Electron-correlated fragment-molecular-orbital calculations for biomolecular and nano systems.

Recent developments in the fragment molecular orbital (FMO) method for theoretical formulation, implementation, and application to nano and biomolecular systems are reviewed. The FMO method has enabled ab initio quantum-mechanical calculations for large molecular systems such as protein-ligand complexes at a reasonable computational cost in a parallelized way. There have been a wealth of application outcomes from the FMO method in the fields of biochemistry, medicinal chemistry and nanotechnology, in which the electron correlation effects play vital roles. With the aid of the advances in high-performance computing, the FMO method promises larger, faster, and more accurate simulations of biomolecular and related systems, including the descriptions of dynamical behaviors in solvent environments. The current status and future prospects of the FMO scheme are addressed in these contexts.

[1]  Takeshi Ishikawa,et al.  Ab initio fragment molecular orbital study of molecular interactions in liganded retinoid X receptor: specification of residues associated with ligand inducible information transmission. , 2008, The journal of physical chemistry. B.

[2]  Svein Saebo,et al.  Avoiding the integral storage bottleneck in LCAO calculations of electron correlation , 1989 .

[3]  Kazuo Kitaura,et al.  Fully analytic energy gradient in the fragment molecular orbital method. , 2011, The Journal of chemical physics.

[4]  T. Nakano,et al.  Fragment interaction analysis based on local MP2 , 2007 .

[5]  Masami Uebayasi,et al.  Pair interaction molecular orbital method: an approximate computational method for molecular interactions , 1999 .

[6]  B. Dijkstra,et al.  Structure and mechanism of bacterial dehalogenases: different ways to cleave a carbon-halogen bond. , 2003, Current opinion in structural biology.

[7]  A. Vallée,et al.  Peptide interactions with metal and oxide surfaces. , 2010, Accounts of chemical research.

[8]  Masato Kobayashi,et al.  Alternative linear-scaling methodology for the second-order Møller-Plesset perturbation calculation based on the divide-and-conquer method. , 2007, The Journal of chemical physics.

[9]  Kazuo Kitaura,et al.  Theoretical analysis of the intermolecular interaction effects on the excitation energy of organic pigments: solid state quinacridone. , 2008, The journal of physical chemistry. A.

[10]  U. Nagashima,et al.  Development of an ab initio MO-MD program based on fragment MO method – an attempt to analyze the fluctuation of protein , 2004 .

[11]  Analysis of solute-solvent interactions in the fragment molecular orbital method interfaced with effective fragment potentials: theory and application to a solvated griffithsin-carbohydrate complex. , 2012, The journal of physical chemistry. A.

[12]  Masato Kobayashi,et al.  Linear-scaling divide-and-conquer second-order Møller–Plesset perturbation calculation for open-shell systems: implementation and application , 2011 .

[13]  Masato Kobayashi,et al.  Second-order Møller-Plesset perturbation energy obtained from divide-and-conquer Hartree-Fock density matrix. , 2006, The Journal of chemical physics.

[14]  G. Forbes.  Molecular Dynamics , 1885, Nature.

[15]  K. Kitaura,et al.  Fragment molecular orbital method: an approximate computational method for large molecules , 1999 .

[16]  Takeshi Ishikawa,et al.  Theoretical study of the prion protein based on the fragment molecular orbital method , 2009, J. Comput. Chem..

[17]  Shigenori Tanaka,et al.  Excitation energy transfer modulated by oscillating electronic coupling of a dimeric system embedded in a molecular environment. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[18]  Yuto Komeiji,et al.  Three-body expansion and generalized dynamic fragmentation improve the fragment molecular orbital-based molecular dynamics (FMO-MD)☆ , 2010 .

[19]  Yuri Alexeev,et al.  Geometry Optimization of the Active Site of a Large System with the Fragment Molecular Orbital Method , 2011 .

[20]  Kaori Fukuzawa,et al.  Fragment molecular orbital method: use of approximate electrostatic potential , 2002 .

[21]  Mark S Gordon,et al.  Structure and dynamics of the 1-hydroxyethyl-4-amino-1,2,4-triazolium nitrate high-energy ionic liquid system. , 2012, The journal of physical chemistry. B.

[22]  Yuichi Inadomi,et al.  PEACH 4 with ABINIT-MP: a general platform for classical and quantum simulations of biological molecules. , 2004, Computational biology and chemistry.

[23]  E. Starikov,et al.  Analysis of electron-transfer rate constant in condensed media with inclusion of inelastic tunneling and nuclear quantum effects. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[24]  Yuichi Inadomi,et al.  Multi-physics Extension of OpenFMO Framework , 2007, ArXiv.

[25]  Makoto Taiji,et al.  Fast and accurate molecular dynamics simulation of a protein using a special‐purpose computer , 1997 .

[26]  H. Nakai,et al.  How does it become possible to treat delocalized and/or open-shell systems in fragmentation-based linear-scaling electronic structure calculations? The case of the divide-and-conquer method. , 2012, Physical chemistry chemical physics : PCCP.

[27]  Y. Mochizuki.  Application of Dyson-corrected second-order perturbation theories , 2009 .

[28]  R. Mata,et al.  An incremental correlation approach to excited state energies based on natural transition/localized orbitals. , 2011, The Journal of chemical physics.

[29]  Dieter Cremer,et al.  Møller–Plesset perturbation theory: from small molecule methods to methods for thousands of atoms , 2011 .

[30]  Yuji Mochizuki,et al.  Configuration interaction singles method with multilayer fragment molecular orbital scheme , 2005 .

[31]  S. Grimme,et al.  A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu. , 2010, The Journal of chemical physics.

[32]  Kaori Fukuzawa,et al.  Large scale FMO-MP2 calculations on a massively parallel-vector computer , 2008 .

[33]  Zhihai Liu,et al.  Evaluation of the performance of four molecular docking programs on a diverse set of protein‐ligand complexes , 2010, J. Comput. Chem..

[34]  Kiyoshi Tanaka,et al.  Application of fragment molecular orbital scheme to silicon-containing systems , 2006 .

[35]  Martin Head-Gordon,et al.  Quadratic configuration interaction. A general technique for determining electron correlation energies , 1987 .

