Coupled Cluster Theory on Graphics Processing Units I. The Coupled Cluster Doubles Method

Abstract

The coupled cluster (CC) ansatz is generally recognized as providing one of the best wave function-based descriptions of electronic correlation in small- and medium-sized molecules. The fact that the CC equations with double excitations (CCD) may be expressed as a handful of dense matrix-matrix multiplications makes it an ideal method to be ported to graphics processing units (GPUs). We present our implementation of the spin-free CCD equations in which the entire iterative procedure is evaluated on the GPU. The GPU-accelerated algorithm readily achieves a factor of 4-5 speedup relative to the multithreaded CPU algorithm on same-generation hardware. The GPU-accelerated algorithm is approximately 8-12 times faster than Molpro, 17-22 times faster than NWChem, and 21-29 times faster than GAMESS for each CC iteration. Single-precision GPU-accelerated computations are also performed, leading to an additional doubling of performance. Single-precision errors in the energy are typically on the order of 10(-6) hartrees and can be improved by about an order of magnitude by performing one additional iteration in double precision.

Quantum Chemistry for Solvated Molecules on Graphical Processing Units Using Polarizable Continuum Models

“…Primitive pairs are prescreened with the density-weighted Schwartz bound of Eq. (18). Each thread is assigned a single primitive pair, and loops over all MS points.…”

Use of graphics processing units for efficient evaluation of derivatives of exchange integrals by means of Fourier transform of the 1/r operator and its numerical quadrature

“…Here, the situation is less clear-cut. A few years ago, the potential of GPUs in quantum chemistry has been recognized, and since then, their merits in applications to evaluation of twoelectron repulsion integrals [13][14][15][16][17], semiempirical methods [18,19], Hartree-Fock calculations [19,20], DFT [21,22], CIS [23], MP2 [24][25][26], CCSD and CCSD(T) [27,28] and Quantum Monte Carlo calculations [29] were reported. Nevertheless, we considered it expedient to note a possible use of our computational scheme also for post-HartreeFock methods.…”

Exploiting GPUs with the Super Instruction Architecture

“…Previous implementations of coupled cluster methods in computational chemistry on GPUs have been reported [3,4,11]. In these papers, the approach was to take a specific algorithm and implement it on a GPU in a highly optimized form.…”