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OpenFMO is an open-architecture program of fragment molecular orbital (FMO) method for massively parallel peta- and exa-scale systems. This chapter provides an overview of OpenFMO program, focusing on its latest capabilities, master-worker execution scheme, MPI+OpenMP hybrid parallelization, GPU acceleration, and benchmark performances. The latest version of OpenFMO program is available through an open-source MIT license and the most recent information, including how to download, compile, and execute it with command-line options, and several examples used as a tutorial and template for the users can be found in the OpenFMO official website, https://openfmo.org.

The parallelization of the fragment molecular orbital (FMO) method implemented in GAMESS is reviewed for Cray/Intel, IBM Blue Gene, and Fujitsu supercomputers. Various strategies for load balancing are compared. A basic OpenMP implementation of FMO is described and its parallel efficiency is reported. The two-level generalized distributed data interface is extended to an arbitrary number of levels and applied using three levels to an FMO Hessian calculation at the level of second-order Moller–Plesset (MP2) theory.

Computational costs with the use of the initial guesses formed by the divide-and-conquer approach are examined. For conventional density functional theory calculations, their computational costs rapidly increase as the system sizes increase, therefore, an efficient methodologies to construct a fine initial molecular orbital guess or a fine density matrix (DM) is quite variable in order to enhance the fast convergence. We examined the DM construction approaches by changing the subsystem buffer sizes and number of divisions, and their computational costs were numerically investigated in order to clarify their characteristic features.

Threonine synthase catalyzes the most complex reaction among the pyridoxal-5'-phosphate (PLP)-dependent enzymes. The important step is the addition of a water molecule to the Cβ-Cα double bond of the PLP-α-aminocrotonate aldimine intermediate. Transaldimination of this intermediate with Lys61 as a side reaction to form α-ketobutyrate competes with the normal addition reaction. We previously found that the phosphate ion released from the O-phospho-l-homoserine substrate plays a critical role in specifically promoting the normal reaction. In order to elucidate the detailed mechanism of this "product-assisted catalysis", we performed comparative QM/MM calculations with an exhaustive search for the lowest-energy-barrier reaction pathways starting from PLP-α-aminocrotonate aldimine intermediate. Satisfactory agreements with the experiment were obtained for the free energy profile and the UV/vis spectra when the PLP pyridine N1 was unprotonated and the phosphate ion was monoprotonated. Contrary to an earlier proposal, the base that abstracts a proton from the attacking water was the ε-amino group of Lys61 rather than the phosphate ion. Nevertheless, the phosphate ion is important for stabilizing the transition state of the normal transaldimination to form l-threonine by making a hydrogen bond with the hydroxy group of the l-threonine moiety. The absence of this interaction may account for the higher energy barrier of the side reaction, and explains the mechanism of the reaction specificity afforded by the phosphate ion product. Additionally, a new mechanism, in which a proton temporarily resides at the phenolate O3' of PLP, was proposed for the transaldimination process, a prerequisite step for the catalysis of all the PLP enzymes.

A parallel Fock matrix construction program for FMO-MO method has been developed with the distributed shared memory model. To construct a large-sized Fock matrix during FMO-MO calculations, a distributed parallel algorithm was designed to make full use of local memory to reduce communication, and was implemented on the Global Array toolkit. A benchmark calculation for a small system indicates that the parallelization efficiency of the matrix construction portion is as high as 93% at 1,024 processors. A large FMO-MO application on the epidermal growth factor receptor (EGFR) protein (17,246 atoms and 96,234 basis functions) was also carried out at the HF/6-31G level of theory, with the frontier orbitals being extracted by a Sakurai-Sugiura eigensolver. It takes 11.3 h for the FMO calculation, 49.1 h for the Fock matrix construction, and 10 min to extract 94 eigen-components on a PC cluster system using 256 processors. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010

