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 H-2(+) and HD+ up to order R-infinity alpha(4). In this work we complete calculations of various contributions to the R-infinity alpha(4) order by computing the relativistic corrections to the binding energy of electron.