Hydrogen (H) atom adsorption and migration over the CeO2-based materials surface are of great importance because of its wide applications to catalytic reactions and electrochemical devices. Therefore, comprehensive knowledge for controlling the H atom adsorption and migration over CeO2-based materials is crucially important. For controlling H atom adsorption and migration, we investigated irreducible divalent, trivalent, and quadrivalent heterocation-doping effects on H atom adsorption and migration over the CeO2(111) surface using density functional theory (DFT) calculations. Results revealed that the electron-deficient lattice oxygen (Olat) and the flexible CeO2matrix played key roles in strong adsorption of H atoms. Heterocations with smaller valence and smaller ionic radius induced the electron-deficient Olat. In addition, smaller cation doping enhanced the CeO2matrix flexibility. Moreover, we confirmed the influence of H atom adsorption controlled by doping on surface proton migration (i.e.surface protonics) and catalytic reaction involving surface protonics (NH3synthesis in an electric field). Results confirmed clear correlation between H atom adsorption energy and surface protonics.

Hydrogen (H) atomic migration over a metal oxide is an important surface process in various catalytic reactions. Control of the interaction between H atoms and the oxide surfaces is therefore important for better catalytic performance. For this investigation, we evaluated the adsorption energies of the H atoms over perovskite-type oxides (Sr1−xBaxZrO3; 0.00 ≤x≤ 0.50) using DFT (Density Functional Theory) calculations, then clarified the effects of cation-substitution in the A-site of perovskite oxides on H atom adsorption, migration, and reaction. Results indicated local distortion at the oxide surface as a key factor governing H atom adsorption. Subtle Ba2+substitution for Sr2+sites provoked local distortion at the Sr1−xBaxZrO3oxide surface, which led to a decrement in the H atom adsorption energy. Furthermore, the effect of Sr2+/Ba2+ratio on the H atoms' reactivities was examined experimentally using a catalytic reaction, which was promoted by activated surface H atoms. Results show that the surface H atoms activated by the substitution of Sr2+sites with a small amount of Ba2+(x= 0.125) contributed to enhancement of ammonia synthesis rate in an electric field, which showed good agreement with predictions made using DFT calculations.

<p>Relativistic quantum chemical calculations are performed based on one of two physical pictures, namely the Dirac picture and the Schrödinger picture. With regard to the latter, the so-called picture-change effect...</p>

The machine-learned electron correlation (ML-EC) model is a regression model in the form of a density functional that reproduces the correlation energy density based on wavefunction theory. In a previous study [T. Nudejima et al., J. Chem. Phys. 151, 024104 (2019)], the ML-EC model was constructed using the correlation energy density from all-electron calculations with basis sets including core polarization functions. In this study, we applied the frozen core approximation (FCA) to the correlation energy density to reduce the computational cost of the response variable used in machine learning. The coupled cluster singles, doubles, and perturbative triples [CCSD(T)] correlation energy density obtained from a grid-based energy density analysis was analyzed within FCA and correlation-consistent basis sets without core polarization functions. The complete basis set (CBS) limit of the correlation energy density was obtained using the extrapolation and composite schemes. The CCSD(T)/CBS correlation energy densities based on these schemes showed reasonable behavior, indicating its appropriateness as a response variable. As expected, the computational time was significantly reduced, especially for systems containing elements with a large number of inner-shell electrons. Based on the density-to-density relationship, a large number of data (5 662 500 points), which were accumulated from 30 molecules, were sufficient to construct the ML-EC model. The valence-electron correlation energies and reaction energies calculated using the constructed model were in good agreement with the reference values, the latter of which were superior in accuracy to density functional calculations using 71 exchange-correlation functionals. The numerical results indicate that the FCA is useful for constructing a versatile model.

Bacteriorhodopsin (BR) is a model protein for light-driven proton pumps, where the vectorial active proton transport results in light-energy conversion. To clarify the microscopic mechanism of primary proton transfer from retinal Schiff base (SB) to Asp85 in BR, herein, we performed quantum-mechanical metadynamics simulations with the isolated BR model (similar to 3750 atoms). The simulations showed a novel proton transfer mechanism, viz. the hydroxide ion mechanism, in which the deprotonation of specific internal water (Wat452) yields the protonation of Asp85 via Thr89, after which the resulting hydroxide ion accepts the remaining proton from retinal SB. Systematic investigations adopting four sequential snapshots obtained by the time-resolved serial femtosecond crystallography revealed that proton transfer took 2-5.25 mu s on the photocycle. The presence of Wat401, which is the main difference between snapshots at 2 and 5.25 mu s, is found to be essential in assisting the primary proton transfer. Furthermore, the hydroxide ion mechanism was confirmed by the minimum energy path for the primary proton transfer in BR obtained by the nudged elastic band calculations with the embedded BR model (10,119 atoms), in which BR was embedded within lipid membranes in between water solvents.

A solvent selection scheme for optimization of reactions is proposed using machine learning, based on the numerical descriptions of solvent molecules. Twenty-eight key solvents were represented using 17 physicochemical descriptors. Clustering analysis results implied that the descriptor represents the chemical characteristics of the solvent molecules. During the assessment of an organometallic reaction system, the regression analysis indicated that learning even a small number of experimental results can be useful for identifying solvents that will produce high experimental yields. Observation of the regression coefficients, and both clustering and regression analysis, can be effective when selecting a solvent to be used for an experiment.

An efficient calculation scheme for obtaining free energy surfaces (FESs) in chemical or biological systems from multiple metadynamics (metaD) simulations was developed. In this study, the biased probability distributions of the collective variables and other degrees of freedom were separately calculated in multiple short-time metaD simulations using the reweighting method. The corresponding equilibrium probability distribution was finally constructed using the weighted histogram analysis method (WHAM). This method was applied for the conformational transitions of alanine dipeptide in the gas phase as an illustrative application. The results confirmed that this method was feasible for efficiently generating the converged FES.

© 2018 Elsevier B.V. Development of a highly efficient ammonia synthesis process is desirable for achieving a sustainable society. Regarding conventional heterogeneous catalysts, Ru-supported catalyst exhibits higher turn-over frequency (TOF) than Fe-supported or Ni-supported catalysts. However, we found that Fe-supported and Ni-supported catalysts show higher TOF than Ru-supported catalyst in an electric field at the low temperature of 373 K. Density functional theory (DFT) calculations revealed that N2 dissociation through the “associative mechanism” plays a key role in the electric field. The ammonia synthesis activity in the electric field is determined by the N2H formation energy at the metal-support interface.

Copyright © 2020 American Chemical Society. For effective utilization of ethane in natural gas, catalytic dehydrogenation of ethane is a promising option that offers better efficiency than ethane cracking to produce ethylene, the most important fundamental chemical. Recently, it was reported that catalytic dehydrogenation of ethane proceeds effectively on doped perovskite oxide via the Mars-van Krevelen (MvK) mechanism. For this work, the reaction mechanism was investigated using density functional theory calculations. Results demonstrated that ethane activation over perovskite (La1-xBaxMnO3-δ) proceeds at the surface lattice oxygen coordinated with Ba, resulting in a low energy barrier of the C-H bond activation. Based on Bader charge analysis, the electron-deficient surface lattice oxygen, which is favorable for hydrogen abstraction from light alkanes, forms around Ba. In addition, the electronic charges of the surface lattice oxygen are important for H2 desorption. The electronic charge depends on hydrogen coverage: electron-rich surface lattice oxygen, which is favorable for H2 desorption, forms at high hydrogen coverage. Therefore, a part of the surface lattice oxygens of perovskite would be covered with hydrogen atoms under the reaction atmosphere, leading to effective H2 desorption and the proceeding catalytic cycle via the MvK mechanism.

The "Relativistic And Quantum Electronic Theory (RAQET)" program was released for academic use. One-component (spin-free) and two-component (spin-dependent) relativistic calculations are possible based on the infinite-order Douglas−Kroll−Hess transformation and local unitary transformation. This review describes available features, registration/installation, and input/output of the RAQET program.

A cationic Ir complex was reported to show specific catalytic activity in C-H bond activation reaction of benzanilides. The present study examined reaction energy profiles of the C-H bond activation with Ir and Rh catalysts based on non-relativistic and relativistic quantum chemical calculations. We found that the relativistic effect is essential to demonstrate the difference in the catalytic activity. In particular, the activation of the d orbital of Ir, which is caused by the s- and p- orbital contraction followed by the self-consistent d-orbital expansion, leads to stabilization of the transition state and product of the C-H bond activation.

© 2019 Author(s). Efficient ammonia synthesis at low temperatures is anticipated for establishing a hydrogen carrier system. We reported earlier that application of an electric field on the Cs/Ru/SrZrO3 catalyst enhanced catalytic ammonia synthesis activity. It is now clear that N2 dissociation is activated by hopping protons in the electric field. Efficient ammonia synthesis proceeds by an "associative mechanism" in which N2 dissociates via an N2H intermediate, even at low temperatures. The governing factor of ammonia synthesis activity in an electric field for active metals differed from that in the conventional mechanism. Also, N2H formation energy played an important role. The effects of dopants (Al, Y, Ba, and Ca) on this mechanism were investigated using activity tests and density functional theory calculations to gain insights into the support role in the electric field. Ba and Ca addition showed positive effects on N2H formation energy, leading to high ammonia synthesis activity. The coexistence of proton-donating and electron-donating abilities is necessary for efficient N2H formation at the Ru-support interface.

The crossing of potential energy surfaces plays an important role in photo-decay processes and photochemical reactions. The energies and geometries of the crossing points have been reported for various molecules using quantum chemical calculations. In this research, excitation energy components of uracil are investigated to understand the characteristics of the crossing points. We revealed that the HOMO−LUMO exchange integral becomes approximately zero at the minimum energy conical intersection between S0 and S1 states. Furthermore, it was found that the HOMO−LUMO gap is close to the HOMO−LUMO Coulomb integral at the crossing structures.

The Relativistic And Quantum Electronic Theory (RAQET) program is a new software package, which is designed for large-scale two-component relativistic quantum chemical (QC) calculations. The package includes several efficient schemes and algorithms for calculations involving large molecules which contain heavy elements in accurate relativistic formalisms. These calculations can be carried out in terms of the two-component relativistic Hamiltonian, wavefunction theory, density functional theory, core potential scheme, and evaluation of electron repulsion integrals. Furthermore, several techniques, which have frequently been used in non-relativistic QC calculations, have been customized for relativistic calculations. This article introduces the brief theories and capabilities of RAQET with several calculation examples.

A semi-local kinetic energy density functional (KEDF) was constructed based on machine learning (ML). The present scheme adopts electron densities and their gradients up to third-order as the explanatory variables for ML and the Kohn-Sham (KS) kinetic energy density as the response variable in atoms and molecules. Numerical assessments of the present scheme were performed in atomic and molecular systems, including first- and second-period elements. The results of 37 conventional KEDFs with explicit formulae were also compared with those of the ML KEDF with an implicit formula. The inclusion of the higher order gradients reduces the deviation of the total kinetic energies from the KS calculations in a stepwise manner. Furthermore, our scheme with the third-order gradient resulted in the closest kinetic energies to the KS calculations out of the presented functionals.

A semi-local kinetic energy density functional (KEDF) was constructed based on machine learning (ML). The present scheme adopts electron densities and their gradients up to third-order as the explanatory variables for ML and the Kohn-Sham (KS) kinetic energy density as the response variable in atoms and molecules. Numerical assessments of the present scheme were performed in atomic and molecular systems, including first- and second-period elements. The results of 37 conventional KEDFs with explicit formulae were also compared with those of the ML KEDF with an implicit formula. The inclusion of the higher order gradients reduces the deviation of the total kinetic energies from the KS calculations in a stepwise manner. Furthermore, our scheme with the third-order gradient resulted in the closest kinetic energies to the KS calculations out of the presented functionals.

This letter proposes an approximate treatment of the harmonic solvation model (HSM) assuming the solute to be a rigid body (RB-HSM). The HSM method can appropriately estimate the Gibbs free energy for condensed phases even where an ideal gas model used by standard quantum chemical programs fails. The RB-HSM method eliminates calculations for intra-molecular vibrations in order to reduce the computational costs. Numerical assessments indicated that the RB-HSM method can evaluate entropies and internal energies with the same accuracy as the HSM method but with lower calculation costs.

We report theoretical calculations of positron-electron annihilation spectra of noble gas atoms and small molecules using the nuclear orbital plus molecular orbital method. Instead of a nuclear wavefunction, the positronic wavefunction is obtained as the solution of the coupled Hartree-Fock or Kohn-Sham equation for a positron and the electrons. The molecular field is included in the positronic Fock operator, which allows an appropriate treatment of the positron-molecule repulsion. The present treatment succeeds in reproducing the Doppler shift, i.e., full width at half maximum (FWHM) of experimentally measured annihilation (γ-ray) spectra for molecules with a mean absolute error less than 10%. The numerical results indicate that the interpretation of the FWHM in terms of a specific molecular orbital is not appropriate.

We report theoretical calculations of positron-electron annihilation spectra of noble gas atoms and small molecules using the nuclear orbital plus molecular orbital method. Instead of a nuclear wavefunction, the positronic wavefunction is obtained as the solution of the coupled Hartree-Fock or Kohn-Sham equation for a positron and the electrons. The molecular field is included in the positronic Fock operator, which allows an appropriate treatment of the positron-molecule repulsion. The present treatment succeeds in reproducing the Doppler shift, i.e., full width at half maximum (FWHM) of experimentally measured annihilation (γ-ray) spectra for molecules with a mean absolute error less than 10%. The numerical results indicate that the interpretation of the FWHM in terms of a specific molecular orbital is not appropriate.

This article proposes a gauge-origin independent formalism of the nuclear magnetic shielding constant in the two-component relativistic framework based on the unitary transformation. The proposed scheme introduces the gauge factor and the unitary transformation into the atomic orbitals. The two-component relativistic equation is formulated by block-diagonalizing the Dirac Hamiltonian together with gauge factors. This formulation is available for arbitrary relativistic unitary transformations. Then, the infinite-order Douglas-Kroll-Hess (IODKH) transformation is applied to the present formulation. Next, the analytical derivatives of the IODKH Hamiltonian for the evaluation of the nuclear magnetic shielding constant are derived. Results obtained from the numerical assessments demonstrate that the present formulation removes the gauge-origin dependence completely. Furthermore, the formulation with the IODKH transformation gives results that are close to those in four-component and other two-component relativistic schemes.

The divide-and-conquer (DC) method was extended to time-dependent density functional tight-binding (TDDFTB) theory to enable excited-state calculations of large systems, as denoted by DC-TDDFTB. In this article, the implementation of TDDFTB and DC-TDDFTB methods into our in-house program, DC-DFTB-K, is explained. Dependence of CPU time on system-size for the DC-TDDFTB calculations indicates significant reduction of computational cost by adopting the DC method. Owing to the feature, excited-state calculations for whole photoactive yellow protein (PYP) surrounded by 4684 water molecules could be carried out in order to examine the hydrogen bond between p-coumaric acid and Glu46 in PYP.

NH3 synthesis on Ru, Os, and Rh nanoparticle catalysts was investigated using density functional theory calculations. The Ru and Os nanoparticles exhibited similar shapes, while that of Rh differed significantly. For all metal species, step sites appeared at nanoparticle diameters (d) &gt
2–4 nm. The calculated activation barriers (Ea) were small at step sites, and Ru and Os step sites exhibited similar Ea values despite the former having a higher turnover frequency. This is likely due to the surface coverage of vacant sites being higher on Ru. Although the increase in NH3 synthesis rate at d = 2–4 nm was common to Ru, Os, and Rh, the reaction rates decreased in the order: Ru &gt
Os &gt
Rh. Our results show that Ea values, surface vacant sites, and the number of step sites are important factors for NH3 synthesis. The Ru nanoparticles exhibited high activity due to satisfying all three factors.

© 2018 American Chemical Society. Detailed reaction mechanisms for the oxidative coupling of methane (OCM) over Ce 2 (WO 4 ) 3 catalysts at low temperatures in an electric field were investigated. The influence of Ce cations in the Ce 2 (WO 4 ) 3 catalyst was evaluated by comparing the OCM activity over various Ln 2 (WO 4 ) 3 (Ln = La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, and Dy) catalysts in an electric field. The electronic states of Ln and W cations and the relationship between the distorted Ce 2 (WO 4 ) 3 structure and methane activation were examined using X-ray absorption fine structure (XAFS) measurements and first-principles calculations. The results reveal that the Ln 2 (WO 4 ) 3 catalysts with redox-active Ln cations (Ce, Pr, Sm, Eu, and Tb) show OCM activity. First-principles calculations indicate that Ce 3+ species in the Ce 2 (WO 4 ) 3 structure are oxidized to Ce 4+ species in an electric field by extracting electrons from the Ce 4f orbitals near the Fermi level; as a result, its structure is distorted. The results indicate that the redox reaction of Ln cations in Ln 2 (WO 4 ) 3 induced by an electric field brings lattice strain and a high OCM activity in an electric field.

Divide-and-conquer-type density-functional tight-binding molecular dynamics simulations of the CO2 absorption process in monoethanolamine (MEA) solution have been performed for systems containing thousands of atoms. The formation of carbamate anions has been widely investigated for neutral systems via ab initio molecular dynamics simulations, yet the present study is aimed at identifying the role of hydroxide ions in acid-base equilibrium. The structural and electronic analyses reveal that the hydroxide ion approaches, via Grotthuss-type shuttling, the zwitterionic intermediates and abstracts a proton from the nitrogen atom of MEA. We also estimated the fraction of reacted CO2 and carbamate formed at different initial CO2 concentrations that confirm a high absorbed CO2 concentration decreases the fraction of MEA(C) formed due to the abundance of MEA(Z) in the solution.

<p>We have proposed a novel quantum chemical model to evaluate condensed-phase thermodynamic properties, that is, the harmonic solvation model (HSM). This paper explains the theoretical background of HSM and the practical procedure to use for the HSM with some sample inputs. Illustrative applications demonstrate the usefulness and accuracy of HSM.</p>

&lt;p&gt;In this letter, effective exchange integrals of radical dimers obtained by density functional calculations are decomposed into atomic-pair components. The bond energy density analysis, which was originally proposed to evaluate the energy of a chemical bond, was found to be a useful tool to analyze the magnetic interaction of radical dimers.&lt;/p&gt;

© 2017 American Chemical Society. The diffusion of the hydroxide ion in bulk water was examined by linear-scaling divide-and-conquer density-functional tight-binding molecular dynamics (DC-DFTB-MD) simulations using three different-sized unit cells that contained 522, 1050, and 4999 water molecules as well as one hydroxide ion. The repulsive potential for the oxygen-oxygen pair was improved by iterative Boltzmann inversion, which adjusted the radial distribution function of DFTB-MD simulations to that of the reference density functional theory-MD one. The calculated diffusion coefficients and the Arrhenius diffusion barrier were in good agreement with experimental results. The results of the hydroxide ion coordination number distribution and potential of mean force analyses supported a dynamical hypercoordination diffusion mechanism. (Graph Presented).

