A practical guide for estimating rates of heterolysis reactions

Chemists are well trained to recognize what controls relative reactivities within a series of compounds. Thus, it is well-known how the rate of ionization of R-X is affected by the stabilization of the carbocation R(+), the nature of the leaving group X(-), or the solvent ionizing power. On the other hand, when asked to estimate the half-life of the ionization of a certain substrate in a certain solvent, most chemists resign. This question, however, is crucial in daily laboratory practice. Can a certain substrate R-X be handled in alcoholic or aqueous solution without being solvolyzed? Can a biologically active tertiary amine or azole be released by ionization of a quaternary ammonium ion? In this Account, we describe a straightforward means of addressing such experimental concerns. A semiquantitative answer to these questions is given by the correlation equation log k(25 °C) = s(f)(N(f) + E(f)), in which carbocations R(+) are characterized by the electrofugality parameter E(f), and leaving groups X(-) in a certain solvent are characterized by the nucleofugality parameter N(f) and the nucleofuge-specific sensitivity parameter s(f). As s(f) is typically around 1 (0.8 < s(f) < 1.2), ionization half-lives of around 1 h at 25 °C can be expected when E(f) + N(f) = -4. This correlation equation is formally analogous to the linear free energy relationship that was used to derive the most comprehensive nucleophilicity and electrophilicity scales presently available (Mayr, H.; Bug, T.; Gotta, M. F.; Hering, N.; Irrgang, B.; Janker, B.; Kempf, B.; Loos, R.; Ofial, A. R.; Remennikov, G.; Schimmel, H. Reference Scales for the Characterization of Cationic Electrophiles and Neutral Nucleophiles. J. Am. Chem. Soc. 2001, 123, 9500-9512). By subjecting 628 solvolysis rate constants k(25 °C) for different benzhydryl derivatives (aryl(2)CH-X) to a least-squares minimization on the basis of the correlation equation, we obtained and tabulate here (i) the electrofugality parameters E(f) for 39 benzhydrylium ions and (ii) the nucleofuge-specific parameters N(f) and s(f) for 101 combinations of common leaving groups and solvents. We show that the E(f) parameters of the reference electrofuges can be used to determine N(f) and s(f) for almost any combination of leaving group and solvent. The nucleofuge-specific parameters of the reference systems can analogously be used to derive the electrofugalities E(f) of other types of carbocations. While it has long been recognized that good nucleophiles are not necessarily poor nucleofuges, it is now reported that there is also no general inverse relationship between electrophilicity and electrofugality. Although more electrophilic methyl- and methoxy-substituted benzhydrylium ions are generally weaker electrofuges, the inverse relationship between electrophilicity and electrofugality breaks down in the series of amino-substituted benzhydrylium ions. Because neither differential solvation of the carbocations nor steric effects are explicitly considered by this treatment, predictions for substrates not belonging to the benzhydrylium series are only reliable within a factor of 10. This is hardly acceptable to physical organic chemists, who are used to high precision within narrow groups of compounds. The synthetic chemist, however, who is seeking orientation in a reactivity range of 25 orders of magnitude, might appreciate the simplicity of this approach, which only requires considering the sum E(f) + N(f) or consulting our summary graphs.