First-Principles Prediction of Nucleophilicity Parameters for pi Nucleophiles: Implications for Mechanistic Origin of Mayr's Equation

Quantitative nucleophilicity scales are fundamental to organic chemistry and are usually constructed on the basis of Mayr's equation [log k=s(N+E)] by using benzhydrylium ions as reference electrophiles. Here an ab initio protocol was developed for the first time to predict the nucleophilicity parameters N of various pi nucleophiles in CH2Cl2 through transition-state calculations. The optimized theoretical model (BH&HLYP/6-311 + G (3df,2p)//B3LYP/6-311 + G(d,p)/PCM/UAHF) could predict the N values of structurally unrelated pi nucleophiles within a precision of ca. 1.14 units and therefore may find applications for the prediction of nucleophilicity of compounds that are not readily amenable to experimental characterization. The success in predicting N parameters from first principles also allowed us to analyze in depth the electrostatic, steric, and solvation energies involved in electrophile nucleophile reactions. We found that solvation does not play an important role in the validity of Mayr's equation. On the other hand, the correlations of the E, N, and log k values with the energies of the frontier molecular orbitals indicated that electrostatic/charge-transfer interactions play vital roles in Mayr's equation. Surprising correlations observed between the electrophile nucleophile C C distances in the transition state, the activation energy barriers, and the E and N parameters indicate the importance of steric interactions in Mayr's equation. A method is then proposed to separate the attraction and repulsion energies in the nucleophile electrophile interaction. It was found that the attraction energy correlated with N + E, whereas the repulsion energy correlated to the s parameter.