Arbitrary Angular Momentum Electron Repulsion Integrals with Graphical Processing Units: Application to the Resolution of Identity Hartree-Fock Method.

A resolution of identity based implementation of the Hartree-Fock method on graphical processing units (GPUs) is presented that is capable of handling basis functions with arbitrary angular momentum. For practical reasons, only functions up to (ff|f) angular momentum are presently calculated on the GPU, thus leaving the calculation of higher angular momenta integrals on the CPU of the hybrid CPU-GPU environment. Speedups of up to a factor of 30 are demonstrated relative to state-of-the-art serial and parallel CPU implementations. Benchmark calculations with over 3500 contracted basis functions (def2-SVP or def2-TZVP basis sets) are reported. The presented implementation supports all devices with OpenCL support and is capable of utilizing multiple GPU cards over either MPI or OpenCL itself.

[1]  Michel Dupuis,et al.  The Rys quadrature revisited: A novel formulation for the efficient computation of electron repulsion integrals over Gaussian functions , 2001 .

[2]  Warren J. Hehre,et al.  Computation of electron repulsion integrals involving contracted Gaussian basis functions , 1978 .

[3]  Joshua A. Anderson,et al.  General purpose molecular dynamics simulations fully implemented on graphics processing units , 2008, J. Comput. Phys..

[4]  Florian Weigend,et al.  Approximated electron repulsion integrals: Cholesky decomposition versus resolution of the identity methods. , 2009, The Journal of chemical physics.

[5]  Vijay S. Pande,et al.  Accelerating molecular dynamic simulation on graphics processing units , 2009, J. Comput. Chem..

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

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

[8]  M J Harvey,et al.  ACEMD: Accelerating Biomolecular Dynamics in the Microsecond Time Scale. , 2009, Journal of chemical theory and computation.

[9]  Florian Weigend,et al.  A fully direct RI-HF algorithm: Implementation, optimised auxiliary basis sets, demonstration of accuracy and efficiency , 2002 .

[10]  Peter M. W. Gill,et al.  The prism algorithm for two-electron integrals , 1991 .

[11]  E. Davidson,et al.  One- and two-electron integrals over cartesian gaussian functions , 1978 .

[12]  Ivan S Ufimtsev,et al.  Quantum Chemistry on Graphical Processing Units. 3. Analytical Energy Gradients, Geometry Optimization, and First Principles Molecular Dynamics. , 2009, Journal of chemical theory and computation.

[13]  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.

[14]  Martin Head-Gordon,et al.  An efficient algorithm for the generation of two‐electron repulsion integrals over gaussian basis functions , 2009 .

[15]  Brett M. Bode,et al.  Uncontracted Rys Quadrature Implementation of up to G Functions on Graphical Processing Units. , 2010, Journal of chemical theory and computation.

[16]  Koji Yasuda,et al.  Accelerating Density Functional Calculations with Graphics Processing Unit. , 2008, Journal of chemical theory and computation.

[17]  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.

[18]  F. Neese,et al.  Comparison of two efficient approximate Hartee–Fock approaches , 2009 .

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

[20]  Peter Schröder,et al.  Quantum Monte Carlo on graphical processing units , 2007, Comput. Phys. Commun..

[21]  Ivan S Ufimtsev,et al.  Quantum Chemistry on Graphical Processing Units. 2. Direct Self-Consistent-Field Implementation. , 2009, Journal of chemical theory and computation.

[22]  Kenneth M. Merz,et al.  Acceleration of High Angular Momentum Electron Repulsion Integrals and Integral Derivatives on Graphics Processing Units. , 2015, Journal of chemical theory and computation.

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

[24]  Yihan Shao,et al.  Accelerating resolution-of-the-identity second-order Møller-Plesset quantum chemistry calculations with graphical processing units. , 2008, The journal of physical chemistry. A.

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

[26]  Klaus Schulten,et al.  Accelerating Molecular Modeling Applications with GPU Computing , 2009 .

[27]  Jean-François Méhaut,et al.  Density functional theory calculation on many-cores hybrid central processing unit-graphic processing unit architectures. , 2009, The Journal of chemical physics.

[28]  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 .

[29]  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.

[30]  S. F. Boys.  Electronic wave functions - I. A general method of calculation for the stationary states of any molecular system , 1950, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.