Complex sentence: The energy of the Rydberg states follows the Rydberg formula converging on the ionization thresholds associated with the energy required to remove an electron from the ionic core of an atom or molecule.
Split into simpler sentences: The energy of the Rydberg states follows the Rydberg formula. The ionization thresholdenergy is the energy required to completely liberate an electron from the ionic core of an atom or molecule.