© 2017 Elsevier B.V. This Letter proposes a density functional treatment based on the two-component relativistic scheme at the infinite-order Douglas-Kroll-Hess (IODKH) level. The exchange-correlation energy and potential are calculated using the electron density based on the picture-change corrected density operator transformed by the IODKH method. Numerical assessments indicated that the picture-change uncorrected density functional terms generate significant errors, on the order of hartree for heavy atoms. The present scheme was found to reproduce the energetics in the four-component treatment with high accuracy.

© 2017 Elsevier B.V.We have derived and implemented a universal formulation of the second-order generalized Møller–Plesset perturbation theory (GMP2) for spin-dependent (SD) two-component relativistic many-electron Hamiltonians, such as the infinite-order Douglas–Kroll–Hess Hamiltonian for many-electron systems, which is denoted as IODKH/IODKH. Numerical assessments for He- and Ne-like atoms and 16 diatomic molecules show that the MP2 correlation energies with IODKH/IODKH agree well with those calculated with the four-component Dirac–Coulomb (DC) Hamiltonian, indicating a systematic improvement on the inclusion of relativistic two-electron terms. The present MP2 scheme for IODKH/IODKH is demonstrated to be computationally more efficient than that for DC.

© 2016 Wiley Periodicals, Inc.This study presents an efficient algorithm to search for the poles of dynamic polarizability to obtain excited states of large systems with nonlocal excitation nature. The present algorithm adopts a homogeneous search with a constant frequency interval and a bisection search to achieve high accuracy. Furthermore, the subtraction process of the information about the detected poles from the total dynamic polarizability is used to extract the undetected pole contributions. Numerical assessments confirmed the accuracy and efficiency of the present algorithm in obtaining the excitation energies and oscillator strengths of all dipole-allowed excited states. A combination of the present pole-search algorithm and divide-and-conquer-based dynamic polarizability calculations was found to be promising to treat nonlocal excitations of large systems. © 2016 Wiley Periodicals, Inc.

© 2017 American Chemical Society. Arylboronic esters can be used as versatile reagents in organic synthesis, as represented by Suzuki-Miyaura cross-coupling. Here we report a serendipitous finding that simple arylboronic esters are phosphorescent in the solid state at room temperature with a lifetime on the order of several seconds. The phosphorescence properties of arylboronic esters are remarkable in light of the general notion that phosphorescent organic molecules require heavy atoms and/or carbonyl groups for the efficient generation of a triplet excited state. Theoretical calculations on phenylboronic acid pinacol ester indicated that this molecule undergoes an out-of-plane distortion at the (pinacol)B-Cipsomoiety in the T1excited state, which is responsible for its phosphorescence. A compound survey with 19 arylboron compounds suggested that the phosphorescence properties might be determined by solid-state molecular packing rather than by the patterns and numbers of boron substituents on the aryl units. The present finding may update the general notion of phosphorescent organic molecules.

© 2017 Author(s). In this study, we developed an excited-state calculation method for large systems using dynamical polarizabilities at the time-dependent density functional theory level. Three equivalent theories, namely, coupled-perturbed self-consistent field (CPSCF), random phase approximation (RPA), and Green function (GF), were extended to linear-scaling methods using the divide-and-conquer (DC) technique. The implementations of the standard and DC-based CPSCF, RPA, and GF methods are described. Numerical applications of these methods to polyene chains, single-wall carbon nanotubes, and water clusters confirmed the accuracy and efficiency of the DC-based methods, especially DC-GF.

© 2017 Elsevier B.V.This Letter examines the enthalpy of formation for 12 transition metal diatomic molecules and 23 transition metal complexes from the viewpoint of effect of the relativistic effect by using the infinite-order Douglas–Kroll–Hess method with the local unitary transformation and three types of pseudopotentials for several levels of theory. The spin-orbit effect contribution to the enthalpy of formation is more than 10 kcal/mol for third transition metal complexes. Frozen orbital approximation at the outermost orbitals in pseudopotential methods shows a contribution to the enthalpy of formation that is more than two times larger than those of inner core orbitals.

© 2017 Wiley Periodicals, Inc. An open-shell Hartree–Fock (HF) theory for spin-dependent two-component relativistic calculations, termed the Kramers-restricted open-shell HF (KROHF) method, is developed. The present KROHF method is defined as a relativistic analogue of ROHF using time-reversal symmetry and quaternion algebra, based on the Kramers-unrestricted HF (KUHF) theory reported in our previous study (Int. J. Quantum Chem., doi:10.1002/qua.25356). As seen in the nonrelativistic ROHF theory, the ambiguity of the KROHF Fock operator gives physically meaningless spinor energies. To avoid this problem, the canonical parametrization of KROHF to satisfy Koopmans&#039; theorem is also discussed based on the procedure proposed by Plakhutin et al. (J. Chem. Phys. 2006, 125, 204110). Numerical assessments confirmed that KROHF using Plakhutin&#039;s canonicalization procedure correctly gives physical spinor energies within the frozen-orbital approximation under spin–orbit interactions.

© 2017 Wiley Periodicals, Inc. An open-shell Hartree–Fock (HF) theory for spin-dependent, two-component relativistic calculations, termed the Kramers-unrestricted HF (KUHF) method, is developed. The present KUHF method, which is formulated as a relativistic counterpart of nonrelativistic UHF, is based on quaternion algebra and partly uses time-reversal symmetry. The fundamental characteristics of KUHF are discussed in this study. From numerical assessments, it was revealed that KUHF gives a corresponding solution to nonrelativistic UHF; furthermore, KUHF properly describes spin-orbit interactions. In addition, KUHF can improve the self-consistent field convergence behavior in spin-dependent calculations, for example, for f-block elements.

© 2017 American Chemical Society. The reduction of NO x is crucial for reducing air pollution from vehicle exhaust. In the presence of Rh-based catalysts, the dissociation of NO and the formation of N 2 O and N 2 constitute the important elementary steps of NO x reduction. The present study used density functional theory (DFT) to investigate the catalytic performances of the Rh(111) surface and Rh 55 and Rh 147 clusters toward these elementary reactions. The NO dissociation reaction was found to have minimum activation barriers (E a ) of 0.63, 0.68, and 1.25 eV on Rh 55 , Rh 147 , and Rh(111), respectively. Therefore, it is the fastest on small Rh clusters. In contrast, the N 2 formation reaction is relatively inefficient on small clusters, with corresponding E a values of 2.14, 1.79, and 1.71 eV. Because of the stronger binding of N atoms to the Rh clusters than to the Rh surface, N 2 formation through the recombination of N atoms has a higher E a value on Rh clusters. The calculated reaction rate constants confirmed that small Rh clusters are less reactive for N 2 formation than Rh(111), especially at low temperatures. Our results also suggest that N 2 O formation is largely end

© 2017 Wiley Periodicals, Inc. We have implemented a linear-scaling divide-and-conquer (DC)-based higher-order coupled-cluster (CC) and Møller–Plesset perturbation theories (MPPT) as well as their combinations automatically by means of the tensor contraction engine, which is a computerized symbolic algebra system. The DC-based energy expressions of the standard CC and MPPT methods and the CC methods augmented with a perturbation correction were proposed for up to high excitation orders [e.g., CCSDTQ, MP4, and CCSD(2) TQ ]. The numerical assessment for hydrogen halide chains, polyene chains, and first coordination sphere (C1) model of photoactive yellow protein has revealed that the DC-based correlation methods provide reliable correlation energies with significantly less computational cost than that of the conventional implementations. © 2017 Wiley Periodicals, Inc.

© 2017 American Chemical Society. Predicting pK a values for different types of amine species with high accuracy and efficiency is of critical importance for the design of high performance and economical solvents in carbon capture and storage with aqueous amine solutions. In this study, we demonstrate that density-functional tight-binding-based metadynamics simulations are a promising approach to calculate the free energy difference between the protonated and neutral states of amines in aqueous solution with inexpensive computational cost. The calculated pK a values were in satisfactory agreement with the experimental values, the mean absolute deviation being only 0.09 pK a units for 34 amines commonly used in CO 2 scrubbing. Such superior reproducibility and correlation compared to estimations by static quantum mechanical calculations highlight the significant effect of dynamical proton transfer processes in explicit solvent molecules for the improvement of the estimation accuracy.

© 2017 American Chemical Society. The structural, dynamical, and energetic properties of the excess proton in ice were studied using density-functional tight-binding molecular dynamics simulations. The ice systems investigated herein consisted of low-density hexagonal and cubic crystalline variants (ice I h and I c ) and high-density structures (ice III and melted ice VI). Analysis of the temperature dependence of radial distribution function and bond order parameters served to characterize the distribution and configuration of hundreds of water molecules in a unit cell. We confirmed that ice I h and I c possess higher hexagonal symmetries than ice III and melted ice VI. The estimated Grotthuss shuttling diffusion coefficients in ice were larger than that of liquid water, indicating a slower proton diffusion process in high-density structures than in low-density systems. The energy barriers calculated on the basis of the Arrhenius plot of diffusion coefficients were in reasonable agreement with experimental measurement for ice I h . Furthermore, the energy barriers for high-density structures were several times larger than those of low-density systems. The simulation results were

© 2017 Wiley Periodicals, Inc. A low-computational-cost algorithm and its parallel implementation for periodic divide-and-conquer density-functional tight-binding (DC-DFTB) calculations are presented. The developed algorithm enables rapid computation of the interaction between atomic partial charges, which is the bottleneck for applications to large systems, by means of multipole- and interpolation-based approaches for long- and short-range contributions. The numerical errors of energy and forces with respect to the conventional Ewald-based technique can be under the control of the multipole expansion order, level of unit cell replication, and interpolation grid size. The parallel performance of four different evaluation schemes combining previous approaches and the proposed one are assessed using test calculations of a cubic water box on the K computer. The largest benchmark system consisted of 3,295,500 atoms. DC-DFTB energy and forces for this system were obtained in only a few minutes when the proposed algorithm was activated and parallelized over 16,000 nodes in the K computer. The high performance using a single node workstation was also confirmed. In addition to liquid wate

核・電子軌道 (NOMO) 法は，原子核に対して軌道の概念を導入した量子化学理論である．NOMO法におけるHartree-Fock方程式の解として得られる原子核軌道エネルギーは，全エネルギーや軌道そのものと比較して注目されていない．本論文では，NOMO法における原子核軌道エネルギーの物理的意味とpost-HF理論への応用を述べる．特に，最近開発されたプロトンプロパゲーター法による束縛エネルギーの見積りについて，計算例を含めて紹介する．

An efficient computational method to evaluate the binding energies of many protons in large systems was developed. Proton binding energy is calculated as a corrected nuclear orbital energy using the second-order proton propagator method, which is based on nuclear orbital plus molecular orbital theory. In the present scheme, the divide-and-conquer technique was applied to utilize local molecular orbitals. This use relies on the locality of electronic relaxation after deprotonation and the electron-nucleus correlation. Numerical assessment showed reduction in computational cost without the loss of accuracy. An initial application to model a protein resulted in reasonable binding energies that were in accordance with the electrostatic environment and solvent effects.

This letter proposes a relaxation scheme for core electrons based on the frozen core potential method at the infinite-order Douglas-Kroll-Hess level, called FCP-CR. The core electrons are self-consistently relaxed using frozen molecular valence potentials after the valence SCF calculation is performed. The efficiency of FCP-CR is confirmed by calculations of gold clusters. Furthermore, FCP-CR reproduces the results of the all-electron method for the energies of coinage metal dimers and the core ionization energies and core level shifts of vinyl acetate and three tungsten complexes at the Hartree Fock and/or symmetry-adapted cluster configuration interaction levels. (C) 2016 Elsevier B.V. All rights reserved.

An efficient computational method to evaluate the binding energies of many protons in large systems was developed. Proton binding energy is calculated as a corrected nuclear orbital energy using the second-order proton propagator method, which is based on nuclear orbital plus molecular orbital theory. In the present scheme, the divide-and-conquer technique was applied to utilize local molecular orbitals. This use relies on the locality of electronic relaxation after deprotonation and the electron-nucleus correlation. Numerical assessment showed reduction in computational cost without the loss of accuracy. An initial application to model a protein resulted in reasonable binding energies that were in accordance with the electrostatic environment and solvent effects.

Energy fitting schemes based on informatics techniques using hierarchical basis sets with small cardinal numbers were numerically investigated to estimate correlation energies at the complete basis set limits. Numerical validations confirmed that the conventional two-point extrapolation models can be unified into a simple formula with optimal parameters obtained by the same test sets. The extrapolation model was extended to two-point fitting models by a relaxation of the relationship between the extrapolation coefficients or a change of the fitting formula. Furthermore, n-scheme fitting models were developed by the combinations of results calculated at several theory levels and basis sets to compensate for the deficiencies in the fitting model at one level of theory. Systematic assessments on the Gaussian-3X and Gaussian-2 sets revealed that the fitting models drastically reduced errors with equal or smaller computational effort. © 2016 Wiley Periodicals, Inc.

© 2016 Wiley Periodicals, Inc.We present an efficient quantum algorithm for beyond-Born–Oppenheimer molecular energy computations. Our approach combines the quantum full configuration interaction method with the nuclear orbital plus molecular orbital method. We give the details of the algorithm and demonstrate its performance by classical simulations. Two isotopomers of the hydrogen molecule (H2, HT) were chosen as representative examples and calculations of the lowest rotationless vibrational transition energies were simulated. © 2016 Wiley Periodicals, Inc.

© 2016 Elsevier B.V. All rights reserved.CO2 chemical absorption and regeneration processes in aqueous amine solutions were investigated using density-functional tight-binding molecular dynamics simulations. Extensive analyses of the structural, electronic, and dynamical properties of 100 independent trajectories supported the contrasting mechanisms in the absorption and regeneration processes. In the CO2 absorption process, bicarbonate formed where the hydroxyl anion migrated through the hydrogen-bond network of water molecules, namely, by a Grotthuss-type mechanism. On the other hand, direct proton transfer from the protonated amine to the hydroxyl group of bicarbonate, which is called the ion-pair mechanism, was the key step to the release of CO2.

<p>This Letter provides an implementation of an efficient and accurate relativistic method based on the infinite-order two-component scheme with the local unitary transformation (LUT-IOTC) to the GAMESS program. The sample input and major capabilities in GAMESS are shown as well as the accuracies and efficiencies in energy and analytical energy gradient calculations. The scheme realizes calculations of molecules containing heavy elements with four-component relativistic accuracy and the non-relativistic computational cost.</p>

地球温暖化の原因であるCO₂の排出量を削減する手段としてCO₂回収貯留（CCS）技術が注目されている。このCCS技術の中でも、広く用いられている化学吸収法は、アミンなど塩基性吸収液へCO₂を吸収させる分離過程と加熱によって高濃度のCO₂を放散させる回収過程からなる。これまでCO₂<br>吸収時に要するエネルギーの削減を目指してアミンの研究・開発が行われている。CO₂吸収効率の良いアミンを探す上で、各アミンについてその化学種濃度の経時変化を予測することは重要である。本研究ではアミン－CO₂反応中の素反応を考慮し、群知能を用いることで実験のローディング依存性から平衡定数を予測する反応シミュレータを開発した。またその平衡定数を量子化学計算による反応自由エネルギーから見積もることで、化学種濃度のローディング依存性の予測も行い、広く1級から3級アミンまで扱えるように拡張した。

これまで、コンピュータを用いて反応物から得られる生成物を予測するシステムが多数開発されてきた。しかし、化学反応の複雑さをコンピュータが表現することは難しく、未だ実験化学者に広く利用されるシステムの開発には至っていない。近年、分子のトポロジカルな情報を中心的な記述子として、機械学習を有機化学反応の予測に応用したシステムが優れた予測能を示した。しかしこの手法は、金属種を含む反応など、分子の立体的構造や電子状態が生成物を左右する反応の予測が困難であると考えられる。そこで本研究では、あらゆる化学種に対する反応予測を目指して、量子化学計算により得られる情報を記述子として機械学習を用いるシステムを開発した。本手法は基本的な有機化学の極性反応およびラジカル反応に対して既存手法と同程度の予測精度を示した。本発表では、本手法の詳細および予測精度の量子化学計算条件に対する依存性について検証した結果を報告する。

<p>アルカノールアミンによるCO₂の化学吸収法は，発電所などの大規模CO₂排出源における排出削減措置として現在最も有効な手段の1つと考えられている．現在，主にCO₂回収過程におけるエネルギーコストの削減を目的として様々な吸収液が開発されており，CO₂吸収液に用いられるアミンの分子設計が実験・理論の両面から精力的に進められている．本稿では，CO₂とアミンの化学反応の理解・分析において理論計算，特に量子化学計算および第一原理分子動力学計算がどのように用いられてきたかを解説する．</p>

<p>We have developed a novel reaction prediction system, which uses machine learning with quantum chemical descriptors. Numerical assessments of the system were performed on basic polar and radical organic chemical reactions. The accuracy of the present system was close to that of a previous system having machine learning with topological information, which is termed ReactionPredictor.</p>

Low density polyethylene (LDPE) and polypropylene (PP) exhibit a photoluminescence (PL) band, which emits photons with an energy of around 4.3 eV when excited by photons with energies around 6.4 eV. The origin of this PL band has been assigned to α, β-unsaturated carbonyl. In this paper, the appearance of PL was examined for four kinds of polyolefin and four kinds of biodegradable polymers. As a result, it has become clear that all the polymers show a PL band with a PL excitation spectrum and a PL spectrum similar to those of the above-mentioned PL band in LDPE and PP. The decay profiles observed for these PL bands indicate that they are fluorescence. Furthermore, the intensity of the PL becomes weak for all the four polyolefin samples and the polylatic acid sample if ultraviolet photons were irradiated to the sample. Quantum chemical calculations carried out by assuming a model of α, β-unsaturated carbonyl have revealed that the PL originates in the π* to π transition of electrons in the carbon-carbon double bond.

© 2016 the Owner Societies. An efficient computational method to evaluate the binding energies of many protons in large systems was developed. Proton binding energy is calculated as a corrected nuclear orbital energy using the second-order proton propagator method, which is based on nuclear orbital plus molecular orbital theory. In the present scheme, the divide-and-conquer technique was applied to utilize local molecular orbitals. This use relies on the locality of electronic relaxation after deprotonation and the electron-nucleus correlation. Numerical assessment showed reduction in computational cost without the loss of accuracy. An initial application to model a protein resulted in reasonable binding energies that were in accordance with the electrostatic environment and solvent effects.

