# Smeared Coulomb potential orbitals for the electron-nucleus mean field configuration interaction method

## TL;DR

This paper introduces a novel approach for electron-nucleus mean field calculations using eigenfunctions of a one-electron model with a smeared Coulomb potential, aiming to improve accuracy in molecular simulations.

## Contribution

It presents a new method employing smeared Coulomb potential eigenfunctions for EN-MFCI calculations, offering a different approximation to the Coulomb interaction.

## Key findings

- Eigenfunctions of the smeared Coulomb potential are effective for EN-MFCI.
- Perturbative solutions are valid for small amplitude vibrations.
- The approach provides a new basis for molecular electronic structure calculations.

## Abstract

We propose to use the eigenfunctions of a one-electron model Hamiltonian to perform electron-nucleus mean field configuration interaction (EN-MFCI) calculations. The potential energy of our model Hamiltonian corresponds to the Coulomb potential of an infinite wire with charge $Z$ distributed according to a Gaussian function. The time independent \sch equation for this Hamiltonian is solved perturbationally in the limit of small amplitude vibration (Gaussian function width close to zero).