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

摘要

An efficient numerical quadrature is proposed for the approximate calculationof the potential energy in the context of pseudo potential electronic structurecalculations with Daubechies wavelet and scaling function basis sets. Ourquadrature is also applicable in the case of adaptive spatial resolution. Ourtheoretical error estimates are confirmed by numerical test calculations of theground state energy and wave function of the harmonic oscillator in onedimension with and without adaptive resolution. As a byproduct we derive afilter, which, upon application on the scaling function coefficients of asmooth function, renders the approximate grid values of this function. Thisalso allows for a fast calculation of the charge density from the wavefunction.