Daubechies wavelets for linear scaling density functional theory
Abstract
We demonstrate that Daubechies wavelets can be used to construct a minimal set of optimized localized adaptively contracted basis functions in which the KohnSham orbitals can be represented with an arbitrarily high, controllable precision. Ground state energies and the forces acting on the ions can be calculated in this basis with the same accuracy as if they were calculated directly in a Daubechies wavelets basis, provided that the amplitude of these adaptively contracted basis functions is sufficiently small on the surface of the localization region, which is guaranteed by the optimization procedure described in this work. This approach reduces the computational costs of density functional theory calculations, and can be combined with sparse matrix algebra to obtain linear scaling with respect to the number of electrons in the system. Calculations on systems of 10 000 atoms or more thus become feasible in a systematic basis set with moderate computational resources. Further computational savings can be achieved by exploiting the similarity of the adaptively contracted basis functions for closely related environments, e.g., in geometry optimizations or combined calculations of neutral and charged systems.
 Authors:

 Institut für Physik, Universität Basel, Klingelbergstr. 82, 4056 Basel (Switzerland)
 Univ. Grenoble Alpes, INACSP2M, F38000 Grenoble, France and CEA, INACSP2M, F38000 Grenoble (France)
 Publication Date:
 OSTI Identifier:
 22304330
 Resource Type:
 Journal Article
 Journal Name:
 Journal of Chemical Physics
 Additional Journal Information:
 Journal Volume: 140; Journal Issue: 20; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 00219606
 Country of Publication:
 United States
 Language:
 English
 Subject:
 37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; ACCURACY; DENSITY FUNCTIONAL METHOD; GROUND STATES; OPTIMIZATION
Citation Formats
Mohr, Stephan, Univ. Grenoble Alpes, INACSP2M, F38000 Grenoble, France and CEA, INACSP2M, F38000 Grenoble, Ratcliff, Laura E., Genovese, Luigi, Caliste, Damien, Deutsch, Thierry, Boulanger, Paul, Institut Néel, CNRS and Université Joseph Fourier, B.P. 166, 38042 Grenoble Cedex 09, and Goedecker, Stefan. Daubechies wavelets for linear scaling density functional theory. United States: N. p., 2014.
Web. doi:10.1063/1.4871876.
Mohr, Stephan, Univ. Grenoble Alpes, INACSP2M, F38000 Grenoble, France and CEA, INACSP2M, F38000 Grenoble, Ratcliff, Laura E., Genovese, Luigi, Caliste, Damien, Deutsch, Thierry, Boulanger, Paul, Institut Néel, CNRS and Université Joseph Fourier, B.P. 166, 38042 Grenoble Cedex 09, & Goedecker, Stefan. Daubechies wavelets for linear scaling density functional theory. United States. doi:10.1063/1.4871876.
Mohr, Stephan, Univ. Grenoble Alpes, INACSP2M, F38000 Grenoble, France and CEA, INACSP2M, F38000 Grenoble, Ratcliff, Laura E., Genovese, Luigi, Caliste, Damien, Deutsch, Thierry, Boulanger, Paul, Institut Néel, CNRS and Université Joseph Fourier, B.P. 166, 38042 Grenoble Cedex 09, and Goedecker, Stefan. Wed .
"Daubechies wavelets for linear scaling density functional theory". United States. doi:10.1063/1.4871876.
@article{osti_22304330,
title = {Daubechies wavelets for linear scaling density functional theory},
author = {Mohr, Stephan and Univ. Grenoble Alpes, INACSP2M, F38000 Grenoble, France and CEA, INACSP2M, F38000 Grenoble and Ratcliff, Laura E. and Genovese, Luigi and Caliste, Damien and Deutsch, Thierry and Boulanger, Paul and Institut Néel, CNRS and Université Joseph Fourier, B.P. 166, 38042 Grenoble Cedex 09 and Goedecker, Stefan},
abstractNote = {We demonstrate that Daubechies wavelets can be used to construct a minimal set of optimized localized adaptively contracted basis functions in which the KohnSham orbitals can be represented with an arbitrarily high, controllable precision. Ground state energies and the forces acting on the ions can be calculated in this basis with the same accuracy as if they were calculated directly in a Daubechies wavelets basis, provided that the amplitude of these adaptively contracted basis functions is sufficiently small on the surface of the localization region, which is guaranteed by the optimization procedure described in this work. This approach reduces the computational costs of density functional theory calculations, and can be combined with sparse matrix algebra to obtain linear scaling with respect to the number of electrons in the system. Calculations on systems of 10 000 atoms or more thus become feasible in a systematic basis set with moderate computational resources. Further computational savings can be achieved by exploiting the similarity of the adaptively contracted basis functions for closely related environments, e.g., in geometry optimizations or combined calculations of neutral and charged systems.},
doi = {10.1063/1.4871876},
journal = {Journal of Chemical Physics},
issn = {00219606},
number = 20,
volume = 140,
place = {United States},
year = {2014},
month = {5}
}