Smooth models for the Coulomb potential

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.