Highly accurate calculation of the energy levels of the molecular ion

Abstract
In this paper we present a new numerical method for the calculation of energy levels of the non-relativistic molecular ion , which is `exact', i.e. beyond the Born-Oppenheimer approximation. It relies on the choice of a suitable basis using the dynamical symmetries of the system, in which the Hamiltonian is a sparse banded matrix. The numerical diagonalization of the Hamiltonian produces well converged energy levels, with a typical accuracy of , and also highly accurate wavefunctions.