Parallel algorithm for the computation of the Hartree-Fock exchange matrix: gas phase and periodic parallel ONX.

In this paper we present an efficient parallelization of the ONX algorithm for linear computation of the Hartree-Fock exchange matrix [J. Chem. Phys. 106, 9708 (1997)]. The method used is based on the equal time (ET) partitioning recently introduced [J. Chem. Phys. 118, 9128 (2003)] and [J. Chem. Phys. 121, 6608 (2004)]. ET exploits the slow variation of the density matrix between self-consistent-field iterations to achieve load balance. The method is presented and some benchmark calculations are discussed for gas phase and periodic systems with up to 128 processors. The current parallel ONX code is able to deliver up to 77% overall efficiency for a cluster of 50 water molecules on 128 processors (2.56 processors per heavy atom) and up to 87% for a box of 64 water molecules (two processors per heavy atom) with periodic boundary conditions.

[1]  Eric Schwegler,et al.  Modern Developments in Hartree-Fock Theory: Fast Methods for Computing the Coulomb Matrix , 1996 .

[2]  David E. Manolopoulos,et al.  Canonical purification of the density matrix in electronic-structure theory , 1998 .

[3]  Eric Schwegler,et al.  Linear scaling computation of the Hartree–Fock exchange matrix , 1996 .

[4]  Eric Schwegler,et al.  Linear scaling computation of the Fock matrix. II. Rigorous bounds on exchange integrals and incremental Fock build , 1997 .

[5]  Shigeru Obara,et al.  Efficient recursive computation of molecular integrals over Cartesian Gaussian functions , 1986 .

[6]  Brendan Vastenhouw,et al.  A Two-Dimensional Data Distribution Method for Parallel Sparse Matrix-Vector Multiplication , 2005, SIAM Rev..

[7]  Gustavo E. Scuseria,et al.  Semiempirical methods with conjugate gradient density matrix search to replace diagonalization for molecular systems containing thousands of atoms , 1997 .

[8]  Mark S. Gordon,et al.  The distributed data SCF , 2002 .

[9]  Umpei Nagashima,et al.  A novel parallel algorithm for large‐scale Fock matrix construction with small locally distributed memory architectures: RT parallel algorithm , 2002, J. Comput. Chem..

[10]  Daw.  Model for energetics of solids based on the density matrix. , 1993, Physical review. B, Condensed matter.

[11]  Evert Jan Baerends,et al.  Towards an order , 1998 .

[12]  G. C. Fox,et al.  Solving Problems on Concurrent Processors , 1988 .

[13]  Michael J. Frisch,et al.  Achieving Linear Scaling for the Electronic Quantum Coulomb Problem , 1996, Science.

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

[15]  M. Head‐Gordon,et al.  A multipole acceptability criterion for electronic structure theory , 1998 .

[16]  Michael E. Colvin,et al.  Parallel direct SCF for large-scale calculations , 1993 .

[17]  Errol Lewars,et al.  Computational chemistry , 2003 .

[18]  Anders M. N. Niklasson,et al.  Trace resetting density matrix purification in O(N) self-consistent-field theory , 2003 .

[19]  Eric Schwegler,et al.  Fast assembly of the Coulomb matrix: A quantum chemical tree code , 1996 .

[20]  Matt Challacombe,et al.  Linear scaling computation of the Fock matrix. VI. Data parallel computation of the exchange-correlation matrix , 2003 .

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

[22]  Benny G. Johnson,et al.  THE CONTINUOUS FAST MULTIPOLE METHOD , 1994 .

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

[24]  Robert J. Harrison,et al.  Toward high‐performance computational chemistry: I. Scalable Fock matrix construction algorithms , 1996 .

[25]  Anders M.N. Niklasson.  Expansion algorithm for the density matrix , 2002 .

[26]  Linear scaling computation of the Fock matrix. VIII. Periodic boundaries for exact exchange at the Gamma point. , 2005, The Journal of chemical physics.

[27]  Martin Head-Gordon,et al.  A method for two-electron Gaussian integral and integral derivative evaluation using recurrence relations , 1988 .

[28]  Thomas R. Furlani,et al.  Implementation of a parallel direct SCF algorithm on distributed memory computers , 1995, J. Comput. Chem..

[29]  Eric Schwegler,et al.  Linear scaling computation of the Fock matrix , 1997 .

[30]  J. Almlöf,et al.  Principles for a direct SCF approach to LICAO–MOab‐initio calculations , 1982 .

[31]  Matt Challacombe,et al.  Linear scaling computation of the Fock matrix. VII. Parallel computation of the Coulomb matrix. , 2004, The Journal of chemical physics.

[32]  Michael J. Frisch,et al.  Achieving linear scaling in exchange-correlation density functional quadratures , 1996 .

[33]  Jerzy Leszczynski,et al.  COMPUTATIONAL CHEMISTRY: Reviews of Current Trends , 2006 .

[34]  Rick Stevens,et al.  Toward high‐performance computational chemistry: II. A scalable self‐consistent field program , 1996 .

[35]  Matt Challacombe,et al.  Linear scaling computation of the Fock matrix. V. Hierarchical Cubature for numerical integration of the exchange-correlation matrix , 2000 .

[36]  Fast evaluation of the Coulomb energy for electron densities , 1997 .

[37]  Kimihiko Hirao,et al.  Semidirect parallel self-consistent field: the load balancing problem in the input/output intensive self-consistent field iterations , 2003 .

[38]  Matt Challacombe,et al.  Linear scaling computation of the Fock matrix. VII. Periodic density functional theory at the Gamma point. , 2005, The Journal of chemical physics.

[39]  Emilio L. Zapata,et al.  Data Distributions for Sparse Matrix Vector Multiplication , 1995, Parallel Comput..

[40]  R. Friesner,et al.  Parallel pseudospectral electronic structure: I. Hartree–Fock calculations , 1998 .

[41]  Weitao Yang,et al.  An algorithm for 3D numerical integration that scales linearly with the size of the molecule , 1995 .

[42]  Matt Challacombe,et al.  A simplified density matrix minimization for linear scaling self-consistent field theory , 1999 .

[43]  Eric Schwegler,et al.  Linear scaling computation of the Fock matrix. IV. Multipole accelerated formation of the exchange matrix , 1999 .