Leading-order relativistic corrections to the hydrogen molecular ion

We present the improved calculations over the results of Korobov [Phys. Rev. A 74, 052506 (2006)] for the energy levels and hyperfine structure of the hydrogen molecular ion H-2+, including the relativistic corrections of orders alpha(2) Ry and alpha(2)m(e)/m(p) Ry, using variationally constructed basis sets in Hylleraas coordinates. In particular, the computational uncertainty of 3 kHz in Korobov's calculation for the alpha(2) Ry correction to the two-photon transition frequency (L=0,v=0)->(L=0,v=1) is eliminated.