Accelerating quantum chemistry with vectorized and batched integrals

Hua Huang, Edmond Chow

Abstract: This paper presents the first quantum chemistry calculations using a recently developed vectorized library for computing electron repulsion integrals. To lengthen the SIMD loop and thus improve SIMD utilization, the approach used in this paper is to batch together multiple integrals that can be computed using the same code path. The standard approach is to compute integrals one at a time, and thus a batching procedure had to be developed. This paper shows proof-of-concept and demonstrates the performance gains possible when the batched approach is used. Batching also enables certain optimizations when the integrals are used to compute the Fock matrix. We further describe several other optimizations that were needed to obtain up to a 270% speedup over the non-batching version of the code, making a compelling case for adopting the presented techniques in quantum chemistry software.