[36]  E. Nobusawa,et al.  Restriction of Amino Acid Change in Influenza A Virus H3HA: Comparison of Amino Acid Changes Observed in Nature and In Vitro , 2003, Journal of Virology.

[37]  Yuichi Inadomi,et al.  Fragment molecular orbital method: application to molecular dynamics simulation, ‘ab initio FMO-MD’ , 2003 .

[38]  T. Yanai,et al.  High-performance ab initio density matrix renormalization group method: applicability to large-scale multireference problems for metal compounds. , 2009, The Journal of chemical physics.

[39]  J. Tomasi,et al.  Quantum mechanical continuum solvation models. , 2005, Chemical reviews.

[40]  Shinichiro Nakamura,et al.  Analytic second derivatives of the energy in the fragment molecular orbital method. , 2013, The Journal of chemical physics.

[41]  R. Feynman,et al.  Quantum Mechanics and Path Integrals , 1965 .

[42]  T. Nakano,et al.  Examination of numerical accuracy on fragment-DFT calculations with integral values of total electron density functions , 2006 .

[43]  W. Hackbusch,et al.  Tensor representation techniques in post-Hartree–Fock methods: matrix product state tensor format , 2013 .

[44]  K. Mori,et al.  Computational Insights into Binding of Bisphosphates to Farnesyl Pyrophosphate Synthase , 2011, Current medicinal chemistry.

[45]  Kazuo Kitaura,et al.  Role of the key mutation in the selective binding of avian and human influenza hemagglutinin to sialosides revealed by quantum-mechanical calculations. , 2010, Journal of the American Chemical Society.

[46]  A Eugene DePrince,et al.  Coupled Cluster Theory on Graphics Processing Units I. The Coupled Cluster Doubles Method. , 2011, Journal of chemical theory and computation.

[47]  Hirotoshi Mori,et al.  Revised model core potentials for third-row transition–metal atoms from Lu to Hg , 2008 .

[48]  Spencer R Pruitt,et al.  Open-Shell Formulation of the Fragment Molecular Orbital Method. , 2010, Journal of chemical theory and computation.

[49]  K. Kitaura,et al.  Definition of molecular orbitals in fragment molecular orbital method , 2002 .

[50]  Kazuya Ishimura,et al.  A new parallel algorithm of MP2 energy calculations , 2006, J. Comput. Chem..

[51]  H. Sekino,et al.  Evaluation of NMR Chemical Shift by Fragment Molecular Orbital Method , 2007 .

[52]  Curtis L. Janssen,et al.  An efficient reformulation of the closed‐shell coupled cluster single and double excitation (CCSD) equations , 1988 .

[53]  Takeshi Ishikawa,et al.  Fragment Molecular Orbital method‐based Molecular Dynamics (FMO‐MD) as a simulator for chemical reactions in explicit solvation , 2009, J. Comput. Chem..

[54]  Mark S. Gordon,et al.  Accurate methods for large molecular systems. , 2009, The journal of physical chemistry. B.

[55]  Lou Massa,et al.  The kernel energy method of quantum mechanical approximation carried to fourth-order terms , 2008, Proceedings of the National Academy of Sciences.

[56]  Claus Ehrhardt,et al.  The coupled pair functional (CPF). A size consistent modification of the CI(SD) based on an energy functional , 1985 .

[57]  D. Truhlar,et al.  The M06 suite of density functionals for main group thermochemistry, thermochemical kinetics, noncovalent interactions, excited states, and transition elements: two new functionals and systematic testing of four M06-class functionals and 12 other functionals , 2008 .

[58]  S. Whitney,et al.  Manipulating ribulose bisphosphate carboxylase/oxygenase in the chloroplasts of higher plants. , 2003, Archives of biochemistry and biophysics.

[59]  Hiroshi Chuman,et al.  Correlation Analyses on Binding Affinity of Sialic Acid Analogues with Influenza Virus Neuraminidase-1 Using ab Initio MO Calculations on Their Complex Structures , 2010, J. Chem. Inf. Model..

[60]  T. Nakano,et al.  Fragment molecular orbital-based molecular dynamics (FMO-MD) simulations on hydrated Zn(II) ion , 2010 .

[61]  D. Mazziotti,et al.  Low-rank spectral expansions of two electron excitations for the acceleration of quantum chemistry calculations. , 2012, The Journal of chemical physics.

[62]  Takashi Nakamura,et al.  Roles of K151 and D180 in L‐2‐haloacid dehalogenase from Pseudomonas sp. YL: Analysis by molecular dynamics and ab initio fragment molecular orbital calculations , 2009, J. Comput. Chem..

[63]  Kazuo Kitaura,et al.  The importance of three-body terms in the fragment molecular orbital method. , 2004, The Journal of chemical physics.

[64]  P Pulay,et al.  Local Treatment of Electron Correlation , 1993 .

[65]  R. Bartlett,et al.  Many – Body Methods in Chemistry and Physics: Introduction , 2009 .

[66]  Y. Mochizuki.  A practical use of self-energy shift for the description of orbital relaxation , 2008 .

[67]  Shigenori Tanaka,et al.  Ab initio study of molecular interactions in higher plant and Galdieria partita Rubiscos with the fragment molecular orbital method. , 2007, Biochemical and biophysical research communications.

[68]  Robert M Parrish,et al.  Tensor hypercontraction density fitting. I. Quartic scaling second- and third-order Møller-Plesset perturbation theory. , 2012, The Journal of chemical physics.

[69]  J. Skehel,et al.  Structural evidence for recognition of a single epitope by two distinct antibodies , 2000, Proteins.

[70]  Manabu Oumi,et al.  A doubles correction to electronic excited states from configuration interaction in the space of single substitutions , 1994 .

[71]  T. Okamoto,et al.  A Minimal Implementation of the AMBER-PAICS Interface for Ab Initio FMO-QM/MM-MD Simulation , 2013 .

[72]  Y. Aoki,et al.  An elongation method for large systems toward bio-systems. , 2012, Physical chemistry chemical physics : PCCP.

[73]  Yuichi Inadomi,et al.  Fragment molecular orbital study of the electronic excitations in the photosynthetic reaction center of Blastochloris viridis , 2009, J. Comput. Chem..

[74]  Kaori Fukuzawa,et al.  Higher-order correlated calculations based on fragment molecular orbital scheme , 2011 .

