Three pillars for achieving quantum mechanical molecular dynamics simulations of huge systems: Divide‐and‐conquer, density‐functional tight‐binding, and massively parallel computation

The linear‐scaling divide‐and‐conquer (DC) quantum chemical methodology is applied to the density‐functional tight‐binding (DFTB) theory to develop a massively parallel program that achieves on‐the‐fly molecular reaction dynamics simulations of huge systems from scratch. The functions to perform large scale geometry optimization and molecular dynamics with DC‐DFTB potential energy surface are implemented to the program called DC‐DFTB‐K. A novel interpolation‐based algorithm is developed for parallelizing the determination of the Fermi level in the DC method. The performance of the DC‐DFTB‐K program is assessed using a laboratory computer and the K computer. Numerical tests show the high efficiency of the DC‐DFTB‐K program, a single‐point energy gradient calculation of a one‐million‐atom system is completed within 60 s using 7290 nodes of the K computer. © 2016 Wiley Periodicals, Inc.

[1]  Wieslaw Nowak,et al.  Elastic properties of single amylose chains in water: a quantum mechanical and AFM study. , 2004, Journal of the American Chemical Society.

[2]  Li,et al.  Density-matrix electronic-structure method with linear system-size scaling. , 1993, Physical review. B, Condensed matter.

[3]  Nicolas Renon,et al.  A Sparse Self-Consistent Field Algorithm and Its Parallel Implementation: Application to Density-Functional-Based Tight Binding. , 2014, Journal of chemical theory and computation.

[4]  A. V. van Duin,et al.  ReaxFF reactive force field for molecular dynamics simulations of hydrocarbon oxidation. , 2008, The journal of physical chemistry. A.

[5]  R B Gerber,et al.  Ab initio and semi-empirical Molecular Dynamics simulations of chemical reactions in isolated molecules and in clusters. , 2014, Physical chemistry chemical physics : PCCP.

[6]  Hiromi Nakai.  Themed issue: Fragment and localized orbital methods in electronic structure theory , 2012 .

[7]  Indiana University-Purdue,et al.  Theory and Applications of Computational Chemistry The First Forty Years , 2005 .

[8]  Keiji Morokuma,et al.  Modeling vibrational spectra using the self-consistent charge density-functional tight-binding method. I. Raman spectra. , 2004, The Journal of chemical physics.

[9]  V Ganesh,et al.  Molecular tailoring approach for geometry optimization of large molecules: energy evaluation and parallelization strategies. , 2006, The Journal of chemical physics.

[10]  A. V. Duin,et al.  ReaxFF: A Reactive Force Field for Hydrocarbons , 2001 .

[11]  Feng Long Gu,et al.  Elongation Method: Towards Linear Scaling for Electronic Structure of Random Polymers and other Quasilinear Materials , 2011 .

[12]  J. Tersoff,et al.  New empirical approach for the structure and energy of covalent systems. , 1988, Physical review. B, Condensed matter.

[13]  Hong Zhang,et al.  Shift‐and‐invert parallel spectral transformation eigensolver: Massively parallel performance for density‐functional based tight‐binding , 2016, J. Comput. Chem..

[14]  Shridhar R. Gadre,et al.  Molecular Tailoring: An Art of the Possible for Ab Initio Treatment of Large Molecules and Molecular Clusters , 2011 .

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

[16]  Michael Gaus,et al.  DFTB3: Extension of the self-consistent-charge density-functional tight-binding method (SCC-DFTB). , 2011, Journal of chemical theory and computation.

[17]  Takeshi Yoshikawa,et al.  Linear‐scaling self‐consistent field calculations based on divide‐and‐conquer method using resolution‐of‐identity approximation on graphical processing units , 2015, J. Comput. Chem..

[18]  T. Frauenheim,et al.  DFTB+, a sparse matrix-based implementation of the DFTB method. , 2007, The journal of physical chemistry. A.

[19]  Hao Hu,et al.  Simulating water with the self-consistent-charge density functional tight binding method: from molecular clusters to the liquid state. , 2007, The journal of physical chemistry. A.

[20]  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.

[21]  Victor Guallar,et al.  Mixed quantum mechanics and molecular mechanics methods: Looking inside proteins , 2011 .

[22]  H. Nakai,et al.  Divide-and-Conquer Approaches to Quantum Chemistry: Theory and Implementation , 2011 .

[23]  Michael A Collins.  Molecular forces, geometries, and frequencies by systematic molecular fragmentation including embedded charges. , 2014, The Journal of chemical physics.

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

[25]  Wei Li,et al.  Generalized energy-based fragmentation approach and its applications to macromolecules and molecular aggregates. , 2014, Accounts of chemical research.

[26]  Stephan Irle,et al.  Density-Functional Tight-Binding Combined with the Fragment Molecular Orbital Method. , 2014, Journal of chemical theory and computation.

