The gas-phase identity nucleophilic substitution reactions of halide anions (X = F, Cl, and Br) with cyclopropenyl halides, X(-) + (CH)(3)X <= => X(CH)(3) + X(-), are investigated theoretically at four levels of theory, B3LYP/6-311+G**, MP2/6-311+G**, G2(+)MP2//MP2/6-311+G**, and G2(+)//MP2/6-311+G**. Four types of reaction paths, the sigma-attack S(N)2, pi-attack S(N)2'-syn, and S(N)2'-anti and sigmatropic 1,2-shift, are possible for all the halides. In the fluoride anion reactions, two types of stable adducts, syn- and anti-1,2-difluorocyclopropyl anions, can exist on the triple-well-type potential energy surface of the identity substitution reactions with rearrangement of double bond (C=C), S(N)2'-syn, and S(N)2'-anti processes. The TSs for the sigma-attack S(N)2 paths have "open" (loose) structures so that the ring positive charges are high rendering strong aromatic cyclopropenyl (delocalized) cation-like character. In contrast, in the pi-attack S(N)2' paths, a lone pair is formed at the unsubstituted carbon (C3), which stabilizes the 1,2-dihalocyclopropyl (delocalized) anion-like TS by two strong n(C)-sigma*(C-F) vicinal charge-transfer delocalization interactions. The barrier height increases in the order S(N)2'-anti < sigma-attack S(N)2 < S(N)2'-syn for X = Cl and Br, whereas for X = F the order is changed to S(N)2'-anti < S(N)2'-syn < sigma-attack S(N)2 due to the stable difluoro adduct formation. The sigmatropic 1,2-shift (circumambulatory) reactions have high activation barriers and cannot interfere with the substitution reactions.