[75]  Hiroshi Chuman,et al.  Correlation Analyses on Binding Affinity of Substituted Benzenesulfonamides with Carbonic Anhydrase Using ab Initio MO Calculations on Their Complex Structures , 2010, J. Chem. Inf. Model..

[76]  Y. Mochizuki,et al.  Modification for spin-adapted version of configuration interaction singles with perturbative doubles , 2007 .

[77]  R. Darnell,et al.  Sequence-Specific RNA Binding by a Nova KH Domain Implications for Paraneoplastic Disease and the Fragile X Syndrome , 2000, Cell.

[78]  Wei Li,et al.  A refined cluster-in-molecule local correlation approach for predicting the relative energies of large systems. , 2012, Physical chemistry chemical physics : PCCP.

[79]  Kazuo Kitaura,et al.  Multiconfiguration self-consistent-field theory based upon the fragment molecular orbital method. , 2005, The Journal of chemical physics.

[80]  K. Kitaura,et al.  Analytic gradient and molecular dynamics simulations using the fragment molecular orbital method combined with effective potentials , 2012, Theoretical Chemistry Accounts.

[81]  Shigenori Tanaka,et al.  Modern methods for theoretical physical chemistry of biopolymers , 2006 .

[82]  Mark Whittaker,et al.  Prediction of cyclin-dependent kinase 2 inhibitor potency using the fragment molecular orbital method , 2011, J. Cheminformatics.

[83]  Y. Mochizuki,et al.  Theoretical study of hydration models of trivalent rare-earth ions using model core potentials , 2010 .

[84]  Masha Sosonkina,et al.  Fragment Molecular Orbital Method Adaptations for Heterogeneous Computing Platforms , 2012, ICCS.

[85]  Martin Head-Gordon,et al.  Higher order singular value decomposition in quantum chemistry , 2010 .

[86]  Tatsuo Kurihara,et al.  Bacterial hydrolytic dehalogenases and related enzymes: occurrences, reaction mechanisms, and applications. , 2008, Chemical record.

[87]  J. Olsen,et al.  A non-linear approach to configuration interaction: The low-rank CI method (LR CI) , 1987 .

[88]  A. Pastore,et al.  Novel RNA-binding motif: the KH module. , 1999, Biopolymers.

[89]  Shigenori Tanaka,et al.  Theoretical analysis of binding specificity of influenza viral hemagglutinin to avian and human receptors based on the fragment molecular orbital method , 2008, Comput. Biol. Chem..

[90]  S. M. Rothstein,et al.  Molecular mechanics and all-electron fragment molecular orbital calculations on mutated polyglutamine peptides , 2010 .

[91]  Garnet Kin-Lic Chan,et al.  Canonical transformation theory from extended normal ordering. , 2007, The Journal of chemical physics.

[92]  Kaori Fukuzawa,et al.  Application of the fragment molecular orbital method for determination of atomic charges on polypeptides. II. Towards an improvement of force fields used for classical molecular dynamics simulations , 2009 .

[93]  K. Kitaura,et al.  Multilayer formulation of the fragment molecular orbital method (FMO). , 2005, The journal of physical chemistry. A.

[94]  Seiichiro Ten-no,et al.  Explicitly correlated wave functions: summary and perspective , 2012, Theoretical Chemistry Accounts.

[95]  M. Head‐Gordon,et al.  Long-range corrected hybrid density functionals with damped atom-atom dispersion corrections. , 2008, Physical chemistry chemical physics : PCCP.

[96]  Kohji Itoh,et al.  Correlation Analyses on Binding Affinity of Sialic Acid Analogues and Anti-Influenza Drugs with Human Neuraminidase Using ab Initio MO Calculations on Their Complex Structures - LERE-QSAR Analysis (IV) , 2011, J. Chem. Inf. Model..

[97]  Koji Ando,et al.  Fragment molecular orbital study on electron tunneling mechanisms in bacterial photosynthetic reaction center. , 2012, The journal of physical chemistry. B.

[98]  Shigenori Tanaka,et al.  Statistical correction to effective interactions in the fragment molecular orbital method , 2013 .

[99]  K. Kitaura,et al.  Energy decomposition analysis in solution based on the fragment molecular orbital method. , 2012, The journal of physical chemistry. A.

[100]  Kazuo Kitaura,et al.  Pair interaction energy decomposition analysis , 2007, J. Comput. Chem..

[101]  Shigenori Tanaka,et al.  Incorporation of solvation effects into the fragment molecular orbital calculations with the Poisson–Boltzmann equation , 2010 .

[102]  T. Nakano,et al.  An application of fragment interaction analysis based on local MP2 , 2008 .

[103]  O. Sugino,et al.  Symmetric tensor decomposition description of fermionic many-body wave functions. , 2012, Physical review letters.

[104]  Hermann Stoll,et al.  The correlation energy of crystalline silicon , 1992 .

[105]  Kaori Fukuzawa,et al.  Ab initio fragment molecular orbital study of molecular interactions between liganded retinoid X receptor and its coactivator; part II: influence of mutations in transcriptional activation function 2 activating domain core on the molecular interactions. , 2008, The journal of physical chemistry. A.

[106]  K. Kitaura,et al.  Fragment-Molecular-Orbital-Method-Based ab Initio NMR Chemical-Shift Calculations for Large Molecular Systems , 2010 .

[107]  Xiaolin Cheng,et al.  Ab initio study of molecular interactions in cellulose Iα. , 2013, The journal of physical chemistry. B.

[108]  Marcel Nooijen,et al.  pCCSD: parameterized coupled-cluster theory with single and double excitations. , 2010, The Journal of chemical physics.

[109]  Stefan Grimme,et al.  Semiempirical GGA‐type density functional constructed with a long‐range dispersion correction , 2006, J. Comput. Chem..

[110]  Robert M Parrish,et al.  Discrete variable representation in electronic structure theory: quadrature grids for least-squares tensor hypercontraction. , 2013, The Journal of chemical physics.

[111]  S. Tanaka.  Variational Quantum Monte Carlo with Inclusion of Orbital Correlations , 2013 .

[112]  Yoshihiro Matsumoto,et al.  Intrinsic Edge Asymmetry in Narrow Zigzag Hexagonal Heteroatomic Nanoribbons Causes their Subtle Uniform Curvature , 2012 .

