  We show that we can predict the first ionization energy of the carbon atom to
within 0.872 cm$^{-1}$ of the experimental value. This is an improvement of
more than a factor of 6.5 over the preceding best prediction in [Phys. Rev. A
81, 022503], and opens the door to achieving sub-cm$^{-1}$ accuracy for
ab-initio predictions in larger elements of the periodic table.
