Theoretical studies on cross interactions in the protonation equilibria ofdiaryl ketones

Cross interactions in the protonation equilibria of diaryl ketones have bee n studied MO theoretically at the MP2/6-31G*//RHF/6-31G* level. The suscept ibility parameters, S, defined by Delta d(X) = S-X x Delta sigma(X)(+) and Delta d(Z) = S-Z x Delta sigma(Z)(+), where d is the length of the bond lin king the ring to the carbonyl carbon (C-alpha), are all positive. However t he cross-interaction terms [GRAPHICS] have different signs indicating that the resonance interaction modes of the two rings in the equilibria are different; the X-ring interacts by pi-pola rization whereas the Z-ring by through-conjugation in the protonated state (P). These two different modes of resonance interactions are supported by t he natural population analysis (NPA). The Hammett cross-interaction constan ts (CIC), rho(XZ), are all negative and the magnitude is of a similar order to that of the susceptibility change, Delta S-Z, upon protonation for the 5-membered heteroaromatic ring. The two different modes of resonance intera ctions within the X- and Z-rings are also reflected in the two different a scales (sigma(X) and sigma(Z)(+)) that give the best fits to the general eq uation defining the CICs rho(XZ) using the reaction energy for the protonat ion reaction, Delta E-XZ(o). The magnitude of the CIC for an equilibrium pr ocess is in general large, especially when the reaction center has a strong cationic charge in the product state.