Lagrange-mesh calculations of the ground-state rotational bands of the H2 and D2 molecular ions

All the energies of the ground-state Σ g rotational band of the H 2 + molecular ion are calculated by solving the three-body Schrödinger equation with the Lagrange-mesh numerical method in the perimetric coordinates system. This method provides the same accuracy as a variational calculation but is much simpler. Energies are obtained with an accuracy of 10 −12 Hartree. The wavefunctions display a strongly dominant axial ( K = 0) symmetry. Calculations including components up to K = 2 show that components beyond K = 1 are negligible at the 10 −10 accuracy. Accurate analytical approximations of the wavefunctions are used to evaluate mean interparticle distances and electric quadrupole moments of these states. The proton–proton distances show a progressive increase accompanied by a corresponding increase of the radius of the electron orbital. For the three bound states of the Σ u rotational band of H 2 + , the interproton distance takes values larger than 17 a 0 . A similar study of the D 2 + ion is also carried out.