Resolutions of the Coulomb operator: VIII. Parallel implementation using the modern programming language X10

Use of the modern parallel programming language X10 for computing long‐range Coulomb and exchange interactions is presented. By using X10, a partitioned global address space language with support for task parallelism and the explicit representation of data locality, the resolution of the Ewald operator can be parallelized in a straightforward manner including use of both intranode and internode parallelism. We evaluate four different schemes for dynamic load balancing of integral calculation using X10's work stealing runtime, and report performance results for long‐range HF energy calculation of large molecule/high quality basis running on up to 1024 cores of a high performance cluster machine. © 2014 Wiley Periodicals, Inc.

[1]  Josh Milthorpe,et al.  Resolutions of the Coulomb Operator: VII. Evaluation of Long-Range Coulomb and Exchange Matrices. , 2013, Journal of chemical theory and computation.

[2]  James R. Larus,et al.  Proceedings of the 19th ACM SIGPLAN symposium on Principles and practice of parallel programming , 2014, PPOPP 2014.

[3]  L. Greengard The Rapid Evaluation of Potential Fields in Particle Systems , 1988 .

[4]  Andrew W. Appel,et al.  An Efficient Program for Many-Body Simulation , 1983 .

[5]  David E. Bernholdt,et al.  Programmability of the HPCS Languages: A case study with a quantum chemistry kernel , 2008, 2008 IEEE International Symposium on Parallel and Distributed Processing.

[6]  I Røeggen,et al.  Cholesky decomposition of the two-electron integral matrix in electronic structure calculations. , 2008, The Journal of chemical physics.

[7]  Peter M W Gill,et al.  Resolutions of the Coulomb operator. , 2007, The Journal of chemical physics.

[8]  Peter M W Gill,et al.  Resolutions of the Coulomb operator. Part III. Reduced-rank Schrödinger equations. , 2009, Physical chemistry chemical physics : PCCP.

[9]  Peter M W Gill,et al.  Resolutions of the Coulomb Operator: V. The Long-Range Ewald Operator. , 2011, Journal of chemical theory and computation.

[10]  Martin Head-Gordon,et al.  Scaled opposite spin second order Møller-Plesset theory with improved physical description of long-range dispersion interactions. , 2005, The journal of physical chemistry. A.

[11]  Henrik Koch,et al.  Method specific Cholesky decomposition: coulomb and exchange energies. , 2008, The Journal of chemical physics.

[12]  Artur F Izmaylov,et al.  Influence of the exchange screening parameter on the performance of screened hybrid functionals. , 2006, The Journal of chemical physics.

[13]  David E. Bernholdt,et al.  Programmability of the HPCS Languages: A Case Study with a Quantum Chemistry Kernel (Extended Version) , 2008 .

[14]  Edward N Brothers,et al.  Accurate solid-state band gaps via screened hybrid electronic structure calculations. , 2008, The Journal of chemical physics.

[15]  N. Handy,et al.  A new hybrid exchange–correlation functional using the Coulomb-attenuating method (CAM-B3LYP) , 2004 .

[16]  G. Scuseria,et al.  Hybrid functionals based on a screened Coulomb potential , 2003 .

[17]  Takao Tsuneda,et al.  Long-range corrected density functional study on weakly bound systems: balanced descriptions of various types of molecular interactions. , 2007, The Journal of chemical physics.

[18]  J. L. Whitten,et al.  Coulombic potential energy integrals and approximations , 1973 .

[19]  S. A. Dodds,et al.  Chemical Physics , 1877, Nature.

[20]  Martin W. Feyereisen,et al.  Use of approximate integrals in ab initio theory. An application in MP2 energy calculations , 1993 .

[21]  Taweetham Limpanuparb,et al.  Applications of Resolutions of the Coulomb Operator in Quantum Chemistry , 2012 .

[22]  Ivan S Ufimtsev,et al.  Quantum Chemistry on Graphical Processing Units. 1. Strategies for Two-Electron Integral Evaluation. , 2008, Journal of chemical theory and computation.

[23]  Thomas Bondo Pedersen,et al.  Reduced scaling in electronic structure calculations using Cholesky decompositions , 2003 .

[24]  J. Almlöf,et al.  Integral approximations for LCAO-SCF calculations , 1993 .

[25]  Stephen W. Taylor,et al.  OPTIMAL PARTITION OF THE COULOMB OPERATOR , 1997 .

[26]  Evert Jan Baerends,et al.  Self-consistent molecular Hartree—Fock—Slater calculations I. The computational procedure , 1973 .

[27]  Michael J Frisch,et al.  Efficient evaluation of short-range Hartree-Fock exchange in large molecules and periodic systems. , 2006, The Journal of chemical physics.

[28]  Peter M W Gill,et al.  Resolutions of the Coulomb Operator: IV. The Spherical Bessel Quasi-Resolution. , 2011, Journal of chemical theory and computation.

[29]  G. G. Stokes "J." , 1890, The New Yale Book of Quotations.

[30]  Peter M W Gill,et al.  Resolutions of the Coulomb operator. VI. Computation of auxiliary integrals. , 2011, The Journal of chemical physics.

[31]  Ross D. Adamson,et al.  Efficient calculation of short‐range Coulomb energies , 1999 .

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

[33]  Roland Lindh,et al.  Atomic Cholesky decompositions: a route to unbiased auxiliary basis sets for density fitting approximation with tunable accuracy and efficiency. , 2009, The Journal of chemical physics.

[34]  Stephen W. Taylor,et al.  KWIK: Coulomb Energies in O(N) Work , 1996 .

[35]  Marco Häser,et al.  Improvements on the direct SCF method , 1989 .

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

[37]  Ross D. Adamson,et al.  Coulomb-attenuated exchange energy density functionals , 1996 .

[38]  F. Neese,et al.  Efficient, approximate and parallel Hartree–Fock and hybrid DFT calculations. A ‘chain-of-spheres’ algorithm for the Hartree–Fock exchange , 2009 .

[39]  G. Scuseria,et al.  Importance of short-range versus long-range Hartree-Fock exchange for the performance of hybrid density functionals. , 2006, The Journal of chemical physics.

[40]  Roland Lindh,et al.  Unbiased auxiliary basis sets for accurate two-electron integral approximations. , 2007, The Journal of chemical physics.

[41]  Benny G. Johnson,et al.  Linear scaling density functional calculations via the continuous fast multipole method , 1996 .

[42]  M. Head‐Gordon,et al.  Attenuated second-order Møller-Plesset perturbation theory: performance within the aug-cc-pVTZ basis. , 2013, Physical chemistry chemical physics : PCCP.

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

[44]  V. Rokhlin Rapid solution of integral equations of classical potential theory , 1985 .

[45]  Martin Head-Gordon,et al.  A Resolution-Of-The-Identity Implementation of the Local Triatomics-In-Molecules Model for Second-Order Møller-Plesset Perturbation Theory with Application to Alanine Tetrapeptide Conformational Energies. , 2005, Journal of chemical theory and computation.