Relativistic corrections ofmα6order to the rovibrational spectrum ofH2+andHD+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 $R_{\infty }{\alpha }^4$. 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.