Search

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.

Molecular orbital calculations of the complex between DNA-ERE (estrogen response element) and ER (estrogen receptor)-DBD (DNA-binding domain) were performed using the fragment molecular orbital (FMO) method, which enables large-scale MO (molecular orbital) calculations by reducing the computational cost and by significantly increasing efficiency for parallel computation. Such a large system, which contains 3354 atoms, is impractical via conventional MO methods due to the immense computational cost. Details of the interaction between DNA-ERE and ER-DBD were revealed in this study as follows by using the FMO calculations to analyze the interfragment interaction energies (IFIEs) and the electrostatic potentials (ESPs). An area with a high positive ESP is identified on the DNA-binding side of ER-DBD and is the main driving force behind access to the DNA. The position of the ER-DBD monomer can be fixed on a phosphate group of DNA-ERE by the strong electrostatic interactions, whereas the rotation cannot be fixed. In contrast, both the position and rotation of the ER-DBD dimer can be fixed and can therefore form the stable (ER-DBD)2...DNA-ERE complex. Dimerization of the ER-DBD monomers, each of which have a charge of +5 , is mainly due to large attractive interaction energies of the second Zn fragments. The base pairs in the consensus sequence of DNA-ERE interact only with the recognition helix located in the major groove due to the large shielding effect of the phosphate groups of DNA. The recognition helix has weaker interactions with the base pairs than the electrostatic interactions with the phosphate groups. Thus, the DNA-binding machinery of the ER-DBD dimer, which can secure the recognition helix in the major groove of DNA, is crucial for interactions between the recognition helix and base pairs.

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。

本論文では、分子軌道計算で最も時間のかかる２電子反発積分の計算を新小原法[6, 7]とVertical Recurrence Relation (VRR)[5]とHorizontal Recurrence Relation (HRR)[8]のhybridアルゴリズムをもちいた2種類のプログラムで行い、Pentium4 (3.6GHz, EM64T, 1GB L2 cache) 上で浮動小数演算数や必要クロックサイクル数などのプロセッサイベントを計測することにより、その性能を評価した。新小原法プログラムの浮動小数点演算数は、hybrid法のそれに比べ20%ほど少ないが、性能はhybrid法プログラムの方が高かった。これは、新小原法プログラムのメモリアクセス回数がhybrid法プログラムに比べ３倍ほど多く、キャッシュミスは25倍も多いことに起因する。このように浮動小数演算数が少なくても、メモリアクセスが多くなることで、計算速度が大きく低下することが分かった。したがって、2電子積分を高速に行うためには、演算数だけでなく、中間積分などを保存、利用するためのメモリアクセス数を減少させる工夫が必要である。

In this paper we consider a method for finding several eigenvalues and corresponding eigenvectors of large-scale generalized eigenvalue problems. In this method, a small matrix pencil that has only the desired eigenvalues is derived using complex moments obtained via numerical integration. Since the process to derive the moments can be performed in parallel and we do not need to exchange data between processes, the presented method is suitable for master-worker programming models. We have implemented and tested the proposed method in a grid RPC (remote procedure call) system. Numerical examples illustrate the properties of our approach. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

A quantum molecular simulation method applicable to biological molecules is proposed. Ab initio fragment molecular orbital method-based molecular dynamics (FMO-MD) combines molecular dynamics simulation with the ab initio fragment molecular orbital method. Here, FMO computes the force acting on each atom’s nucleus while MD computes the nuclei’s time-dependent evolutions. FMO-MD successfully simulated a small polypeptide, demonstrating the method’s applicability to biological molecules.

We propose an explicit definition of molecular orbitals in the fragment molecular orbital (FMO) method. We evaluated the accuracy of this method by using a conventional MO method and the FMO method to compare the calculated molecular orbitals and their orbital energies for four poly glycine molecules. These comparisons show that the molecular orbitals and their orbital energies calculated with the FMO method are within about 1% difference of those calculated with the conventional method. Therefore, the molecular orbitals calculated with the FMO method can be used for accurate calculations of chemical properties of large molecules.

2進数における循環小数である10進数の0.1を109回逐次加えるプログラムと104回の部分和をとり、これを105回加え最終的に109回加えるプログラムを作成し、メッセージ通信ライブラリMPIを用いてプログラムの並列化を行った。これらプログラムをAlta Technology AltaCluster、Hitachi SR8000、IBM RS/6000 SP、SGI Origin2000の計4種類の並列計算機を用いて8CPUまでの実行速度および計算精度の評価を行った。その結果、通信量が演算量に比べて小さいため、いずれの並列計算機でもほぼCPU数に応じた高速化が図ることができた。また、計算精度はそれぞれのプログラムとも4つの並列計算機で全く同一であった。逐次加えていく場合は、情報落ちにより正確な解が得られないが、並列化により精度向上が観測された。104回の部分和を加える場合は、逐次計算でも正しい解が得られるが、並列処理によりわずかな精度劣化が見られた。

