3D01

グリッド技術を用いた大規模分子シミュレーションプログラムの開発
Development of a Large Scale Molecular Simulation Programfor A Large Scale Molecular Orbital Calculation
using Fragment Molecular Orbital Method and Grid Computation TechniqueUmpei Nagashimaa, Yuichi Inadomia, Hiroaki Umedaa, Toshio Watanabea, Takayoshi Ishimotoa, Tetsuya
Sakuraia,b , Tsuneo Hiranoa, Mutsumi Tomonaria,ca

Grid Technology Research Center, National Institute of Advanced Industrial Science and Technolog,, and Core

Research for Evolutional Science and Technology (CREST), Japan Science and Technology Agency (JST)bc

Department of Computer Science, Tsukuba University.

Fundamental and Environmental Res. Labs., NEC Corporation.

1. Introduction
We have been developing the computational tool to obtain the molecular orbitals for large molecules
such as proteins and molecular clusters without excessive calculation costs. The most time consuming stepof Hartree-Fock calculation is the molecular integral evaluation and Fock matrix gereration (O(n4)). The
actual cost of these steps has been reduced to O(n2~3) by the fragment molecular orbital method [1] andparallel processing technique. The cost became the same or less for Fock matrix diagonalization (O(n3)).
We have proposed FMO-MO method to obtain important MOs of large molecules cost-effectively [2].
In our method, the entire Fock matrix is generated by the technique based on the fragment molecular orbital
method, which is applicable to large systems and suitable for the parallel processing. To solve the large
scale generalized eigenproblem, we use the Sakurai-Sugiura method [3]. Because this method solves
several number of liner equation which has a large granularity and master-worker type of execution, themethod is sufficient for parallel processing on the computers of the distributed memory parallel architecture.
And the method is favorable to calculate only a small number of eigenvalues and corresponding
eigenvectors of the large scale matrix. Our method has high parallelization efficiency and thecommunication cost is negligible to the total calculation costs. Thus, this is one of the right applications forusing the Grid technology.
2. Results
Elapsed time of FMO/HF/STO-3G of Lyzozyme (129 amino-acid residues, 1961 atoms, 6005 basis
functions) and DNA model system (40 base pairs, 2636 atoms and 10108 basis functions)areshown in Table 1 where all calculation were executed on a PC cluster, AIST super-cluster system P32
consists of Opteron model 246, 2GHz x 1024 CPUs.
Total elapsed time for FMO-MO calculation of Lyzozyme is only about 17min. Since the elapsed timeof the conventional method by GAMESS is almost 1 week (7 days = ~170 hours) on a PC cluster (ItaniumII 3.06GHz x 64 CPUs), improvement of performance is more than 600 times..
Total elapsed time of DNA model is only about 56 min (~1 hour). Though the number ofbasis set of DNA is about twice of Lyzozyme, ratio of elapsed time is 3.3 times. It is suggested
that the computational cost of FMO is proportional to square of the number of basis functionsor less. Note that the computational cost of Fock matrix diagonalization of DNA model is thesame as the Lyzozyme.

Table 1 E-time (sec.) for FMO-MO calc. of Lysozyme and DNA model system on a PC cluster
consists of Opteron model 246, 2GHz x 1024 CPUs.

Lyzozyme
No. ofE-time

DNA model system

HOMO and LUMO of Lyzozyme

No. ofare depicted in Figure 1. Reaction

E-timeprocessor sec.

processor sec.

FMO calculation

544

454

640

1182

shown in the figure 1.

Fock matrix gen.

512515256

1839

HOMO and LUMO of DNA model

Fock matrix diag.

16

64

1664

system are depicted in Figure 2.

3085

Because the molecular symmetry

Total E-time1033

centers of Lyzozyme are clearly

was slightly deformed, the LUMO islocalized at the left hand side whereas
the HOMO is at the center. The
LUMO+1 is located at the right handside though LUMO+1 is not shown in
the figure 2.

This work is supported by the research
project, “Development of MO calculation
system for large molecule on Grid”,
CREST, JST. All numerical calculations
were performed on the AIST supercluster.

Figure 1. HOMO and LUMO of Lyzozyme[1] [T. Nakano, T. Kaminuma, T. Sato, K. Fukuzawa, Y. Akiyama, M. Uebayasi, and K. Kitaura, Chem. Phys. Lett., 2002, 351 , 475.
[2] Y. inadomi, T. Nakano, K. Kitaura and U. Nagashima, Chem. Phys. Lett., 2002, 364 139-.
[3] T. Sakurai and H. Sugiura, J. Comput. Appl. Math., 2003, 159 119-.

Figure 2. HOMO and LUMO of a model of DNA model consist of 40 base pairs