Low density polyethylene (LDPE) and polypropylene (PP) exhibit a photoluminescence (PL) band, which emits photons with an energy of around 4.3 eV when excited by photons with energies around 6.4 eV. The origin of this PL band has been assigned to α, β -unsaturated carbonyl. In this paper, the appearance of PL was examined for four kinds of polyolefin and four kinds of biodegradable polymers. As a result, it has become clear that all the polymers show a PL band with a PL excitation spectrum and a PL spectrum similar to those of the above-mentioned PL band in LDPE and PP. The decay profiles observed for these PL bands indicate that they are fluorescence. Furthermore, the intensity of the PL becomes weak for all the four polyolefin samples and the polylatic acid sample if ultraviolet photons were irradiated to the sample. Quantum chemical calculations carried out by assuming a model of α, β -unsaturated carbonyl have revealed that the PL originates in the π∗to π transition of electrons in the carbon-carbon double bond.

© 2015 American Chemical Society.The process of proton diffusion in liquid water was investigated using molecular dynamics (MD) simulations, and the total energy and atomic forces were evaluated by the divide-and-conquer-type density-functional tight-binding (DC-DFTB) method. The effectiveness of this approach was confirmed by comparing the computational time of water clusters with conventional treatments. The unit cell employed herein, which contained 523 water molecules and 1 excess proton, was moderately large in comparison with those used in previous studies. The reasonable accuracy obtained by using this unit cell was confirmed by examining the temperature fluctuation. The diffusion coefficients for the vehicular and Grotthuss processes were accurately reproduced by the DC-DFTB-MD simulations with the unit cell containing 523 water molecules. Furthermore, the energy barriers were evaluated from the temperature dependence of the diffusion coefficient for each process. The calculated barrier for Grotthuss diffusion was in good agreement with the experimental value.

© 2016 Elsevier B.V. All rights reserved. Gibbs free energy of hydration of a proton and standard hydrogen electrode potential were evaluated using high-level quantum chemical calculations. The solvent effect was included using the cluster-continuum model, which treated short-range effects by quantum chemical calculations of proton-water complexes, and the long-range effects by a conductor-like polarizable continuum model. The harmonic solvation model (HSM) was employed to estimate enthalpy and entropy contributions due to nuclear motions of the clusters by including the cavity-cluster interactions. Compared to the commonly used ideal gas model, HSM treatment significantly improved the contribution of entropy, showing a systematic convergence toward the experimental data.

© 2016 American Chemical Society.An analytical energy gradient for the spin-dependent general Hartree-Fock method based on the infinite-order Douglas-Kroll-Hess (IODKH) method was developed. To treat realistic systems, the local unitary transformation (LUT) scheme was employed both in energy and energy gradient calculations. The present energy gradient method was numerically assessed to investigate the accuracy in several diatomic molecules containing fifth- and sixth-period elements and to examine the efficiency in one-, two-, and three-dimensional silver clusters. To arrive at a practical calculation, we also determined the geometrical parameters of fac-tris(2-phenylpyridine)iridium and investigated the efficiency. The numerical results confirmed that the present method describes a highly accurate relativistic effect with high efficiency. The present method can be a powerful scheme for determining geometries of large molecules, including heavy-element atoms.

© 2016 Elsevier B.V. All rights reserved.This Letter assesses the self-consistent field (SCF) convergence behavior in the generalized Hartree-Fock (GHF) method. Four acceleration algorithms were implemented for efficient SCF convergence in the GHF method: the damping algorithm, the conventional direct inversion in the iterative subspace (DIIS), the energy-DIIS (EDIIS), and a combination of DIIS and EDIIS. Four different systems with varying complexity were used to investigate the SCF convergence using these algorithms, ranging from atomic systems to metal complexes. The numerical assessments demonstrated the effectiveness of a combination of DIIS and EDIIS for GHF calculations in comparison with the other discussed algorithms.

© 2016 Elsevier B.V. All rights reserved.The harmonic solvation model (HSM) was applied to the solvation of gaseous molecules and compared to a procedure based on the ideal gas model (IGM). Examination of 25 molecules showed that (i) the accuracy of ΔGsolv was similar for both methods, but the HSM shows advantages for calculating ΔHsolv and TΔSsolv; (ii) TΔSsolv contributes more than ΔHsolv to ΔGsolv in the HSM, i.e. the solvation of gaseous molecules is entropy-driven, which agrees well with experimental understanding (the IGM does not show this); (iii) the temperature dependence of Henry&#039;s law coefficient was correctly reproduced with the HSM.

© 2016 Wiley Periodicals, Inc.The linear-scaling divide-and-conquer (DC) quantum chemical methodology is applied to the density-functional tight-binding (DFTB) theory to develop a massively parallel program that achieves on-the-fly molecular reaction dynamics simulations of huge systems from scratch. The functions to perform large scale geometry optimization and molecular dynamics with DC-DFTB potential energy surface are implemented to the program called DC-DFTB-K. A novel interpolation-based algorithm is developed for parallelizing the determination of the Fermi level in the DC method. The performance of the DC-DFTB-K program is assessed using a laboratory computer and the K computer. Numerical tests show the high efficiency of the DC-DFTB-K program, a single-point energy gradient calculation of a one-million-atom system is completed within 60 s using 7290 nodes of the K computer. © 2016 Wiley Periodicals, Inc.

© 2016 Elsevier B.V.This letter proposes a relaxation scheme for core electrons based on the frozen core potential method at the infinite-order Douglas–Kroll–Hess level, called FCP-CR. The core electrons are self-consistently relaxed using frozen molecular valence potentials after the valence SCF calculation is performed. The efficiency of FCP-CR is confirmed by calculations of gold clusters. Furthermore, FCP-CR reproduces the results of the all-electron method for the energies of coinage metal dimers and the core ionization energies and core level shifts of vinyl acetate and three tungsten complexes at the Hartree–Fock and/or symmetry-adapted cluster configuration interaction levels.

© 2016 Elsevier B.V.Gibbs free energy of hydration of a proton and standard hydrogen electrode potential were evaluated using high-level quantum chemical calculations. The solvent effect was included using the cluster-continuum model, which treated short-range effects by quantum chemical calculations of proton-water complexes, and the long-range effects by a conductor-like polarizable continuum model. The harmonic solvation model (HSM) was employed to estimate enthalpy and entropy contributions due to nuclear motions of the clusters by including the cavity-cluster interactions. Compared to the commonly used ideal gas model, HSM treatment significantly improved the contribution of entropy, showing a systematic convergence toward the experimental data.

An efficient algorithm for the rapid evaluation of electron repulsion integrals is proposed. The present method, denoted by accompanying coordinate expansion and transferred recurrence relation (ACE-TRR), is constructed using a transfer relation scheme based on the accompanying coordinate expansion and recurrence relation method. Furthermore, the ACE-TRR algorithm is extended for the general-contraction basis sets. Numerical assessments clarify the efficiency of the ACE-TRR method for the systems including heavy elements, whose orbitals have long contractions and high angular momenta, such as f- and g-orbitals.

The extrapolation scheme of correlation energy is revisited to evaluate the complete basis set limit from double-zeta (DZ) and triple-zeta levels of calculations. The DZ level results are adjusted to the standard asymptotic behavior with respect to the cardinal number, observed at the higher levels of basis sets. Two types of adjusting schemes with effective scaling factors, which recover errors in extrapolations with the DZ level basis set, are examined. The first scheme scales the cardinal number for the DZ level energy, while the second scheme scales the prefactor of the extrapolation function. Systematic assessments on the Gaussian-3X and Gaussian-2 test sets reveal that these calibration schemes successfully and drastically reduce errors without additional computational efforts. (c) 2015 Wiley Periodicals, Inc.

The extrapolation scheme of correlation energy is revisited to evaluate the complete basis set limit from double-zeta (DZ) and triple-zeta levels of calculations. The DZ level results are adjusted to the standard asymptotic behavior with respect to the cardinal number, observed at the higher levels of basis sets. Two types of adjusting schemes with effective scaling factors, which recover errors in extrapolations with the DZ level basis set, are examined. The first scheme scales the cardinal number for the DZ level energy, while the second scheme scales the prefactor of the extrapolation function. Systematic assessments on the Gaussian-3X and Gaussian-2 test sets reveal that these calibration schemes successfully and drastically reduce errors without additional computational efforts. (c) 2015 Wiley Periodicals, Inc.

We report the implementation of the local response dispersion (LRD) method in an electronic structure program package aimed at periodic systems and an assessment combined with the Perdew-Burke-Ernzerhof (PBE) functional and its revised version (revPBE). The real-space numerical integration was implemented and performed exploiting the electron distribution given by the plane-wave basis set. The dispersioncorrected density functionals revPBE1LRD was found to be suitable for reproducing energetics, structures, and electron distributions in simple substances, molecular crystals, and physical adsorptions.

Using energy density analysis, total energy is partitioned into the atomic energy densities of constituent elements. The atomization energy of each element is then evaluated by subtracting the atomic energy density from the energy of the isolated neutral atom. This recent approach to the energy expression is reviewed of the chemical bond between atoms in hydrides and oxides. For various hydrides, the atomization energies, ΔE H for H atom and ΔE M for metal atom, are evaluated and the ΔE H vs. ΔE M diagram called atomization energy diagram is made. All the hydrides including complex hydrides and metal hydrides can be located on this diagram, although there are significant differences in the nature of the chemical bond among them. Also, for hydrocarbons, CmH, the atomization energy for carbon, ΔE C, increases linearly with the ratio of carbon number to hydrogen number, m/n, while keeping ΔE H constant. It is no longer needed for us to give expression for the C-C bond to be either single, or double or triple bond in CmHn. For metal oxides, the atomization energies, ΔE M for metal atom and ΔE O for O atom, reflect the average structure as well as the local structure. As a result, their values change with the overall density of binary metal oxides. For perovskite-type oxides, the ΔE O value increases by the phase transition from cubic to tetragonal phase, regardless of the tilting-type or the &lt
100&gt
displacement-type transition. One of the applications of this approach is the quantitative evaluation for the catalytic activities of metal oxides (e.g., Nb2O5) on the dehydrogenation reaction of magnesium hydride (MgH2), MgH2 → Mg + H2. The atomization energy concept will provide us a new clue to materials design, for example, catalysts design.

:An efficient algorithm for the rapid evaluation of electron repulsion integrals is proposed. The present method, denoted by accompanying coordinate expansion and transferred recurrence relation (ACE-TRR), is constructed using a transfer relation scheme based on the accompanying coordinate expansion and recurrence relation method. Furthermore, the ACE-TRR algorithm is extended for the general-contraction basis sets. Numerical assessments clarify the efficiency of the ACE-TRR method for the systems including heavy elements, whose orbitals have long contractions and high angular momenta, such as f- and g-orbitals.

:The extrapolation scheme of correlation energy is revisited to evaluate the complete basis set limit from double-zeta (DZ) and triple-zeta levels of calculations. The DZ level results are adjusted to the standard asymptotic behavior with respect to the cardinal number, observed at the higher levels of basis sets. Two types of adjusting schemes with effective scaling factors, which recover errors in extrapolations with the DZ level basis set, are examined. The first scheme scales the cardinal number for the DZ level energy, while the second scheme scales the prefactor of the extrapolation function. Systematic assessments on the Gaussian-3X and Gaussian-2 test sets reveal that these calibration schemes successfully and drastically reduce errors without additional computational efforts.

:The intramolecular magnetic coupling constant (J) of diradical systems linked with five- or six-membered aromatic rings was calculated to obtain the scaling factor (experimental J/calculated J ratio) for various density functional theory (DFT) functionals. Scaling factors of group A (PBE, TPSSh, B3LYP, B97-1, X3LYP, PBE0, and BH&HLYP) and B (M06-L, M06, M06-2X, and M06-HF) were shown to decrease as the amount of Hartree-Fock exact exchange (HFx) increases, in other words, overestimation of calculated J becomes more severe as the HFx increases. We further investigated the effect of HFx fraction of DFT functional on J value, spin contamination, and spin density distributions by comparing the B3LYP analogues containing different amount of HFx. It was revealed that spin contamination and spin densities at each atom increases as the HFx increases. Above all, newly developed BLYP-5 functional, which has 5% of HFx, was found to have the scaling factor of 1.029, indicating that calculated J values are very close to that of experimental values without scaling. BLYP-5 has potential to be utilized for accurate evaluation of intramolecular magnetic coupling constant (J) of diradicals linked by five- or six-membered aromatic ring couplers.

:Graphical processing units (GPUs) are emerging in computational chemistry to include Hartree-Fock (HF) methods and electron-correlation theories. However, ab initio calculations of large molecules face technical difficulties such as slow memory access between central processing unit and GPU and other shortfalls of GPU memory. The divide-and-conquer (DC) method, which is a linear-scaling scheme that divides a total system into several fragments, could avoid these bottlenecks by separately solving local equations in individual fragments. In addition, the resolution-of-the-identity (RI) approximation enables an effective reduction in computational cost with respect to the GPU memory. The present study implemented the DC-RI-HF code on GPUs using math libraries, which guarantee compatibility with future development of the GPU architecture. Numerical applications confirmed that the present code using GPUs significantly accelerated the HF calculations while maintaining accuracy.

完全基底関数極限における高精度な電子相関を含んだ電子相関エネルギーを高効率に算出することは化学的精度（1 kcal/mol以内）での量子化学計算を実現するために重要である。これまで種々の電子相関エネルギーの完全基底関数極限への外挿手法や、幾つかの計算レベル・基底関数でのエネルギーを組み合わせた複合法が提案されてきた。本研究では情報学手法を用いてより効率的に、完全基底関数極限におけるCCSD(T)レベルの電子相関エネルギーを算出する手法を提案する。

The origin of the stability of diamondoid dimers containing very long carbon–carbon bonds was examined using density functional theory (DFT) calculations with local response dispersion correction. It has been suggested that noncovalent CH···HC contacts are the probable source of their extraordinary stability as evidenced by dispersion-corrected DFT calculations. In this work, we numerically proved that the small radical stabilization energy, which was achieved through the geometric relaxation of cleaved radicals, led to the high stability of diamondoid dimers compared to other hydrocarbons. The bond energy density analysis showed that the CH···HC contacts are repulsive though the dispersion force somewhat stabilizes the dimer. We further decomposed CH···HC interaction energies to discover strong attractive interaction between C&lt;sup&gt;δ−&lt;/sup&gt;···H&lt;sup&gt;δ+&lt;/sup&gt; intermonomer contacts.

The authors group has developed the program named DC-DFTB-K for the on-the-fly quantum mechanical molecular dynamics (MD) simulation of huge systems using the density-functional tight binding (DFTB) method. The combination with the divide-and-conquer (DC) method enables linear-scaling calculation of DFTB energy and its derivatives. Due to the massively parallel implementation, the program can treat systems containing one million atoms on the K computer. In this paper, the recent extension of DC-DFTB-MD technique is outlined together with the illustrative application to chemical reaction dynamics in lithium-ion device.

© 2015 AIP Publishing LLC. An efficient algorithm for the rapid evaluation of electron repulsion integrals is proposed. The present method, denoted by accompanying coordinate expansion and transferred recurrence relation (ACE-TRR), is constructed using a transfer relation scheme based on the accompanying coordinate expansion and recurrence relation method. Furthermore, the ACE-TRR algorithm is extended for the general-contraction basis sets. Numerical assessments clarify the efficiency of the ACE-TRR method for the systems including heavy elements, whose orbitals have long contractions and high angular momenta, such as f- and g-orbitals.

© 2015, Springer-Verlag Berlin Heidelberg. This study proposes two efficient algorithms of the linear-scaling divide-and-conquer self-consistent field (DC-SCF) method for parallel computations. These algorithms minimize the amount of network communication required for determining the common Fermi level by adopting an approximate Fermi level. One algorithm adopts the quasi-converged Fermi level during DC-SCF iterations, while the other uses the quasi-converged electron numbers of individual subsystems. A numerical assessment demonstrates the high parallel efficiency for both methods without loss in accuracy.

© 2015 AIP Publishing LLC.This paper reviews a series of theoretical studies to develop efficient two-component (2c) relativistic method for large systems by the author&#039;s group. The basic theory is the infinite-order Douglas-Kroll-Hess (IODKH) method for many-electron Dirac-Coulomb Hamiltonian. The local unitary transformation (LUT) scheme can effectively produce the 2c relativistic Hamiltonian, and the divide-and-conquer (DC) method can achieve linear-scaling of Hartree-Fock and electron correlation methods. The frozen core potential (FCP) theoretically connects model potential calculations with the all-electron ones. The accompanying coordinate expansion with a transfer recurrence relation (ACE-TRR) scheme accelerates the computations of electron repulsion integrals with high angular momenta and long contractions.

DNAは電荷輸送特性を有し，生理的な機能のみならず電荷輸送デバイスとしての応用が期待されている．電荷輸送特性のうち，ホール移動に関して，実験的・理論的研究から多くの知見が得られてきた．しかしながら，過剰電子移動(EET)に対する知見は限定的である．本研究ではMarcus理論に基づいて，密度汎関数理論(DFT)レベルの量子化学計算によるDNA内EET速度の算出を試みた．隣接チミン間のEET速度の計算値(2.31 − 3.49 × 10&lt;sup&gt;10&lt;/sup&gt; s&lt;sup&gt;−1&lt;/sup&gt;)は，実験値(4.4 ± 0.3 × 10&lt;sup&gt;10&lt;/sup&gt; s&lt;sup&gt;−1&lt;/sup&gt;)を良く再現した．また，ミスマッチ(MM)塩基対を含む系に本手法を適用し，MM塩基対の挿入によるEET速度低下のメカニズムを明らかにした．

PicoGreen (PG) is used as a probe to selectively quantitate double-stranded (ds-) DNA because it shows unique fluorescence enhancement when complexed with DNA. By binding to ds- and single-stranded (ss-) DNA, the quantum yields of PG-DNA complexes become remarkably larger than that of a free molecule. In the present theoretical study, the fluorescence enhancement mechanism of PG-DNA complexes was investigated using molecular docking simulations and ab initio quantum chemical methods. The binding energies between PG and ds-DNA were calculated to be larger than those in the case of PG and ss-DNA owing to the existence of an extra pi-pi stacking interaction. Nonradiative deactivation paths through conical intersections between the ground and the first excited states were obtained for a free PG molecule, while steric repulsions between PG and DNA hindered such deactivation processes in the case of PG-DNA complexes.

