Radial Gausslets

TL;DR

This paper introduces radial gausslets, a compact basis set for atomic electronic structure calculations that maintains diagonal electron-electron interactions, extending the original Cartesian-based gausslets to three-dimensional radial coordinates.

Contribution

The authors generalize gausslet construction from 1D Cartesian coordinates to 3D radial coordinates, enabling efficient atomic basis sets with diagonal interactions.

Findings

Radial gausslets provide a compact basis with fewer functions.

They achieve accurate Hartree--Fock and exact diagonalization results.

The basis maintains diagonal electron-electron interaction terms.

Abstract

Gausslets are one of the few examples of basis sets for electronic structure which allow for two-index/diagonal electron-electron interaction terms. A weakness of gausslets is that, because of their 1D origin, they have been tied to Cartesian coordinates. Here we generalize the gausslet construction for the radial coordinate in three dimensions for atomic basis sets. These radial gausslets make a very compact radial basis with a relatively modest number of functions, with diagonal interaction terms. We illustrate the accuracy of this construction with Hartree--Fock and exact diagonalization on atomic systems.