Adaptively Compressed Exchange Operator

TL;DR

The paper introduces the adaptively compressed exchange (ACE) operator, significantly reducing the computational cost of Fock exchange calculations in quantum chemistry without sacrificing accuracy, applicable to various system types.

Contribution

The ACE formulation is a novel method that reduces exchange operator costs, compatible with existing electronic structure codes, and effective for small to large systems.

Findings

ACE reduces exchange calculation costs by orders of magnitude.

ACE is applicable to insulating, semiconducting, and metallic systems.

ACE achieves near-GGA computational efficiency in Hartree-Fock-like calculations.

Abstract

The Fock exchange operator plays a central role in modern quantum chemistry. The large computational cost associated with the Fock exchange operator hinders Hartree-Fock calculations and Kohn-Sham density functional theory calculations with hybrid exchange-correlation functionals, even for systems consisting of hundreds of atoms. We develop the adaptively compressed exchange operator (ACE) formulation, which greatly reduces the computational cost associated with the Fock exchange operator without loss of accuracy. The ACE formulation does not depend on the size of the band gap, and thus can be applied to insulating, semiconducting as well as metallic systems. In an iterative framework for solving Hartree-Fock-like systems, the ACE formulation only requires moderate modification of the code, and can be potentially beneficial for all electronic structure software packages involving exchange calculations. Numerical results indicate that the ACE formulation can become advantageous even for small systems with tens of atoms. In particular, the cost of each self-consistent field iteration for the electron density in the ACE formulation is only marginally larger than that of the generalized gradient approximation (GGA) calculation, and thus offers orders of magnitude speedup for Hartree-Fock-like calculations.