Relativistic corrections of mα⁶ order to the ro-vibrational spectrum of H₂^+ and HD^+ molecular ions

The major goal of the high-precision studies of ro-vibrational 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 ro-vibrational states of H_2^+ and HD^+ up to order R_\infty\alpha^4. In this work we complete calculations of various contributions to the R_\infty\alpha^4 order by computing the relativistic corrections to the binding energy of electron.