The gas-phase Lewis acidity of group 13 element aryl and perfluorinated aryl derivatives E(C₆H₅)₃, E(C ₆H₄F)₃, and E(C₅F₅) ₃ (E = B, Al, Ga) toward different donor molecules (NH₃, H₂O, PH₃, H^-, CH₃^-, F^-) has been theoretically studied at the RI-BP86/def2-TZVPP level of theory. The following order of the acceptor ability has been established: E(C₆H₅)₃ ≈ E(C₆H ₄F)₃ < E(C₆F₅)₃ ≈ ECl₃. The acceptor strengths of E(C₆H₅) ₃ and E(C₆H₄F)₃ are comparable to each other but much weaker compared to E(C₆H₅) ₃, which has a similar acceptor strength to those of the corresponding trihalides ECl₃. The acceptor ability of ER₃ decreases in the order Al > Ga > B. In the gas phase, Al(C ₆F₅)₃ is found to be a stronger Lewis acid than B(C₆F₅)₃ toward all electron donors but H ^-. In contrast to AlCl₃, which forms stable dimers, Al(C₆F₃)₃ is monomelic and tiierefore has a much higher Lewis acid reactivity . The reactivity of perfluorinated derivatives E(C₅F₅)₃ (E = B, Al, Ga) toward ammonolysis and hydrolysis processes and L₂ZrMe₂ (L = Cl, Cp, Cp*) as cocatalysts in olefin polymerization is also discussed.