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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