DNAは電荷輸送特性を有し，生理的な機能のみならず電荷輸送デバイスとしての応用が期待されている．電荷輸送特性のうち，ホール移動に関して，実験的・理論的研究から多くの知見が得られてきた．しかしながら，過剰電子移動(EET)に対する知見は限定的である．本研究ではMarcus理論に基づいて，密度汎関数理論(DFT)レベルの量子化学計算によるDNA内EET速度の算出を試みた．隣接チミン間のEET速度の計算値(2.31 − 3.49 × 1010 s−1)は，実験値(4.4 ± 0.3 × 1010 s−1)を良く再現した．また，ミスマッチ(MM)塩基対を含む系に本手法を適用し，MM塩基対の挿入によるEET速度低下のメカニズムを明らかにした．

本稿では，大規模な重元素化合物を高効率・高精度に計算するための理論を取り上げる．まず相対論的量子化学の現状を概観し，それを踏まえて目的を遂行するためにどの部分を考察しなければならないのかを述べたい．次にこれらの問題点を解決すべく，著者らが開発した高効率・高精度な2成分相対論計算手法，無限次Douglas-Kroll-Hess変換に基づく局所ユニタリー変換法の理論について解説し，数値検証を行うことで有用性を示す．さらに本手法を分割統治法へと拡張することにより，計算全体の線形スケーリングを達成する手法となることを示す．本手法に基づけば，非相対論と同等の計算コストで (スピン非依存の) 4成分相対論と同程度の精度を与えることができるため，従来の非相対論的なSchrödinger方程式から相対論的なDirac方程式へのパラダイムシフトが可能となる．

:We propose a novel quantum chemical method, called the harmonic solvation model (HSM), for calculating thermochemical parameters in the condensed phase, particularly in the liquid phase. The HSM represents translational and rotational motions of a solute as vibrations interacting with a cavity wall of solvent molecules. As examples, the HSM and the ideal-gas model (IGM) were used for the standard formation reaction of liquid water, combustion reactions of liquid formic acid, methanol, and ethanol, vapor-liquid equilibration of water and ethanol, and dissolution of gaseous CO2 in water. The numerical results confirmed the reliability and applicability of the HSM. In particular, the temperature dependence of the Gibbs energy of liquid molecules was accurately reproduced by the HSM; for example, the boiling point of water was reasonably determined using the HSM, whereas the conventional IGM treatment failed to obtain a crossing of the two Gibbs energy curves for gaseous and liquid water.

:An algorithm of the accompanying coordinate expansion and recurrence relation (ACE-RR), which is used for the rapid evaluation of the electron repulsion integral (ERI), has been extended to the general-contraction (GC) scheme. The present algorithm, denoted by GC-ACE-RR, is designed for molecular calculations including heavy elements, whose orbitals consist of many primitive functions with and without higher angular momentum such as d- and f-orbitals. The performance of GC-ACE-RR was assessed for (ss|ss)-, (pp|pp)-, (dd|dd)-, and (ff|ff)-type ERIs in terms of contraction length and the number of GC orbitals. The present algorithm was found to reduce the central processing unit time compared with the ACE-RR algorithm, especially for higher angular momentum and highly contracted orbitals. Compared with HONDOPLUS and GAMESS program packages, GC-ACE-RR computations for ERIs of three-dimensional gold clusters Aun (n = 1, 2, …, 10, 15, 20, and 25) are more than 10 times faster.

:The Lagrange interpolation of molecular orbital (LIMO) method, which reduces the number of self-consistent field iterations in ab initio molecular dynamics simulations with the Hartree-Fock method and the Kohn-Sham density functional theories, is extended to the theory of multiconfigurational wave functions. We examine two types of treatments for the active orbitals that are partially occupied. The first treatment, as denoted by LIMO(C), is a simple application of the conventional LIMO method to the union of the inactive core and the active orbitals. The second, as denoted by LIMO(S), separately treats the inactive core and the active orbitals. Numerical tests to compare the two treatments clarify that LIMO(S) is superior to LIMO(C). Further applications of LIMO(S) to various systems demonstrate its effectiveness and robustness.

MK-4965, 3-{5-[(6-Amino-1H-pyrazolo[3,4-b]pyridine-3-yl)methoxy]-2- chlorophenoxy}-5-chloro-benzonitrile, is a novel non-nucleoside reverse transcriptase inhibitor (NNRTI) revealing high levels of potency against wild-type (WT) the human immunodeficiency virus type-1 (HIV-1) and some important mutants. The divide-and-conquer (DC) based Hartree-Fock (HF) and second-order Møller-Plesset perturbation theory (MP2) calculations were performed for the binding modes of MK-4965 in the reverse transcriptase (RT) of the WT HIV-1 and a mutant Y181C, 181 tyrosine mutated by cysteine. The binding pockets of MK-4965 consisting of 19 residues are selected for the study. Numerical assessments confirmed the efficiency and accuracy of the DC-MP2 method in comparison with the conventional MP2 one. Subsystem interaction energies obtained by the DC-MP2 calculations clarified the key parts of the binding between MK-4965 and HIV-1: hydrogen bonding with 102 lysine, which is apart from mutated 181 residue. The present information can give a helpful guide for the future inhibitor design. © 2012 Wiley Periodicals, Inc.

This study presents the self-consistent field (SCF) treatment of the local response dispersion (LRD) method. The implementation of SCF involves the modification of the KohnSham Fock matrix by adding the dispersion potential. The derivatives of atomic pseudo-polarizabilities with respect to the density variables, which are required for evaluating the dispersion potential, are efficiently updated in the SCF procedure. Analytical energy gradient of the LRD method is also developed based on the SCF treatment. Numerical assessments of the present treatment clarified that the SCF effect brings about minor changes in both energy and electronic structure. The computational time, and number of SCF iterations, are essentially unaffected by moving from a non-self-consistent implementation to a self-consistent one. For the geometry optimizations for weakly interacting systems, the inclusion of the LRD energy gradients is shown to be essential for accurately demonstrating the intermolecular geometric parameters. (c) 2012 Wiley Periodicals, Inc.

:In this study, the analytical energy gradient for the spin-free infinite-order Douglas-Kroll-Hess (IODKH) method at the levels of the Hartree-Fock (HF), density functional theory (DFT), and second-order Møller-Plesset perturbation theory (MP2) is developed. Furthermore, adopting the local unitary transformation (LUT) scheme for the IODKH method improves the efficiency in computation of the analytical energy gradient. Numerical assessments of the present gradient method are performed at the HF, DFT, and MP2 levels for the IODKH with and without the LUT scheme. The accuracies are examined for diatomic molecules such as hydrogen halides, halogen dimers, coinage metal (Cu, Ag, and Au) halides, and coinage metal dimers, and 20 metal complexes, including the fourth-sixth row transition metals. In addition, the efficiencies are investigated for one-, two-, and three-dimensional silver clusters. The numerical results confirm the accuracy and efficiency of the present method.

:We proposed a novel kinetic energy decomposition analysis based on information theory. Since the Hirshfeld partitioning for electron densities can be formulated in terms of Kullback-Leibler information deficiency in information theory, a similar partitioning for kinetic energy densities was newly proposed. The numerical assessments confirm that the current kinetic energy decomposition scheme provides reasonable chemical pictures for ionic and covalent molecules, and can also estimate atomic energies using a correction with viral ratios.

:In order to perform practical electron correlation calculations, the local unitary transformation (LUT) scheme at the spin-free infinite-order Douglas-Kroll-Hess (IODKH) level [J. Seino and H. Nakai, J. Chem. Phys. 136, 244102 (2012); and ibid. 137, 144101 (2012)], which is based on the locality of relativistic effects, has been combined with the linear-scaling divide-and-conquer (DC)-based Hartree-Fock (HF) and electron correlation methods, such as the second-order Mo̸ller-Plesset (MP2) and the coupled cluster theories with single and double excitations (CCSD). Numerical applications in hydrogen halide molecules, (HX)n (X = F, Cl, Br, and I), coinage metal chain systems, Mn (M = Cu and Ag), and platinum-terminated polyynediyl chain, trans,trans-{(p-CH3C6H4)3P}2(C6H5)Pt(C≡C)4Pt(C6H5){(p-CH3C6H4)3P}2, clarified that the present methods, namely DC-HF, MP2, and CCSD with the LUT-IODKH Hamiltonian, reproduce the results obtained using conventional methods with small computational costs. The combination of both LUT and DC techniques could be the first approach that achieves overall quasi-linear-scaling with a small prefactor for relativistic electron correlation calculations.

:In this study, the divide-and-conquer (DC) method is extended to configuration-interaction singles, time-dependent density functional, and symmetry-adapted cluster configuration interaction (SACCI) theories for enabling excited-state calculations of large systems. In DC-based excited-state theories, one subsystem is selected as the excitation subsystem and analyzed via excited-state calculations. Test calculations for formaldehyde in water and a conjugated aldehyde demonstrate the high accuracy and effectiveness of these methods. To demonstrate the efficiency of the method, we calculated the π-π* excited state of photoactive yellow protein (PYP). The numerical applications to PYP confirm that the DC-SACCI method significantly accelerates the excited-state calculations while maintaining high accuracy.

:This study presents a numerical assessment of total energy related physical quantities estimated using the orbital-specific (OS) global and range-separated hybrid functionals, designed to satisfy the linearity condition for orbital energies (LCOE). The numerical assessment demonstrates that accurate evaluation of the reaction energies, reaction barrier, and dissociation curve can be achieved via the OS hybrid functional, for systems in which self-interaction is expected to be dominant. Therefore, the LCOE offers an accurate description of orbital energies as well as total energies for self-interaction dominant systems.

:We recently proposed a linear-scaling evaluation scheme for the second-order Mo̸ller-Plesset perturbation (MP2) energy based on the divide-and-conquer (DC) method [M. Kobayashi, Y. Imamura, and H. Nakai, J. Chem. Phys. 127, 074103 (2007)]. In this paper, we propose an approximate but effective expression for the first derivative of the DC-MP2 energy. The present scheme evaluates the one- and two-body density matrices, which appear in the MP2 gradient formula, in the DC manner; that is, the entire matrix is obtained as the sum of subsystem matrices masked by the partition matrix. Therefore, the method requires solving only the local Z-vector equations. Illustrative applications to three types of systems, peptides, Si surface model, and delocalized polyenes, reveal the effectiveness of the present method.

A new xenicane diterpenoid, cristaxenicin A (1), has been isolated from the deep sea gorgonian Acanthoprimnoa cristata. The structure of 1 was elucidated on the basis of spectral analysis including NMR and MS. The absolute configuration of 1 was determined on the basis of quantum chemical calculation of CD spectra. Cristaxenicin A (1) showed antiprotozoal activities against Leishmania amazonensis and Trypanosoma congolense with IC50 values of 0.088 and 0.25 μM, respectively. © 2012 American Chemical Society.

Direct alkoxysilylation, which is a powerful tool to provide explicit alkoxysiloxanes, is developed and its versatility is investigated. Siloxane pentamers Si[OSiR1(OMe)(2)](4) having various functional groups (R-1 = methyl, vinyl, phenyl, chloropropyl and n-butyl groups) were successfully obtained by direct alkoxysilylation of Si(OR)(4) (R= t-Bu, CHPh2). Thus, the versatility of the reaction is confirmed on organic functional groups R-1. Functional group tolerance of the reaction is discussed on the basis of electro-negativity of the R-1 groups. Alkoxysilylation of Si(Ot-Bu)(2)(OMe)(2) and Si(Ot-Bu)(OMe)(3) selectively gives trimer (MeO)(2)Si[OSiMe(OMe)(2)](2) and dimer (MeO)(3)SiOSiMe(OMe)(2), respectively. Thus, the feasibility on siloxane structure is also confirmed. Various siloxane compounds are synthesized by this newly developed reaction for the first time. (C) 2012 Published by Elsevier B.V.

We report the extension of the local response dispersion (LRD) method to the excited-state calculation based on time-dependent density functional theory. The difference density matrix, which is usually used for excited-state response properties, enables a state-specific dispersion correction. The numerical assessment proves that interaction energies of exciton-localized molecular complexes and their shifts from the ground state are accurately reproduced by the LRD method. Furthermore, we find that the dispersion correction is important in reproducing binding energies of aromatic excimers, despite the existence of other attractive forces such as exciton delocalization and charge-transfer interaction. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4754508]

An accurate and efficient scheme for two-component relativistic calculations at the spin-free infinite-order Douglas-Kroll-Hess (IODKH) level is presented. The present scheme, termed local unitary transformation (LUT), is based on the locality of the relativistic effect. Numerical assessments of the LUT scheme were performed in diatomic molecules such as HX and X 2 (X = F, Cl, Br, I, and At) and hydrogen halide clusters, (HX) n (X = F, Cl, Br, and I). Total energies obtained by the LUT method agree well with conventional IODKH results. The computational costs of the LUT method are drastically lower than those of conventional methods since in the former there is linear-scaling with respect to the system size and a small prefactor. © 2012 American Institute of Physics.

The influence of water molecules on the reaction behavior of hypophosphite ion, which acts as a reducing agent for electroless deposition, on metal surfaces was elucidated by calculating the adsorption structure of hydrated hypophosphite ion on a Pd surface using Monte-Carlo simulation and density functional theory calculations. Through geometrical optimization, the most favorable structure of the hydrated hypophosphite ion was obtained, in which six water molecules interact with the oxygen of hypophosphite ion and no water interacts with the hydrogen of hypophosphite ion. Further calculations indicated that the hydrated hypophosphite ion adsorbed on the Pd surface via hydrogen. (C) The Electrochemical Society of Japan, All rights reserved.

This Letter proposes a scheme to incorporate electron-electron (e-e) correlation for the explicitly correlated Gaussian-nuclear orbital plus molecular orbital (ECG-NOMO) theory, which offers accurate descriptions for electronic and nuclear states. The second order Moller-Plesset perturbation theory and coupled-cluster theory with singles and doubles in the ECG-NOMO framework are adopted for evaluating the e-e correlation. Illustrative applications for dihydrogen, trihydrogen cation molecules, and their isotopomers confirm significant improvement for the total energies and zero-point energies. (C) 2012 Elsevier B. V. All rights reserved.

This Letter explores the potential utility of the constrained self-consistent field (CSCF) method as an efficient methodology for estimating the external fields that reproduce desired physical quantities. Using the fact that a Lagrange multiplier introduced in CSCF corresponds to an external field (perturbation), numerical assessments of CSCF were carried out on the benzene molecule. The activation energies and critical electric fields that reverse the polarizations of the ferroelectric material tetrathiafulvalene-p-chloranil (TTF-CA) were efficiently estimated. The numerical assessments demonstrate the potential applicability of CSCF for the practical designs of materials possessing certain desired physical quantities induced by external fields. (C) 2012 Elsevier B. V. All rights reserved.

We report a linear-scaling computation method for evaluating the dynamic first hyperpolarizability beta based on the divide-and-conquer (DC) method. In the present scheme, we utilized the quasi-density-matrix expression derived from Wigner's (2n + 1) rule for beta, where the quasi-density matrices are constructed from the solution obtained via the DC time-dependent self-consistent field (TD-SCF) method [T. Touma, M. Kobayashi, and H. Nakai, Chem. Phys. Lett. 485, 247 (2010)]. Numerical evaluation of pi-conjugated and saturated organic chain systems verified that the present scheme considerably reduces the computational time for the beta evaluation with a slight loss of accuracy, even around the singular frequency appearing at the electronic excitation energy. This evaluation indicates that the present linear-scaling TD-SCF scheme can also be used to estimate the molecular excitation energy. Furthermore, we succeeded in accurately evaluating the macroscopic second-harmonic generation coefficient of the polyvinylidene fluoride from the molecular (hyper)polarizabilities. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.3687341]

本稿では，化学研究において言わば道標の役割を果たす化学原理(概念・法則・規則・仮説)を取り上げる．まず量子化学の歴史を概観し，今日の理論研究者が化学原理をどのように捉えているかを問いかけたい．次に，著者らが見出した縮重系励起の対称則を解説し，発見の経緯・数値検証・理論的解釈について述べる．

:The local unitary transformation (LUT) scheme at the spin-free infinite-order Douglas-Kroll-Hess (IODKH) level [J. Seino and H. Nakai, J. Chem. Phys. 136, 244102 (2012)], which is based on the locality of relativistic effects, has been extended to a four-component Dirac-Coulomb Hamiltonian. In the previous study, the LUT scheme was applied only to a one-particle IODKH Hamiltonian with non-relativistic two-electron Coulomb interaction, termed IODKH/C. The current study extends the LUT scheme to a two-particle IODKH Hamiltonian as well as one-particle one, termed IODKH/IODKH, which has been a real bottleneck in numerical calculation. The LUT scheme with the IODKH/IODKH Hamiltonian was numerically assessed in the diatomic molecules HX and X(2) and hydrogen halide molecules, (HX)(n) (X = F, Cl, Br, and I). The total Hartree-Fock energies calculated by the LUT method agree well with conventional IODKH/IODKH results. The computational cost of the LUT method is reduced drastically compared with that of the conventional method. In addition, the LUT method achieves linear-scaling with respect to the system size and a small prefactor.

:We report the extension of the local response dispersion (LRD) method to the excited-state calculation based on time-dependent density functional theory. The difference density matrix, which is usually used for excited-state response properties, enables a state-specific dispersion correction. The numerical assessment proves that interaction energies of exciton-localized molecular complexes and their shifts from the ground state are accurately reproduced by the LRD method. Furthermore, we find that the dispersion correction is important in reproducing binding energies of aromatic excimers, despite the existence of other attractive forces such as exciton delocalization and charge-transfer interaction.

:An accurate and efficient scheme for two-component relativistic calculations at the spin-free infinite-order Douglas-Kroll-Hess (IODKH) level is presented. The present scheme, termed local unitary transformation (LUT), is based on the locality of the relativistic effect. Numerical assessments of the LUT scheme were performed in diatomic molecules such as HX and X(2) (X = F, Cl, Br, I, and At) and hydrogen halide clusters, (HX)(n) (X = F, Cl, Br, and I). Total energies obtained by the LUT method agree well with conventional IODKH results. The computational costs of the LUT method are drastically lower than those of conventional methods since in the former there is linear-scaling with respect to the system size and a small prefactor.

:The authors have developed a fragmentation-based linear-scaling electronic structure calculation strategy named the divide-and-conquer (DC) method, which has been implemented into the Gamess program package. Although there are many sorts of fragmentation-based linear-scaling schemes, most of them require the charge and spin multiplicity of each fragment a priori. Therefore, their applications to delocalized and/or open-shell systems have been limited. However, the DC method is a notable exception because the distribution of electrons in the entire system is automatically determined by the universal Fermi level. In this perspective, the authors have summarized the performance of the linear-scaling self-consistent field (SCF) and post-SCF calculations of delocalized and/or open-shell systems based on the DC method. Furthermore, some future prospects of the method have been discussed.

