Accelerating Fock build via hybrid analytical-numerical integration

TL;DR

This paper introduces a hybrid analytical-numerical method, aMECP+aCOSx, to accelerate Fock matrix construction in quantum chemistry calculations, achieving high accuracy and efficiency especially for large molecules.

Contribution

The paper presents a novel hybrid approach combining analytical and numerical techniques to significantly speed up Fock build in HF/DFT calculations with maintained accuracy.

Findings

Achieves less than 1 μEh/atom error in total energies.

Provides acceleration in Fock build for small and large molecules.

Effective with medium and coarse grids for high efficiency.

Abstract

A very robust and efficient hybrid analytic-numerical Fock build, aMECP+aCOSx, has been developed for accelerating HF/DFT calculations. The essential idea is to extract those portions of the Fock matrix that can readily be evaluated analytically, so as to minimize numerical noises arising from the semi-numerical and numerical integrations. As a result, the combination of aMECP with a medium grid and aCOSx with a coarse grid is already sufficient to achieve an accuracy of less than 1{\mu}Eh/atom in total energies. The acceleration of aMECP+aCOSx over the analytic Fock build is already seen in calculations of small molecular systems and is more enhanced in calculations of large molecules with extended basis sets.