Theoretical studies on empirical structure–reactivity relationship: the Yukawa–Tsuno equation

The substituent‐dependent stabilization energies (δ X Δ E ) of a series of α,α‐R 1 R 2 benzyl cations were determined by means of ab initio calculation at the MP2/6–31G*//RHF/6–31G* + ZPE (scaled 0.8929) level, based on the isodesmic hydride transfer reactions between ring X‐substituted and unsubstituted R 1 R 2 benzyl cations. Substituent stabilities (δ X Δ E ) of α,α‐dimethylbenzyl cations were determined in the same way, to define a reference set of the ab initio σ + values. The (δ X Δ E ) of α,α‐dimethylbenzyl cations of which the cation center is set orthogonal to the benzene π‐system were correlated linearly with σ 0 (solution). Based on this correlation, a set of ab initio σ 0 constants [(σ 0 ) ab ] was determined. The ab initio resonance substituent constants $(\Delta \overline{\sigma}_{\rm R}^{+})_{ab}$ were defined as (σ + ) ab  − (σ 0 ) ab . Employing the present ab initio set of (σ 0 ) ab and $(\Delta \overline{\sigma}_{\rm R}^{+})_{ab}$ constants, the ab initio Yukawa–Tsuno (Y–T) equation was applied to 18 sets of cation stabilities δ X Δ E associated with hydride transfer reaction systems. Successful applications of the ab initio Y–T equation confirm the theoretical validity of the empirical Y–T relationship; in practice, the Y–T equation makes it possible to divide the electronic substituent effect into the non‐resonance and resonance contributions. Copyright © 2003 John Wiley & Sons, Ltd.