Quantum states of a confined hydrogen atom calculated in a basis of explicitly correlated Gaussians

A quantum-mechanical model for describing a hydrogen atom confined to a soft-wall cuboidal potential energy trap is implemented. Explicitly correlated Gaussian functions are used to expand the hydrogen wave functions that are symmetry-adapted with respect to the symmetry elements of the trapping potential. The calculations are performed without assuming the Born-Oppenheimer approximation. The electronic and nuclear densities of the calculated states are visualized using one-particle density plots. The approach enables to describe the behavior of a trapped hydrogen atom and, when extended to multiple hydrogen molecules, has potential for application in the theoretical modeling of the hydrogen storage phenomenon.