We are investigated substitution effects of titanium heteroatoms on band gap, charge and local reactivity of C20-nTin heterofullerenes (n = 1–5), at different levels and basis sets. The C18Ti2-2 nanocage is considered as the most kinetically stable species with the widest band gap of 2.86 eV, in which two carbon atoms are substituted by two Ti atoms in equatorial position, individually. The charges on carbon atoms of C20 are roughly zero, while high positive charge (1.256) on the surface of C19Ti1 prompts this heteofullerene for hydrogen storage. The positive atomic charge on Ti atoms and negative atomic charge on their adjacent C atoms implies that these sites can be influenced more readily by nucleophilic and electrophilic regents, respectively. We examined the usefulness of local reactivity descriptors to predict the reactivity of Ti–C atomic sites on the external surface of the heterofullerenes. The properties determined include Fukui function (F.F.); f (k) and local softness s (k) on the surfaces of the investigated hollow cages. Geometry optimization results reveal that titanium atoms can be comfortably incorporated into the CC network of fullerene. It is most likely associated with the triple-coordination characteristic of titanium atoms, which can well match with the sp2-hybridized carbon bonding structure. According to the values of f (k) and s (k) for the C15Ti5 heterofullerene; the carbon atoms in the cap regions exhibit a different reactivity pattern than those in the equatorial portion of the heterofullerene. The titanium impurity can significantly improve the fullerene's surface reactivity and it allows controlling their surface properties. The band gap of C20-nTin …..(H2)n structures is decreased with increasing n. Hence, C15Ti5 is found as the best hydrogen adsorbent.