The influence of relativistic effects on the structure, vibrational modes, and reactivity of recently discovered tertrahedral gold clusters (Au(19) and Au(20)) are investigated using density functional methods. The intramolecular reactivity of the clusters was analyzed using density functional-based reactivity descriptors. The work shows that whereas the structural properties and vibrational modes are considerably affected by the relativistic effects, the reactivity trends based on Fukui function calculation on various atoms within this cluster remain unaffected by the absence or presence of relativistic effects. The reactivity descriptors reveal that the vertex atoms are the most reactive ones in Au(20) toward a nucleophilic attack. On the other hand, atoms connecting the missing vertex edge with the pyramid base along with the vertex atom are the most reactive for a nucleophilic attack in Au(19). The atoms lying at the center of each face are favorable for an electrophilic attack in both cases. Interestingly, the atoms with a missing cap in Aulg are highly favorable for electrophilic attack, and Au(20) has more sites for a favorable nucleophilic attack.