[27]  Keiji Morokuma,et al.  Systematic study of vibrational frequencies calculated with the self‐consistent charge density functional tight‐binding method , 2004, J. Comput. Chem..

[28]  D. Brenner,et al.  Empirical potential for hydrocarbons for use in simulating the chemical vapor deposition of diamond films. , 1990, Physical review. B, Condensed matter.

[29]  Ying Wang,et al.  Atomistic Mechanism of Carbon Nanostructure Self-Assembly as Predicted by Nonequilibrium QM/MD Simulations , 2012 .

[30]  D R Bowler,et al.  Atomic force algorithms in density functional theory electronic-structure techniques based on local orbitals. , 2004, The Journal of chemical physics.

[31]  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.

[32]  S. Goedecker.  Linear scaling electronic structure methods , 1999 .

[33]  D. Bowler,et al.  O(N) methods in electronic structure calculations. , 2011, Reports on progress in physics. Physical Society.

[34]  Sándor Suhai,et al.  Self-consistent-charge density-functional tight-binding method for simulations of complex materials properties , 1998 .

[35]  Tai-Sung Lee,et al.  A variational linear-scaling framework to build practical, efficient next-generation orbital-based quantum force fields. , 2013, Journal of chemical theory and computation.

[36]  Masato Kobayashi,et al.  Second-order Møller–Plesset perturbation (MP2) theory at finite temperature: relation with Surján’s density matrix MP2 and its application to linear-scaling divide-and-conquer method , 2015, Theoretical Chemistry Accounts.

[37]  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.

[38]  D R Bowler,et al.  Calculations for millions of atoms with density functional theory: linear scaling shows its potential , 2009, Journal of physics. Condensed matter : an Institute of Physics journal.

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

[40]  K. Morokuma,et al.  Insights into carbon nanotube and graphene formation mechanisms from molecular simulations: a review , 2015, Reports on progress in physics. Physical Society.

[41]  Hiromi Nakai,et al.  A divide-and-conquer method with approximate Fermi levels for parallel computations , 2015, Theoretical Chemistry Accounts.

[42]  Xin Li,et al.  The ONIOM method: its foundation and applications to metalloenzymes and photobiology , 2012 .

[43]  Michael A Collins,et al.  Approximate ab initio energies by systematic molecular fragmentation. , 2005, The Journal of chemical physics.

[44]  Masato Kobayashi,et al.  Implementation of divide‐and‐conquer method including Hartree‐Fock exchange interaction , 2007, J. Comput. Chem..

[45]  Lichang Wang,et al.  Molecular Dynamics - Theoretical Developments and Applications in Nanotechnology and Energy , 2012 .

[46]  M Elstner,et al.  Quantum mechanics simulation of protein dynamics on long timescale , 2001, Proteins.

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

[48]  Stephan Irle,et al.  Analytical second-order geometrical derivatives of energy for the self-consistent-charge density-functional tight-binding method. , 2004, The Journal of chemical physics.

[49]  Masato Kobayashi,et al.  Divide‐and‐conquer‐based symmetry adapted cluster method: Synergistic effect of subsystem fragmentation and configuration selection , 2013 .

[50]  Henryk A. Witek,et al.  Modeling vibrational spectra using the self-consistent charge density-functional tight-binding method. I. Raman spectra , 2004 .

[51]  Yuriko Aoki,et al.  Interaction of OH− with xylan and its hydrated complexes: structures and molecular dynamics study using elongation method , 2015, Journal of Molecular Modeling.

[52]  Tsuyoshi Miyazaki,et al.  Large-scale DFT simulations with a linear-scaling DFT code CONQUEST on K-computer , 2014 .

[53]  Masato Kobayashi,et al.  Divide-and-conquer-based linear-scaling approach for traditional and renormalized coupled cluster methods with single, double, and noniterative triple excitations. , 2009, The Journal of chemical physics.

[54]  Weitao Yang,et al.  A density‐matrix divide‐and‐conquer approach for electronic structure calculations of large molecules , 1995 .

[55]  Masato Kobayashi,et al.  Reconsidering an analytical gradient expression within a divide-and-conquer self-consistent field approach: exact formula and its approximate treatment. , 2011, The Journal of chemical physics.

[56]  Masato Kobayashi,et al.  Two‐level hierarchical parallelization of second‐order Møller–plesset perturbation calculations in divide‐and‐conquer method , 2011, J. Comput. Chem..

[57]  S. Stuart,et al.  A reactive potential for hydrocarbons with intermolecular interactions , 2000 .

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

[59]  Jürg Hutter,et al.  Ab Initio Molecular Dynamics: Basic Theory and Advanced Methods , 2009 .

[60]  A. V. Duin,et al.  A Divide-and-Conquer/Cellular-Decomposition Framework for Million-to-Billion Atom Simulations of Chemical Reactions , 2007 .