Smooth models for the Coulomb potential

TL;DR

This paper introduces smooth model potentials that approximate the Coulomb potential, accurately reproducing atomic spectra and demonstrating transferability to other systems, offering a practical alternative to the singular Coulomb potential.

Contribution

It presents a method for constructing smooth potentials that replicate Coulomb spectra and discusses their transferability across different atomic and electronic systems.

Findings

Smooth potentials reproduce atomic spectra within chemical accuracy.

Higher angular momentum states are modeled more accurately.

Transferability from attractive to repulsive systems is feasible.

Abstract

Smooth model potentials with parameters selected to reproduce the spectrum of one-electron atoms are used to approximate the singular Coulomb potential. Even when the potentials do not mimic the Coulomb singularity, much of the spectrum is reproduced within the chemical accuracy. For the Hydrogen atom, the smooth approximations to the Coulomb potential are more accurate for higher angular momentum states. The transferability of the model potentials from an attractive interaction (Hydrogen atom) to a repulsive one (Harmonium and the uniform electron gas) is discussed.