Distributed memory, GPU accelerated Fock construction for hybrid, Gaussian basis density functional theory

Abstract

With the growing reliance of modern supercomputers on accelerator-based architecture such a graphics processing units (GPUs), the development and optimization of electronic structure methods to exploit these massively parallel resources has become a recent priority. While significant strides have been made in the development GPU accelerated, distributed memory algorithms for many modern electronic structure methods, the primary focus of GPU development for Gaussian basis atomic orbital methods has been for shared memory systems with only a handful of examples pursing massive parallelism. In the present work, we present a set of distributed memory algorithms for the evaluation of the Coulomb and exact exchange matrices for hybrid Kohn–Sham DFT with Gaussian basis sets via direct density-fitted (DF-J-Engine) and seminumerical (sn-K) methods, respectively. The absolute performance and strong scalability of the developed methods are demonstrated on systems ranging from a few hundred to over one thousand atoms using up to 128 NVIDIA A100 GPUs on the Perlmutter supercomputer.

High-Performance Evaluation of High Angular Momentum 4-Center Gaussian Integrals on Modern Accelerated Processors

“…Thus, the question remains: what is a better way to evaluate 2-electron integrals over high- l Gaussian AOs on GPUs? Our recent work on the density-fitting-accelerated J-matrix engine implementation for GPUs based on McMurchie–Davidson (MD) recurrences hinted that the MD recurrences recast in matrix form might be the way to go for some classes of integrals; that development also provided many fundamental elements that we reused in this work. We were not alone in thinking that the SHARK integral engine developed by Frank Neese and recently incorporated into the public release of ORCA program illustrated how efficient the MD scheme can be when expressed as a matrix multiplication (matmul) on conventional CPUs, at least when used for integrals over high angular momenta (SHARK supplements the MD approach with traditional Obara-Saika-based kernels implemented in the Libint library).…”

“…A possible workaround for the challenge of high-l integrals is the use of real-space factorization of 2-electron integrals, as illustrated recently by us and collaborators 24 via the use of realspace quadrature ("pseudospectral", 25 also known as chain-ofspheres 26 or seminumerical 27 ) approximation to the exact exchange, which trades the problem of computing 4-center 2electron integrals for evaluation of cheaper but much more numerous 2-center 1-electron Gaussian AO integrals. Nevertheless, these and other numerical approximations that avoid the 4-center integrals cannot entirely eliminate the need to evaluate 4-center 2-electron integrals; thus, their efficient evaluation, especially for high angular momenta, remains a critical challenge on modern HPC platforms.…”