Daubechies wavelets as a basis set for density functional pseudopotential calculations.

By L. Genovese, A. Neelov, Stefan Goedecker, T. Deutsch, S. Ghasemi, Alexander Willand, D. Caliste, Oded Zilberberg, M. Rayson, A. Bergman and 1 more. Journal of Chemical Physics, 2008

333 citations recorded by the source corpus.

Daubechies wavelets are a powerful systematic basis set for electronic structure calculations because they are orthogonal and localized both in real and Fourier space. We describe in detail how this basis set can be used to obtain a highly efficient and accurate method for density functional electronic structure calculations. An implementation of this method is available in the ABINIT free software package. This code shows high systematic convergence properties, very good performances, and an excellent efficiency for parallel calculations.

Subfields: Atomic and Molecular Physics, and Optics, Spectroscopy

View Paper: https://www.semanticscholar.org/paper/c74ce27419b0bc2ac7fe1d3d06f15e2843ea387b

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Citations in the corpus

A perspective on conventional high-temperature superconductors at high pressure: Methods and materials (2019, methodology): “unctions of the position operator, that is, points on a uniform mesh in real-space. Actual implementations of this idea may use ﬁnite dierences, ﬁnite elements or Lagrange sine-functions or wavelets [352]. Other mixed-basis sets, such (linear) augmented plane waves, have proven to be able to achieve”
Computational Physics on Graphics Processing Units (2012, methodology): “They used double precision arithmetic and a Daubechies wavelet based code called BIGDFT [51].”
Numerical Solution of the Hartree - Fock Equation in Multilevel Tensor-Structured Format (2011, methodology): “The simplified models based on the appropriately adjusted pseudopotentials, can be solved by using the grid-oriented methods over n × n × n spacial grid via the traditional plane waves, wavelet or finite element discretizations at the expense that scales at least linear in the volume size, NV = n (3”
Numerical solution of the Hartree-Fock equation by multilevel tensor-structured methods (2011, background): “These include the traditional plane waves, wavelet or finite element discretizations, at the expense that scales linearly in the volume size, Nvol = n(3), [4, 5].”
Numerical Methods for Electronic Structure Calculations of Materials (2010, background): “Wavelet bases hold great promise because of their localized nature in both real space and reciprocal space; see, for example, [69, 182, 65, 84, 38].”
QTT Representation of the Hartree and Exchange Operators in Electronic Structure Calculations (2011, background): “It concerns both the Gaussian-type basis sets, and the plane waves bases, which in spite of intrinsic limitations, are the cornerstone for the DFT calculations [10, 41].”
The analysis of a plane wave pseudopotential density functional theory code on a GPU machine (2013, methodology): “We note that the overall parallelization scheme used here is similar to that used in the BigDFT code [16].”
Recent developments in the ABINIT software package (2016, methodology): “Inspired by the BigDFT method [111], the 3D integrals are simplified into a sum of products of 1D integrals in the three cartesian directions, ”
Versatile, scalable, and accurate simulation of distributed applications and platforms (2014, neutral): “…makes it possible to simulate MPI applications, for both benchmarks and complex applications, including the full LinPACK suite [30], the Sweep3D [3] benchmark, the BigDFT Density Functional Theory application [37], and the SpecFEM3D geodynamics application [64] that is part of the PRACE benchmark.”
Wavelet Scattering Regression of Quantum Chemical Energies (2016, methodology): “Multiscale wavelet transforms are used in some DFT software to reduce computations by providing sparse representations of atomic wavefunctions [3, 37, 21, 44, 39, 48].”