[113]  Edward F. Valeev,et al.  Explicitly correlated R12/F12 methods for electronic structure. , 2012, Chemical reviews.

[114]  H. Hieronymus,et al.  A systems view of mRNP biology. , 2004, Genes & development.

[115]  Kaori Fukuzawa,et al.  Sialic acid recognition of the pandemic influenza 2009 H1N1 virus: binding mechanism between human receptor and influenza hemagglutinin. , 2011, Protein and peptide letters.

[116]  K. Kitaura,et al.  Systematic study of the embedding potential description in the fragment molecular orbital method. , 2010, The journal of physical chemistry. A.

[117]  Feng Xu,et al.  Fragment Molecular Orbital Molecular Dynamics with the Fully Analytic Energy Gradient. , 2012, Journal of chemical theory and computation.

[118]  Jirí Cerný,et al.  Scaled MP3 non-covalent interaction energies agree closely with accurate CCSD(T) benchmark data. , 2009, Chemphyschem : a European journal of chemical physics and physical chemistry.

[119]  K. Fujimura,et al.  The Role of Fluorine Atoms in a Fluorinated Prostaglandin Agonist , 2010, ChemMedChem.

[120]  Kiyotaka Shiba,et al.  A hexapeptide motif that electrostatically binds to the surface of titanium. , 2003, Journal of the American Chemical Society.

[121]  Y. Mochizuki.  A size-extensive modification of super-CI for orbital relaxation , 2005 .

[122]  Kazuo Kitaura,et al.  Extending the power of quantum chemistry to large systems with the fragment molecular orbital method. , 2007, The journal of physical chemistry. A.

[123]  Takeshi Ishikawa,et al.  Fragment molecular orbital calculation using the RI-MP2 method , 2009 .

[124]  Kaori Fukuzawa,et al.  Modeling of peptide–silica interaction based on four-body corrected fragment molecular orbital (FMO4) calculations , 2013 .

[125]  Yuji Mochizuki,et al.  Large scale MP2 calculations with fragment molecular orbital scheme , 2004 .

[126]  T. Nakano,et al.  Fragment molecular orbital calculations for excitation energies of blue- and yellow-fluorescent proteins , 2011 .

[127]  Kaori Fukuzawa,et al.  Accuracy of fragmentation in ab initio calculations of hydrated sodium cation , 2009 .

[128]  Kaori Fukuzawa,et al.  Large-scale FMO-MP3 calculations on the surface proteins of influenza virus, hemagglutinin (HA) and neuraminidase (NA) , 2010 .

[129]  Noriyuki Kurita,et al.  Molecular orbital analysis based on fragment molecular orbital scheme , 2003 .

[130]  Takeshi Ishikawa,et al.  Partial energy gradient based on the fragment molecular orbital method: Application to geometry optimization , 2010 .

[131]  Yutaka Akiyama,et al.  Fragment molecular orbital method: application to polypeptides , 2000 .

[132]  Frédéric H.-T. Allain,et al.  Sequence-specific binding of single-stranded RNA: is there a code for recognition? , 2006, Nucleic acids research.

[133]  T. Nakano,et al.  Dynamic polarizability calculation with fragment molecular orbital scheme , 2006 .

[134]  Mark S. Gordon,et al.  General atomic and molecular electronic structure system , 1993, J. Comput. Chem..

[135]  Yuichi Inadomi,et al.  Fragment Molecular Orbital (FMO) and FMO-MO Calculations of DNA: Accuracy Validation of Energy and Interfragment Interaction Energy , 2009 .

[136]  K. Ando,et al.  Electronic coupling calculation and pathway analysis of electron transfer reaction using ab initio fragment-based method. I. FMO-LCMO approach. , 2011, The Journal of chemical physics.

[137]  Trygve Helgaker,et al.  Ab Initio Methods for the Calculation of NMR Shielding and Indirect Spin-Spin Coupling Constants , 1999 .

[138]  Y. Aoki,et al.  Linear-scaled excited state calculations at linear response time-dependent Hartree–Fock theory , 2010 .

[139]  P. Fulde,et al.  An incremental coupled-cluster approach to metallic lithium , 2009 .

[140]  Mark S Gordon,et al.  Geometry optimizations of open-shell systems with the fragment molecular orbital method. , 2012, The journal of physical chemistry. A.

[141]  Daniel Kats,et al.  Sparse tensor framework for implementation of general local correlation methods. , 2013, The Journal of chemical physics.

[142]  Yuto Komeiji,et al.  Change in a protein's electronic structure induced by an explicit solvent: An ab initio fragment molecular orbital study of ubiquitin , 2007, J. Comput. Chem..

[143]  Kazuo Kitaura,et al.  Coupled-cluster theory based upon the fragment molecular-orbital method. , 2005, The Journal of chemical physics.

[144]  K. Kitaura,et al.  Unrestricted Hartree-Fock based on the fragment molecular orbital method: energy and its analytic gradient. , 2012, The Journal of chemical physics.

[145]  Kazuo Kitaura,et al.  Derivatives of the approximated electrostatic potentials in the fragment molecular orbital method , 2009 .

[146]  Kaori Fukuzawa,et al.  Development of the four-body corrected fragment molecular orbital (FMO4) method , 2012 .

[147]  Junwei Zhang,et al.  VISCANA: Visualized Cluster Analysis of Protein-Ligand Interaction Based on the ab Initio Fragment Molecular Orbital Method for Virtual Ligand Screening , 2006, J. Chem. Inf. Model..

[148]  Yang,et al.  Direct calculation of electron density in density-functional theory. , 1991, Physical review letters.

[149]  Shinichiro Nakamura,et al.  Octahedral point-charge model and its application to fragment molecular orbital calculations of chemical shifts , 2014 .

[150]  Alistair P. Rendell,et al.  A direct coupled cluster algorithm for massively parallel computers , 1997 .

[151]  Arieh Warshel,et al.  Simulation of enzyme reactions using valence bond force fields and other hybrid quantum/classical approaches , 1993 .

[152]  Kaori Ueno-Noto,et al.  CHEMICAL DESCRIPTION OF THE INTERACTION BETWEEN GLYCAN LIGAND AND SIGLEC-7 USING AB INITIO FMO METHOD AND CLASSICAL MD SIMULATION , 2013 .

