Spherically confined H${}_2^{+}$: ${}^2{\mathrm{\Sigma }}_g^{+}$ and ${}^2{\mathrm{\Sigma }}_u^{+}$ states

The molecular ion H${}_2^{+}$ is studied under strong confinement conditions produced by a spherical barrier centered in the gravity center of the molecule. Results for the potential curves are obtained by diffusion Monte Carlo methods for the ground state (X${}^2{\mathrm{\Sigma }}_g^{+}$) and the first excited state (A${}^2{\mathrm{\Sigma }}_u^{+}$), and reported as functions of the internuclear distance d for different values of the confinement radius. Results show that the compressed state corresponding to both ${}^2{\mathrm{\Sigma }}_g^{+}$ and ${}^2{\mathrm{\Sigma }}_u^{+}$ present deep minima in their potential curves, due to the increased space for electron wave-functions when the protons are displaced from the barrier surface.