Importance of Three-Body Interactions in Molecular Dynamics Simulations of Water Demonstrated with the Fragment Molecular Orbital Method.

The analytic first derivative with respect to nuclear coordinates is formulated and implemented in the framework of the three-body fragment molecular orbital (FMO) method. The gradient has been derived and implemented for restricted second-order Møller-Plesset perturbation theory, as well as for both restricted and unrestricted Hartree-Fock and density functional theory. The importance of the three-body fully analytic gradient is illustrated through the failure of the two-body FMO method during molecular dynamics simulations of a small water cluster. The parallel implementation of the fragment molecular orbital method, its parallel efficiency, and its scalability on the Blue Gene/Q architecture up to 262,144 CPU cores are also discussed.

[1]  Clemens C. J. Roothaan,et al.  New Developments in Molecular Orbital Theory , 1951 .

[2]  K. Kitaura,et al.  Derivatives of the approximated electrostatic potentials in unrestricted Hartree–Fock based on the fragment molecular orbital method and an application to polymer radicals , 2014, Theoretical Chemistry Accounts.

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

[4]  Mark S. Gordon,et al.  Approximate second order method for orbital optimization of SCF and MCSCF wavefunctions , 1997 .

[5]  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.

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

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

[8]  S. Hirata,et al.  Second-order many-body perturbation and coupled-cluster singles and doubles study of ice VIII. , 2014, The Journal of chemical physics.

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

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

[11]  Kenneth M Merz,et al.  Divide-and-Conquer Hartree-Fock Calculations on Proteins. , 2010, Journal of chemical theory and computation.

[12]  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.

[13]  S. Xantheas,et al.  Development of transferable interaction models for water. I. Prominent features of the water dimer potential energy surface , 2002 .

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

[15]  Spencer R Pruitt,et al.  Hexamers and witchamers: Which hex do you choose? , 2013 .

[16]  M. Gordon,et al.  Accurate first principles model potentials for intermolecular interactions. , 2013, Annual review of physical chemistry.

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

[18]  Michael A Collins,et al.  Systematic fragmentation of large molecules by annihilation. , 2012, Physical chemistry chemical physics : PCCP.

[19]  T. Exner,et al.  Toward the Quantum Chemical Calculation of NMR Chemical Shifts of Proteins. 2. Level of Theory, Basis Set, and Solvents Model Dependence. , 2012, Journal of chemical theory and computation.

[20]  Robert J. Harrison,et al.  Development of transferable interaction models for water. II. Accurate energetics of the first few water clusters from first principles , 2002 .

[21]  Michael W. Schmidt,et al.  Efficient molecular dynamics simulations of multiple radical center systems based on the fragment molecular orbital method. , 2014, The journal of physical chemistry. A.

[22]  W. Kohn,et al.  Self-Consistent Equations Including Exchange and Correlation Effects , 1965 .

[23]  Gregory S. Tschumper,et al.  CCSD(T) complete basis set limit relative energies for low-lying water hexamer structures. , 2009, The journal of physical chemistry. A.

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

[25]  H. C. Andersen.  Rattle: A “velocity” version of the shake algorithm for molecular dynamics calculations , 1983 .

[26]  Mark S Gordon,et al.  The fragment molecular orbital and systematic molecular fragmentation methods applied to water clusters. , 2012, Physical chemistry chemical physics : PCCP.

[27]  So Hirata,et al.  Second-order many-body perturbation study of ice Ih. , 2012, The Journal of chemical physics.

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

[29]  Masato Kobayashi,et al.  An effective energy gradient expression for divide-and-conquer second-order Møller-Plesset perturbation theory. , 2013, The Journal of chemical physics.

[30]  J. Ladik,et al.  Investigation of the interaction between molecules at medium distances: I. SCF LCAO MO supermolecule, perturbational and mutually consistent calculations for two interacting HF and CH2O molecules , 1975 .

