How does the s(E plus N) equation work? Comparisons with a modified Swain-Scott equation (E plus sN) and revision of the N1 scale of solvent nucleophilicity

Modifications of the Swain-Scott equation (log k/k(0)) = sn) give an equation log k(1) = (E + sN(1)'); k(1) is the rate constant, E is an electrophilicity parameter, N-1' is a solvent nucleophilicity parameter and s is an electrophile-specific sensitivity parameter. The equation is tested using over 300 published first-order rate constants (k(1)) for decay of a range of benzhydrylium cations in various solvents, on which the published N-1 scale of solvent nucleophilicity is based (S. Minegishi, S. Kobayashi and H. Mayr, J. Am. Chem. Soc. 2004, 126, 5174-5181) using the alternative equation log k = s(E + N-1), in which s is a nucleophile-specific parameter. The modified (E + sN(1)') equation provides a revised N-1' scale of solvent nucleophilicity, and a more precise fit, with less than half the number of adjustable parameters. It is found that the sensitivities of the benzhydrylium cations to changes in solvent nucleophilicity decrease slightly as reactivity increases, in contrast to s(E + N) equations, which show no trends in s values. It is proposed that more reliable N scales can be defined using (E + sN), because N is determined directly from definitions, and residual errors (e.g. experimental or due to solvation effects) can be incorporated into the slope and intercept. The complex reasons for the success of equations of the type log k = s(E + N) are discussed. Copyright (C) 2009 John Wiley & Sons, Ltd.