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 Δd_X = S_X × Δσ_X⁺ and Δd_Z = S_Z × Δσ_Z⁺, where d is the length of the bond linking the ring to the carbonyl carbon (C_α), are all positive. However the cross-interaction terms S_XZ = 

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 > 0 and S_ZX = 

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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), ρ_XZ, are all negative and the magnitude is of a similar order to that of the susceptibility change, ΔS_Z, 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 (σ_X and σ_Z⁺) that give the best fits to the general equation defining the CICs ρ_XZ 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.