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

Abstract

An efficient numerical quadrature is proposed for the approximate calculation of the potential energy in the context of pseudo potential electronic structure calculations with Daubechies wavelet and scaling function basis sets. Our quadrature is also applicable in the case of adaptive spatial resolution. Our theoretical error estimates are confirmed by numerical test calculations of the ground state energy and wave function of the harmonic oscillator in one dimension with and without adaptive resolution. As a byproduct we derive a filter, which, upon application on the scaling function coefficients of a smooth function, renders the approximate grid values of this function. This also allows for a fast calculation of the charge density from the wave function.

35 pages, 9 figures. Submitted to: Journal of Computational Physics

References in corpus (2)

• Multiresolution analysis for efficient, high precision all-electron density-functional calculations
• Robust ab initio calculation of condensed matter: transparent convergence through semicardinal multiresolution analysis

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• Wavelet-Based Linear-Response Time-Dependent Density-Functional Theory
• Accurate Complex Scaling of Three Dimensional Numerical Potentials
• Multipole-Preserving Quadratures for Discretization of Functions in Real-Space Electronic Structure Calculations
• Wavelets for Density-Functional Theory and Post-Density-Functional-Theory Calculations
• Towards 1ULP evaluation of Daubechies Wavelets