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Flexibilities of Wavelets as a Computational Basis Set for Large-Scale Electronic Structure Calculations

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Density Functional Theory

Part of the book series: Mathematics and Molecular Modeling ((MAMOMO))

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Abstract

The BigDFT project started in 2005 with the aim of testing the advantages of using a Daubechies wavelet basis set for Kohn–Sham density functional theory with pseudopotentials. This project led to the creation of the BigDFT code, which employs a computational approach with optimal features for flexibility, performance and precision of the results. In particular, the employed formalism has enabled the implementation of an algorithm able to tackle DFT calculations of large systems, up to many thousands of atoms, with a computational effort which scales linearly with the number of atoms. In this work we show how the localised description of the Kohn–Sham problem, emerging from the features of the basis set, are helpful in providing a simplified description of large-scale electronic structure calculations. We recall some of the features that have been made possible by the peculiar mathematical properties of Daubechies wavelets and also interpolating scaling functions.

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  1. Univ. Grenoble Alpes, CEA, IRIG-MEM, Grenoble, France

    Luigi Genovese & Thierry Deutsch

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  1. Luigi Genovese
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  1. CERMICS, Ecole des Ponts and Inria Paris, Marne-la-Vallée, France

    Eric Cancès

  2. Department of Mathematics, Technische Universität München, Garching bei München, Germany

    Gero Friesecke

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Genovese, L., Deutsch, T. (2023). Flexibilities of Wavelets as a Computational Basis Set for Large-Scale Electronic Structure Calculations. In: Cancès, E., Friesecke, G. (eds) Density Functional Theory. Mathematics and Molecular Modeling. Springer, Cham. https://doi.org/10.1007/978-3-031-22340-2_11

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