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Title: Analytic second derivative of the energy for density functional theory based on the three-body fragment molecular orbital method

Abstract

Analytic second derivatives of the energy with respect to nuclear coordinates have been developed for spin restricted density functional theory (DFT) based on the fragment molecular orbital method (FMO). The derivations were carried out for the three-body expansion (FMO3), and the two-body expressions can be obtained by neglecting the three-body corrections. Also, the restricted Hartree-Fock (RHF) Hessian for FMO3 can be obtained by neglecting the density-functional related terms. In both the FMO-RHF and FMO-DFT Hessians, certain terms with small magnitudes are neglected for computational efficiency. The accuracy of the FMO-DFT Hessian in terms of the Gibbs free energy is evaluated for a set of polypeptides and water clusters and found to be within 1 kcal/mol of the corresponding full (non-fragmented) ab initio calculation. The FMO-DFT method is also applied to transition states in S{sub N}2 reactions and for the computation of the IR and Raman spectra of a small Trp-cage protein (PDB: 1L2Y). Some computational timing analysis is also presented.

Authors:
 [1];  [2];  [2];  [3]; ; ;  [4];  [5];  [6]
  1. Center for Biological Resources and Informatics, Tokyo Institute of Technology, B-62 4259 Nagatsuta-cho, Midori-ku, Yokohama 226-8501 (Japan)
  2. (Japan)
  3. NRI, National Institute of Advanced Industrial Science and Technology (AIST), 1-1-1 Umezono, Tsukuba, Ibaraki 305-8568 (Japan)
  4. Department of Chemistry and Ames Laboratory, US-DOE, Iowa State University, Ames, Iowa 50011 (United States)
  5. Graduate School of System Informatics, Kobe University, 1-1 Rokkodai-cho, Nada-ku, Kobe 657-8501 (Japan)
  6. RIKEN, Research Cluster for Innovation, Nakamura Lab, 2-1 Hirosawa, Wako, Saitama 351-0198 (Japan)
Publication Date:
OSTI Identifier:
22415549
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Chemical Physics; Journal Volume: 142; Journal Issue: 12; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; CHEMICAL REACTIONS; CORRECTIONS; DENSITY FUNCTIONAL METHOD; EFFICIENCY; FREE ENTHALPY; HARTREE-FOCK METHOD; MOLECULAR ORBITAL METHOD; POLYPEPTIDES; RAMAN SPECTRA; SPIN; THREE-BODY PROBLEM; TWO-BODY PROBLEM; WATER

Citation Formats

Nakata, Hiroya, E-mail: nakata.h.ab@m.titech.ac.jp, RIKEN, Research Cluster for Innovation, Nakamura Lab, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan Society for the Promotion of Science, Kojimachi Business Center Building, 5-3-1 Kojimachi, Chiyoda-ku, Tokyo 102-0083, Fedorov, Dmitri G., E-mail: d.g.fedorov@aist.go.jp, Zahariev, Federico, Schmidt, Michael W., Gordon, Mark S., Kitaura, Kazuo, and Nakamura, Shinichiro. Analytic second derivative of the energy for density functional theory based on the three-body fragment molecular orbital method. United States: N. p., 2015. Web. doi:10.1063/1.4915068.
Nakata, Hiroya, E-mail: nakata.h.ab@m.titech.ac.jp, RIKEN, Research Cluster for Innovation, Nakamura Lab, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan Society for the Promotion of Science, Kojimachi Business Center Building, 5-3-1 Kojimachi, Chiyoda-ku, Tokyo 102-0083, Fedorov, Dmitri G., E-mail: d.g.fedorov@aist.go.jp, Zahariev, Federico, Schmidt, Michael W., Gordon, Mark S., Kitaura, Kazuo, & Nakamura, Shinichiro. Analytic second derivative of the energy for density functional theory based on the three-body fragment molecular orbital method. United States. doi:10.1063/1.4915068.
Nakata, Hiroya, E-mail: nakata.h.ab@m.titech.ac.jp, RIKEN, Research Cluster for Innovation, Nakamura Lab, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan Society for the Promotion of Science, Kojimachi Business Center Building, 5-3-1 Kojimachi, Chiyoda-ku, Tokyo 102-0083, Fedorov, Dmitri G., E-mail: d.g.fedorov@aist.go.jp, Zahariev, Federico, Schmidt, Michael W., Gordon, Mark S., Kitaura, Kazuo, and Nakamura, Shinichiro. Sat . "Analytic second derivative of the energy for density functional theory based on the three-body fragment molecular orbital method". United States. doi:10.1063/1.4915068.
@article{osti_22415549,
title = {Analytic second derivative of the energy for density functional theory based on the three-body fragment molecular orbital method},
author = {Nakata, Hiroya, E-mail: nakata.h.ab@m.titech.ac.jp and RIKEN, Research Cluster for Innovation, Nakamura Lab, 2-1 Hirosawa, Wako, Saitama 351-0198 and Japan Society for the Promotion of Science, Kojimachi Business Center Building, 5-3-1 Kojimachi, Chiyoda-ku, Tokyo 102-0083 and Fedorov, Dmitri G., E-mail: d.g.fedorov@aist.go.jp and Zahariev, Federico and Schmidt, Michael W. and Gordon, Mark S. and Kitaura, Kazuo and Nakamura, Shinichiro},
abstractNote = {Analytic second derivatives of the energy with respect to nuclear coordinates have been developed for spin restricted density functional theory (DFT) based on the fragment molecular orbital method (FMO). The derivations were carried out for the three-body expansion (FMO3), and the two-body expressions can be obtained by neglecting the three-body corrections. Also, the restricted Hartree-Fock (RHF) Hessian for FMO3 can be obtained by neglecting the density-functional related terms. In both the FMO-RHF and FMO-DFT Hessians, certain terms with small magnitudes are neglected for computational efficiency. The accuracy of the FMO-DFT Hessian in terms of the Gibbs free energy is evaluated for a set of polypeptides and water clusters and found to be within 1 kcal/mol of the corresponding full (non-fragmented) ab initio calculation. The FMO-DFT method is also applied to transition states in S{sub N}2 reactions and for the computation of the IR and Raman spectra of a small Trp-cage protein (PDB: 1L2Y). Some computational timing analysis is also presented.},
doi = {10.1063/1.4915068},
journal = {Journal of Chemical Physics},
number = 12,
volume = 142,
place = {United States},
year = {Sat Mar 28 00:00:00 EDT 2015},
month = {Sat Mar 28 00:00:00 EDT 2015}
}