title: 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 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.
authors.affiliation: Institut für Physik, Universität Basel, Klingelbergstr. 82, 4056 Basel, Switzerland.
authors.forename: Stephan
authors.initials: S
authors.lastname: Mohr
authors.affiliation: Univ. Grenoble Alpes, INAC-SP2M, F-38000 Grenoble, France and CEA, INAC-SP2M, F-38000 Grenoble, France.
authors.forename: Laura E
authors.initials: LE
authors.lastname: Ratcliff
authors.affiliation: Univ. Grenoble Alpes, INAC-SP2M, F-38000 Grenoble, France and CEA, INAC-SP2M, F-38000 Grenoble, France.
authors.forename: Paul
authors.initials: P
authors.lastname: Boulanger
authors.affiliation: Univ. Grenoble Alpes, INAC-SP2M, F-38000 Grenoble, France and CEA, INAC-SP2M, F-38000 Grenoble, France.
authors.forename: Luigi
authors.initials: L
authors.lastname: Genovese
authors.affiliation: Univ. Grenoble Alpes, INAC-SP2M, F-38000 Grenoble, France and CEA, INAC-SP2M, F-38000 Grenoble, France.
authors.forename: Damien
authors.initials: D
authors.lastname: Caliste
authors.affiliation: Univ. Grenoble Alpes, INAC-SP2M, F-38000 Grenoble, France and CEA, INAC-SP2M, F-38000 Grenoble, France.
authors.forename: Thierry
authors.initials: T
authors.lastname: Deutsch
authors.affiliation: Institut für Physik, Universität Basel, Klingelbergstr. 82, 4056 Basel, Switzerland.
authors.forename: Stefan
authors.initials: S
authors.lastname: Goedecker