We demonstrate that Daubechies wavelets can be used to construct a minimal set of optimized localized adaptively contracted basis functions in which the Kohn-Sham 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.
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28 May 2014
Research Article|
May 28 2014
Daubechies wavelets for linear scaling density functional theory
Stephan Mohr;
Stephan Mohr
1Institut für Physik,
Universität Basel
, Klingelbergstr. 82, 4056 Basel, Switzerland
2
Univ. Grenoble Alpes
, INAC-SP2M, F-38000 Grenoble, France and CEA, INAC-SP2M, F-38000 Grenoble, France
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Laura E. Ratcliff;
Laura E. Ratcliff
2
Univ. Grenoble Alpes
, INAC-SP2M, F-38000 Grenoble, France and CEA, INAC-SP2M, F-38000 Grenoble, France
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Paul Boulanger;
Paul Boulanger
2
Univ. Grenoble Alpes
, INAC-SP2M, F-38000 Grenoble, France and CEA, INAC-SP2M, F-38000 Grenoble, France
3Institut Néel, CNRS and
Université Joseph Fourier
, B.P. 166, 38042 Grenoble Cedex 09, France
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Luigi Genovese;
Luigi Genovese
2
Univ. Grenoble Alpes
, INAC-SP2M, F-38000 Grenoble, France and CEA, INAC-SP2M, F-38000 Grenoble, France
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Damien Caliste;
Damien Caliste
2
Univ. Grenoble Alpes
, INAC-SP2M, F-38000 Grenoble, France and CEA, INAC-SP2M, F-38000 Grenoble, France
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Thierry Deutsch;
Thierry Deutsch
2
Univ. Grenoble Alpes
, INAC-SP2M, F-38000 Grenoble, France and CEA, INAC-SP2M, F-38000 Grenoble, France
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Stefan Goedecker
Stefan Goedecker
1Institut für Physik,
Universität Basel
, Klingelbergstr. 82, 4056 Basel, Switzerland
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J. Chem. Phys. 140, 204110 (2014)
Article history
Received:
January 29 2014
Accepted:
April 08 2014
Citation
Stephan Mohr, Laura E. Ratcliff, Paul Boulanger, Luigi Genovese, Damien Caliste, Thierry Deutsch, Stefan Goedecker; Daubechies wavelets for linear scaling density functional theory. J. Chem. Phys. 28 May 2014; 140 (20): 204110. https://doi.org/10.1063/1.4871876
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