Molecular Orbital Calculation for Large Molecule

Toshio WATANABEa,b, Yuichi INADOMIc, Takayoshi ISHIMOTOa,b, Hiroaki UMEDAa,b, Tetsuya SAKURAIa,b,d and Umpei NAGASHIMAa,b*

aCore Research for Evolutional Science and Technology (CREST), Japan Science and Technology Agency (JST)
Kawaguchi Center Building,4-1-8, Honcho, Kawaguchi, Saitama 332-0012 Japan
bResearch Institute for Computational Science, National Institute of Advanced Industrial Science and Technology
1-1-1 Umezono, Tsukuba, Ibaraki 305-8568, Japan
cComputing & Communications Center, Kyushu University
3-8-33-710 Momochihama, Sawara-ku, Fukuoka 814-0001 Japan
dInstitute of Information Sciences and Electronics, University of Tsukuba
1-1-1 Ten-nodai, Tsukuba, Ibaraki, Japan

(Received: June 7, 2007; Accepted for publication: July 20, 2007; Published on Web: August 30, 2007)

We have been developing a computational tool to obtain the molecular orbitals for large molecules such as proteins and molecular clusters without excessive calculation costs. In our method, the entire Fock matrix is generated using density matrix obtained from the fragment molecular orbital method, which is applicable to large systems and suitable for parallel processing. To solve the large scale generalized eigenproblem, we use the Sakurai-Sugiura method. This method solves several liner equations which have large granularity and is well suited to master-worker type execution. It is sufficient for parallel processing on computers of distributed memory parallel architecture. The method is favorable for calculation of only a small number of eigenvalues and corresponding eigenvectors of a large scale matrix. Our method has high parallelization efficiency and the communication cost is negligible to the total calculation costs. Thus, this is one of the right applications for using Grid technology.
Elapsed times to obtain MOs close to HOMO-LUMO of Lysozyme (129 amino-acid residues and solvent molecules, total 8258 atoms) with FMO/HF/STO-3G (20758 basis functions)) and model DNA (40 A-T base pairs, total 2636 atoms with FMO/HF/STO-3G (10108 basis functions)) are less than about 5 hours and 1 hour, respectively, on only 128 Dual Opteron cluster.@The position of HOMO and LUMO in the Lysozyme and water cluster case is strongly dependent on distribution and the number of solvent water molecules. Careful treatment for solvent molecules is required to have consistent results. In the case of model DNA, HOMO and LUMO are located at the center and the terminal of the DNA chain, respectively.

Keywords: Fragment Molecular Orbital method, Large scale molecule, Parallel processing, Lysozyme, Model DNA

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