Study of Quantum Confinement of $$ {\text{H}}_{2}^{ + } $$ Ion and H2 Molecule with Monte Carlo. Respective Role of the Electron and Nuclei Confinement

Abstract

The effect of quantum confinement on the H2 molecular ion and on the H2 molecule is analyzed. Simple approximate trial wave functions are employed to study within a variational approach these molecules when confined by impenetrable surfaces. The study is carried out beyond the Born-Oppenheimer approximation so that the motion of the nuclei is included in the trial wave function. The molecules are studied in their lowest rovibrational state. Confinement in considered in the approximation by including cut-off functions to fulfill the Dirichlet boundary conditions. The optimized variational wave functions are used as guiding functions in a Diffusion Monte Carlo calculation. The results show an increase of the energy when both the confinement of the electron or the nuclei becomes stronger. The electronic constrain is found to be much more efficient to increase the energy than nuclear confinement. The present study reveals that a metastable bound state of these molecular systems, above the energy corresponding to the dissociation limit, can be obtained when the electron constrain is present. Expectation values of the internuclear distance and the mean electron to nuclear center of mass distance are also calculated and show a rapid decrease when the confinement is stronger. Finally the variation in quantum pressure with the confinement radius is also estimated. A rapid raise of the pressure value when the confinement is below 3 au is observed.