  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.
