Efficient Hybrid Density Functional Calculations for Large Periodic Systems Using Numerical Atomic Orbitals

TL;DR

This paper introduces a linear-scaling, parallel implementation of hybrid density functional calculations for large periodic systems using numerical atomic orbitals, significantly improving efficiency and scalability.

Contribution

The authors develop a highly efficient, parallelized method for constructing the Hartree-Fock exchange matrix in periodic systems with linear scaling, tailored for numerical atomic orbitals.

Findings

Achieves linear scaling with system size for HFX matrix construction.

Demonstrates high efficiency and scalability up to 4096 atoms.

Provides detailed algorithms and implementation in ABACUS code.

Abstract

We present an efficient, linear-scaling implementation for building the (screened) Hartree-Fock exchange (HFX) matrix for periodic systems within the framework of numerical atomic orbital (NAO) basis functions. Our implementation is based on the localized resolution of the identity approximation by which two-electron Coulomb repulsion integrals can be obtained by only computing two-center quantities -- a feature that is highly beneficial to NAOs. By exploiting the locality of basis functions and efficient prescreening of the intermediate three- and two-index tensors, one can achieve a linear scaling of the computational cost for building the HFX matrix with respect to the system size. Our implementation is massively parallel, thanks to a MPI/OpenMP hybrid parallelization strategy for distributing the computational load and memory storage. All these factors add together to enable highly efficient hybrid functional calculations for large-scale periodic systems. In this work we describe the key algorithms and implementation details for the HFX build as implemented in the ABACUS code package. The performance and scalability of our implementation with respect to the system size and the number of CPU cores are demonstrated for selected benchmark systems up to 4096 atoms.