All the energies of the ground-state Σg rotational bandof the H2+molecular ion are calculated by solving the three-body Schrödinger equationwith the Lagrange-mesh numerical method in the perimetric coordinatessystem. This method provides the same accuracy as a variational calculationbut is much simpler. Energies are obtained with an accuracy of 10−12Hartree. The wavefunctions display a strongly dominant axial (K = 0)symmetry. Calculations including components up toK = 2 show thatcomponents beyond K = 1are negligible at the 10−10 accuracy. Accurate analytical approximations of thewavefunctions are used to evaluate mean interparticle distances and electricquadrupole moments of these states. The proton–proton distances show aprogressive increase accompanied by a corresponding increase of the radius ofthe electron orbital. For the three bound states of the Σu rotational bandof H2+,the interproton distance takes values larger than 17a0. A similar studyof the D2+ion is also carried out.