[153]  Noriyuki Kurita,et al.  DENSITY FUNCTIONAL CALCULATIONS ON THE INTERACTION BETWEEN CATABOLITE ACTIVATOR PROTEIN AND CYCLIC AMP USING THE FRAGMENT MOLECULAR ORBITAL METHOD , 2005 .

[154]  Yuto Komeiji,et al.  FMO-MD simulations on the hydration of formaldehyde in water solution with constraint dynamics. , 2012, Chemistry.

[155]  Martin Head-Gordon,et al.  Scaled opposite-spin second order Møller-Plesset correlation energy: an economical electronic structure method. , 2004, The Journal of chemical physics.

[156]  Paulus,et al.  Electron correlations for ground-state properties of group-IV semiconductors. , 1995, Physical review. B, Condensed matter.

[157]  H. Stoll.  Can incremental expansions cope with high-order coupled-cluster contributions? , 2010 .

[158]  Mark S. Gordon,et al.  Diffusion energy profiles in silica mesoporous molecular sieves modelled with the fragment molecular orbital method , 2013 .

[159]  U. Dräger,et al.  Retinoids in embryonal development. , 2000, Physiological reviews.

[160]  Nuclear-Electronic Orbital Method within the Fragment Molecular Orbital Approach† , 2010 .

[161]  Tetsuya Sakurai,et al.  Parallel Fock matrix construction with distributed shared memory model for the FMO‐MO method , 2010, J. Comput. Chem..

[162]  Mahito Chiba,et al.  Electronic excitation energy calculation by the fragment molecular orbital method with three-body effects. , 2010, The Journal of chemical physics.

[163]  Jing Ma,et al.  Linear scaling local correlation approach for solving the coupled cluster equations of large systems , 2002, J. Comput. Chem..

[164]  Kazuo Kitaura,et al.  A combined effective fragment potential-fragment molecular orbital method. II. Analytic gradient and application to the geometry optimization of solvated tetraglycine and chignolin. , 2011, The Journal of chemical physics.

[165]  M. Klobukowski,et al.  Model potentials for molecular calculations. I. The sd‐MP set for transition metal atoms Sc through Hg , 2022 .

[166]  Y. Mochizuki,et al.  4f-in-core model core potentials for trivalent lanthanides , 2011 .

[167]  Jan H. Jensen,et al.  Covalent bond fragmentation suitable to describe solids in the fragment molecular orbital method. , 2008, The journal of physical chemistry. A.

[168]  F. Verstraete,et al.  Complete-graph tensor network states: a new fermionic wave function ansatz for molecules , 2010, 1004.5303.

[169]  Mark Whittaker,et al.  Compound Design by Fragment‐Linking , 2011, Molecular informatics.

[170]  T. Nakano,et al.  Does amination of formaldehyde proceed through a zwitterionic intermediate in water? Fragment molecular orbital molecular dynamics simulations by using constraint dynamics. , 2010, Chemistry.

[171]  Kazuo Kitaura,et al.  CHAPTER 1 – Theoretical development of the fragment molecular orbital (FMO) method , 2006 .

[172]  Yuto Komeiji,et al.  Fragment molecular orbital-based molecular dynamics (FMO-MD) method with MP2 gradient , 2011 .

[173]  Yuto Komeiji,et al.  Fragment molecular orbital method: analytical energy gradients , 2001 .

[174]  Y. Aoki,et al.  Theoretical study on static (hyper)polarizabilities for polyimide by the elongation finite-field method , 2009 .

[175]  Kenneth M Merz,et al.  Acceleration of Electron Repulsion Integral Evaluation on Graphics Processing Units via Use of Recurrence Relations. , 2013, Journal of chemical theory and computation.

[176]  P. J. Andralojc,et al.  Manipulation of Rubisco: the amount, activity, function and regulation. , 2003, Journal of experimental botany.

[177]  Umpei Nagashima,et al.  Ab Initio MO-MD Simulation Based on the Fragment MO Method. A Case of (−)-Epicatechin Gallate with STO-3G Basis Set , 2008 .

[178]  Martin Karplus,et al.  Calculation of ground and excited state potential surfaces of conjugated molecules. I. Formulation and parametrization , 1972 .

[179]  M. Shiga,et al.  Ab initio path integral Monte Carlo simulations for water trimer with electron correlation effects , 2012 .

[180]  Takeshi Ishikawa,et al.  Fragment molecular orbital calculations on large scale systems containing heavy metal atom , 2006 .

[181]  Michiel Sprik,et al.  Free energy from constrained molecular dynamics , 1998 .

[182]  Masami Uebayasi,et al.  The fragment molecular orbital method for geometry optimizations of polypeptides and proteins. , 2007, The journal of physical chemistry. A.

[183]  Kazuo Kitaura,et al.  Importance of the hybrid orbital operator derivative term for the energy gradient in the fragment molecular orbital method , 2010 .

[184]  Kotoko Nakata,et al.  Ab initio quantum mechanical study of the binding energies of human estrogen receptor α with its ligands: An application of fragment molecular orbital method , 2005, J. Comput. Chem..

[185]  A. Becke.  Density-functional thermochemistry. III. The role of exact exchange , 1993 .

[186]  Mika Ito,et al.  Ab initio quantum-chemical study on emission spectra of bioluminescent luciferases by fragment molecular orbital method , 2009 .

[187]  A. Kitao,et al.  A theoretical study of the two binding modes between lysozyme and tri-NAG with an explicit solvent model based on the fragment molecular orbital method. , 2013, Physical chemistry chemical physics : PCCP.

[188]  Kaori Fukuzawa,et al.  Counterpoise-corrected interaction energy analysis based on the fragment molecular orbital scheme , 2011 .

[189]  Kaori Fukuzawa,et al.  Fragment molecular orbital (FMO) study on stabilization mechanism of neuro-oncological ventral antigen (NOVA)–RNA complex system , 2010 .

[190]  Masato Kobayashi,et al.  Extension of linear-scaling divide-and-conquer-based correlation method to coupled cluster theory with singles and doubles excitations. , 2008, The Journal of chemical physics.