:We report a linear-scaling computation method for evaluating the dynamic first hyperpolarizability β based on the divide-and-conquer (DC) method. In the present scheme, we utilized the quasi-density-matrix expression derived from Wigner's (2n + 1) rule for β, where the quasi-density matrices are constructed from the solution obtained via the DC time-dependent self-consistent field (TD-SCF) method [T. Touma, M. Kobayashi, and H. Nakai, Chem. Phys. Lett. 485, 247 (2010)]. Numerical evaluation of π-conjugated and saturated organic chain systems verified that the present scheme considerably reduces the computational time for the β evaluation with a slight loss of accuracy, even around the singular frequency appearing at the electronic excitation energy. This evaluation indicates that the present linear-scaling TD-SCF scheme can also be used to estimate the molecular excitation energy. Furthermore, we succeeded in accurately evaluating the macroscopic second-harmonic generation coefficient of the polyvinylidene fluoride from the molecular (hyper)polarizabilities.

The authors have developed a fragmentation-based linear-scaling electronic structure calculation strategy named the divide-and-conquer (DC) method, which has been implemented into the GAMESS program package. Although there are many sorts of fragmentation-based linear-scaling schemes, most of them require the charge and spin multiplicity of each fragment a priori. Therefore, their applications to delocalized and/or open-shell systems have been limited. However, the DC method is a notable exception because the distribution of electrons in the entire system is automatically determined by the universal Fermi level. In this perspective, the authors have summarized the performance of the linear-scaling self-consistent field (SCF) and post-SCF calculations of delocalized and/or open-shell systems based on the DC method. Furthermore, some future prospects of the method have been discussed.

This Letter proposes two schemes for the efficient evaluation of electron repulsion integrals required for the explicitly correlated Gaussian-nuclear orbital plus molecular orbital (ECG-NOMO) theory, which offers accurate descriptions for electrons and nuclei. Two schemes, i.e., fully analytical and hybrid schemes for analytical and numerical integrations, for the ECG-NOMO/Hartree-Fock theory are assessed. Illustrative applications of these schemes to two-electron diatomic molecules demonstrate that the ECG-NOMO/HF theory provides significantly accurate zero-point energies within 123.5 cm(-1) deviation when compared with the experimental data. (C) 2011 Elsevier B.V. All rights reserved.

This article describes the finite-field (FF) approach for calculating static (hyper)polarizabilities based on the divide-and-conquer (DC) method. The method is assessed by the Hartree-Fock (HF) and post-HF calculations of pi-conjugated model systems: a terminal donor or acceptor substituent on polyene chains. The DC-FF approach enables the evaluation of molecular polarizabilities with highly accurate coupled-cluster theory. Numerical assessments demonstrate that the (hyper)polarizabilities calculated by the present DC-FF method agree with the conventional FF results to within a few percent by employing an appropriate buffer size.

A two-level hierarchical parallelization scheme including the second-order Moller-Plesset perturbation (MP2) theory in the divide-and-conquer method is presented. The scheme is a combination of coarse-grain parallelization assigning each subsystem to a group of processors, with fine-grain parallelization, where the computational tasks for evaluating MP2 correlation energy of the assigned subsystem are distributed among processors in the group. Test calculations demonstrate that the present scheme shows high parallel efficiency and makes MP2 calculations practical for very large molecules. (C) 2011 Wiley Periodicals, Inc. J Comput Chem 32: 2756-2764, 2011

We have developed the spin-unrestricted divide-and-conquer (DC)-based linear-scaling self-consistent field method for treating open-shell systems (Kobayashi et al. in Chem Phys Lett 500:172, 2010). Because the method does not require the position of excess spins or charges, it made the treatment of large spin-delocalized systems tractable. The present study extends the DC-based unrestricted open-shell scheme to the correlated second-order Moller-Plesset perturbation (MP2) theory. Numerical applications to polyene cations demonstrate that the present method gives highly accurate results with less computational costs even for spin-delocalized systems.

We have previously proposed the linearity condition for orbital energies (LCOE) in density functional theory for constructing orbital-specific exchange-correlation (XC) functionals and reported promising results in the case of range-separated functionals [24]. This Letter applies the LCOE to global hybrid functionals of which the OS Hartree-Fock exchange portions are determined by the LCOE. The numerical assessment demonstrates accurate descriptions of core and valence orbital energies for all global hybrid functionals. Thus, the LCOE is generally an effective and essential condition for constructing XC functionals. (C) 2011 Elsevier B. V. All rights reserved.

The present study theoretically revisits and numerically assesses two-body energy decomposition schemes including a newly proposed one. The new decomposition scheme is designed to make the equilibrium bond distance equivalent with the minimum point of bond energies. Although the other decomposition schemes generally predict the wrong order of the C-C bond strengths of C(2)H(2), C(2)H(4), and C(2)H(6), the new decomposition scheme is capable of reproducing the C-C bond strengths. Numerical assessment on a training set of molecules demonstrates that the present scheme exhibits a stronger correlation with bond dissociation energies than the other decomposition schemes do, which suggests that the new decomposition scheme is a reliable and powerful analysis methodology. (C) 2011 American Institute of Physics. [doi:10.1063/1.3636387]

The present study proposes a rigorous non-Born-Oppenheimer theory combining between the explicitly correlated Gaussian (ECG) method and the nuclear orbital plus molecular orbital (NOMO) method. The new method, called ECG-NOMO, adopts the ECG functions between the electronic and nuclear coordinates and, therefore, is capable of describing the nucleus-electron correlation effect accurately. The basic formalism of the ECG-NOMO method is close to the NOMO method, which starts with the Hartree-Fock type equations for NOs and MOs. The present method requires more computational cost than the original NOMO method. However, its cost is significantly smaller than that of the ECG method. The numerical tests was performed for hydrogen-like atoms (H-Ne9+) and dihydrogen cations (H2+, D2+ and T2+), and clarified that the ECG-NOMO method shows the sufficient accuracy. (C) 2011 American Institute of Physics. [doi: 10.1063/1.3609806]

The chemical bond between atoms in metal oxides is expressed in an energy scale. Total energy is partitioned into the atomic energy densities of constituent elements in the metal oxide, using energy density analysis. The atomization energies, Delta E-M for metal atom and Delta E-O for O atom, are then evaluated by subtracting the atomic energy densities from the energy of the isolated neutral atom, M and O, respectively. In this study, a Delta E-O vs. Delta E-M diagram called atomization energy diagram is first proposed and used for the understanding of the nature of chemical bond in various metal oxides. Both Delta E-M and Delta E-O values reflect the average structure as well as the local structure. For example their values vary depending on the vertex, edge or face sharing of MO6 octahedron, and also change with the overall density of binary metal oxides. For perovskite-type oxides it is shown that the Delta E-O value tends to increase by the phase transition from cubic to tetragonal phase, regardless of the tilting-type or the &lt; 100 &gt; displacement-type transition. The bond formation in spinel-type oxides is also understood with the aid of the atomization energies. The present approach based on the atomization energy concept will provide us a new clue to the design of metal oxides. (C) 2011 Elsevier Ltd. All rights reserved.

A hexacoordinate hypervalent carbon compound with an ideal octahedral structure was proposed theoretically in a previous study (Chem. Phys. Lett. 2008, 460, 37). However, there is no report telling of success in synthesizing the compound and/or its derivatives. In order to perform a theoretical design for stronger hypervalent bonds, the present study systematically investigated the substituent effects at the para position of phenyl groups of axial C-C and equatorial C-O bonds by adopting 14 functional groups involving both electron-donating and -withdrawing groups. The results showed that the substituent effect at the former position is more influential than that at the latter. In the former case, a good correlation between the C-C and C-O distances is found and the hypervalent C-O bonds are strengthened as the substituent becomes more electron-withdrawing. In the latter case, both electron-donating and -withdrawing groups slightly weaken the hypervalent C-O bonds.

The intermolecular geometric isotope effect (GIE) in hydrogen bond A-X⋯B (X = H and D) is investigated theoretically using the nuclear orbital plus molecular orbital (NOMO) theory. To interpret the GIE in terms of physically meaningful energy components such as electrostatic and exchange-repulsion interactions, the reduced variational space self-consistent-field method is extended to the NOMO scheme. The intermolecular GIE is analyzed as a two-stage process: the intramolecular bond shrinkage and the intermolecular bond elongation. According to the isotopic shifts of energy components described by the NOMO/MP2 method, the intermolecular GIE is approximately interpreted as a process reducing the exchange-repulsion interaction after the decrease of electrostatic interaction. © 2011 American Chemical Society.

This study proposes a novel approach to construct the orbital-specific (OS) hybrid exchange-correlation functional by imposing the linearity condition: theta E-2/theta f(i)(2)vertical bar(0 &lt;= fi &lt;= 1) = theta epsilon i/theta fi vertical bar(0 &lt;= fi &lt;= 1) = 0, where E, epsilon(i), and f(i) represent the total energy, orbital energy, and occupation number of the ith orbital. The OS hybrid exchange-correlation functional, of which the OS Hartree-Fock exchange (HFx) portion is determined by the linearity condition, reasonably reproduces the ionization potentials not only from valence orbitals but also from core ones in a sense of Koopmans' theorem. The obtained short-range HFx portions are consistent with the parameters empirically determined in core-valence-Rydberg-Becke-3-parameter-Lee-Yang-Parr hybrid functional [Nakata et al., J. Chem. Phys., 124, 094105 (2006); ibid, 125, 064109 (2006)]. (C) 2011 American Institute of Physics. [doi:10.1063/1.3569030]

:The present study theoretically revisits and numerically assesses two-body energy decomposition schemes including a newly proposed one. The new decomposition scheme is designed to make the equilibrium bond distance equivalent with the minimum point of bond energies. Although the other decomposition schemes generally predict the wrong order of the C-C bond strengths of C(2)H(2), C(2)H(4), and C(2)H(6), the new decomposition scheme is capable of reproducing the C-C bond strengths. Numerical assessment on a training set of molecules demonstrates that the present scheme exhibits a stronger correlation with bond dissociation energies than the other decomposition schemes do, which suggests that the new decomposition scheme is a reliable and powerful analysis methodology.

:This study proposes a novel approach to construct the orbital-specific (OS) hybrid exchange-correlation functional by imposing the linearity condition: ∂(2)E/∂f(i)(2)|(0≤f(i)≤1) = ∂ɛ(i)/∂f(i)|(0≤f(i)≤1) = 0, where E, ε(i), and f(i) represent the total energy, orbital energy, and occupation number of the ith orbital. The OS hybrid exchange-correlation functional, of which the OS Hartree-Fock exchange (HFx) portion is determined by the linearity condition, reasonably reproduces the ionization potentials not only from valence orbitals but also from core ones in a sense of Koopmans' theorem. The obtained short-range HFx portions are consistent with the parameters empirically determined in core-valence-Rydberg-Becke-3-parameter-Lee-Yang-Parr hybrid functional [Nakata et al., J. Chem. Phys., 124, 094105 (2006); ibid, 125, 064109 (2006)].

:An analytical energy gradient formula for the density-matrix-based linear-scaling divide-and-conquer (DC) self-consistent field (SCF) method was proposed in a previous paper by Yang and Lee (YL) [J. Chem. Phys. 103, 5674 (1995)]. Since the formula by YL does not correspond to the exact gradient of the DC-SCF energy, we derive the exact formula by direct differentiation, which requires solving the coupled-perturbed equations while including the inter-subsystem coupling terms. Next, we present an alternative formula for approximately evaluating the DC-SCF energy gradient, assuming the variational condition for the subsystem density matrices. Numerical assessments confirmed that the DC-SCF energy gradient values obtained by the present formula are in reasonable agreement with the conventional SCF values when adopting a reliable buffer region. Furthermore, the performance of the present method was found to be better than that of the YL method.

An analytical energy gradient formula for the density-matrix-based linear-scaling divide-and-conquer (DC) self-consistent field (SCF) method was proposed in a previous paper by Yang and Lee (YL) [J. Chem. Phys. 103, 5674 (1995)]. Since the formula by YL does not correspond to the exact gradient of the DC-SCF energy, we derive the exact formula by direct differentiation, which requires solving the coupled-perturbed equations while including the inter-subsystem coupling terms. Next, we present an alternative formula for approximately evaluating the DC-SCF energy gradient, assuming the variational condition for the subsystem density matrices. Numerical assessments confirmed that the DC-SCF energy gradient values obtained by the present formula are in reasonable agreement with the conventional SCF values when adopting a reliable buffer region. Furthermore, the performance of the present method was found to be better than that of the YL method. (C) 2011 American Institute of Physics. [doi:10.1063/1.3524337]

:The intermolecular geometric isotope effect (GIE) in hydrogen bond A-X···B (X = H and D) is investigated theoretically using the nuclear orbital plus molecular orbital (NOMO) theory. To interpret the GIE in terms of physically meaningful energy components such as electrostatic and exchange-repulsion interactions, the reduced variational space self-consistent-field method is extended to the NOMO scheme. The intermolecular GIE is analyzed as a two-stage process: the intramolecular bond shrinkage and the intermolecular bond elongation. According to the isotopic shifts of energy components described by the NOMO/MP2 method, the intermolecular GIE is approximately interpreted as a process reducing the exchange-repulsion interaction after the decrease of electrostatic interaction.

The elementary steps of the reactions of hypophosphite ions with Cu, Ni, and Pd were calculated theoretically using Density Functional Theory (DFT) to demonstrate the reaction mechanism and gain insight at the molecular level. The elementary steps of these reactions are adsorption, dehydrogenation, and oxidation (hydroxyl base attack). In the adsorption step, hypophosphite ions adsorb onto each surface spontaneously with stabilities in the order of Ni (111) &gt; Pd (111) &gt; Cu (111). In the dehydrogenation step, hypophosphite ions dehydrogenate on Ni (111) and Pd (111) with small reaction barriers, whereas they react on Cu (111) with a large reaction barrier. The large reaction barrier on Cu (111) is not compensated for by the adsorption energy on the surface. In the oxidation step, dehydrogenated anions on each metal surface react spontaneously with the hydroxyl base. The reaction barriers on each metal surface in this step are not so significant compared to the adsorption energies on each surface, suggesting that a reaction barrier of hypophosphite ion oxidation should exist in the dehydrogenation step and only be observed for Cu (111). This proposition elucidates the experimental catalytic behaviors of metal surfaces in the electroless deposition process using hypophosphite ions. (C) 2011 The Electrochemical Society. [DOI: 10.1149/1.3609000] All rights reserved.

Recently introduced local response dispersion method [T. Sato and H. Nakai, J. Chem. Phys. 131, 224104 (2009)], which is a first-principles alternative to empirical dispersion corrections in density functional theory, is implemented with generalized multicenter interactions involving both atomic and atomic pair polarizabilities. The generalization improves the asymptote of intermolecular interactions, reducing the mean absolute percentage error from about 30% to 6% in the molecular C-6 coefficients of more than 1000 dimers, compared to experimental values. The method is also applied to calculations of potential energy curves of molecules in the S22 database [P. Jurecka et al., Phys. Chem. Chem. Phys. 8, 1985 (2006)]. The calculated potential energy curves are in a good agreement with reliable benchmarks recently published by Molnar et al. [J. Chem. Phys. 131, 065102 (2009)]. These improvements are achieved at the price of increasing complexity in the implementation, but without losing the computational efficiency of the previous two-center (atom-atom) formulation. A set of different truncations of two-center and three-or four-center interactions is shown to be optimal in the cost-performance balance. (C) 2010 American Institute of Physics. [doi:10.1063/1.3503040]

In this Letter, the divide-and-conquer (DC) linear-scaling self-consistent field method is extended to the spin-unrestricted Hartree-Fock (UHF) method or Kohn-Sham density functional theory (UDFT) for treating large open-shell systems. Although the DC method is one of the fragmentation-based linear-scaling schemes, the present DC-UHF/UDFT framework can avoid specifying the number of up-and down-spin electrons in each fragment by introducing up-and down-spin Fermi levels. Test calculations for oligoth-iophenes demonstrate the high efficiency and accuracy of the DC-UHF/UDFT method even for spin-delocalized systems. (C) 2010 Elsevier B.V. All rights reserved.

To understand the phase transition from perovskite to postperovskite MgSiO3, total energy is partitioned into atomic energy densities of constituent elements in the oxide, using the energy density analysis. The atomization energies, delta E-Mg for Mg atom, delta E-Si for Si atom, and delta E-O for O atom, are then evaluated by subtracting the atomic energy density from the energy of the isolated neutral atom, Mg, Si, and O, respectively. It is found that delta E-Si and delta E-Mg are much larger than delta E-O in the perovskite phase, but delta E-O is much larger than delta E-Si and delta E-Mg in the postperovskite phase. This means that most of the energies partitioned into Mg and Si atoms in the perovskite phase transfer to the O atoms in the postperovskite phase during the transition. Such an extremely stable O-atom state is formed by the introduction of edge-shared SiO6 octahedra into the postperovskite structure. This is because the edge-sharing makes the Si-O interatomic distances longer even in very high pressure conditions. The unusual energy balance between atoms is also seen in the other postperovskite, MgGeO3 and NaMgF3.

The present study theoretically investigated hypervalent bonding systems with the skeleton of pentalene. Geometries and energetics were examined by density functional theory calculations with triple-zeta class basis sets. The bond energies of the O-X and N-X hypervalent three-center four-electron bonds were estimated. Furthermore, the relationships between the bond-switching equilibration reactions and the stabilities of the hypervalent bonding intermediates were examined.

Two perturbation (PT) theories are developed starting from a multiconfiguration (MC) zero-order function. To span the configuration space, the theories employ biorthogonal vector sets introduced in the MCPT framework. At odds with previous formulations, the present construction operates with the full Fockian corresponding to a principal determinant, giving rise to a nondiagonal matrix of the zero-order resolvent. The theories provide a simple, generalized Moller-Plesset (MP) second-order correction to improve any reference function, corresponding either to a complete or incomplete model space. Computational demand of the procedure is determined by the iterative inversion of the Fockian, similarly to the single reference MP theory calculated in a localized basis. Relation of the theory to existing multireference (MR) PT formalisms is discussed. The performance of the present theories is assessed by adopting the antisymmetric product of strongly orthogonal geminal (APSG) wave functions as the reference function.

Theoretical study of the mechanism of bond-switching of 5-(1-aminoethylimino)-3-methyl-1,2,4-thiadiazole and 5-(2-aminovinyl)isothiazole was carried out by using simplified models of 1,6-dihydro-6a-thia-1,6-diazapentalene (10-S-3) systems and corresponding oxygen analogs. Geometries and energetics were examined along unimolecular and bimolecular reaction paths by hybrid density functional theory (DFT) calculations with triple-zeta class basis sets by taking into account solvent effects which is estimated by the polarizable continuum model. It was clarified that the unimolecular reactions cannot proceed due to the high energy barriers around 70 kcal mol(-1). On the other hand, the bimolecular processes in neutral and acidic conditions can be accomplished for the sulfur compounds, not for the oxygen ones. The differences of the reactivities between the sulfur and oxygen compounds were found to be due to the difference of the stability of the symmetric intermediates with the hypervalent three-center four-electron bonds.

