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

All the energies of the ground-state Sigma(g) rotational band of the H-2(+) molecular 2 ion are calculated by solving the three-body Schrodinger 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 Sigma(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.