Optimal Fourier filtering of a function that is strictly confined within a sphere

TL;DR

This paper introduces a new Fourier filtering method for functions confined within a sphere, optimizing their Fourier transform confinement, with applications in electronic structure calculations.

Contribution

The paper proposes an alternative Fourier filtering technique that enhances confinement properties for functions within a sphere, aiding electronic structure computations.

Findings

Effective confinement of functions within a sphere achieved

Optimized Fourier transform confinement demonstrated

Potential improvements in pseudopotential generation

Abstract

We present an alternative method to filter a distribution, that is strictly confined within a sphere of given radius $r_c$, so that its Fourier transform is optimally confined within another sphere of radius $k_c$. In electronic structure methods, it can be used to generate optimized pseudopotentials, pseudocore charge distributions, and pseudo atomic orbital basis sets.