The CVB3LYP functional, which has been developed for evaluating both core and valence excitation energies with high accuracy, is applied to real-time time-dependent density functional theory (RT-TDDFT) calculations. The core excitation energies from the Is orbitals of several second-row atoms obtained by RT-TDDFT with the CVB3LYP functional were demonstrated and compared with those of the frequency-domain TDDFT.

We propose a novel acceleration method for self-consistent-field calculations in direct ab initio molecular dynamics/Monte Carlo (AIMD/AIMC) simulations and geometry optimization. This acceleration method, so-called LSMO, predicts an initial guess of molecular orbitals (MOs) for the next simulation step by using the geometric information with the least-squares technique. Numerical tests confirm that the LSMO method is both effective and feasible in the AIMD/AIMC simulations and geometry optimization. (C) 2010 Elsevier B.V. All rights reserved.

Energy density analysis (EDA), which partitions the total energy of a molecular system into atomic contributions, has been extended to periodic-boundary-condition calculations carried out by density-functional theory using plane-wave (PW) basis functions and pseudopotentials. The present analysis method, called PW-EDA, allows us to extract local-energy information by estimating atomic energy contributions. Numerical applications to an isolated molecule H2O and the adsorption of C2H2 on the Si(001)-(2x1) surface confirm the reliability and usefulness of PW-EDA.

We propose a novel analysis of real-time (RT) time-dependent Hartree-Fock and time-dependent density functional theory (TDHF/TDDFT) calculations using a short-time Fourier transform (STFT) technique. RT-TDHF/TDDFT calculations of model dimers were carried out and analyzed using the STFT technique, in addition to the usual Fourier transform (FT). STFT analysis revealed that the induced polarization propagated between the molecules through the intermolecular interaction; that is, it directly showed the electron dynamics of the excited system. The dependence of the propagation period on the intermolecular distance of the dimer was investigated. We also proved the possibility of describing, not just the valence, but also the core excitations by FT analysis of the RT-TDHF/TDDFT calculations of a formaldehyde monomer with Gaussian basis functions compared with conventional TDHF/TDDFT results. (c) 2010 American Institute of Physics. [doi:10.1063/1.3300127]

:Recently introduced local response dispersion method [T. Sato and H. Nakai, J. Chem. Phys. 131, 224104 (2009)], which is a first-principles alternative to empirical dispersion corrections in density functional theory, is implemented with generalized multicenter interactions involving both atomic and atomic pair polarizabilities. The generalization improves the asymptote of intermolecular interactions, reducing the mean absolute percentage error from about 30% to 6% in the molecular C(6) coefficients of more than 1000 dimers, compared to experimental values. The method is also applied to calculations of potential energy curves of molecules in the S22 database [P. Jurečka et al., Phys. Chem. Chem. Phys. 8, 1985 (2006)]. The calculated potential energy curves are in a good agreement with reliable benchmarks recently published by Molnar et al. [J. Chem. Phys. 131, 065102 (2009)]. These improvements are achieved at the price of increasing complexity in the implementation, but without losing the computational efficiency of the previous two-center (atom-atom) formulation. A set of different truncations of two-center and three- or four-center interactions is shown to be optimal in the cost-performance balance.

:We propose a novel analysis of real-time (RT) time-dependent Hartree-Fock and time-dependent density functional theory (TDHF/TDDFT) calculations using a short-time Fourier transform (STFT) technique. RT-TDHF/TDDFT calculations of model dimers were carried out and analyzed using the STFT technique, in addition to the usual Fourier transform (FT). STFT analysis revealed that the induced polarization propagated between the molecules through the intermolecular interaction; that is, it directly showed the electron dynamics of the excited system. The dependence of the propagation period on the intermolecular distance of the dimer was investigated. We also proved the possibility of describing, not just the valence, but also the core excitations by FT analysis of the RT-TDHF/TDDFT calculations of a formaldehyde monomer with Gaussian basis functions compared with conventional TDHF/TDDFT results.

2H- and 13C-labelling studies on skeletal reorganization of 1,6-enynes having a terminal alkyne moiety have been performed with various catalysts. The products are 1-vinylcyclopentenes, but two possible isomers, type I and II products, can be formed. The formation of type I involves the cleavage of the original C-C double bonds and migration of the terminal alkene carbon atom to the terminus of the alkyne. On the other hand, the formation of type II involves a double cleavage of the C-C double bond and the C-C triple bond, which is an anomalous bond connection. The product ratio is affected by the nature of the catalyst used. Type II is obtained as a major isomer in the case of late transition metal halides. On the other hand, the type I product forms exclusively in the presence of a typical element halide, such as InCl3. Copyright © 2007 The Chemical Society of Japan.

本研究では、凝縮相の熱力学計算に対する高精度量子化学計算法の確立を目指して、我々が開発した新しい理論モデルである調和溶媒和モデル(HSM)の実践的応用を行った。その他、本目的に必要な理論的検討を行った。具体的には、以下の4つのテーマを実践した。
①剛体近似型調和溶媒和モデル(RB-HSM)の開発、②量子化学計算による気液平衡の理論的検討、③気体の溶解度に対する量子化学計算、④量子化学計算による標準水素電極電位(SHE)の算出、⑤CO2化学吸収法における反応自由エネルギーの理論的検討、⑥遷移金属錯体の生成エンタルピーの理論的検討。

本研究では、ガウス型軌道(GTO)基底を用いた実時間発展形式-時間依存密度汎関数理論(RT-TDDFT)の計算手法を開発した。特に、高次の非線形過程にも対応した一般式を導出し、また、原子核の時間発展も考慮した定式化も行った。さらに、単に理論・プログラム開発だけでなく、高次の非線形励起過程や励起状態の超高速な緩和過程についても理論的に解明した

本研究では、ガウス型軌道(GTO)基底を用いた実時間発展形式-時間依存密度汎関数理論(RT-TDDFT)の計算手法を開発した。特に、高次の非線形過程にも対応した一般式を導出し、また、原子核の時間発展も考慮した定式化も行った。さらに、単に理論・プログラム開発だけでなく、高次の非線形励起過程や励起状態の超高速な緩和過程についても理論的に解明した。

本研究では、ガウス型軌道(GTO)基底を用いた実時間発展形式-時間依存密度汎関数理論(RT-TDDFT)の計算手法を開発した。特に、高次の非線形過程にも対応した一般式を導出し、また、原子核の時間発展も考慮した定式化も行った。さらに、単に理論・プログラム開発だけでなく、高次の非線形励起過程や励起状態の超高速な緩和過程についても理論的に解明した。

本研究では,AIMD計算のボトルネックである電子状態理論計算の高速化,大規模化を目指した理論開発を行った。また,原子核の量子効果を考慮したダイナミックスについては,核・電子軌道(NOMO)法を発展させることにより研究を進めた。さらに実在系に対する様々な応用計算のため,エネルギー密度解析(EDA)を発展させ,計算結果の効果的な解析を行った。

1、6配位のアニオンであるリン化合物(12-P-6)は一般に不安定であり、単離は困難である。
これを安定化するために、2座配位子であるMartinリガンド(ヘキサフルオロベンジルアルコール)を2個用いて4配位のリンのアニオンであるボスホラニドアニオン(10-P-4)を系中に発生させた。これに共役アルデヒドや1,2-ジケトンを付加させ、リンの原子価を拡張し、6配位のボスファートアニオン(12-P-6)を生成させ、それらの単離と安定化を試みた。1,2-ジケトンであるフェナントレンキノンの場合は付加体が安定に単離され、X線回折により、構造を決定した。その他の場合は、系中で6配位のホスファートアニオン(12-P-6)の生成を確認できた場合もあるが、一般的には、加水分解されたアルデヒドとして、5配位の付加体(10-P-5)が高い収率が得られた。これらは2,4-ジニトロフェニルヒドラゾンとして構造を確認した。
2、17年度に、5配位の炭素化合物(10-C-5)の合成と構造決定を報告した。さらに、中心原子をホウ素にした超原子価化合物を種々合成して、超原子価結合に対する置換基の電子的影響を明らかにした。本年度は、それに続いて6配位の炭素化合物(12-C-6)の合成に挑戦した。これは極めて新規でユニークな化合物であるので、種々な系を設計し、その可能性を検討した。その結果、チオキサンテン骨格を1,3-位にもつアレンを合成し、その2個の硫黄原子をともにメチル化することにより、6配位の炭素化合物(12-C-6)の創製に成功した。このメチル化には、リード教授(Riverside, California, USA)の開発したカルボランを用いて、初めて成功した。
3、パラトリル基とパラトリフルオロフェニル基を1価の置換基とするベンタアリールアンチモンの全ての置換体を合成し、それらの気相熱分解により、両置換基のリガンドカップリング反応の選択性を実験的に決定した。この結果から、アピカル位の置換基同士が選択的にカップリングすることを見出した。
これにより、カップリング反応における置換基の[memory effect]を提唱した。

現在広く用いられている分子軌道(MO)法や密度汎関数理論(DFT)は、原子核と電子の運動を分離するBorn-Oppenheimer (BO)近似に基づいている。このBO近似を用いることで、ポテンシャルエネルギー曲面(PES)の概念が導かれ、分子の物性や反応性の解釈に対し大きな成果を上げてきた。しかし、非断熱遷移が起こる領域などBO近似が破綻する場合も数多く、BO近似を超えた取り扱いが必要である。また、原子核の同位体効果・量子効果を議論する場合には、原子核の波動関数は不可欠である。その場合、BO近似に基づく限りPESを予め求める必要があるが、PESの計算は原子数の増加に伴い計算コストが指数関数的に増加する。一方、本申請者が提案してきた電子および原子核の波動関数を同時に決定できる理論であるNOMO法は、BO近似を用いておらず、計算コストの急激な増加はない。また、電子と原子核のカップリング、つまり非断熱効果も考慮することができる。しかし、我々のNOMO法は、必ずしも計算精度が高くないという欠点を持っていた。そこで本研究では、NOMO法の計算精度の向上を第1の目的とした。この点については、NOMO-Hamiltonianに混入している並進・回転運動を分離することで大幅な精度向上に成功した。さらに、多体摂動法との組合せにより更なる高制度化に成功した。本研究ではさらに、NOMO法をより有用な方法へと発展させるために、構造最適化の実現、励起状態への拡張、動力学法との組み合わせ、解析手法の充実などを行った。

本研究では、種々の量子化学計算に対するUnear-Scaling(LS)法あるいは効果的な計算アルゴリズムを提案することを目指した。
(1)分子積分の高速計算プログラム開発:分子積分、とりわけ電子間反発積分(ERI)の計算は、いまなお量子化学計算のボトルネックの一つである。本研究では、昨年度提案したACE-RRアルゴリズムに基づくプログラムを作成し、GAMESSプログラムと組合せることにより汎用性の向上を目指した。実際、本手法は従来のアルゴリズムより20%程度高速化していることが確かめられた。
(2)Divide-and-Conquer(DC)法の検証:Yangによって提案された:LS法の一つであるDC法は、主にDFTに適用されてきた。しかし、原理的にはHF交換項を含むハイブリッド法にも応用できる。本研究では、DC-HFプログラムを作成し、HF交換項に対するDC法の是非を検討した。その結果、HF交換項の非局所性のため、十分な相互作用領域を用いる必要があること、打ち切りによるSCF収束性が悪化することが明らかとなった。
(3)AIMD法におけるSCF収束性の向上:AIMD法は時間ステップごとにMO/DFT計算を行うため、膨大な計算時間を必要とする。本研究では、MOの時間発展を考慮することにより、効果的な初期MOを推定し、SCF収束性の向上を達成した。多くの系で、2-4倍程度の高速化が実現された。
(4)NOMO法の高精度化:電子と核の波動関数を同時に決定するNOMO法は、我々が提案してきた独自の方法で、世界的にも注目されている。しかし、その精度は従来のMO法に比べ劣る。その原因は、電子-核および核-核相関といった特殊な多体効果に加えて、並進・回転運動の混入が挙げられる。本研究では、並進・回転運動の寄与を取り除く効果的なスキームを提案し、それによる高精度化を図った。

固体表面及び表面吸着種の励起プロセスは、光触媒、光エネルギー変換、半導体材料の製造など多くの応用分野で盛んに研究されている。理論的に表面励起プロセスを研究しようとすると、既存の方法論やプログラムだけでは必ずしも十分ではない。本研究では、それらの理論的手法を自ら開発し、いくつかの興味ある対象に応用した。具体的には以下のような理論的研究を展開してきた。(1)活性部位のエネルギー変化を見積るための解析法の開発、(2)固体表面の効果的なモデリングの検討、(3)Ab Initio Molecular Dynamics(AIMD)法による励起状態ダイナミクスの検討、(4)TDDFT法による光化学反応の解明、(5)二酸化チタンの結晶構造と電子状態の研究を行ってきた。テーマ(1)では、全系のエネルギーを構成原子に分割するための新しい解析法(EDA ; Energy Density Analysis)を提案した。テーマ(2)では、EDA法を使ってモデルの妥当性及び効果的な取り扱いを検討した。テーマ(3)では、ソラレン化合物の励起状態に対するAIMDシミュレーションを行った。テーマ(4)では、ポルフィリンアンチモン錯体の光解離反応について検討した。テーマ(5)では、二酸化チタンに対する周期境界条件(PBC ; Periodic Boundary Condition)計算を行うことにより、結晶構造と電子状態の関係を理論的に検討した。

本研究では、励起分子や固体触媒の構造や振動状態、さらにそれらが引き起こす種々の化学反応を理論的手法により検討し、そのメカニズムの解明を目指した。本年度はこの目的にしたがって、(1)ab initio NO+MO法による振動励起状態の解析、(2)ソラレン化合物のDNA光付加反応に関する理論的研究、(3)分子衝突のMDシミュレーションと化学反応性の理論的予測、等の研究を行った。(1)では、これまでに我々が開発したBorn-Oppenheimer近似に基づかない理論、ab initio NO+MO法に励起状態の理論を適用し、電子励起状態だけでなく振動励起状態に関する知見を得ることに成功した。特に、振動波動関数から得られる核密度分布は、分子振動やプロトントンネリングなどの現象を、視覚的・直感的に理解するうえで有用であることがわかった。(2)では、乾癬などの皮膚病治療に用いられるソラレン化合物がDNAとどのように光付加するかを理論的に検討した。その結果、ソラレン化合物のひとつである8-MOPは、T_1状態において特異な開環構造をすることが初めて示され、それが治療効果と密接な関係があることも明らかとなった。(3)では、アンモニアクラスターイオンとアンモニアモノマーの衝突反応に対して、種々の反応条件に対してab initio MDシミュレーションを行い、その結果から衝突実験で報告されている反応断面積を理論的に見積ることに成功した。さらに、衝突サイトと反応性との関連も明らかにすることができた。

本研究では、固体表面および金属錯体の関与する反応に対して、その触媒作用のメカニズムを理論的に解明することを目指した。固体表面に対しては、クラスターモデルによる取り扱いで問題となる、クラスターサイズ依存性に関して系統的に調べた。その結果、吸着分子の構造や振動数などは金属原子数個のクラスターを用いた計算でも収束しているが、生成熱などエネルギーは40個のクラスターを用いても収束が見られない、という興味深い結果が得られた。その原因として、クラスターを切り出したことによる不安定性が直接エネルギー計算に影響していることが示された。具体的な触媒反応としては、銅表面におけるメタノール合成を取り上げ、吸着活性種の特定、反応経路の決定、銅の触媒作用、蒸着亜鉛の助触媒効果などを検討した。特に本年度は、律速段階であるフオーメートからジオキソメチレンに至る過程を重点的に調べ、一般にその特定が困難とされる固体表面反応の遷移状態を理論的に求めることに成功した。金属錯体の関与する反応としては、昨年度から取り組んでいるRu(II)-Sn(II)複核錯体における酢酸合成反応を引き続き検討した。本研究を通して、異種金属間結合が触媒反応に果たす多種多様な機能の解明に、理論的にはどのようなアプローチが可能かを検討することができた。

本研究では、励起分子の構造や振動状態、さらにはそれが引き起こす種々の反応を理論的な手法を用いて検討し、そのメカニズムを解明することを目指した。本年度は、この目的に従って、(1)BO近似に基づかないNO+MO理論、(2)アンモニアクラスターイオンの構造と反応性、(3)励起分子のメチル基内部回転運動、に関して研究を行った。(1)では、先に我々のグループで提案した核と電子の波動関数と同時に決定する方法、NO+MO/HF法の定量性を向上するために、多体摂動論を用いて解析した。その結果、核-核相関に比べ電子-核相関が圧倒的に大きいこと、低次の摂動では収束しないこと、リング型の相互作用より梯子型の相互作用が重要なこと、などが示された。この結果に基づいて、Bruecknerタイプの有効相互作用を用いる必要性があることがわかった。(2)では、アンモニアクラスターイオンとアンモニアモノマーの衝突断面積を、ab initioポテンシャルを用いて求めた。その結果、実験的に観測されているクラスターサイズ依存性や衝突エネルギー依存性を再現することに成功した。特に、衝突断面積が極小となるサイズが、中心のアンモニウムイオンの周りをアンモニアモノマーがすべて取り囲んだ構造、つまり第1溶媒和圏が閉じた状態に相当するという興味深い結果も得られた。(3)では、S_0,S_1状態における置換トルエンの回転障壁は、HF/CIS計算でまずまず実験値を再現できた。この計算結果の解析から、S_0→S_1励起による回転障壁の変化は、LUMOにみられる新しいタイプの超共役に由来していることがわかった。この超共役相互作用により、置換基の配向や電子供与性の違いによる回転障壁の変化を、系統的に理解することに成功した。