Fragment molecular orbital (FMO) and FMO-MO (MOs of the FMO) calculations with three typical fragmentations were performed for DNA molecules with various lengths up to 40 base pairs (bps) to validate the accuracy of the total energy and the interfragment interaction energy (IFIE). The respective accuracies of the FMO energies are 5.8 × 10−5, 1.3 × 10−4, and 5.0 × 10−3 hartree/bp for large, medium, and small fragmentations with HF/STO-3G, all sufficiently satisfying chemical accuracy. Two iterative calculations of the FMO-MO methods gave sufficient accuracy as less than 6.6 × 10−5 hartree/bp even with small fragmentation. The IFIE validations showed that IFIE, even with small fragmentation, has sufficient accuracy for chemical analyses. Small fragmentation is useful for the interaction analysis, not only for the hydrogen bonding interaction of base pairs but also for the stacking interaction of bases. For analyses of DNA molecules, IFIE analysis with small fragmentation is expected to be a powerful tool. Some frontier MOs of the largest model DNA examined in this study were delocalized over multiple base pairs, which well reflected the conductivity of DNA by a coherent mechanism. Such delocalized MO cannot be obtained in terms of the usual FMO calculation. This is a typical demonstration of the advantages of the FMO-MO calculation. These fundamental data for validation of the total energy and IFIE are expected to promote FMO and FMO-MO applications to biosystems related to DNA molecules.

2,6,10-Tris[5′-(5-hexyloxyphenyl-2,2′-bithiophenyl)]-3,7,11-tris(hexyloxy)tripheneylene (2) was designed and synthesized as a π-conjugated platform to produce its tris(cationic radical) derivative (1) in a non-Kekule and nondisjoint fashion. An electrochemical study revealed the chemically reversible redox property of 2. Gaseous antimony pentachloride-doping of 2 dispersed in a polystyrene matrix gave its cationic radical. It was chemically stable with a half-life >2 weeks and displayed a triplet ground state based on an ESR measurement. A high-spin state with S = 3/2 for 1 was proved by the magnetization and magnetic susceptibility.

This paper deals with the H ∞ norm and frequency response gain analysis of sampled-data systems and provides a new approach, which we call modified fast-sample/fast-hold approximation. The new approximation approach discretizes the continuous-time generalized plant in a “γ-independent fashion” and leads to a discrete-time generalized plant with a similar structure to what is obtained by the conventional fast-sample/fast-hold approximation approach. Unlike the conventional approach, however, the modified fast-sample/fast-hold approximation approach can give both the upper and lower bounds of the H ∞ -norm and/or the frequency response gain for sampled-data systems. Furthermore, the gap between the upper and lower bounds can be bounded from above directly from the fast-sample/fast-hold parameter N and is independent of the controller. These features are quite useful when it is applied to control system design, and this study indeed has very close relation with the control system design via noncausal periodically time-varying scaling, a novel notion introduced recently.

フラグメント分子軌道（FMO）法に基づいた大規模系の分子軌道（FMO-MO）計算についての概要と、Lysozyme分子およびモデルDNA分子への適用結果を示す。FMO-MO法は、FMO計算によって得られた密度行列を基にFock行列を生成し、それを一度だけ対角化することによって近似的な分子軌道を得る方法である。本方法は巨大な分子全体に対する反復解法を行わずにすむため、従来の分子軌道法では非常に困難であった2000原子程度の大規模分子の分子軌道計算を、比較的短時間で行うことができる。また新たに開発した対角化法を用いると化学反応に重要なHOMO-LUMO付近のみの軌道エネルギーと軌道を得ることが可能であり、従来法に比較して大幅な時間短縮が可能である。Dual Opteron 246, 2GHz × 128台を用いた並列計算では、Lysozyme分子（129 アミノ酸残基, 1961 原子）と溶媒（8258原子、STO-3G 20758基底関数）に対するFMO-MO計算を、5時間程度で行うことができた。このとき、水分子の配置の仕方でHOMO-LUMOの位置が大きく変化することが確認された。また同じシステムを用いるとDNAのモデル（40核酸対、2636原子、STO-3G 10108基底関数）を1時間以内で計算可能であった。この場合、HOMOはDNAの中央に大きな振幅を持ち、LUMOはDNAの末端近くに大きな振幅を持っていた。

Steady state and laser flash photolytic experiments with precursors 6 and 11 revealed that diphenyl substitution affects the lifetime and reaction mode of cyclobutylidene. 2,2-Diphenylcyclobutylidene 3 ( τ 1 via 1,2-carbon in significant preference to the positional isomer 2 or cyclobutene 4 . On the other hand, 3,3-diphenylcyclobutylidene 5 ( τ = ca. 4 ns) gives 1,2-hydrogen shift product 4 more favorably than 1,2-carbon shift product 2 together with formal carbene dimer 14 . MRMP2//MP2 calculations afford useful results to understand the interrelationship among substitution, structure, and reactivity.

