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 SN2 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.affiliation: Center for Biological Resources and Informatics, Tokyo Institute of Technology, B-62 4259 Nagatsuta-cho, Midori-ku, Yokohama 226-8501, Japan.
authors.forename: Hiroya
authors.initials: H
authors.lastname: Nakata
authors.affiliation: NRI, National Institute of Advanced Industrial Science and Technology (AIST), 1-1-1 Umezono, Tsukuba, Ibaraki 305-8568, Japan.
authors.forename: Dmitri G
authors.initials: DG
authors.lastname: Fedorov
authors.affiliation: Department of Chemistry and Ames Laboratory, US-DOE, Iowa State University, Ames, Iowa 50011, USA.
authors.forename: Federico
authors.initials: F
authors.lastname: Zahariev
authors.affiliation: Department of Chemistry and Ames Laboratory, US-DOE, Iowa State University, Ames, Iowa 50011, USA.
authors.forename: Michael W
authors.initials: MW
authors.lastname: Schmidt
authors.affiliation: Graduate School of System Informatics, Kobe University, 1-1 Rokkodai-cho, Nada-ku, Kobe 657-8501, Japan.
authors.forename: Kazuo
authors.initials: K
authors.lastname: Kitaura
authors.affiliation: Department of Chemistry and Ames Laboratory, US-DOE, Iowa State University, Ames, Iowa 50011, USA.
authors.forename: Mark S
authors.initials: MS
authors.lastname: Gordon
authors.affiliation: RIKEN, Research Cluster for Innovation, Nakamura Lab, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan.
authors.forename: Shinichiro
authors.initials: S
authors.lastname: Nakamura