High accuracy results for the energy levels of the molecular ions H+2, D+2 and HD+, up to J = 2

We present a nonrelativistic calculation of the rotation-vibration levels of the molecular ions H+2, D+2 and HD+, relying on the diagonalization of the exact three-body Hamiltonian in a variational basis. The J = 2 levels are obtained with a very high accuracy of 10−14 au (for most levels) representing an improvement by five orders of magnitude over previous calculations. The accuracy is also improved for the J = 1 levels of H+2 and D+2 with respect to earlier works. Moreover, we have computed the sensitivities of the energy levels with respect to the mass ratios, allowing these levels to be used for metrological purposes.