Occupied-orbital fast multipole method for efficient exact exchange evaluation

TL;DR

This paper introduces an efficient algorithm leveraging the fast multipole method to compute exact exchange contributions in quantum chemistry, significantly reducing computational costs for large molecules.

Contribution

The paper presents a novel FMM-based algorithm for exact exchange evaluation that is more efficient than traditional methods, especially for large systems.

Findings

Far-field exchange evaluation for Crambin costs about 3% of SCF iteration

Algorithm effectively handles large molecules like proteins and graphene

Timing benchmarks demonstrate substantial efficiency gains

Abstract

We present an efficient algorithm for computing the exact exchange contributions in the Hartree-Fock and hybrid density functional theory models on the basis of the fast multipole method (FMM). Our algorithm is based on the observation that FMM with hierarchical boxes can be efficiently used in the exchange matrix construction, when at least one of the indices of the exchange matrix is constrained to be an occupied orbital. Timing benchmarks are presented for alkane chains (C400H802 and C150H302), a graphene sheet (C150H30), a water cluster [(H2O)100], and a protein Crambin (C202H317O64N55S6). The computational cost of the far-field exchange evaluation for Crambin is roughly 3% that of a self-consistent field iteration when the multipoles up to rank 2 are used.