the QM/MM calculations have elucidated the hydrogen-bonding O···O(N) and O···H distances and O(N)–H···O angles in PRP, together with the Cl–O(N) and Cl···H distances and O(N)–H···Cl angles for chloride anions. The optimised hydrogen-bonding networks are well consistent with the XRD results and available experiments such as extended X-ray absorption fine structure, showing the reliability of channel structures of OEC of PSII revealed by the XRD exp...

We here formulate and implement linear response function (LRF) of the Mayer bond order (MBO), which is expected to be a new indicator to describe intrinsic chemical reactivity of molecules. We calculate LRFs of the MBOs of para-substituted benzoic acids, and compare the results with the Hammett substituent constants and computational results of acid dissociation constants that were previously reported. The results are discussed from the viewpoint of the applicability of LRF of the MBO to estimate the relative reactivity of the substituted benzoic acids.

Domain-based local pair natural orbital (DLPNO) coupled cluster single and double (CCSD) methods with perturbative triples (T) correction with NormalPNO were used to compute energies for twelve different S1 structures of the CaMn4O5 cluster in the oxygen evolving complex (OEC) of photosystem II (PSII). The DLPNO-CCSD(T0) calculations with TightPNO for the important six structures among them revealed that the right (R)-opened S1XYZW structures were more stable than the corresponding left (L)-opened structures (X = O(5), Y = W2, Z = W1, and W = O(4)) of CaMn4O5. The three different S1 structures belonging to the R-opened type (S1acca, S1bbca, and S1abcb, where O2- = a, OH- = b and H2O = c) were found nearly degenerated in energy, indicating the possibility of the coexistence of different structures in the S1 state. The DLPNO-CCSD(T0) calculations with TightPNO supported the proposal of a dynamic equilibrium model based on the multi-intermediate structures for the S1 state, which is also in agreement with EPR and other experimental and hybrid DFT computational results. Implications of the computational results are discussed in relation to scope and applicability of NormalPNO and TightPNO for the CCSD(T0) calculations of strongly correlated electron systems such as 3d transition-metal complexes.

Mukherjee's type of multireference coupled-cluster (MkMRCC), approximate spin-projected spin-unrestricted CC (APUCC), and AP spin-unrestricted Brueckner's (APUBD) methods were applied to didehydronated ethylene, allyl cation, cis-butadiene, and naphthalene. The focus is on descriptions of magnetic properties for these diradical species such as S-T gaps and diradical characters. Several types of orbital sets were examined as reference orbitals for MkMRCC calculations, and it was found that the change of orbital sets do not give significant impacts on computational results for these species. Comparison of MkMRCC results with APUCC and APUBD results show that these two types of methods yield similar results. These results show that the quantum spin corrected UCC and UBD methods can effectively account for both nondynamical and dynamical correlation effects that are covered by the MkMRCC methods. It was also shown that appropriately parameterized hybrid density functional theory (DFT) with AP corrections (APU...

We present simple CAS-DFT approaches for degenerate and nearly degenerate systems. In this method, we do not employ any auxiliary variables, but employ the effective CASCI-DFT and CASSCF-DFT equations for the ground and excited states. Simple applications for fundamental systems such as atomic multiplet states (C, N+n , and O+n ), the transition metal complex V(III)L6 (L = H2O and CO) and the Cu(II) acetate dimer Cu(II)2(Ac)4(H2O)2 are presented. The results are discussed from the viewpoint of the shapes of the potential curves of several nearly degenerate spin states, the theory of molecular magnetism and the reliability of the CAS space employed. The computational results are fully compatible with the experimental results available, and also with those of ligand field theory.

Static molecular second hyperpolarizabilities γ of several donor-π-acceptor molecules have been examined using an ab initio molecular orbital (MO) method to evaluate the effects of substituents and molecular distortion on γ. It was found that γ values of the donor-π-acceptor compounds are affected by the degree of π electron delocalization more than the donor or acceptor strength of the substituents. Also it was found that contributions from higher order excitation process are not negligible for γ values of the donor-π-acceptor molecules.

The effective exchange integrals (J ab(M)) between two cation radicals of title compounds in the Heisenberg model were calculated by ab initio molecular orbital (MO) and density functional theory (DFT) methods, together with hybrid DFT methods. The J ab(D) values between two dimer mono-cation radicals were also estimated assuming J ab(D) = J ab(M)/2. It is found that the spin lattice obtained by the ab initio method is square planar and linear in BEDT-TTF and BETS planes, respectively, although other previous calculations show that spin lattice in the BEDT-TTF plane is a triangular one. The J ab and overlap integrals (sab ) values by the ab initio methods were used to determine transfer integral (tab ) and Coulomb repulsion (Ucff ) parameters of the Hubbard model, which were compared with those of the previous results. Implications of the calculated results are discussed in relation to the spin-mediated mechanism for superconductivity.

The molecular second hyperpolarizabilities γ of cationic 3- or 4-substituted pyridine derivatives have been investigated. The γ values are calculated by an ab initio molecular orbital (MO) method at correlated levels including CCSD(T). The magnitude of γ for the pyridinium cation is shown to be smaller than that of pyridine. It is found that γ for the pyridinium cation changes dramatically with substitution, whereas γ for neutral pyridine does not show such large substituent effects. This remarkable substituent effect on γ of cationic pyridine derivatives is one of the special features of cationic species.

Potential curves and high and low spin energy gaps for radical clusters were calculated by spin polarized molecular orbital methods. Through-space effective exchange integrals (J ab) and relative energies of spin projected low spin states by post-Hartree-Fock (HF) calculation were reproduced by the hybrid density functional theory (DFT) method. The hybrid parameters that could reproduce post-HF values such as UCCSD(T)'s for each model had close relations with the instabilities of those systems. Information entropy and related chemical indices were used to estimate the magnitude of the instabilities. A magnetic effective density functional (MEDF) scheme for spin clusters was proposed for practical computation of J ab values in molecular magnetic materials.

Activation barrier heights for concerted and non-concerted transition structures between butadiene and ethylene have been calculated by the broken-symmetry Hartree-Fock (HF), QCISD(T), and CCSD(T) methods with and without approximate spin projection, and the spin-restricted CASCI, CASSCF UNO MP2 and MR MP2 methods. They also have been calculated by the density functional theory (DFT) and hybrid DFT (HDFT) methods such as B2LYP and B3LYP. The reliability and utility of the HDFT methods have been investigated, and compared with the post-HF and MR MP2 results. The information entropy and related electron correlation indices also have been examined in relation to the polyradical character of the transition structures. Implications of the present results are discussed concerning the applicability of HDFT to large systems.