# Monte Carlo calculation of the potential energy surface for octahedral confined H$_2^+$

## TL;DR

This paper uses Diffusion Monte Carlo to calculate the potential energy surface of H$_2^+$ confined within an octahedral well, exploring effects of geometry and well width relevant to high-pressure and nanoscale systems.

## Contribution

It presents the first detailed PES calculations for H$_2^+$ in octahedral confinement using DMC, adaptable to complex geometries and nuclear positions.

## Key findings

- PES varies with well geometry and size.
- Electron compression influences energy levels.
- Correlation with semi-confined atomic orbitals observed.

## Abstract

A rich literature has been produced on the quantum states of atoms and molecules confined into infinite potential wells with a specified symmetry. Apart from their interest as basic quantum systems, confined atoms and molecules are useful models for extreme high pressure states of matter, spectroscopically active defects in solid lattices and chemical species in molecular cages. A most important case is that of H$_2^+$ for which little or no results are available in the case of polyhedral confinement. The approach of the authors makes use of the Diffusion Monte Carlo (DMC) method. The advantage of this method is that previously developed codes are readily adapted to new, even complex, well geometries and nuclear positions. In this paper the potential energy surface (PES) of H$_2^+$ confined inside an octahedral well is reported for restricted D$_{4h}$ and D$_{3d}$ geometries and different well widths. The results are discussed using the concept of electron compression and the correlation with semi-confined atomic orbitals.