Quantum confinement study of the H+2ion with the Monte Carlo approach. Respective role of electron and nuclei confinement

A simple approximate trial wavefunction is used to study, within a variational approach and beyond the Born–Oppenheimer approximation, the molecular ion H+2 confined by impenetrable spherical surfaces. This wavefunction describes explicitly the motion of the nuclei and the electron of this three-body system in its lowest rovibrational state. Two cut-off functions are introduced to fulfil the Dirichlet boundary conditions, respectively, for the electron and the nuclei. The results show an increase of the energy of the ion when both the confinement radius of the electron and of the nuclei become smaller. The electron constraint is found to be much more efficient to increase the energy than the nuclei confinement. This study shows that a metastable bound state of the ion, above the energy corresponding to the dissociation limit, can be obtained when the electron constraint is present. Expectation values of the internuclear and electron-to-origin distances are also calculated and show a rapid decrease when the confinement is stronger. Finally, the quantum pressure versus the confinement radius is also estimated. A rapid rise of the pressure value when is less than 3 au is observed.