  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.