[191]  Tjerk P. Straatsma,et al.  NWChem: A comprehensive and scalable open-source solution for large scale molecular simulations , 2010, Comput. Phys. Commun..

[192]  M. Head‐Gordon,et al.  Systematic optimization of long-range corrected hybrid density functionals. , 2008, The Journal of chemical physics.

[193]  Takeshi Ishikawa,et al.  RI-MP2 Gradient Calculation of Large Molecules Using the Fragment Molecular Orbital Method. , 2012, The journal of physical chemistry letters.

[194]  G. Chan,et al.  Entangled quantum electronic wavefunctions of the Mn₄CaO₅ cluster in photosystem II. , 2013, Nature chemistry.

[195]  Takao Otsuka,et al.  Trimer effects in fragment molecular orbital-linear combination of molecular orbitals calculation of one-electron orbitals for biomolecules. , 2013, The Journal of chemical physics.

[196]  Jun Zhang,et al.  Third-Order Incremental Dual-Basis Set Zero-Buffer Approach: An Accurate and Efficient Way To Obtain CCSD and CCSD(T) Energies. , 2013, Journal of chemical theory and computation.

[197]  T. Nakano,et al.  Parallelized integral-direct CIS(D) calculations with multilayer fragment molecular orbital scheme , 2007 .

[198]  Shinichiro Nakamura,et al.  Ab initio NMR chemical shift calculations on proteins using fragment molecular orbitals with electrostatic environment , 2007 .

[199]  Kazuya Ishimura,et al.  Accuracy of the three‐body fragment molecular orbital method applied to Møller–Plesset perturbation theory , 2007, J. Comput. Chem..

[200]  Yuto Komeiji,et al.  Fragment molecular orbital-based molecular dynamics (FMO-MD), a quantum simulation tool for large molecular systems , 2009 .

[201]  D. Yamaki,et al.  The extension of the fragment molecular orbital method with the many-particle Green's function. , 2006, The Journal of chemical physics.

[202]  S. Tanaka.  Modulation of excitation energy transfer by conformational oscillations in biomolecular systems , 2011 .

[203]  Wei Li,et al.  Local correlation calculations using standard and renormalized coupled-cluster approaches. , 2009, The Journal of chemical physics.

[204]  Dick B Janssen,et al.  Bacterial degradation of xenobiotic compounds: evolution and distribution of novel enzyme activities. , 2005, Environmental microbiology.

[205]  Mark S. Gordon,et al.  The Distributed Data Interface in GAMESS , 2000 .

[206]  E. Nobusawa,et al.  Accumulation of Amino Acid Substitutions Promotes Irreversible Structural Changes in the Hemagglutinin of Human Influenza AH3 Virus during Evolution , 2005, Journal of Virology.

[207]  Mark S Gordon,et al.  Large-Scale MP2 Calculations on the Blue Gene Architecture Using the Fragment Molecular Orbital Method. , 2012, Journal of chemical theory and computation.

[208]  Kazuo Kitaura,et al.  Time-dependent density functional theory based upon the fragment molecular orbital method. , 2007, The Journal of chemical physics.

[209]  Kazuo Kitaura,et al.  Analytic gradient for second order Møller-Plesset perturbation theory with the polarizable continuum model based on the fragment molecular orbital method. , 2012, The Journal of chemical physics.

[210]  S. Miyachi,et al.  Ribulose-1,5-bisphosphate carboxylase/oxygenase from thermophilic red algae with a strong specificity for CO2 fixation. , 1997, Biochemical and biophysical research communications.

[211]  Mark S. Gordon,et al.  New Multithreaded Hybrid CPU/GPU Approach to Hartree-Fock. , 2012, Journal of chemical theory and computation.

[212]  J. V. Von Roenn,et al.  Antitumor activity of oral 9-cis-retinoic acid in HIV-associated Kaposi's sarcoma , 2002, AIDS.

[213]  R. Bartlett,et al.  Singular value decomposition approach for the approximate coupled-cluster method , 2003 .

[214]  L. Regan,et al.  Structure and function of KH domains , 2008, The FEBS journal.

[215]  Kaori Fukuzawa,et al.  Ab initio fragment molecular orbital study of molecular interactions between liganded retinoid X receptor and its coactivator: roles of helix 12 in the coactivator binding mechanism. , 2007, The journal of physical chemistry. B.

[216]  Christine M. Isborn,et al.  Excited-State Electronic Structure with Configuration Interaction Singles and Tamm–Dancoff Time-Dependent Density Functional Theory on Graphical Processing Units , 2011, Journal of chemical theory and computation.

[217]  D. Macfarlane,et al.  Large-scale ab initio calculations of archetypical ionic liquids. , 2012, Chemical communications.

[218]  Werner Kutzelnigg,et al.  How many‐body perturbation theory (MBPT) has changed quantum chemistry , 2009 .

[219]  Kaori Fukuzawa,et al.  A configuration analysis for fragment interaction , 2005 .

[220]  Hiroaki Tokiwa,et al.  Theoretical study of intramolecular interaction energies during dynamics simulations of oligopeptides by the fragment molecular orbital-Hamiltonian algorithm method. , 2005, The Journal of chemical physics.

[221]  Roland Lindh,et al.  Utilizing high performance computing for chemistry: parallel computational chemistry. , 2010, Physical chemistry chemical physics : PCCP.

[222]  Pekka Pyykkö,et al.  Relativistic effects in structural chemistry , 1988 .

[223]  S. Grimme.  Improved second-order Møller–Plesset perturbation theory by separate scaling of parallel- and antiparallel-spin pair correlation energies , 2003 .

[224]  Michael A Collins,et al.  Accuracy and efficiency of electronic energies from systematic molecular fragmentation. , 2006, The Journal of chemical physics.

[225]  M. Parrinello,et al.  AB INITIO PATH INTEGRAL MOLECULAR DYNAMICS : BASIC IDEAS , 1996 .

[226]  K. Umesono,et al.  The nuclear receptor superfamily: The second decade , 1995, Cell.

[227]  D. Jordan,et al.  Species variation in the specificity of ribulose biphosphate carboxylase/oxygenase , 1981, Nature.

[228]  Kaori Fukuzawa,et al.  Possibility of mutation prediction of influenza hemagglutinin by combination of hemadsorption experiment and quantum chemical calculation for antibody binding. , 2009, The journal of physical chemistry. B.