STMによる表面の観察は、これまで現象論的な理解が先行していた電極反応において、基礎的な理解を与える手段として期待されている。しかし、これらの解釈には、表面-探針間の相互作用を考慮する必要がある。そこで本研究では、電極表面のSTMシミュレーションを行い、正しい理解を理論的に与えることを目指した。まず、Bardeenの摂動論に基づくSTMシミュレーションプログラムを開発し、これを金表面に吸着した硫酸イオンに適応した。その結果、印加電圧が小さい場合には硫酸イオンに対応するSTM像が得られないが、ある電圧を境にSTM像が見えることがわかった。その場合、原子レベルの分解能はなく、硫酸イオン全体で一つのスポットとなることも示された。次に、電極表面反応の一つとして無電解鍍金を取り上げ、その反応機構を理論的に検討した。その結果、ジメチルアミンボランや次亜リン酸などの還元剤については、脱水素より水酸基の配位が先行して生成される5配位化合物を経由することが示された。還元剤の酸化反応は溶媒の誘導率が増加するとともに進行しにくいことも示された。これは、還元剤が極性溶媒中では自発的に酸化されないが、バルク溶液に比べ誘導率が小さい電気二重層中では酸化されやすくなっていることを示している。さらに、表面上では反応全体が発熱的であることより、析出金属の自己触媒作用により還元剤の酸化が起こりやすくなっていることが理論的に示された。

クロルプロマジンの光化学: フェノチアジン、クロルフェノチアジン、プロマジン、クロルプロマジン光化学において、クロル誘導体ではカチオンラジカルから560nmに吸収をもつ過渡分子種Xが、更にXから380nmに吸収をもつ過渡分子種Yが生成することを明らかにし、Xが主要な生理活性種である可能性を示した。
サリチルアニリドの光化学: 時間分解赤外吸収スペクトルにより、サリチルアニリドの光反応において、寿命8μsの過渡分子種の存在を明らかにた。また、この過渡分子種ではアミドIIに対応する赤外バンドが観測されないことから、キノイド構造をとっていると結論した。
ルシフェリンの光化学: 電子励起一重項状態S_1のピコ秒時間分解吸収/蛍光スペクトルの時間依存性は4順位モデルを仮定することにより説明できることが分かった。このことから、ルシフェリンのS_1にはコンフォーメーションの異なる2種の異性体が存在すると結論した。すなわち、基底状態と同様の構造を持つFranck-Condon状態は180psの寿命で基底状態に戻るとともに、50psの寿命で構造の異なる別のS_1へと変化する。この状態は480psの寿命で最初とは異なる基底状態へ落ちる。なお、この基底状態から最初の基底状態への戻り反応はナノ秒の時間領域で起こる。
ジベンスアゼピンの光励起状態の構造とダイナミックス: ピコ秒時間分解吸収スペクトルにおいて,3種類の過渡分子種が観測されたが,これらはS_2状態,S_1のFranck-Condon状態およびS_1の緩和状態に帰属できる.この分子は基底状態S_0では,2個のフェニル基がバタフライ状に折れ曲がった構造をとっており,Franck-Condon状態のS_1も同様に折れ曲がった構造をとっている.これに対して,緩和した状態のS_1は平面形を取っていることが,ピコ秒時間分解ラマンスペクトルおよび蛍光スペクトルから明らかになった.なお,この構造変化は光励起後20ピコ秒以内に起こる.
ビフェニルの光化学反応: 励起一重項状態S_1の構造が中央のC-C結合周りでねじれた構造から平面トランス形に変化することを明らかにした.この構造変化の時定数は20ピコ秒以下でる.S_1状態のラマンスペクトルはT_1状態のラマンスペクトルに極めて似ていることが分かった.このことは,S_1状態の構造がT_1状態の構造と類似していることを示唆している.ナノ秒時間分解赤外吸収スペクトルとナノ秒時間分解ラマンスペクトルとの比較から,T_1状態は対称中心を持つトランス平面構造をとっていることが分かった.従って,S_1状態も同様の平面構造をとっていると考えらる.
カルバゾールの光化学反応: 光励起により、極性溶媒中ではラジカルカチオンとカルバジルラジカルが生成し、無極性溶媒中ではカルバジルラジカルのみが生成することを明らかにした。なお、ラジカルカチオンはS_1経由の2光子過程で生成するが、N-H結合の切断によりカルバジルラジカルが生成する過程は308nm励起の場合、S_1状態経由の1光子過程で起こることが分かった。

本研究では、触媒反応の活性点における吸着種の構造・電子状態・エネルギーを量子化学計算により求め、触媒作用の解明を目指してきた。さらに、その結果に基づいて分子・原子あるいは電子レベルで触媒設計を行うことを最終目標とした。以下に具体的な研究成果を報告する。
1.Cu/ZnO触媒によるメタノール合成反応: 気相中のCO_2とH_2からメタノールを生成する反応は、工業的にも重要であり、多くの実験的研究がなされてきた。しかしながら、反応メカニズムや触媒作用の本質など未解決な問題も多く残されていた。本研究では、Cu_4およびCu_3Znクラスターを用いて、それぞれ清浄表面および亜鉛蒸着表面のモデルとし、吸着フォーメートの水素化反応を重点的に調べた。その結果、Zn-Cuに橋掛けしたフォーメート中間体の存在が確認され、安定性・反応性ともに清浄表面のものよりも有利であることがわかった。吸着フォーメートの水素化反応過程では、ジオキソメチレン中間体、メトキシ中間体を経て、メタノールが生成することがわかった。Cu表面の触媒作用やZnの助触媒効果には、種々の吸着種への多彩な電子移動が密接に関与していることが明らかとなった。
2.[V_4O_<12>]^<4->上に坦持されたアリル-ロジウム錯体によるC-Cカップリング反応: 分子性酸化物[V_4O_<12>]^<4->上に坦持されたアリル-ロジウム錯体は、C-Cカップリング反応を引き起こしヘキサジエンを生成することが知られている。本研究では、この反応過程における構造変化と触媒活性の関係を明らかにすることを目指した。その結果、C-Cカップリング反応が起らないアセチルアセトナート上に坦持されたアリル-ロジウム錯体に比べて、遷移状態に大きな差異が見られた。この違いは、ロジウム錯体部位への電子移動の違いに由来していることが明らかとなった。構造面では、フリーな酸化バナジウム錯体はV_4O_4という8員環はπ共役により平面構造を有しているが、ロジウム錯体がこれに配位すると平面構造は崩れることが示された。2個のロジウム錯体が配位する場合、V_4O_4の8員環を通した長距離相互作用が働き、これがC-Cカップリング反応をサポートしていることも明らかとなった。

固体表面及び表面吸着種の励起ダイナミックスは、光触媒、光エネルギー変換、半導体材料の製造など多くの応用分野において、また、これらの電子論的理解という点では基礎研究としても多いに注目されている。しかしながら、これらは励起状態における表面一分子系の構造変化、エネルギー移動、電子移動などを含んでおり、実験的に全課程を理解することは非常に困難である。本研究では、理論的な立場からこの様な表面励起ダイナミックスの電子過程を明らかにすることを目指した。具体的には、(1)固体表面の触媒作用、(2)表面吸着種のSTM像、(3)金属錯体の励起状態と光化学反応に関して、これらを取り扱う理論や方法論の構築および各現象の電子的マカニズムの解明を試みた。(1)では、銀触媒によるエチレンの部分酸化反応を対象とした。本研究により、これまで未解決であった活性酸素種の特定に成功した。また、触媒設計の観点から、そもそも銀なのか、銀以外の金属では触媒と成り得ないのか、また、エチレンなのか、他のオレフィンではどうなのか、などについても検討した。(2)では、Bardeenの摂動論を分子軌道法に適用し、STMの分子軌道モデルを提案した。さらに、この手法を吸着ベンゼンに適用し、吸着構造の違いによって炭素の6個のピークが見られる場合と3個のピークしか現われない場合があることを理論的に示した。(3)では、高い対称性を持つ金属錯体の励起状態に関して系統的に研究し、その結果からこれらの励起状態のエネルギー準位や分裂幅に一般則があることを見いだした。さらに、この規則は金属錯体に限らず、縮退軌道間の遷移に基ずく励起状態に関する一般則であり、直線分子やベンゼン錯p-p^*励起状態、正20面体構造のC_<60>の励起状態などにも適用できることを確認した。白金およびイリジウム錯体が示す光異性化や光分解などの光化学反応についても理論的に検討した。

(1)高速化:大型ベクトル計算機の能力、容量を最大限に引き出すようにアルゴリズムの改良、ベクトル化を行った。まず、SAC85プログラムにおいて最も計算時間を要するバミルトニアン行列の計算とその対角化部分を重点的に行った。前者では、従来のものとは全く異なるアルゴリズムを提案し、それを採用することにより5倍程度の加速に成功した。後者では、ベクトル化率の向上により20倍、更に収束性の改善により10倍程度の加速に成功した。また、収束性の改善によりこれまで求まらなかった解も計算できるようになった。これらの成果から現在の制約は計算時間よりもむしろ一時的に保存するデータの取り扱いに移行した。
(2)ワークステーション化:ワークステーションユーザーが急速に増加していることを考慮し、SAC/SAC-CI法のプログラム(SAC85)がUNIX環境で作動するように全てのステップを変更した。その際、入出力ファイルの取り扱いを自動化し、また、計算規模に関係なく一つのモジュールで計算できるようにメモリーアクセスに変更を加えた。更に、結果解析プログラムなどを追加した上で、プログラム全体の統一を行った。その際、マシン依存性がある箇所について対応できるように整備を行った。
(3)プログラム使用法の簡略化:理論を十分理解していないユーザーでも無理なく使用でき、正しい結果を得ることができるように配慮した入力方法に変更した。このため、計算パラメーターは我々の経験から得たデフォルト値を設定し、不要なパラメーターは入力から除外した。また、中間データを保存する外部ファイルをユーザーが意識しないで計算ができるようにファイル構造を改善した。更に、入力についてはプログラムマニュアルの再整備を行った。結果の出力内容については再検討を行い、一般ユーザーに分かり易い出力を行うように変更した。
(4)応用計算:大規模分子に対する応用として、(a)光合成反応中心を構成するスペシャルペア、Bacteriochloro-phyll、Bacteriopheophytinなどの励起状態の研究、(b)フタロシアニンなどの色素化合物の研究、(c)過酸化水素分解酵素であるHRPCOおよびHRPのcompound IIのモデル系の研究などで成果を挙げた。また、(d)SAC-CI法を用いた構造最適化法の開発に成功し、励起状態反応面の精密な解析を行った。

本研究では、いくつかの固体触媒反応に対して理論的な手法を用いてその触媒作用を解明し、その結果に基づいて触媒設計の指針を理論的研究から与えることを目指した。ここでは、このような目的で行った研究のうち、ホルムアルデヒド合成反応に対する銀の触媒作用に関する研究を報告する。本研究は、これまでに行ってきた銀表面における酸素活性化の研究を基礎としており、また、昨年本重点領域研究で報告したエチレンのエポキシ化反応に対する銀の触媒作用との対比としても興味深いテーマである。
本研究では、ホルムアルデヒド合成反応に対して、反応メカニズムと吸着酸素種の役割を明らかにした。ホルムアルデヒド合成反応は、理論的にも二段階(O-H解離とC-H解離)で進むことが示され、ともに吸着酸素は活性種として働くことがわかった。しかし、C-H解離の際、吸着酸素が存在すると副反応を導く可能性が示された。さらに、吸着酸素は生成物であるホルムアルデヒドを再吸着させ、さらなる分解を引き起こすことが示された。この吸着酸素種の二面性のため、反応プロセスではメタノール過剰つまり酸素不足の条件が用いられている。反応温度が高いのは、酸素不足によりあまり有利でない過程を経る必要があるためである。熱力学的にも有利な酸素過剰で反応させるためには、効果的にホルムアルデヒド生成物を反応場から取り除く必要がある。本研究の結果は、今後の触媒設計へ重要な指針を与えるものであろう。

本研究では、いくつかの固体触媒反応に対して理論的な手法を用いてその触媒作用を解明し、その結果に基づいて触媒設計の指針を理論的研究から与えることを目的とした。ここでは、このような目的で行った研究のうち、エチレンのエポキシ化反応に対する銀の触媒作用に関する研究を報告する。
(1)エポキシ化反応の電子的メカニズム
銀は、エチレンを部分酸化してエチレンオキサイドを生成する唯一高活性で高選択的な触媒である。しかし、この反応に有効な酸素種が何であるかさえ未だ明らかでない。本研究では、エチレンのエポキシ化および燃焼反応両方のメスニズムを解明し、それぞれの活性酸素種は何であるのかを検討した。その結果、分子状吸着酸素は選択的にエチレンオキサイドを生成し、原子状吸着酸素は両方を導くことがわかった。これにより、実験的に示唆されていた選択率の上限(85.7%)は存在しないことになり、理想的には100%の選択率を持つ触媒設計が可能であることがわかった。
(2)銅および金触媒の可能性
上記の研究から、エポキシ化反応には酸素の解離能の小さい表面が、触媒として有利であることがわかる。つまり、d電子が不活性な金属表面の方が有利である。そこで本研究では、銀と同族の銅および金表面におけるエポキシ化反応を理論的に検討した。その結果、いずれの表面上のスーパーオキソ種も銀表面のものと類似の反応性が示された。しかし、スーパーオキソ種の安定性に違いが見られ、この点を改良すれば銅および金でも触媒と成り得ることがわかった。
(3)Ag (111)面とAg (110)面における触媒活性
銀触媒の選択性に対する面依存性を調べるために、Ag (111)面とAg (110)面上における酸素活性化の比較を行った。その結果、解離のバリアに大きな差が現れ、Ag (110)面の方が解離吸着を導きやすいことが示された。このため、Ag (110)面では高選択性を示すスーパーオキソ種の相対安全性が減少する。この差が選択性に対する面依存性に対する面依存性の起源である。

本研究の目的は、論理的な立場から表面光化学の電子プロセスを明らかにすることである。表面-分子系の理論モデルとしてクラスラ-モデルとDipped Adcluster Model(DAM)を用いて、その系の基底状態と励起状態の電子構造およびエネルギーをSAC-CI法などの量子化学計算により求めた。以下に具体的な研究成果を述べる。
1.金属表面上の表面励起プロセス:発光や電子放出を伴う吸着現象(Cl/K系)、Pt表面からの吸着CO,NO分子の光刺脱離に対して、SAC-CI法により励起状態のポテンシャルカーブを描き、そのダイナミックスを研究した。表面-分子系の励起状態や電子移動状態が関与する現象として、SERS(表面補強ラマン散乱)やSTM(走査型トンネル顕微鏡)についても研究し、新しい理論モデルを提案することによりそのメカニズムを明らかにした。2.金属および金属酸化物表面上における触媒反応:金属および金属酸化物表面上で起こる吸着や分解反応の反応は、熱反応であるにもかかわらずしばしば励起状態の関与が見られる。今回、そのような触媒反応として、酸素、水素の吸着、ギ酸の分解、GaAs表面のエピタキシャル成長に関して研究を行った。
3.金属醋体の電子スペクトル:金属表面と金属醋体のアナロジーから、種々の金属醋体の励起状態の理論計算を行った。SAC-CI法による結果は、いずれの場合も実験スペクトルを良く再現し、それに基づいて信頼できるアサインメントができた。
4.金属醋体の光化学反応:金属醋体に対しては、更に、光励起に引き続いて起こる光分解や光異性化反応について研究した。具体的には、MnO_4とNi(CO)_4の光分解、Pt-アセチレン、エチレン醋体の光異性化反応に大して、関与する励起状態の特定、中間体の構造決定などを行った。

本研究では、エチレンの部分酸化反応における銀の触媒作用の電子的オリジンを、量子化学的なアプローチにより解明することを目指し、以下のテーマを実行した。表面-分子相互作用系のモデルには、先に我々が提案したDipped Adcluster Model(DAM)を用いた。
(1)エポキシ化反応の電子的メカニズムの解明:銀の清浄表面には、エチレンは吸着しないことが知られている。そのため、エポキシ化反応は、吸着酸素種と気相中のエチレンとの間で進行すると考えられる。そこで本研究では、先に申請者らが理論的に存在を確認した4種の吸着酸素種について、それぞれエチレンとの反応を調べた。その結果、スーパーオキソ種から導かれる非常に活性な反応中間体の存在が確かめられた。この中間体を経る反応は、気相中での反応に比べ殆どバリアーなく進行し、銀の触媒作用が理論的に示された。他に原子状酸素種からもエチレンオキサイドが生成することが示された。これにより、実験的に示唆されている選択率の上限(6/7)は存在しないことになり、理想的には100%の選択率をもつ触媒設計が可能であることがわかった。
(2)燃焼反応の電子的メカニズムの解明:エチレンの燃焼反応は、部分酸化の副反応として起こり、結果として選択性を減少させる。触媒開発では、この燃焼反応を如何に抑えるかが鍵となっている。本研究では燃焼反応の第1ステップであるアセトアルデヒド生成反応を調べた。その結果、分子状吸着酸素種からこの反応は起こらないが、原子状吸着種からは比較的容易に起こることが示された。すなわち、原子状酸素種からはエポキシ化反応と燃焼反応が競争的に起こっていることがわかる。従って、前者をより起こり易くするような触媒設計が今後必要となろう。また、エポキシ化反応に最も有効なスーパーオキソ種が他の吸着酸素種に移行しないようにすることも、重要な触媒設計の指針である。

表面増強ラマン散乱(SERS)とは、特定の金属表面上で吸着分子のラマン強度が通常の10^6倍も大きくなる現象である。本研究では、このSERSの電子的発現機構を量子化学的なアプローチにより解明することを目指した。
(1)遷移金属表面に吸着したCO,NO分子の電子状態:SERSの発現機構は、表面-分子間の相互作用と密接な関係があり、吸着分子の基底状態及び励起状態の電子構造が反映されると考えられる。そこで本研究では、遷移金属Ag,Pt表面に吸着したCO(下),NO(下)分子に対し、クラスターモデルを用いてHF/SE-CI法あるいはSAC/SAC-CI法によりその基底状態及び励起状態の電子構造を調べた。その結果、Ag_2,Pt_2表面にCO,NO分子が吸着している場合、クラスターの二電子励起状態と相互作用していることが示された。Ag_2表面ではその二電子励起状態はかなり不安定であり、結果として吸着安定化は得られないことがわかった。一方、Pt_2表面ではCO,NO分子ともに吸着安定化がみられた。そして、自由なCO,NO分子の最低励起エネルギーがそれぞれ8.5,5.5eV程度であるのに対し、Pt_2表面に吸着した系では2.5,1.8eVとかなり小さくなっていることが示された。これは、SERSの発現機構の一つと考えられている共鳴効果を容易にしていることを表している。一方、吸着系の電荷はCO,NOがそれぞれ+0.27,+0.31と比較的小さく、電磁気的効果は小さいことを示唆している。
(2)吸着分子のラマン散乱強度の計算:気相及び吸着CO分子のラマン散乱強度を、時間依存ハートリーフォック(TDHF)法を用いて計算した。その結果、気相CO分子では入射光が1eVから6eVに変化するにしたがって次第に増加することが示された。しかし、7eV以上では計算が発散し、この方法では解が得られなかった。同様に、吸着CO分子の場合は1eVですでに発散が起こった。そこで本研究では、中間状態の寿命に対応する項を加えた計算をし、その寿命がゼロである極限値を用いる方法を提案した。

