Daubechies wavelets for linear scaling density functional theory

2014/01/31 by Stephan Mohr, Laura E. Ratcliff, P Boulanger +5
Chemistry · Mathematics · Physics and Astronomy · #Advanced Chemical Physics Studies #Advanced NMR Techniques and Applications #Algorithm #Artificial intelligence #Basis (linear algebra) #Basis function #Basis set #Computer science #Daubechies wavelet #Density functional theory #Discrete wavelet transform #Geometry #Linear scale #Mathematical analysis #Mathematics #Physics #Quantum mechanics #Scaling #Spectroscopy and Quantum Chemical Studies #Statistical physics #Wavelet #Wavelet transform #cond-mat.mtrl-sci

paper · pdf · doi:10.1063/1.4871876

openalex publication_date 2014/05/28 · arxiv created 2014/06/03 · arxiv updated 2014/06/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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.

Citations

• Self-consistent first-principles technique with linear scaling
• Energy Landscape of Fullerene Materials: A Comparison of Boron to Boron Nitride and Carbon
• NWChem: A comprehensive and scalable open-source solution for large scale molecular simulations
• Generalized Gradient Approximation Made Simple
• Relativistic separable dual-space Gaussian pseudopotentials from H to Rn
• Calculations for millions of atoms with density functional theory: linear scaling shows its potential
• Quickstep: Fast and accurate density functional calculations using a mixed Gaussian and plane waves approach
• Critical assessment of the self-interaction-corrected–local-density-functional method and its algorithmic implementation
• QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials
• Efficient index handling of multidimensional periodic boundary conditions
• Maximally-localized generalized Wannier functions for composite energy bands
• First-principles simulation: ideas, illustrations and the CASTEP code
• Self-Consistent Equations Including Exchange and Correlation Effects