High-Performance, High-Angular-Momentum J Engine on Graphics Processing Units

Efficient evaluation of electron repulsion integrals (ERIs) involving high-angular-momentum Gaussian basis functions is computationally challenging on graphical processing units (GPUs), as traditional recurrence-based integral algorithms generate numerous intermediates, causing significant register pressure and memory bottlenecks. In this Article, we present a high-performance, high-angular-momentum Coulomb-matrix (J) engine specifically optimized for GPU execution. Our approach introduces a GPU-optimized McMurchie-Davidson recurrence algorithm combined with a tailored integral batching scheme, designed specifically to jointly minimize intermediate storage requirements and redundant computation. By strategically partitioning high-angular-momentum ERIs classes into several carefully selected sub-batches, our approach transitions the associated integral evaluation kernels from memory-bound to compute-bound regimes, significantly enhancing computational throughput and reducing time to solution. Implemented in the Extreme-scale Electronic Structure System (EXESS), our algorithm achieves individual kernel speedups of up to 9× and improves overall J-matrix formation performance by up to 64% across a variety of increasing-size chemical systems, including polyglycine chains, water clusters, and boron nitride crystals, when using the cc-pVQZ quadruple-ζ basis set on an NVIDIA A100 GPU.