We present two hybrid solvation models for the calculation of the solvation structure with model 1 in a confined nanospace in bulk materials and model 2 at solid/liquid interfaces where an electrode is in contact with an electrolyte and a membrane is immersed into a solution. The hybrid theory is based on the reference interaction site method (RISM) for the solvent region. The electronic structure of a bulk material, an electrode, and a membrane is treated by density functional theory with the plane-wave basis and pseudopotentials technique. For model 1, we use the three-dimensional RISM (3D-RISM) by imposing a 3D periodic boundary condition on the system. However, for model 2, we reformulate the RISM by means of a two-dimensional boundary condition parallel to the surface and an open boundary condition normal to the surface. Four benchmark calculations are performed for the formaldehyde-water system, water packed into a zeolite framework, a NaCl solution in contact with an Al electrode, and an Al thin film immersed in a NaCl solution with different concentrations. The calculations are shown to be efficient and stable. Because of the flexibility of the RISM theory, the models are considered to be applicable to a wide range of solid/liquid interfaces.

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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.

ABSTRACT:We have investigated the reaction pathways for the primary hydroxylation reaction of trimethylmethane by a high-valent Fe(IV)AO porphyrincation radical species known as compound I at the B3LYP/CEP-31G level. The isoelectronic analogy of the Fe(IV)AO core of compound I to a molecular oxygen (O 2 ) has been successfully used to clarify the important roles of the singlet excited state of the Fe(IV)AO core in the alkane hydroxylation, which has hitherto been neglected. The reaction is initiated by the rate-determining hydrogen-atom abstraction from the substrate to give a discrete radical intermediate complex, in accordance with the conventional radical rebound mechanism. Similar to the chemistry of O 2 , however, one of the singlet excited states, i.e., the diradical component of the 1 ⌬ state of the Fe(IV)AO core intercepts the triplet ground state (the 3 ⌺ state) in the region of the transition state for the hydrogen abstraction. Our findings strongly indicate that the exchange polarization or intersystem crossing for the nonradiative transition to the locally singlet state is highly important to enhance the reactivity of compound I.

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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.

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Reaction mechanisms of oxygen evolution in native and artificial photosynthesis II (PSII) systems have been investigated on the theoretical grounds, together with experimental results. First of all, our previous broken-symmetry (BS) molecular orbitals (MO) calculations are reviewed to elucidate the instability of the dp-pp bond in high-valent (HV) Mn(X)¼ ¼O systems and the dp-pp-dp bond in HV Mn¼ ¼O¼ ¼Mn systems. The triplet instability of these bonds entails strong or intermediate diradical characters: Mn(IV)¼ ¼O and MnAOAMn; the BS MO resulted from strong electron correlation, leading to the concept of electron localizations and local spins. The BS computations have furthermore revealed guiding principles for derivation of selection rules for radical reactions of local spins. As a continuation of these theoretical results, the BS MO interaction diagrams for oxygen-radical coupling reactions in the oxygen evolution complex (OEC) in the PSII have been depicted to reveal scope and applicability of local singlet diradical (LSD) and local triplet diradical (LTD) mechanisms that have been successfully utilized for theoretical understanding of oxygenation reactions mechanisms by p450 and methane monooxygenase (MMO). The manganese-oxide cluster models examined are London, Berlin, and Berkeley models of CaMn 4 O 4 and related clusters Mn 4 O 4 and Mn 3 Ca. The BS MO interaction diagrams have revealed the LSD and/or LTD mechanisms for generation of molecular oxygen in the total low-, intermediate and highspin states of these clusters. The spin alignments are found directly corresponding to the spin-coupling mechanisms of oxygen-radical sites in these clusters. The BS UB3LYP calculations of the clusters have been performed to confirm the comprehensive guiding principles for oxygen evolution; charge and spin densities by BS UB3LYP are utilized for elucidation and confirmation of the LSD and LTD mechanisms. Applicability of the proposed selection rules are examined in comparison with a lot of accumulated experimental and theoretical results for oxygen evolution reactions in native and artificial PSII systems.