Scales of Lewis Basicities toward C‑Centered Lewis Acids (Carbocations)

Equilibria for the reactions of benzhydryl cations (Ar₂CH⁺) with phosphines, <i>tert</i>-amines, pyridines, and related Lewis bases were determined photometrically in CH₂Cl₂ and CH₃CN solution at 20 °C. The measured equilibrium constants can be expressed by the sum of two parameters, defined as the Lewis Acidity (LA) of the benzhydrylium ions and the Lewis basicity (LB) of the phosphines, pyridines, etc. Least-squares minimization of log <i>K</i> = LA + LB with the definition LA = 0 for (4-MeOC₆H₄)₂CH⁺ gave a Lewis acidity scale for 18 benzhydrylium ions covering 18 orders of magnitude in CH₂Cl₂ as well as Lewis basicities (with respect to C-centered Lewis acids) for 56 bases. The Lewis acidities correlated linearly with the quantum chemically calculated (B3LYP/6-311++G­(3df,2pd)//B3LYP/6-31G­(d,p) level) methyl anion affinities of the corresponding benzhydrylium ions, which can be used as reference compounds for characterizing a wide variety of Lewis bases. The equilibrium measurements were complemented by isothermal titration calorimetry studies. Rates of S_N1 solvolyses of benzhydryl chlorides, bromides, and tosylates derived from <b>E­(13–33)</b>⁺, i.e., from highly reactive carbocations, correlate excellently with the corresponding Lewis acidities and the quantum chemically calculated methyl anion affinities. This correlation does not hold for solvolyses of derivatives of the better stabilized amino-substituted benzhydrylium ions <b>E­(1–12)</b>⁺. In contrast, the correlation between electrophilic reactivities and Lewis acidities (or methyl anion affinities) is linear for all donor-substituted benzhydrylium ions <b>E­(1–21)</b>⁺, while the acceptor-substituted benzhydrylium ions <b>E­(26–33)</b>⁺ react more slowly than expected from their thermodynamic stabilities. The boundaries of linear rate-equilibrium relationships were thus defined