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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14 December 2021
Research Article|
December 09 2021
Massively parallel linear-scaling Hartree–Fock exchange and hybrid exchange–correlation functionals with plane wave basis set accuracy
Special Collection:
Beyond GGA Total Energies for Solids and Surfaces
Jacek Dziedzic
;
Jacek Dziedzic
1
School of Chemistry, Highfield, University of Southampton
, Southampton SO17 1BJ, United Kingdom
2
Faculty of Applied Physics and Mathematics, Gdańsk University of Technology
, Gdańsk 80-233, Poland
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James C. Womack
;
James C. Womack
1
School of Chemistry, Highfield, University of Southampton
, Southampton SO17 1BJ, United Kingdom
3
Research Software Engineering, Advanced Computing Research Centre, University of Bristol
, Bristol BS1 5QD, United Kingdom
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Rozh Ali;
Rozh Ali
2
Faculty of Applied Physics and Mathematics, Gdańsk University of Technology
, Gdańsk 80-233, Poland
4
Applied Physics Department, College of Medical and Applied Science, Charmo University
, Chamchamal, 46023 Sulaimania, Iraq
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Chris-Kriton Skylaris
Chris-Kriton Skylaris
a)
1
School of Chemistry, Highfield, University of Southampton
, Southampton SO17 1BJ, United Kingdom
a)Author to whom correspondence should be addressed: C.Skylaris@soton.ac.uk
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a)Author to whom correspondence should be addressed: C.Skylaris@soton.ac.uk
Note: This paper is part of the JCP Special Topic on Beyond GGA Total Energies for Solids and Surfaces.
J. Chem. Phys. 155, 224106 (2021)
Article history
Received:
August 19 2021
Accepted:
November 22 2021
Citation
Jacek Dziedzic, James C. Womack, Rozh Ali, Chris-Kriton Skylaris; Massively parallel linear-scaling Hartree–Fock exchange and hybrid exchange–correlation functionals with plane wave basis set accuracy. J. Chem. Phys. 14 December 2021; 155 (22): 224106. https://doi.org/10.1063/5.0067781
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