# Spherically confined H$_2^+$: $^2\Sigma_g^+$ and $^2\Sigma_u^+$ states

## TL;DR

This study investigates the effects of spherical confinement on the electronic states of the H$_2^+$ molecular ion using diffusion Monte Carlo methods, revealing deep potential minima under strong confinement conditions.

## Contribution

It provides new potential energy curves for H$_2^+$ under spherical confinement, highlighting how confinement alters molecular electronic states.

## Key findings

- Deep minima in potential curves under confinement.
- Increased electron wave-function space with proton displacement.
- Potential curves depend on confinement radius.

## Abstract

The molecular ion H$_2^+$ is studied under strong confinement conditions produced by a spherical barrier centered in the gravity center of the molecule. Results for the potential curves are obtained by diffusion Monte Carlo methods for the ground state (X$^2\Sigma_g^+$) and the first excited state (A$^2\Sigma_u^+$), and reported as functions of the internuclear distance d for different values of the confinement radius. Results show that the compressed state corresponding to both $^2\Sigma_g^+$ and $^2\Sigma_u^+$ present deep minima in their potential curves, due to the increased space for electron wave-functions when the protons are displaced from the barrier surface.