本研究の目的は、金属及び金属酸化物からなる固体触媒、および金属クラスターの表面反応や金属錯体の触媒作用を理論的に研究し、それらの電子的過程を解析することによって、固体表面の触媒活性と反応選択性を明らかにすることである。この目的に沿って以下の研究を行った。
まず、表面一分子系を扱う理論の開発を行った。従来のクラスターモデルでは固体-吸着分子間の電子移動を十分に記述できなかった。我々は、バルク固体の中に分子を吸着したクラスターを埋め込み、バルク固体の働きをその自由電子の流入・流出で代表させるモデルーーDipped Adcluster Model(DAM)ーーを考案し、この方法が固体金属触媒を良く表現することを示した。また、固体金属表面では鏡映力(image force)という正電的相互作用が重要あることを示した。
上記の方法を用い、銀表面における酸素分子の解離吸着の電子的メカニズムを明らかにした。この反応はエチレンの部分酸化の初期過程として重要である。我々は、この反応を理論的に記述することに初めて成功した。銀表面で酸素分子は、superoxide(O2^-)とperoxide(O2^<2->)の状態でも存在し、後者が解離状態に至ることを明らかにした。さらにハロゲン分子が化学発光を伴ってアルカリ金属表面に吸着する現象を解明した。我々の方法のは、電子のHapooningと発光に電子的過程を再現した。
また、酸化亜鉛表面やリチウム金属表面での水素分子の解離吸着過程について研究した。酸化ジルコニウム表面で、水素分子が分子状と解離状に吸着することを示した。この結果は実験的示唆と良く一致している。
さらに、過マンガン酸イオンの基底状態および励起状態を詳細に解析し、この分子が光解離反応によって酸素を発生するメカニズムを理論的に明らかにした。Os-WやOs-Crといった複核金属錯体が金属ー金属間配位結合を持つことを理論的に示し、その構造や反応性を解析した。

本研究の最終目標は、インシリコ・ケミストリーの確立である。まず、それに必要な高精度な大規模計算手法を開発するため，本研究では，理論の構築，プログラムの開発，そして実践という3段階で研究を進めた。当研究室ではこれまでに，全系を部分系に分割して計算することにより計算コストを削減する手法，分割統治(DC)法に基づくHF，hybrid-DFT，MP2，CCSD法の理論および計算アルゴリズムを提案し，これら計算プログラムの開発を行ってきた。本研究では，現在標準的に用いられている計算方法のうち最も高精度なCCSD(T)にDC法を適用した(DC-CCSD(T))。また，エネルギー計算だけでなく動的分極率を計算するための計算手法にもDC法を拡張した。比較的低コストである密度汎関数理論(DFT)は，標準的な交換相関汎関数を用いる場合，分散力を記述できないという致命的な問題があった。本研究では局所応答近似に基づいて分散力を非経験的に算出するLRD法を考案し，弱い相互作用の高精度かつ効率的な計算を可能にした。また，量子化学計算に基づく分子シミュレーション手法を用いて，生体関連分子の立体構造の探索を行った。その際，当研究室で開発した分子構造の類似性の指標を用いて効率的に探索するMSMC法を用いた。

本研究の最終目標は、理論的手法に基づいた実用的分子デバイスの設計と制御である。そのために、ナノリンク分子の接合安定性と量子輸送現象を取り扱うための高精度な理論的手法の開発を目的とした。具体的には、電子および原子核の取り扱いに対する3種類のアプローチと電流に対する2種類のアプローチの融合を目指した。前者は主に量子化学理論を基盤としており、次のようなものである。第1が、Born-Oppenheimer(BO)近似により原子核の運動は分離して電子状態のみを扱う通常の分子軌道(MO)法や密度汎関数理論(DFT)などの量子化学計算である。第2は、原子核の運動を取り込むために、分子動力学(MD)法と組み合わせた方法がAIMD法である。更に、原子核の運動も量子的に扱えるものとして申請者らによるNOMO法があり、これが第3の方法である。後者は物性物理理論を基盤としておりKeldyshの摂動論に基づく非平衡グリーン関数(NEGF)法とKosovの定常電流Schr&ouml;dinger方程式(CCSE)を直接解く方法である。本年度は、第1のアプローチに関して、従来定常状態にしか適用できなかったNOMO法を時間依存形式に拡張し、原子核の量子効果を考慮したダイナミックス（量子ダイナミックス）手法の基礎を確立した。また、第2のアプローチについては、AIMDシミュレーションのボトルネックである電子状態計算の高速化手法（LI-MO,LS-MO）を開発し、従来法に比べ3～5倍の計算時間の短縮に成功した。その他、分子－電極間安定接合の検証するために、我々が先に提案したエネルギー密度解析（EDA）を周期境界条件（PBC）計算に拡張した。さらに、このPBC-EDAが、表面構造の違いによる安定性・反応性の差異を定量的に評価できることを数値的に確認することができた。

本特定課題研究では、酸化チタン表面上での光エネルギー変換及び光触媒作用の本質を分子軌道(MO)法や密度汎関数理論(DFT)などの第一原理計算手法により解明することを目指した。具体的には、 (1) 修飾された酸化チタン表面の幾何構造及び電子状態、および(2) 酸化チタン表面における光分解反応、を検討課題とした。研究テーマ(1)では、ガウス基底を用いた周期境界条件(PBC)計算によって天然に存在する酸化チタンが持つ3つの結晶構造（ルチル、アナターゼ、ブルッカイト）に電子状態を検討した。特に、各結晶構造に対してそれぞれ3種類の表面構造のPBC計算を行った。特に、これらの理論的解析において、我々が独自に開発したエネルギー密度解析(EDA)をPBC計算と組み合わせること(PBC-EDA)で、表面とバルクの違い、結晶構造および結晶表面の違いによる安定性や反応性の違いを定量的に評価することに成功した。また、酸化チタンにB, C, Sなどの半金属や非金属イオンを注入することにより、可視光領域に吸収を示すことが期待されている。そこで、酸素欠陥型TiO2-X(X=B,C,S)に対するPBC計算を行い、それらのバンド構造を検討した。特に、BおよびCの注入により、価電子帯の上部に新たに準位が生じ、結果としてバンドギャップが小さくなることが示された。研究テーマ(2)では、クラスターモデルを用いて、水、メタノール、そしてギ酸の分解反応を理論的に検討した。熱反応（基底状態）に加えて、光反応のモデルとして、イオン化したクラスターの反応性を検討した。その結果、熱反応に比べ光反応では容易に反応が進行することが確かめられた。

本特定課題研究では、分子軌道(MO)法や密度汎関数理論(DFT)などの第一原理手法を用いて、固体及びクラスター表面の触媒作用や機能発現の電子的機構を明らかにすることを目指した。さらに、第一原理計算に基づいた力場を利用して分子動力学シミュレーションを行うAIMD法により、表面反応のダイナミクスに関しても定量的な解析を目指した。具体的には、 (1)歪みシリコン表面の機能発現機構、および(2)星間分子衝突反応のダイナミクスとエネルギー移動、を当初の検討課題としていた。研究テーマ(1)では、ガウス基底を用いた周期境界条件(PBC)計算によって歪みシリコン表面の幾何構造及び電子状態を解明し、機能発現機構を理論的に検討した。特に、これらの理論的解析において、我々が独自に開発したエネルギー密度解析(EDA)をPBC計算と組み合わせること(PBC-EDA)の有効性が確かめられた。PBC-EDAの開発は、本プロジェクトと平行して行われ、まず種々のMgO表面(100)および(n10) (n=1-6)に対して応用された。そこでは、キンクやステップといった表面の各サイトの安定性や反応性を定量的に評価することに成功した。歪みシリコン表面に対しても、PBC-EDAにより歪みの影響を定量化することができた。研究テーマ(2)では、シアノラジカルとさまざまな不飽和炭化水素の衝突反応についてAIMDシミュレーションを実行し、そのダイナミクスとエネルギー移動を検討した。ここでは、上記のEDAをAIMDと組み合わせることにより、局所エネルギー変化の自己相関関数を求めることができ、さらにそれを短時間フーリエ変換(STFT)することにより化学反応におけるモード選択的なエネルギー分配のメカニズムを明らかすることができた。

本研究では、衝突や励起によって引き起こされるクラスター内部自由度の変化を理論的に評価することにより、それに伴う化学反応を解明・予測・設計することを目指した。具体的には、(1)アンモニアクラスターイオンの衝突反応と(2)ソラレン化合物のDNA光付加反応を検討した。(1)については、理研のグループにより、サイズ選別したアンモニアクラスターイオンと重水素化したアンモニアモノマーの衝突実験が報告されている。さらに、吸着および分解過程に対する反応断面積の衝突エネルギーおよびクラスターサイズ依存性も報告されている。そこで本研究では、衝突過程のAb Initio Molecular Dynamics (AIMD)シミュレーションを行い、その結果から分子衝突と化学反応性の関連を検討した。衝突反応の初期条件を変化させたトラジェクトリーを走らせ、その結果から吸着・分解・非反応性衝突・非衝突を判断した。この結果を統計処理することにより得られた反応断面積は、まずまず実験値を再現した。さらに、吸着と分解を導く場合では、衝突サイトには系統的な違いがあることが初めて示された。(2)では、乾癬などの皮膚病に対する光療法の薬として用いられるソラレン化合物を扱った。ソラレン化合物単体での励起状態ダイナミックスを調べる目的で、励起三重項状態におけるAIMDシミュレーションを行った。その結果、無置換ソラレンや5-メトキシソラレン(5-MOP)には見られなかったピロン環の開環が、8-メトキシソラレン(8-MOP)で起こることが初めて明らかとなった。この開環構造は、DNAにフラン環側で付加した場合にも見られ、2段階目の付加反応が抑制されていることがわかる。実際、DNAへのモノ付加体は治療効果があるが、ジ付加体は結合が強固なためDNAが再生されにくく副作用があると考えられている。本研究の結果を踏まえると、8-MOPは副作用という点では最も優れた薬であると判断される。

　本研究では、固体表面および金属錯体の関与する反応に対して、その触媒作用のメカニズムを理論的に解明することを目指した。固体表面に対しては、クラスターモデルによる取り扱いで問題となる、クラスターサイズ依存性に関して系統的に調べた。その結果、吸着分子の構造や振動数などは金属原子数個のクラスターを用いた計算でも収束しているが、生成熱などエネルギーは40個のクラスターを用いても収束が見られない、という興味深い結果が得られた。その原因として、クラスターを切り出したことによる不安定性が直接エネルギー計算に影響していることが示された。具体的な触媒反応としては、銅表面におけるメタノール合成を取り上げ、吸着活性種の特定、反応経路の決定、銅の触媒作用、蒸着亜鉛の助触媒効果などを検討した。特に本年度は、律速段階であるフォーメートからジオキソメチレンに至る過程を重点的に調べ、一般にその特定が困難とされる固体表面反応の遷移状態を理論的に求めることに成功した。金属錯体の関与する反応としては、Ru(II)－Sn(II)複核錯体における酢酸合成反応を検討した。本研究を通して、異種金属間結合が触媒反応に果たす多種多様な機能の解明に、理論的にはどのようなアプローチが可能かを検討することができた。

　本研究では、（1）電極表面のSTMシミュレーションを行い、正しい理解を理論的に与えること、（2）電極表面で起こる触媒反応と電子移動を理論計算により検討し、そのメカニズムの解明を目指した。テーマ（1）として、Au（111）面に吸着したSulfateに対して、吸着構造とそのSTM像を理論計算により決定することを試みた。吸着構造はon-top-site eclipse型＜hollow-site staggered型＜hollow-site eclipse型という順に安定となることがわかった。この結論は、OsawaらのSEIRASの結果とも一致している。さらに、eclipse型吸着構造についてSTM像について検討した。吸着SulfateのバンドはFermi準位付近には現われていないため、通常考えられているTipと吸着系の間のHOMO-LUMO遷移では吸着Sulfateの像は得られない。しかし、電極表面特有の遷移を考えることにより、吸着SulfateのSTM像の再現に成功した。テーマ（2）として、無電解鍍金における還元剤の酸化反応メカニズムについて検討した。その結果、ジメチルアミンボランや次亜リン酸などの還元剤については、これまで広く受け入れられてきた脱水素が先行し３配位化合物を経由するというMeerakker機構よりも、水酸基の配位が先行し５配位化合物を経由するという新たな反応機構が理論的に支持された。溶媒効果を考慮した計算結果から、還元剤が極性溶媒中では自発的に酸化されないが、バルク溶液に比べ誘電率が小さい電気二重層中では酸化されやすくなっていることが示された。さらに、析出金属の自己触媒作用により還元剤の酸化が起こりやすいことが理論的に示された。

本研究では、多自由度のプロトン・トンネリングが関係する系に対して、理論的なアプローチにより、そのメカニズムの解明を行った。具体的には、(1)置換トルエンにおける励起状態のメチル基回転障壁、(2)マロンアルデヒドにおけるプロトン・トンネリング分裂、について研究を行った。(1)では、基底(S0)および励起(S1)状態にある置換トルエンのメチル基分子内回転に対するポテンシャルカーブを分子軌道(MO)計算により求め、実験的に観測されているようなS0→S1励起に伴う回転障壁の劇的な変化を理論的に再現した。計算結果の解析より、この劇的な変化はLUMOにおける新しいタイプの超共役が原因であることが示された。このメカニズムによると、これまで明らかにされなかった置換基の位置や種類による回転障壁の変化も矛盾なく説明できることもわかった。(2)では、多自由度のプロトン・トンネリングを取り扱えるようにするために、従来のMO法に替わるNO+MO法を提案し、その理論に基づいた計算プログラムの開発を行った。本研究では、このNO+MO法を適用することにより、マロンアルデヒドのトンネリング分裂幅を理論的に予測することに成功した。特に、重水素置換することで分裂幅が1オーダー減少することが報告されているが、理論的にもこのことが再現された。また、より多くの分子をこのNO+MO法で取り扱えるように、原子核の波動関数(NO)を記述するための基底関数の開発も同時に行った。

本研究では、励起ダイナミックスおよび触媒反応の電子過程を明らかにすることを目的とした。以下に具体的な研究成果を報告する。　１．Cu/ZnO触媒によるメタノール合成反応：本研究では、清浄表面(Cu4)および亜鉛蒸着表面(Cu3Zn)上でCO2とH2からメタノールを生成する反応について理論的に調べた。その結果、 Zn-Cuに橋掛けしたフォーメート中間体の存在が確認され、安定性・反応性ともに清浄表面のものよりも有利であることがわかった。吸着フォーメートの水素化反応過程では、ジオキソメチレン中間体、メトキシ中間体を経て、メタノールが生成することがわかった。Cu表面の触媒作用やZnの助触媒効果には、種々の吸着種への多彩な電子移動が密接に関与していることが明らかとなった。　２．[V4O12]4-担持アリル－ロジウム錯体によるC-Cカップリング反応：本研究では、アリル－ロジウム錯体がC-Cカップリング反応を起してヘキサジエンを生成する過程を理論的に調べた。その結果、C-Cカップリング反応のエネルギー障壁は、アセチルアセトナート上に担持されたものに比べて、分子性酸化物[V4O12]4-上では半分程度であった。この違いは、ロジウム錯体部位への電子移動の違いに由来しており、次のような構造変化とも関係している。フリーな [V4O12]4-では、V4O4という８員環はπ共役により平面構造を有しているが、ロジウム錯体がこれに配位すると平面構造は崩れる。この崩れによりπ電子が局在化され、ロジウム錯体部位への電子移動を容易にしているのである。また、２個のロジウム錯体が配位する場合、V4O4の８員環を通した長距離相互作用によりC-Cカップリング反応をサポートしていることも明らかとなった。研究成果の発表：[1] Mechanism of the Partial Oxidation of Ethylene on an Ag Surface：Dipped Adcluster Model Study, H. Nakatsuji, H. Nakai, K. Ikeda, and Y.Yamamoto, Surf. Sci., 384, 315-333 (1997). [2] Activation of O2 on Cu, Ag, and Au Surfaces for the Epoxidation of Ethylene： Dipped Adcluster Model Study, H. Nakatsuji, Z. Hu, H. Nakai, and K. Ikeda, Surf. Sci., 387, 328-341 (1997). [3] Theoretical Study on the Catalytic Activity of Ag Surface for the Oxidation of Olefins, H. Nakatsuji, Z.M. Hu, and H. Nakai, Int. J. Quant. Chem., 65, 839-855 (1997). [4] Electronic Structures of the Ground and Excited States of Mo(CO)6：SAC-CI Calculation and Frozen Orbital Analysis, H. Morita, H. Nakai, H. Hanada, and H. Nakatsuji, Mol. Phys., 92 (3), 523-534 (1997). [5] Electronic Structures of the Ground and Excited States of MoF6 and MoOF4： SAC-CI Calculation and Frozen Orbital Analysis, H. Nakai, H. Morita, P. Tomasello, and H. Nakatsuji, J. Phys. Chem., in press (1998).

　本研究では、金属錯体の励起状態の量子化学計算から、それらを一般的に理解するための規則を見い出すことに成功した。また、励起状態のポテンシャル面の計算から、Mo(CO)6の光分解反応や白金テトラシアノエチレン錯体の光異性化反応の電子的メカニズムを解明した。ここでは、前者の研究について、その概要を報告する。　金属錯体の励起状態に関する一般則：多くの金属錯体は高い対称性を持つため、二重あるいは三重に縮退した分子軌道を持つ。それらの縮退軌道間の遷移に基づく励起状態は、複数個現われる。我々は、これら励起状態の順序や分裂幅には、一般則があることを見い出した。すなわち、「同じ主配置を持つ複数の励起状態のうち、許容遷移に相当する状態は最も高いエネルギー準位に位置し、しかも他の準位との分裂幅も最も大きい。」実際に我々は、この規則が、正四面体(Td)構造のオキソ錯体、MO4(M=Cr，Mo，Mn，Tc，Ru，Os)、正八面体(Oh)構造のMoF6やMo(CO)6などについて成り立つことを確認した。さらに、この規則は金属錯体に限らず、縮退軌道間の遷移に基づく励起状態に関する一般則であることも確認した。例えば、直線分子やD6h構造のベンゼンのpai-pai*励起状態、正20面体構造のC60やB12H122-の励起状態などである。このように、この規則が任意の分子について成り立つのは、エネルギー準位や分裂幅が分子の性質には関係なく、遷移に関係する分子軌道の重なりにのみ依存しているためである。さらに、この規則は、ちょうどHund則が同じ主配置を持つ異なるスピン状態に関するものであるのに対し、同じスピン状態内で成り立つ規則として注目に値する。