Ab initio restricted Hartree-Fock calculations were performed on the ground and excited states of C28H4, Hf@C28H4, and their positive and negative ions. Relativistic core potentials were included in the calculations to take account of the relativistic effects of the heavy atom. Symmetry-adapted functions were used to reduce the time and effort of the computation. Ionization potentials, electron affinities, MO interaction diagrams, and population analyses of the systems were obtained. These results and those from our previous studies of Hf@C-28 were used to interpret the mode of bonding in C28H4 and Hf@C28H4, the mutual weakening of the bonding of Hf and 4H to C-28, and the factors that affect the bonding. These results can also shed light on the characteristics of the bonding of endohedral and exohedral complexes of fullerenes in general.