Quantum states of confined hydrogen plasma species: Monte Carlo calculations

The diffusion Monte Carlo method with symmetry-based state selection is used to calculate the quantum energy states of H${}_2^{+}$ confined into potential barriers of atomic dimensions (a model for these ions in solids). Special solutions are employed permitting one to obtain satisfactory results with rather simple native code. As a test case, ${}^2{\mathrm{\Pi }}_u$ and ${}^2{\mathrm{\Pi }}_g$ states of H${}_2^{+}$ ions under spherical confinement are considered. The results are interpreted using the correlation of H${}_2^{+}$ states to atomic orbitals of H atoms lying on the confining surface and perturbation calculations. The method is straightforwardly applied to cavities of any shape and different hydrogen plasma species (at least one-electron ones, including H) for future studies with real crystal symmetries.