Theoretical studies on cross interactions in the protonation equilibria of diaryl ketones
Abstract
Cross interactions in the protonation equilibria of diaryl ketones have been studied MO theoretically at the MP2/6-31G*//RHF/6-31G* level. The susceptibility parameters, S, defined by ΔdX = SX × ΔσX+ and ΔdZ = SZ × ΔσZ+, where d is the length of the bond linking the ring to the carbonyl carbon (Cα), are all positive. However the cross-interaction terms SXZ =
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> 0 and SZX =
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< 0, have different signs indicating that the resonance interaction modes of the two rings in the equilibria are different; the X-ring interacts by π-polarization whereas the Z-ring by through-conjugation in the protonated state (P). These two different modes of resonance interactions are supported by the natural population analysis (NPA). The Hammett cross-interaction constants (CIC), ρXZ, are all negative and the magnitude is of a similar order to that of the susceptibility change, ΔSZ, upon protonation for the 5-membered heteroaromatic ring. The two different modes of resonance interactions within the X- and Z-rings are also reflected in the two different σ scales (σX and σZ+) that give the best fits to the general equation defining the CICs ρXZ using the reaction energy for the protonation reaction, ΔE°XZ. The magnitude of the CIC for an equilibrium process is in general large, especially when the reaction center has a strong cationic charge in the product state.