The dynamic and static nature of the XH-∗-π and YX-∗-π (X = F, Cl, Br, and I; Y = X and F) interactions in the distorted π-system of corannulene (π(C20H10)) is elucidated with a QTAIM dual functional analysis (QTAIM-DFA), where asterisks emphasize the presence of bond critical points (BCPs) on the interactions. The static and dynamic nature originates from the data of the fully optimized and perturbed structures, respectively, in QTAIM-DFA. On the convex side, H in F–H-∗-π(C20H10) and each X in Y–X-∗-π(C20H10) join to C of the central five-membered ring in π(C20H10) through a bond path (BP), while each H in X–H-∗-π(C20H10) does so to the midpoint of C=C in the central five-membered ring for X = Cl, Br, or I. On the concave side, each X in F–X-∗-π(C20H10) also joins to C of the central five-membered ring with a BP for X = H, Cl, Br, and I; however, the interactions in other adducts are more complex than those on the convex side. Both H and X in X–H-∗-π(C20H10) (X = Cl and Br) and both Fs in F–F-∗-π(C20H10) connect to the three C atoms in each central five-membered ring (with three BPs). Two, three, and five BPs were detected for the Cl–Cl, I–H, Br–Br, and I–I adducts, where some BPs do not stay on the central five-membered ring in π(C20H10). The interactions are predicted to have a vdW to CT-MC nature. The interactions on the concave side seem weaker than those on the convex side for X–H-∗-π(C20H10), whereas the inverse trend is observed for Y–X-∗-π(C20H10) as a whole. The nature of the interactions in the π(C20H10) adducts of the convex and concave sides is examined in more detail, employing the adducts with X–H and F–X placed on their molecular axis together with the π(C24H12) and π(C6H6) adducts.