[229]  Spencer R Pruitt,et al.  Fragmentation methods: a route to accurate calculations on large systems. , 2012, Chemical reviews.

[230]  Yuji Mochizuki,et al.  Acceleration of fragment molecular orbital calculations with Cholesky decomposition approach , 2010 .

[231]  K. Kitaura,et al.  Mathematical Formulation of the Fragment Molecular Orbital Method , 2011 .

[232]  K. Kitaura,et al.  Analytic energy gradient for second-order Møller-Plesset perturbation theory based on the fragment molecular orbital method. , 2011, The Journal of chemical physics.

[233]  Robert M Parrish,et al.  Tensor hypercontraction. II. Least-squares renormalization. , 2012, The Journal of chemical physics.

[234]  Hui Li,et al.  Energy gradients in combined fragment molecular orbital and polarizable continuum model (FMO/PCM) calculation , 2009, J. Comput. Chem..

[235]  Heather Netzloff,et al.  Ab initio energies of nonconducting crystals by systematic fragmentation. , 2007, The Journal of chemical physics.

[236]  Daniel Kats,et al.  Communication: The distinguishable cluster approximation. , 2013, The Journal of chemical physics.

[237]  Michael J. Frisch,et al.  Toward a systematic molecular orbital theory for excited states , 1992 .

[238]  T. Sakurai,et al.  A projection method for generalized eigenvalue problems using numerical integration , 2003 .

[239]  Mark S. Gordon,et al.  A new hierarchical parallelization scheme: Generalized distributed data interface (GDDI), and an application to the fragment molecular orbital method (FMO) , 2004, J. Comput. Chem..

[240]  G. Varani,et al.  Recent advances in RNA-protein recognition. , 2001, Current opinion in structural biology.

[241]  Takeshi Ishikawa,et al.  Fragment molecular orbital calculations on red fluorescent proteins (DsRed and mFruits). , 2009, The journal of physical chemistry. B.

[242]  Kazuo Kitaura,et al.  Analytic gradient for the embedding potential with approximations in the fragment molecular orbital method , 2012 .

[243]  Kaori Fukuzawa,et al.  Application of the fragment molecular orbital method for determination of atomic charges on polypeptides , 2007 .

[244]  K. Kitaura,et al.  The Fragment Molecular Orbital–Based Time- Dependent Density Functional Theory for Excited States in Large Systems , 2009 .

[245]  Le Chang,et al.  Protein‐specific force field derived from the fragment molecular orbital method can improve protein–ligand binding interactions , 2013, J. Comput. Chem..

[246]  Yuto Komeiji,et al.  Visualization analysis of inter-fragment interaction energies of CRP-cAMP-DNA complex based on the fragment molecular orbital method. , 2007, Biophysical chemistry.

[247]  Kazuo Kitaura,et al.  Polarizable continuum model with the fragment molecular orbital‐based time‐dependent density functional theory , 2008, J. Comput. Chem..

[248]  The role of the exchange in the embedding electrostatic potential for the fragment molecular orbital method. , 2009, The Journal of chemical physics.

[249]  Nicholas J Mayhall,et al.  Many-Overlapping-Body (MOB) Expansion: A Generalized Many Body Expansion for Nondisjoint Monomers in Molecular Fragmentation Calculations of Covalent Molecules. , 2012, Journal of chemical theory and computation.

[250]  Takeshi Ishikawa,et al.  A fully quantum mechanical simulation study on the lowest n-π* state of hydrated formaldehyde , 2007 .

[251]  Low-rank configuration interaction with orbital optimization - the LR SCF approach , 1988 .

[252]  R. Bartlett,et al.  Coupled-cluster theory in quantum chemistry , 2007 .

[253]  Wei Li,et al.  Improved design of orbital domains within the cluster-in-molecule local correlation framework: single-environment cluster-in-molecule ansatz and its application to local coupled-cluster approach with singles and doubles. , 2010, The journal of physical chemistry. A.

[254]  K. Kitaura,et al.  Open-shell pair interaction energy decomposition analysis (PIEDA): formulation and application to the hydrogen abstraction in tripeptides. , 2013, The Journal of chemical physics.

[255]  Koji Yasuda,et al.  Two‐electron integral evaluation on the graphics processor unit , 2008, J. Comput. Chem..

[256]  Markus Reiher,et al.  New electron correlation theories for transition metal chemistry. , 2011, Physical chemistry chemical physics : PCCP.

[257]  Kaori Ueno-Noto,et al.  A theoretical study of the physicochemical mechanisms associated with DNA recognition modulation in artificial zinc-finger proteins. , 2011, The journal of physical chemistry. B.

[258]  Frederick R Manby,et al.  Tensor factorizations of local second-order Møller-Plesset theory. , 2010, The Journal of chemical physics.

[259]  Kaori Fukuzawa,et al.  Three- and four-body corrected fragment molecular orbital calculations with a novel subdividing fragmentation method applicable to structure-based drug design. , 2013, Journal of molecular graphics & modelling.

[260]  Takeshi Ishikawa,et al.  Fragment molecular orbital calculations on red fluorescent protein (DsRed) , 2007 .

[261]  M. Gordon,et al.  A combined effective fragment potential-fragment molecular orbital method. I. The energy expression and initial applications. , 2009, The Journal of chemical physics.

[262]  Poul Jørgensen,et al.  The divide-expand-consolidate family of coupled cluster methods: numerical illustrations using second order Møller-Plesset perturbation theory. , 2012, The Journal of chemical physics.

[263]  Kazuo Kitaura,et al.  Exploring chemistry with the fragment molecular orbital method. , 2012, Physical chemistry chemical physics : PCCP.

[264]  Umpei Nagashima,et al.  A parallelized integral-direct second-order Møller–Plesset perturbation theory method with a fragment molecular orbital scheme , 2004 .

[265]  Heather J Kulik,et al.  Ab initio quantum chemistry for protein structures. , 2012, The journal of physical chemistry. B.

[266]  J. Olsen,et al.  Linear and nonlinear response functions for an exact state and for an MCSCF state , 1985 .

[267]  Hui Li,et al.  The polarizable continuum model (PCM) interfaced with the fragment molecular orbital method (FMO) , 2006, J. Comput. Chem..

