An efficient numerical quadrature for the calculation of the potential energy of wavefunctions expressed in the Daubechies wavelet basis

Neelov, Alexey; Goedecker, Stefan

doi:10.1016/j.jcp.2006.01.003

Cited by 31 publications

(36 citation statements)

References 41 publications

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“…As described in Refs. 15,16,32 , from the expression of φ T α in a Daubechies wavelets basis set, the so-called "magic-filter" transformation can be used to define a real space representation of the basis functions, given in terms of one-dimensional interpolating scaling functions (ISF)…”

Section: E Reformatting Scheme For Roto-translationsmentioning

confidence: 99%

Fragment approach to constrained density functional theory calculations using Daubechies wavelets

Ratcliff

Genovese

Mohr

et al. 2015

The Journal of Chemical Physics

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In a recent paper we presented a linear scaling Kohn-Sham density functional theory (DFT) code based on Daubechies wavelets, where a minimal set of localized support functions is optimized in situ and therefore adapted to the chemical properties of the molecular system. Thanks to the systematically controllable accuracy of the underlying basis set, this approach is able to provide an optimal contracted basis for a given system: accuracies for ground state energies and atomic forces are of the same quality as an uncontracted, cubic scaling approach. This basis set offers, by construction, a natural subset where the density matrix of the system can be projected. In this paper we demonstrate the flexibility of this minimal basis formalism in providing a basis set that can be reused as-is, i.e. without reoptimization, for charge-constrained DFT calculations within a fragment approach. Support functions, represented in the underlying wavelet grid, of the template fragments are roto-translated with high numerical precision to the required positions and used as projectors for the charge weight function. We demonstrate the interest of this approach to express highly precise and efficient calculations for preparing diabatic states and for the computational setup of systems in complex environments.

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Section: E Reformatting Scheme For Roto-translationsmentioning

confidence: 99%

Fragment approach to constrained density functional theory calculations using Daubechies wavelets

Ratcliff

Genovese

Mohr

et al. 2015

The Journal of Chemical Physics

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“…it has a rather low number of continuous derivatives. A. Neelov and S. Goedecker (22) have shown that one should not try to approximate a single matrix element as accurately as possible but that one should try instead to approximate directly the expectation value of the local potential. The reason for this strategy is that the wavefunction expressed in the Daubechy basis is smoother than a single Daubechies basis function.…”

Section: Treatment Of Local Potential Energymentioning

confidence: 99%

Daubechies wavelets as a basis set for density functional pseudopotential calculations

Genovese¹,

Neelov²,

Goedecker³

et al. 2008

The Journal of Chemical Physics

327

306

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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.

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“…An integration scheme proposed in [40] has been employed successfully for computations involving smooth pseudopotentials in 3D with Daubechies wavelets, but is not suitable for our purposes due to its smoothness requirements on both potentials and wavefunctions.…”

Section: Evaluation Of Integralsmentioning

confidence: 99%

Hyperbolic wavelet discretization of the two-electron Schrödinger equation in an explicitly correlated formulation

Bachmayr

2012

ESAIM: M2AN

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Abstract. In the framework of an explicitly correlated formulation of the electronic Schrödinger equation known as the transcorrelated method, this work addresses some fundamental issues concerning the feasibility of eigenfunction approximation by hyperbolic wavelet bases. Focusing on the two-electron case, the integrability of mixed weak derivatives of eigenfunctions of the modified problem and the improvement compared to the standard formulation are discussed. Elements of a discretization of the eigenvalue problem based on orthogonal wavelets are described, and possible choices of tensor product bases are compared especially from an algorithmic point of view. The use of separable approximations of potential terms for applying operators efficiently is studied in detail, and estimates for the error due to this further approximation are given.Mathematics Subject Classification. 35B65, 35J10, 65T60, 81Q05.

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An efficient numerical quadrature for the calculation of the potential energy of wavefunctions expressed in the Daubechies wavelet basis

Cited by 31 publications

References 41 publications

Fragment approach to constrained density functional theory calculations using Daubechies wavelets

Fragment approach to constrained density functional theory calculations using Daubechies wavelets

Daubechies wavelets as a basis set for density functional pseudopotential calculations

Hyperbolic wavelet discretization of the two-electron Schrödinger equation in an explicitly correlated formulation

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