Adaptive local basis set for Kohn–Sham density functional theory in a discontinuous Galerkin framework II: Force, vibration, and molecular dynamics calculations
Recently, we have proposed the adaptive local basis set for electronic structure calculations based on Kohn–Sham density functional theory in a pseudopotential framework. The adaptive local basis set is efficient and systematically improvable for total energy calculations. In this paper, we present the calculation of atomic forces, which can be used for a range of applications such as geometry optimization and molecular dynamics simulation. We demonstrate that, under mild assumptions, the computation of atomic forces can scale nearly linearly with the number of atoms in the system using the adaptive local basis set. We quantify the accuracy of the Hellmann–Feynman forces for a range of physical systems, benchmarked against converged planewave calculations, and find that the adaptive local basis set is efficient for both force and energy calculations, requiring at most a few tens of basis functions per atom to attain accuracies required in practice. Sin ce the adaptive local basis set has implicit dependence on atomic positions, Pulay forces are in general nonzero. However, we find that the Pulay force is numerically small and systematically decreasing with increasing basis completeness, so that the Hellmann–Feynman force is sufficient for basis sizes of a few tens of basis functions per atom.more »
 Authors:

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 Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
 Univ. of California, Berkeley, CA (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
 Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
 Publication Date:
 Grant/Contract Number:
 AC0205CH11231; AC5207NA27344
 Type:
 Accepted Manuscript
 Journal Name:
 Journal of Computational Physics
 Additional Journal Information:
 Journal Volume: 335; Journal Issue: C; Journal ID: ISSN 00219991
 Publisher:
 Elsevier
 Research Org:
 Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
 Sponsoring Org:
 USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC21)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 74 ATOMIC AND MOLECULAR PHYSICS; 97 MATHEMATICS AND COMPUTING; Electronic structure; Kohn–Sham density functional theory; Discontinuous Galerkin; Adaptive local basis set; Hellmann–Feynman force; Pulay force; Molecular dynamics
 OSTI Identifier:
 1379809
 Alternate Identifier(s):
 OSTI ID: 1397834
Zhang, Gaigong, Lin, Lin, Hu, Wei, Yang, Chao, and Pask, John E. Adaptive local basis set for Kohn–Sham density functional theory in a discontinuous Galerkin framework II: Force, vibration, and molecular dynamics calculations. United States: N. p.,
Web. doi:10.1016/j.jcp.2016.12.052.
Zhang, Gaigong, Lin, Lin, Hu, Wei, Yang, Chao, & Pask, John E. Adaptive local basis set for Kohn–Sham density functional theory in a discontinuous Galerkin framework II: Force, vibration, and molecular dynamics calculations. United States. doi:10.1016/j.jcp.2016.12.052.
Zhang, Gaigong, Lin, Lin, Hu, Wei, Yang, Chao, and Pask, John E. 2017.
"Adaptive local basis set for Kohn–Sham density functional theory in a discontinuous Galerkin framework II: Force, vibration, and molecular dynamics calculations". United States.
doi:10.1016/j.jcp.2016.12.052. https://www.osti.gov/servlets/purl/1379809.
@article{osti_1379809,
title = {Adaptive local basis set for Kohn–Sham density functional theory in a discontinuous Galerkin framework II: Force, vibration, and molecular dynamics calculations},
author = {Zhang, Gaigong and Lin, Lin and Hu, Wei and Yang, Chao and Pask, John E.},
abstractNote = {Recently, we have proposed the adaptive local basis set for electronic structure calculations based on Kohn–Sham density functional theory in a pseudopotential framework. The adaptive local basis set is efficient and systematically improvable for total energy calculations. In this paper, we present the calculation of atomic forces, which can be used for a range of applications such as geometry optimization and molecular dynamics simulation. We demonstrate that, under mild assumptions, the computation of atomic forces can scale nearly linearly with the number of atoms in the system using the adaptive local basis set. We quantify the accuracy of the Hellmann–Feynman forces for a range of physical systems, benchmarked against converged planewave calculations, and find that the adaptive local basis set is efficient for both force and energy calculations, requiring at most a few tens of basis functions per atom to attain accuracies required in practice. Sin ce the adaptive local basis set has implicit dependence on atomic positions, Pulay forces are in general nonzero. However, we find that the Pulay force is numerically small and systematically decreasing with increasing basis completeness, so that the Hellmann–Feynman force is sufficient for basis sizes of a few tens of basis functions per atom. We verify the accuracy of the computed forces in static calculations of quasi1D and 3D disordered Si systems, vibration calculation of a quasi1D Si system, and molecular dynamics calculations of H2 and liquid Al–Si alloy systems, where we show systematic convergence to benchmark planewave results and results from the literature.},
doi = {10.1016/j.jcp.2016.12.052},
journal = {Journal of Computational Physics},
number = C,
volume = 335,
place = {United States},
year = {2017},
month = {1}
}