近年、分子シミュレーションのような大規模科学技術計算が盛んに行われるようになっている。特に、非経験的分子軌道法は、新素材、高性能材料、医薬品等の開発に利用されており、これからもますます発展する分野である。しかし非経験的分子軌道法に基づく分子シミュレーションは、その計算量が膨大であるために、研究者が設計したい大規模分子への適用が容易ではない。そこで我々は、「現実を反映した大規模分子系」の分子軌道計算を、「低コスト＝パーソナルユース」で実現すべく、非経験的分子軌道法による分子軌道計算を高速に実行する専用並列計算機システムの開発に取り組んでいる。本稿では、我々が開発した分子軌道計算専用並列計算機システム、および、専用計算機システムに搭載する、電子反発積分計算専用 LSIの概要を紹介する。

The dissociation energy curves of low-lying spin-mixed states for Group 5 hydrides (VH, NbH, and TaH), as well as Group 3 hydrides (ScH, YH, and LaH), have been calculated by using both effective core potential (ECP) and all-electron (AE) approaches. The two approaches are based on the multiconfiguration self-consistent field (MCSCF) method, followed by second-order configuration interaction (SOCI) calculations: the first method employs an ECP basis set proposed by Stevens and co-workers (SBKJC) augmented by a set of polarization functions, and spin−orbit coupling effects are estimated with a one-electron approximation, using effective nuclear charges. The second method employs a double-ζ basis set developed by Huzinaga (MIDI) and three sets of p functions are added to both transition element and hydrogen and one set of f functions is also added to the transition element. The relativistic elimination of small components (RESC) scheme and full Breit−Pauli Hamiltonian are employed in the AE approaches to i...

The results of a theoretical study are presented on quantum control of a chiral exchange reaction of a polyatomic molecule by using infrared laser pulses. Difluorobenzo[c]phenanthrene was chosen to be the simplest model for its helical chirality exchange reaction. This molecule has two stable configurations: M and P forms. From the viewpoint of chemical reaction dynamics, isomerization is regarded as the movement of one of the two representative points that initially correspond to the two forms to the position of the other representative point, while the other representative point remains in its initial position. The ground-state potential energy surface and dipole moment functions required to control this reaction were evaluated at the MP2/6-31+G(d,p) and MP2/TZV+(d,p) levels of molecular orbital (MO) theory. An effective potential energy surface (PES) that is a function of twisting motion of the benzene rings and wagging motion of the CF(2) group was constructed on the basis of the MO results. An analytical expression for the effective PES and that for the dipole moment functions were prepared to make the isomerization control tractable. A quantum control method in a classical way was applied to the isomerization of preoriented difluorobenzo[c]phenanthrene in low temperature limits. The time evolution of the representative point of the M form and that of the P form are separately evaluated to determine the optimal laser fields. This means that the laser control produces pure helical enantiomers from a racemic mixture. Representative points are replaced by the corresponding nuclear wave packets in this treatment. The derived control laser field consists of two linearly polarized E(x)() and E(z)() components that are perpendicular to each other. These components are pi-phase-shifted when the representative point is in the transition-state regions. Under the irradiation of this laser pulse, one of the two representative points of the isomerization is transferred to the target position along the intrinsic reaction path between the enantiomers, while the other representative point remains in its initial potential well. This results in one-way isomerization control, that is, the M(P) to P(M) form. The isomerization is completed with yields of ca. 70% within a few picoseconds. Temporal behaviors of the nuclear wave packet whose center corresponds to the representative point are drawn to see how the desired chiral exchange reaction proceeds in the presence of the control field, while its reverse process is suppressed.

