The University of Southampton
University of Southampton Institutional Repository

Massively parallel linear-scaling Hartree–Fock exchange and hybrid exchange–correlation functionals with plane wave basis set accuracy

Massively parallel linear-scaling Hartree–Fock exchange and hybrid exchange–correlation functionals with plane wave basis set accuracy
Massively parallel linear-scaling Hartree–Fock exchange and hybrid exchange–correlation functionals with plane wave basis set accuracy
We extend our linear-scaling approach for the calculation of Hartree–Fock exchange energy using localized in situ optimized orbitals [Dziedzic et al., J. Chem. Phys. 139, 214103 (2013)] to leverage massive parallelism. Our approach has been implemented in the onetep (Order-N Electronic Total Energy Package) density functional theory framework, which employs a basis of non-orthogonal generalized Wannier functions (NGWFs) to achieve linear scaling with system size while retaining controllable near-complete-basis-set accuracy. For the calculation of Hartree–Fock exchange, we use a resolution-of-identity approach, where an auxiliary basis set of truncated spherical waves is used to fit products of NGWFs. The fact that the electrostatic potential of spherical waves (SWs) is known analytically, combined with the use of a distance-based cutoff for exchange interactions, leads to a calculation cost that scales linearly with the system size. Our new implementation, which we describe in detail, combines distributed memory parallelism (using the message passing interface) with shared memory parallelism (OpenMP threads) to efficiently utilize numbers of central processing unit cores comparable to, or exceeding, the number of atoms in the system. We show how the use of multiple time-memory trade-offs substantially increases performance, enabling our approach to achieve superlinear strong parallel scaling in many cases and excellent, although sublinear, parallel scaling otherwise. We demonstrate that in scenarios with low available memory, which preclude or limit the use of time-memory trade-offs, the performance degradation of our algorithm is graceful. We show that, crucially, linear scaling with system size is maintained in all cases. We demonstrate the practicability of our approach by performing a set of fully converged production calculations with a hybrid functional on large imogolite nanotubes up to over 1400 atoms. We finish with a brief study of how the employed approximations (exchange cutoff and the quality of the SW basis) affect the calculation walltime and the accuracy of the obtained results.
0021-9606
Dziedzic, Jacek
8e2fdb55-dade-4ae4-bf1f-a148a89e4383
Womack, James C
ef9e1954-4a38-4e89-bf25-741a0738e85b
Ali, Rozh
597b45cf-4f99-4b9d-afff-0d29d79ae5db
Skylaris, Chris-Kriton
8f593d13-3ace-4558-ba08-04e48211af61
Dziedzic, Jacek
8e2fdb55-dade-4ae4-bf1f-a148a89e4383
Womack, James C
ef9e1954-4a38-4e89-bf25-741a0738e85b
Ali, Rozh
597b45cf-4f99-4b9d-afff-0d29d79ae5db
Skylaris, Chris-Kriton
8f593d13-3ace-4558-ba08-04e48211af61

Dziedzic, Jacek, Womack, James C, Ali, Rozh and Skylaris, Chris-Kriton (2021) Massively parallel linear-scaling Hartree–Fock exchange and hybrid exchange–correlation functionals with plane wave basis set accuracy. The Journal of Chemical Physics, 155 (22), [224106]. (doi:10.1063/5.0067781).

Record type: Article

Abstract

We extend our linear-scaling approach for the calculation of Hartree–Fock exchange energy using localized in situ optimized orbitals [Dziedzic et al., J. Chem. Phys. 139, 214103 (2013)] to leverage massive parallelism. Our approach has been implemented in the onetep (Order-N Electronic Total Energy Package) density functional theory framework, which employs a basis of non-orthogonal generalized Wannier functions (NGWFs) to achieve linear scaling with system size while retaining controllable near-complete-basis-set accuracy. For the calculation of Hartree–Fock exchange, we use a resolution-of-identity approach, where an auxiliary basis set of truncated spherical waves is used to fit products of NGWFs. The fact that the electrostatic potential of spherical waves (SWs) is known analytically, combined with the use of a distance-based cutoff for exchange interactions, leads to a calculation cost that scales linearly with the system size. Our new implementation, which we describe in detail, combines distributed memory parallelism (using the message passing interface) with shared memory parallelism (OpenMP threads) to efficiently utilize numbers of central processing unit cores comparable to, or exceeding, the number of atoms in the system. We show how the use of multiple time-memory trade-offs substantially increases performance, enabling our approach to achieve superlinear strong parallel scaling in many cases and excellent, although sublinear, parallel scaling otherwise. We demonstrate that in scenarios with low available memory, which preclude or limit the use of time-memory trade-offs, the performance degradation of our algorithm is graceful. We show that, crucially, linear scaling with system size is maintained in all cases. We demonstrate the practicability of our approach by performing a set of fully converged production calculations with a hybrid functional on large imogolite nanotubes up to over 1400 atoms. We finish with a brief study of how the employed approximations (exchange cutoff and the quality of the SW basis) affect the calculation walltime and the accuracy of the obtained results.

Text
paper - Accepted Manuscript
Download (2MB)
Text
Massively parallel linear-scaling - Version of Record
Download (6MB)

More information

Accepted/In Press date: 22 November 2021
e-pub ahead of print date: 14 December 2021
Additional Information: This work was funded by the Engineering and Physical Sciences Research Council (EPSRC), UK, as part of a flagship project of the CCP9 consortium (EPSRC Grant No. EP/P02209X/1). We acknowledge the support of the high-performance computing centers where we ran the calculations: Iridis5 at the University of Southampton (UK) and tryton at the TASK Academic Computer Centre (Gdańsk, Poland). We also acknowledge the UKCP for access to ARCHER and ARCHER2 (EPSRC Grant No. EP/P022030/1) and the MMM hub for access to Young (EPSRC Grant No. EP/T022213/1). J.D. would like to thank Gilberto Teobaldi and Emiliano Poli for fruitful discussions regarding the imogolite nanotube systems and for making their structures available.

Identifiers

Local EPrints ID: 454217
URI: http://eprints.soton.ac.uk/id/eprint/454217
ISSN: 0021-9606
PURE UUID: bbce9e1f-7e20-4f2f-b5e7-1e11661ebdfb
ORCID for Jacek Dziedzic: ORCID iD orcid.org/0000-0003-4786-372X
ORCID for James C Womack: ORCID iD orcid.org/0000-0001-5497-4482
ORCID for Chris-Kriton Skylaris: ORCID iD orcid.org/0000-0003-0258-3433

Catalogue record

Date deposited: 02 Feb 2022 17:52
Last modified: 17 Mar 2024 07:05

Export record

Altmetrics

Contributors

Author: Jacek Dziedzic ORCID iD
Author: James C Womack ORCID iD
Author: Rozh Ali

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of http://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×