Ab initio MO GB theory which includes the continuum model of solvent effect using generalized Born formula has been applied to the dimerization reaction of HCN in aqueous solution which is the starting step in prebiotic synthesis of purine precursors from aqueous hydrogen cyanide. Three steps considered were: (i) the reaction of HCN and H 2 O to produce the CN − anion, (ii) the reaction of CN − with HCN to give the NC–CHN − anion, and (iii) the addition of a proton to the anion to give iminoacetonitrile. The formation of CN − ion from HCN in aqueous solution requires 15.1 kcal/mol (the experimental value estimated from the dissociation constant of HCN in water is 14.8 kcal/mol). The reaction of CN − with HCN requires the activation energy of 32.2 kcal/mol (MP2/6-31++G ∗∗ //HF/6-31++G ∗∗ ) to give the dimer. This barrier height is reduced to 26.1 kcal/mol when HCN is associated with H 3 O + . In the presence of NH 3 in aqueous solution, CN − is produced easily by the reaction of HCN and NH 3 with a low activation energy of 4.3 kcal/mol. It was shown that the formation of CN − becomes easier in ammoniacal solution, and the dimerization occurs efficiently in aqueous solutions which contain NH 3 .

Ab initio RHF and ROHF methods including solvent effects based on the generalized Born formula (GB) were applied to a typical push–pull azobenzene, 4-(dimethylamino)-4′-nitroazobenzene (DMANAB), and the solvent effect on the inversion and rotation mechanisms of thermal cis – trans isomerization of DMANAB was examined. The pull-group inversion path was more favorable than the push-group one in the gas phase and in solution, and the calculated activation energies were compared well with experimental values. Analysis of two-dimensional potential energy map and electron configurations of the transition states indicated that the transition state of the rotation path, if it exists, resembles closely to that of the inversion path, and it is unlikely that both transition states are found separately in the potential energy surface of the closed-shell electronic state. Although large stabilization by solvent was expected for the rotation transition state, searching for such a transition state on the closed-shell electronic state gave the inversion transition state even in polar solvent. The transition state for the rotation path in the diradical electronic state was calculated to be comparable in terms of energy to the transition state for the pull-group inversion path in the closed-shell electronic state.

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.

The fragmentation pattern dependence of the total energy and atomic charge difference between the fragment MO method and conventional ab initio Hartree–Fock SCF-MO method (HFMO) was investigated us...

Geometry optimizations at the UHF/6-31G* and UMP2/6-31G* levels of theory were performed to find the transition state in the interconversion between norbornadiene (N) and quadricyclane (Q) radical cations. Two transition structures, TS + · 1 and TS + · 2 , were obtained which have C1 and C2 symmetry, respectively. Vibrational analysis at the UHF and UMP2 levels of theory and IRC calculation showed that TS + · 1 is the true transition state connecting N+· and Q+·, while TS + · 2 is a second order saddle point.

Geometrical optimizations for the radical cation of 1,3,5-cycloheptatriene (CHT+) were performed at different levels of theory, UHF, UMP2, CASSCF and DFT/B3LYP, with the 6–31G(d) basis set. In all cases, planar structures with the C2ν symmetry were obtained. Vibrational analyses showed that the C2ν planar structure is at a local minimum and not very rigid for the ring inversion. Using the optimized structure, the hyperfine coupling constants for hydrogen atoms in CHT+ were calculated and were compared with the experimental values. The UHF and UMP2 calculations failed to predict the hyperfine coupling constants (hfcc) correctly, while DFT hfcc agreed well with experiments.

Hemi-π-bond properties of the sulfursulfur bond in organodisulfide radical cations of 1,2-dithietane ( 1 ), 1,2-dithiolane ( 2 ), and 1,2-dithiete ( 3 ) were examined by ab initio MO calculations. The UHF/MIDI-4(d) calculations predicted that 1 + and 2 + have a two-center three-electron π-bonding character between the sulfur atoms, while the π-anti-bonding character is dominant in the SS bond of 3 + .

Various processor architectures have been proposed until today, and the performance has improved remarkably. Recently, the Chip Multi‐processors (CMPs), which has many processor cores onto a chip, are proposed for further performance improvement. The Cell processor is one of such CMP and shows high computational performance. Although this processor is designed for the multimedia, that high performance character can be utilized to molecular orbital calculation. In this study we implemented Fock matrix construction program on the Cell processor, and evaluated computational performance. As a result, there were two kinds of main stalls by the branch prediction and the data alignment, which are controlled by software mechanism for the simplification of the Cell processor hardware. It is possible to improve the performance about 30%, if the branch prediction hit ratio could be improved to 99%. For data alignment stall, a part of stalls, which is originated by data shuffle pipeline, could be decreased by prepari...

A program package for molecular simulations of biological molecules was developed. The package, "PEACH version 4 with ABINIT-MP version 20021029," was constructed by incorporating ABINIT-MP, a program for the fragment molecular orbital (FMO) method [Chem.Phys. Lett. 313 (1999) 701], into PEACH, a program package for classical molecular dynamics simulations (MD). A few capabilities of the package were demonstrated. First, high parallel efficiency of FMO was demonstrated in a single point calculation of a protein. Second,FMO-MD simulations [Chem. Phys. Lett. 372 (2003) 342] of a peptide were performed with and without explicit solvent, and the simulations showed the influence of the solvent on the electronic state of the peptide.