[268]  G. Voth,et al.  Multi-state Approach to Chemical Reactivity in Fragment Based Quantum Chemistry Calculations. , 2013, Journal of chemical theory and computation.

[269]  Yuri Alexeev,et al.  GAMESS as a free quantum-mechanical platform for drug research. , 2012, Current topics in medicinal chemistry.

[270]  Alán Aspuru-Guzik,et al.  Accelerating Correlated Quantum Chemistry Calculations Using Graphical Processing Units , 2010, Computing in Science & Engineering.

[271]  J. Schwabe,et al.  Mechanism of the nuclear receptor molecular switch. , 2004, Trends in biochemical sciences.

[272]  K. Kitaura,et al.  Time-dependent density functional theory with the multilayer fragment molecular orbital method , 2007 .

[273]  Shridhar R. Gadre,et al.  Molecular tailoring approach in conjunction with MP2 and Ri‐MP2 codes: A comparison with fragment molecular orbital method , 2010, J. Comput. Chem..

[274]  N. H. Beebe,et al.  Simplifications in the generation and transformation of two‐electron integrals in molecular calculations , 1977 .

[275]  Noriyuki Kurita,et al.  Fragment molecular orbital method with density functional theory and DIIS convergence acceleration , 2003 .

[276]  Kaori Fukuzawa,et al.  Prediction of probable mutations in influenza virus hemagglutinin protein based on large-scale ab initio fragment molecular orbital calculations. , 2011, Journal of molecular graphics & modelling.

[277]  Branislav Jansík,et al.  Linear scaling coupled cluster method with correlation energy based error control. , 2010, The Journal of chemical physics.

[278]  Kiyoyuki Terakura,et al.  Molecular orbital calculation of biomolecules with fragment molecular orbitals , 2009 .

[279]  M. Levitt,et al.  Theoretical studies of enzymic reactions: dielectric, electrostatic and steric stabilization of the carbonium ion in the reaction of lysozyme. , 1976, Journal of molecular biology.

[280]  R. J. Spreitzer.  Questions about the complexity of chloroplast ribulose-1,5-bisphosphate carboxylase/oxygenase , 1999, Photosynthesis Research.

[281]  Kaori Fukuzawa,et al.  Antigen–antibody interactions of influenza virus hemagglutinin revealed by the fragment molecular orbital calculation , 2011 .

[282]  Shigenori Tanaka,et al.  Intra‐ and intermolecular interactions between cyclic‐AMP receptor protein and DNA: Ab initio fragment molecular orbital study , 2006, J. Comput. Chem..

[283]  Kazuo Kitaura,et al.  Second order Møller-Plesset perturbation theory based upon the fragment molecular orbital method. , 2004, The Journal of chemical physics.

[284]  Jan H. Jensen,et al.  Analytic gradient for the adaptive frozen orbital bond detachment in the fragment molecular orbital method , 2009 .

[285]  Michio Katouda.  Application of resolution of identity approximation of second-order Møller–Plesset perturbation theory to three-body fragment molecular orbital method , 2011 .

[286]  Nicholas J Mayhall,et al.  Molecules-in-Molecules: An Extrapolated Fragment-Based Approach for Accurate Calculations on Large Molecules and Materials. , 2011, Journal of chemical theory and computation.

[287]  Michael Dolg,et al.  Implementation and performance of a domain-specific basis set incremental approach for correlation energies: applications to hydrocarbons and a glycine oligomer. , 2008, The Journal of chemical physics.

[288]  Y. Komeiji,et al.  Differences in hydration between cis- and trans-platin: Quantum insights by ab initio fragment molecular orbital-based molecular dynamics (FMO-MD) , 2012 .

[289]  Shigenori Tanaka,et al.  Ab initio Path Integral Molecular Dynamics Based on Fragment Molecular Orbital Method , 2009 .

[290]  Dmitri G. Fedorov,et al.  Reducing the scaling of the fragment molecular orbital method using the multipole method , 2012 .

[291]  Takeshi Ishikawa,et al.  How does an S(N)2 reaction take place in solution? Full ab initio MD simulations for the hydrolysis of the methyl diazonium ion. , 2008, Journal of the American Chemical Society.

[292]  Michael Dolg,et al.  Fully automated implementation of the incremental scheme: application to CCSD energies for hydrocarbons and transition metal compounds. , 2007, The Journal of chemical physics.

[293]  Feng Long Gu,et al.  Describing electron correlation effects in the framework of the elongation method—Elongation‐MP2: Formalism, implementation and efficiency , 2009, J. Comput. Chem..

[294]  Tetsuya Sakurai,et al.  A parallel eigensolver using contour integration for generalized eigenvalue problems in molecular simulation , 2010 .

[295]  Kazuo Kitaura,et al.  On the accuracy of the 3-body fragment molecular orbital method (FMO) applied to density functional theory , 2004 .

[296]  M. Reiher,et al.  Decomposition of density matrix renormalization group states into a Slater determinant basis. , 2007, The Journal of chemical physics.

[297]  Shigenori Tanaka,et al.  Fragment molecular orbital calculations under periodic boundary condition , 2011 .

[298]  Christof Hättig,et al.  Explicitly correlated electrons in molecules. , 2012, Chemical reviews.

[299]  Kazuo Kitaura,et al.  The three-body fragment molecular orbital method for accurate calculations of large systems , 2006 .

[300]  Ryo Maezono,et al.  Fragmentation Method Combined with Quantum Monte Carlo Calculations(Atomic and molecular physics) , 2007 .

[301]  Kaori Fukuzawa,et al.  Partial geometry optimization with FMO-MP2 gradient: Application to TrpCage , 2012 .

[302]  Sriram Krishnamoorthy,et al.  GPU-Based Implementations of the Noniterative Regularized-CCSD(T) Corrections: Applications to Strongly Correlated Systems. , 2011, Journal of chemical theory and computation.

[303]  Nicholas C. Handy,et al.  Size-consistent Brueckner theory limited to double substitutions , 1989 .

[304]  K. Kitaura,et al.  Excited state geometry optimizations by time-dependent density functional theory based on the fragment molecular orbital method , 2009 .

[305]  Roland Lindh,et al.  Density fitting with auxiliary basis sets from Cholesky decompositions , 2009 .