Bethe logarithm for the H2+ and HD+ molecular ions

The Bethe logarithm is calculated for the lowest rotational-vibrational states of H-2(+) and HD+ hydrogen molecular ions in a wide range of vibrational (v = 0-4) and total orbital momentum (L = 0-4) quantum numbers. Numerical results with eight to nine significant digits are obtained for all the states within this range. This allows us to reduce an error in the leading-order radiative contribution, which results eventually in the relative uncertainty of rovibrational frequency intervals at a level lower than 10(-11). This high precision is important for the rovibrational spectroscopy experiments of hydrogen molecular ions aiming to determine the electron-to-proton mass ratio.