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Mathematical Formulation of the Fragment Molecular Orbital Method

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Linear-Scaling Techniques in Computational Chemistry and Physics

Part of the book series: Challenges and Advances in Computational Chemistry and Physics ((COCH,volume 13))

Abstract

The fragment molecular orbital (FMO) method is a computational scheme applied to the conventional molecular orbital theories, which reduces their scaling from N 3… N 7 to a nearly linear scaling, where N is the system size. FMO provides an accurate treatment of large molecules such as proteins and molecular clusters, and it can be efficiently parallelized to achieve high scaling on massively parallel computers. The main purpose of this chapter is to focus on the derivation of the equations and to provide a concise mathematical description of FMO. A brief summary of the recent applications of FMO is also given.

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Acknowledgments

This work was funded in part by the Next Generation SuperComputing Project, Nanoscience Program (MEXT, Japan).

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Authors and Affiliations

  1. NRI, National Institute of Advanced Industrial Science and Technology (AIST), 1-1-1 Umezono, Tsukuba, Ibaraki, 305-8568, Japan

    Takeshi Nagata & Dmitri G. Fedorov

  2. Graduate School of Pharmaceutical Sciences, Kyoto University, Sakyo-ku, Kyoto, 606-8501, Japan

    Kazuo Kitaura

  3. NRI, National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba, Ibaraki, 305-8568, Japan

    Kazuo Kitaura

Authors
  1. Takeshi Nagata
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  2. Dmitri G. Fedorov
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  3. Kazuo Kitaura
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Correspondence to Takeshi Nagata .

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Editors and Affiliations

  1. Inst. Physical & Theoretical Chemistry, Wroclaw University of Technology, Wyb. Wyspianskiego 27, Warszawa, 50-370, Poland

    Robert Zalesny

  2. Institute of Organic &, Pharmaceutical Chemistry, National Hellenic Research Foundation, Vas. Constantinou Ave. 48, Athens, 116 35, Greece

    Manthos G. Papadopoulos

  3. Dept. Chemistry, University of Saskatchewan, Saskatoon, S7N 0W0, Saskatchewan, Canada

    Paul G. Mezey

  4. Jackson State University, J. R. Lynch St. 1325, Jackson, 39217, Mississippi, USA

    Jerzy Leszczynski

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Nagata, T., Fedorov, D.G., Kitaura, K. (2011). Mathematical Formulation of the Fragment Molecular Orbital Method. In: Zalesny, R., Papadopoulos, M., Mezey, P., Leszczynski, J. (eds) Linear-Scaling Techniques in Computational Chemistry and Physics. Challenges and Advances in Computational Chemistry and Physics, vol 13. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-2853-2_2

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