Efficient Evaluation of Coulomb Interactions for Large-Scale Quantum Chemistry

Author: Li, Rui

Year: 2026

Degree: Dissertation (Ph.D.)

Advisor: Chan, Garnet K.

Committee Members: Goddard, William A., III; Chan, Garnet K.; Minnich, Austin J.; Sharma, Sandeep

Option: Chemistry

Abstract

Evaluating the Coulomb interaction remains a fundamental computational bottleneck in electronic structure theory, dictating the scaling and efficiency of quantum chemical simulations. While recent advancements in graphics processing units (GPUs) offer immense theoretical peak performance, translating traditional, memory-intensive CPU algorithms for evaluating electron repulsion integrals to GPU architectures presents significant challenges due to memory bandwidth limitations and warp divergence.

This thesis presents the development of algorithms to efficiently evaluate Coulomb interactions across diverse chemical systems. Chapter 2 describes the GPU implementation of Coulomb interaction for molecular systems at Hartree-Fock level of theory. Chapter 3 shows how multigrid Gaussian-Plane-Wave algorithm can better utilize GPU compute performance by a two-level parallelization scheme and grid-based screening of orbital pairs in the real space. Chapter 4 illustrates the issues of the original modified Coulomb potential from GFN-xTB in periodic systems, and the effectiveness of a new generalized Ewald summation scheme for the potential in X23 molecular crystal dataset and a range of prototypical bulk semiconductors.