Optimizing computational kernels in quantum chemistry

Abstract

Density fitting is a rank reduction technique popularly used in quantum chemistry in order to reduce the computational cost of evaluating, transforming, and processing the 4-center electron repulsion integrals (ERIs). By utilizing the resolution of the identity technique, density fitting reduces the 4-center ERIs into a 3-center form. Doing so not only alleviates the high storage cost of the ERIs, but it also reduces the computational cost of operations involving them. Still, these operations can remain as computational bottlenecks which commonly plague quantum chemistry procedures. The goal of this thesis is to investigate various optimizations for density-fitted version of computational kernels used ubiquitously throughout quantum chemistry. First, we detail the spatial sparsity available to the 3-center integrals and the application of such sparsity to various operations, including integral computation, metric contractions, and integral transformations. Next, we investigate sparse memory layouts and their implication on the performance of the integral transformation kernel. Next, we analyze two transformation algorithms and how their performance will vary depending on the context in which they are used. Then, we propose two sparse memory layouts and the resulting performance of Coulomb and exchange evaluations. Since the memory required for these tensors grows rapidly, we frame these discussions in the context of their in-core and disk performance. We implement these methods in the P SI 4 electronic structure package and reveal the optimal algorithm for the kernel should vary depending on whether a disk-based implementation must be used.