Ab initio calculation of the J=0 and J=1 states of the H-2(+), D-2(+) and HD+ molecular ions

A new, non adiabatic, description of the H-2(+) molecular ion and its isoto pomers is proposed: the molecular system is treated as a three body Coulomb system, in the framework of non relativistic quantum mechanics. The method takes advantage of the dynamical symmetries of the system. It relies on th e choice of the perimetric coordinates to describe the system, and of a gen eralized Hylleraas basis, in which the Hamiltonian exhibits strong coupling rules. The method is described in detail both for S and P states (i.e., st ates of total angular momentum J = 0 or 1). We calculate the energies of J = 0 or 1 vibrational levels of the H-2(+) and D-2(+) molecular ions with a very high accuracy (typically 10(-14) atomic unit). This a considerable imp rovement over previous calculations. The dependence of these results on the proton to electron mass ratio is also discussed.