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.
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).
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.
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Massively parallel linear-scaling
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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.
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Local EPrints ID: 454217
URI: http://eprints.soton.ac.uk/id/eprint/454217
ISSN: 0021-9606
PURE UUID: bbce9e1f-7e20-4f2f-b5e7-1e11661ebdfb
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Date deposited: 02 Feb 2022 17:52
Last modified: 17 Mar 2024 07:05
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Author:
James C Womack
Author:
Rozh Ali
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