Two-dimensional confinement of hydrogen molecular ion

Abstract

Using the Born – Oppenheimer approximation, and considering the nuclei fixed at the foci, a study of the hydrogen molecular ion (H2+), confined strongly in two dimensions by ellipses of different size ξ0, is done. The Schrödinger equation is solved numerically in elliptic coordinates (ξ, η), applying the separation of variables method. The equations for ξ and η are solved following an iterative process, until the energy and separation constant become consistent with the size of the confining ellipse characterized by the parameter ξ0 and the internuclear distance R. The energies for the ion at its ground state and the equilibrium distance between the nuclei are obtained, for different values of ξ0, as well as the polarizability of the molecule.