[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]  Peng Bai,et al.  Water 26-mers Drawn from Bulk Simulations: Benchmark Binding Energies for Unprecedentedly Large Water Clusters and Assessment of the Electrostatically Embedded Three-Body and Pairwise Additive Approximations. , 2014, The journal of physical chemistry letters.

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

[34]  J. S. Binkley,et al.  Derivative studies in hartree-fock and møller-plesset theories , 2009 .

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

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

[37]  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.

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

[39]  T. Dunning,et al.  The structure of the water trimer from ab initio calculations , 1993 .

[40]  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..

[41]  Mark S Gordon,et al.  Fully Integrated Effective Fragment Molecular Orbital Method. , 2013, Journal of chemical theory and computation.

[42]  G. Schenter,et al.  A quantitative account of quantum effects in liquid water. , 2006, The Journal of chemical physics.

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

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

[45]  P. Hohenberg,et al.  Inhomogeneous Electron Gas , 1964 .

[46]  Jiali Gao,et al.  Communication: variational many-body expansion: accounting for exchange repulsion, charge delocalization, and dispersion in the fragment-based explicit polarization method. , 2012, The Journal of chemical physics.

[47]  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 .

[48]  Jiali Gao,et al.  Toward a Molecular Orbital Derived Empirical Potential for Liquid Simulations , 1997 .

[49]  Jacob Kongsted,et al.  Ligand Affinities Estimated by Quantum Chemical Calculations. , 2010, Journal of chemical theory and computation.

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

[51]  S. Bulusu,et al.  Lowest-energy structures of water clusters (H2O)11 and (H2O)13. , 2006, The journal of physical chemistry. A.

[52]  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 .

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

[54]  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.

[55]  M. Gordon,et al.  Analytic Gradient for Density Functional Theory Based on the Fragment Molecular Orbital Method. , 2014, Journal of chemical theory and computation.

[56]  Hirotoshi Mori,et al.  Theoretical Study on the Hydration Structure of Divalent Radium Ion Using Fragment Molecular Orbital–Molecular Dynamics (FMO–MD) Simulation , 2014, Journal of Solution Chemistry.

[57]  Sotiris S. Xantheas,et al.  Ab initio studies of cyclic water clusters (H2O)n, n=1–6. II. Analysis of many‐body interactions , 1994 .

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

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

[60]  S. Harvey,et al.  The flying ice cube: Velocity rescaling in molecular dynamics leads to violation of energy equipartition , 1998, J. Comput. Chem..

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

[62]  S. Hirata,et al.  Ab initio molecular crystal structures, spectra, and phase diagrams. , 2014, Accounts of chemical research.

[63]  Masato Kobayashi,et al.  Divide-and-conquer self-consistent field calculation for open-shell systems: Implementation and application , 2010 .

[64]  Lucas Visscher,et al.  Quantum-Chemical Electron Densities of Proteins and of Selected Protein Sites from Subsystem Density Functional Theory. , 2013, Journal of chemical theory and computation.

[65]  A. Stone,et al.  Contribution of Many-Body Terms to the Energy for Small Water Clusters: A Comparison of ab Initio Calculations and Accurate Model Potentials , 1997 .

[66]  Mark S Gordon,et al.  Ab initio investigation of the aqueous solvation of the nitrate ion. , 2015, Physical chemistry chemical physics : PCCP.

[67]  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.

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

[69]  M. Plesset,et al.  Note on an Approximation Treatment for Many-Electron Systems , 1934 .

[70]  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.

[71]  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.

[72]  Marat Valiev,et al.  Fast electron correlation methods for molecular clusters in the ground and excited states , 2005 .

[73]  So Hirata,et al.  Ab initio molecular dynamics of liquid water using embedded-fragment second-order many-body perturbation theory towards its accurate property prediction , 2015, Scientific Reports.

[74]  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.

[75]  Ye Mei,et al.  QUANTUM CALCULATION OF PROTEIN SOLVATION AND PROTEIN–LIGAND BINDING FREE ENERGY FOR HIV-1 PROTEASE/WATER COMPLEX , 2009 .

[76]  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..