Quantum control of chemical reaction dynamics in a classical way derived in a previous study [J. Chem. Phys. 113 (2000) 3510] is extended by taking into account the distribution of the classical particles. Three types of control field expression are considered. The first type is designed to control a specific particle that is initially located at the center of the distribution in phase space. The second one is designed to control an effective particle with ensemble-averaged coordinates and their conjugate momentum. The third one is obtained by averaging over the fields controlling each particle of the ensemble. These are applied to a reaction system whose potential is of a one-dimensional double well. The third type of control field significantly improves the reaction yield in the presence of a bifurcation compared with the case in which the distribution is not considered. A control field for quantum wave packet dynamics is obtained by replacing the classical ensemble-averaged position and momentum with quantum mechanically averaged ones. The reaction control is explained in terms of a quantum state-to-state transition mechanism. This is proved by analyzing the time-resolved spectrum of the control field.

A simplified approach to quantum control of chemical reaction dynamics based on a classical, local control theory was developed. The amplitude of the control pulse is proportional to the linear momentum of the reaction system within the dipole approximation for the system-radiation field interaction. The kinetic energy of the system is the controlling parameter. That is, the reaction is controlled by accelerating the representative point on a potential energy surface before crossing over a potential barrier and then by deaccelerating it to the target after passing over the potential barrier. The classical treatment was extended to control of wave packet dynamics by replacing the classical momentum by a quantum mechanically averaged momentum on the basis of the Ehrenfest theorem. The present method was applied to a quantum system of a simple one-dimensional, double-well potential for checking its validity. A restriction of the applicability of the simplified method was also discussed. An isomerization of H...

FMO-MO (Molecular orbitals (MOs) of the fragment MO (FMO) method) for (−)-epicatechin gallate were calculated to examine the dependency of the accuracy on the fragmentation patterns and on the basis set, and the results were compared to those obtained using conventional MO calculations. Results also show that the FMO-MO can be used as the initial guess in self-consistent field calculations.

Nitrous oxide (N2O), with a greenhouse effect 300 times that of CO2, is increasingly eliminated into the atmosphere. Using a hybrid quantum mechanics/molecular mechanics (QM/MM) method, we examined nitric oxide reductase-catalysed N2O formation, which includes two important chemical reactions of N–N bond formation and N–O bond cleavage. The N–N bond formation has no activation barrier, but N–O bond cleavage exhibits an activation barrier of 20.9 kcal·mol−1 at the QM/MM level. We show that the N–O bond cleavage occurs via a hyponitrous intermediate (FeB (II; s = 4/2)/N2O2 (−1; s = 1/2)/ (III; s = −1/2)), with bidentate coordination between Glu211 and a non-heme iron atom. The Glu211 coordination decreases the N–O bond cleavage energy barrier by inhibiting the formation of stable, five-membered ring intermediate (FeB–O1–N1–N2–O2–).

A theory of coherent control of reaction dynamics by pulse shaping is developed based on optimization of a linear time invariant system with complex variables. This theory is an extension of a previous control theory based on a linear time-invariant system for real variables [J. Chem. Phys., 100 (1994) 5646]. The theory is successfully applied to HCN → HNC in a one dimensional model. The isomerization takes place along a minimum energy path in which several vibrational levels below the potential barrier are selected as intermediate levels. Upper two levels of them are associated with tunneling dynamics. The effects of the tunneling dynamics on the coherent isomerization are discussed.

Toray had been developing highly-reliable hydrocarbon-based (HC) membrane for PEFC in NEDO FY2013-2014 Next Generation Project. Newly-developed HC membrane using newly-developed organic peroxide decomposition catalysts showed higher cell performance under high temperature and low humidity condition, and more than 5.2 times higher chemical durability, in comparison with the reinforced PFSA membrane NafionHPas a reference membrane. Consequently, newly-developed HCmembrane accomplished the FY2014 target of NEDO Project on both cell performance and chemical/mechanical durability. Acknowledgement: This work was partially supported by the New Energy and Industrial Technology Development Organization (NEDO) of Japan.

