Relativistic corrections of mα6 order to the rovibrational spectrum of H2+ and HD+ molecular ions

The major goal of high-precision studies of rovibrational states in the hydrogen molecular ions is to provide an alternative way for improving the electron-to-proton mass ratio, or the atomic mass of electron. By now the complete set of relativistic and radiative corrections have been obtained for a wide range of rovibrational states of $\text{H}_{2}{}^{+}$ and ${\text{HD}}^{+}$ up to order ${R}_{\ensuremath{\infty}}{\ensuremath{\alpha}}^{4}$. In this work we complete calculations of various contributions to the ${R}_{\ensuremath{\infty}}{\ensuremath{\alpha}}^{4}$ order by computing the relativistic corrections to the binding energy of electron.