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Title: Self-consistent implementation of meta-GGA functionals for the ONETEP linear-scaling electronic structure package

Accurate and computationally efficient exchange-correlation functionals are critical to the successful application of linear-scaling density functional theory (DFT). Local and semi-local functionals of the density are naturally compatible with linear-scaling approaches, having a general form which assumes the locality of electronic interactions and which can be efficiently evaluated by numerical quadrature. Presently, the most sophisticated and flexible semi-local functionals are members of the meta-generalized-gradient approximation (meta-GGA) family, and depend upon the kinetic energy density, τ, in addition to the charge density and its gradient. In order to extend the theoretical and computational advantages of τ-dependent meta-GGA functionals to large-scale DFT calculations on thousands of atoms, we have implemented support for τ-dependent meta-GGA functionals in the ONETEP program. In this paper we lay out the theoretical innovations necessary to implement τ-dependent meta-GGA functionals within ONETEP's linear-scaling formalism. We present expressions for the gradient of the τ-dependent exchange-correlation energy, necessary for direct energy minimization. We also derive the forms of the τ-dependent exchange-correlation potential and kinetic energy density in terms of the strictly localized, self-consistently optimized orbitals used by ONETEP. To validate the numerical accuracy of our self-consistent meta-GGA implementation, we performed calculations using the B97M-V and PKZB meta-GGAs on a varietymore » of small molecules. Using only a minimal basis set of self-consistently optimized local orbitals, we obtain energies in excellent agreement with large basis set calculations performed using other codes. Finally, to establish the linear-scaling computational cost and applicability of our approach to large-scale calculations, we present the outcome of self-consistent meta-GGA calculations on amyloid fibrils of increasing size, up to tens of thousands of atoms.« less
Authors:
ORCiD logo [1] ;  [2] ;  [3] ;  [1]
  1. School of Chemistry, University of Southampton, Highfield, Southampton SO17 1BJ, United Kingdom
  2. Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, California 94720, USA
  3. Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, California 94720, USA; Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
Publication Date:
Grant/Contract Number:
AC02-05CH11231
Type:
Accepted Manuscript
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 145; Journal Issue: 20; Related Information: © 2016 Author(s).; Journal ID: ISSN 0021-9606
Publisher:
American Institute of Physics (AIP)
Research Org:
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Sponsoring Org:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22), Chemical Sciences, Geosciences & Biosciences Division (SC-22.1); USDOE
Country of Publication:
United States
Language:
English
OSTI Identifier:
1477254
Alternate Identifier(s):
OSTI ID: 1333761

Womack, James C., Mardirossian, Narbe, Head-Gordon, Martin, and Skylaris, Chris-Kriton. Self-consistent implementation of meta-GGA functionals for the ONETEP linear-scaling electronic structure package. United States: N. p., Web. doi:10.1063/1.4967960.
Womack, James C., Mardirossian, Narbe, Head-Gordon, Martin, & Skylaris, Chris-Kriton. Self-consistent implementation of meta-GGA functionals for the ONETEP linear-scaling electronic structure package. United States. doi:10.1063/1.4967960.
Womack, James C., Mardirossian, Narbe, Head-Gordon, Martin, and Skylaris, Chris-Kriton. 2016. "Self-consistent implementation of meta-GGA functionals for the ONETEP linear-scaling electronic structure package". United States. doi:10.1063/1.4967960. https://www.osti.gov/servlets/purl/1477254.
@article{osti_1477254,
title = {Self-consistent implementation of meta-GGA functionals for the ONETEP linear-scaling electronic structure package},
author = {Womack, James C. and Mardirossian, Narbe and Head-Gordon, Martin and Skylaris, Chris-Kriton},
abstractNote = {Accurate and computationally efficient exchange-correlation functionals are critical to the successful application of linear-scaling density functional theory (DFT). Local and semi-local functionals of the density are naturally compatible with linear-scaling approaches, having a general form which assumes the locality of electronic interactions and which can be efficiently evaluated by numerical quadrature. Presently, the most sophisticated and flexible semi-local functionals are members of the meta-generalized-gradient approximation (meta-GGA) family, and depend upon the kinetic energy density, τ, in addition to the charge density and its gradient. In order to extend the theoretical and computational advantages of τ-dependent meta-GGA functionals to large-scale DFT calculations on thousands of atoms, we have implemented support for τ-dependent meta-GGA functionals in the ONETEP program. In this paper we lay out the theoretical innovations necessary to implement τ-dependent meta-GGA functionals within ONETEP's linear-scaling formalism. We present expressions for the gradient of the τ-dependent exchange-correlation energy, necessary for direct energy minimization. We also derive the forms of the τ-dependent exchange-correlation potential and kinetic energy density in terms of the strictly localized, self-consistently optimized orbitals used by ONETEP. To validate the numerical accuracy of our self-consistent meta-GGA implementation, we performed calculations using the B97M-V and PKZB meta-GGAs on a variety of small molecules. Using only a minimal basis set of self-consistently optimized local orbitals, we obtain energies in excellent agreement with large basis set calculations performed using other codes. Finally, to establish the linear-scaling computational cost and applicability of our approach to large-scale calculations, we present the outcome of self-consistent meta-GGA calculations on amyloid fibrils of increasing size, up to tens of thousands of atoms.},
doi = {10.1063/1.4967960},
journal = {Journal of Chemical Physics},
number = 20,
volume = 145,
place = {United States},
year = {2016},
month = {11}
}

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