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

Self-consistent implementation of meta-GGA functionals for the ONETEP linear-scaling electronic structure package
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, tau, in addition to the charge density and its gradient. In order to extend the theoretical and computational advantages of tau-dependent meta-GGA functionals to large-scale DFT calculations on thousands of atoms, we have implemented support for tau-dependent meta-GGA functionals in the ONETEP program. In this paper we lay out the theoretical innovations necessary to implement tau-dependent meta-GGA functionals within ONETEP's linear-scaling formalism. We present expressions for the gradient of the tau-dependent exchange-correlation energy, necessary for direct energy minimization. We also derive the forms of the tau-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.
0021-9606
1-21
Womack, James C.
ef9e1954-4a38-4e89-bf25-741a0738e85b
Mardirossian, Narbe
6dc65ee1-19a9-490e-83e6-6984a64bb7f9
Head-Gordon, Martin
f203c934-60ff-4c19-a2ff-b1f6ec2ad05a
Skylaris, Chris
8f593d13-3ace-4558-ba08-04e48211af61
Womack, James C.
ef9e1954-4a38-4e89-bf25-741a0738e85b
Mardirossian, Narbe
6dc65ee1-19a9-490e-83e6-6984a64bb7f9
Head-Gordon, Martin
f203c934-60ff-4c19-a2ff-b1f6ec2ad05a
Skylaris, Chris
8f593d13-3ace-4558-ba08-04e48211af61

Womack, James C., Mardirossian, Narbe, Head-Gordon, Martin and Skylaris, Chris (2016) Self-consistent implementation of meta-GGA functionals for the ONETEP linear-scaling electronic structure package. The Journal of Chemical Physics, 1-21. (doi:10.1063/1.4967960).

Record type: Article

Abstract

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, tau, in addition to the charge density and its gradient. In order to extend the theoretical and computational advantages of tau-dependent meta-GGA functionals to large-scale DFT calculations on thousands of atoms, we have implemented support for tau-dependent meta-GGA functionals in the ONETEP program. In this paper we lay out the theoretical innovations necessary to implement tau-dependent meta-GGA functionals within ONETEP's linear-scaling formalism. We present expressions for the gradient of the tau-dependent exchange-correlation energy, necessary for direct energy minimization. We also derive the forms of the tau-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.

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More information

Submitted date: 31 August 2016
Accepted/In Press date: 5 November 2016
e-pub ahead of print date: 29 November 2016
Published date: November 2016
Organisations: Computational Systems Chemistry

Identifiers

Local EPrints ID: 402421
URI: http://eprints.soton.ac.uk/id/eprint/402421
ISSN: 0021-9606
PURE UUID: 7bc20418-98d7-4b38-b70d-3988237d751e
ORCID for James C. Womack: ORCID iD orcid.org/0000-0001-5497-4482
ORCID for Chris Skylaris: ORCID iD orcid.org/0000-0003-0258-3433

Catalogue record

Date deposited: 09 Nov 2016 16:27
Last modified: 15 Mar 2024 06:03

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Contributors

Author: James C. Womack ORCID iD
Author: Narbe Mardirossian
Author: Martin Head-Gordon
Author: Chris Skylaris ORCID iD

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