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

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.