The unimolecular reaction dynamics of hydrogen cyanide (HCN) induced by IR multiphoton, femtosecond excitations was studied on the basis of the nuclear wavepacket theory. Both hydrogen dissociation and migration of HCN are taken into account. In evaluating the propagation of the wavepackets in the two-dimensional potential surface, position grid and eigenfunction basis sets were adopted for the dissociation and hydrogen migration coordinates, respectively. The ground state potential energy function and the dipole moment function calculated by using a MCSCF ab-initio procedure were used. Laser-intensity dependencies of the dissociation and hydrogen migration probabilities were evaluated. Effects of mode-couplings on the hydrogen migration were examined.

In molecular orbital calculations, one of the high performance applications, execution time of Fock matrix construction is approximately 99% of all execution time. We propose a communication method for a parallel Fock matrix construction program on a compact embedded cluster (called EMDC: Embedded Middle Density Cluster). The parallel Fock matrix construction program was developed on EHPC project, and EMDC has been developing for low power and small space. Network architecture (tree-base network) of EMDC conforms to parallel Fock matrix construction program. In order to communicate among the system, we developed a communication library for tree-base network. In evaluations, EMDC system achieved high parallelization efficiency (13.2 speed-up ratios at 14 nodes).

A full electron calculation for the photosynthetic reaction center of Rhodopseudomonas viridis was performed by using the fragment molecular orbital (FMO) method on a massive cluster computer. The target system contains 20,581 atoms and 77,754 electrons, which was divided into 1,398 fragments. According to the FMO prescription, the calculations of the fragments and pairs of the fragments were conducted to obtain the electronic state of the system. The calculation at RHF/6-31G* level of theory took 72.5 hours with 600 CPUs. The CPUs were grouped into several workers, to which the calculations of the fragments were dispatched. An uneven CPU grouping, where two types of workers are generated, was shown to be efficient.

One of the major cost drivers in polymer electrolyte fuel cells (PEFCs), particularly for automotive application, is the use of platinum-based electrodes to facilitate electrochemical reactions such as hydrogen oxidation and oxygen reduction. Improving the durability of Pt and PtCo alloy catalyst shall reduce total active area and/or Pt loading per unit active area without any sacrifice in performance of fuel cell stacks, and it can also significantly be beneficial to the reduction of total Pt usage on fuel cell vehicles (FCVs). Catalyst durability during fuel cell operation remains a key challenge to developing the fuel cell system with acceptable overall cost in automotive applications. Toray has been developing advanced hydrocarbon (HC) membranes to give a better total solution in terms of overall cost reduction of fuel cell systems, which includes i) the potentiality for durability improvement of Pt and PtCo alloy catalyst and Pt loading reduction due to less Pt particle dissolution, ii) no emission of super acids such as HF and perfluorosulfonic acids, iii) low gas crossover, and iv) environmental friendliness, in comparison with conventional PFSA membranes. We will describe in the meeting that Toray HC membrane would potentially improve the durability of PtCo alloy catalyst owing to less Pt particle dissolution, and thereby reduce total active area and/or Pt loading per unit active area by 45% ((1-0.24V/0.43V)x100) vs Nafion HP as a reference in case judging at 1000 hours in the accelerated chemical and mechanical durability test. We hope Toray HC membranes could help to form a pathway toward FCV wide commercialization. ACKNOWLEDGEMENT This work was partially supported by the New Energy and Industrial Technology Development Organization (NEDO) of Japan.

This paper is concerned with new discretization methods of continuous-time controllers taking account of the intersample behavior of the resulting sampled-data systems. We first state how to evaluate the controller discretization error based on the Hilbert-Schmidt norm of the sampled-data frequency response, and introduce what we call the desirable frequency response of the discretized controller. We then show that the desirable frequency response can be determined in a closed form in terms of the state-space representations of the original continuous-time controller and the frequency-domain weight. We further discuss some important properties of the desirable frequency response, whereby we propose a heuristic method for controller discretization. We further propose a more sophisticated method, and the effectiveness of these proposed methods is demonstrated by numerical examples. The relationship of the proposed methods with (as well as difference and advances from) similar existing studies are clarified from the viewpoint of the modern theory on the frequency response of sampled-data systems, and the roles and choice of the frequency-domain weight are discussed for better recovery of control performance.