Bernard Denegri

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.

Method for Estimating SN1 Rate Constants: Solvolytic Reactivity of Benzoates

Nucleofugalities of pentafluorobenzoate (PFB) and 2,4,6-trifluorobenzoate (TFB) leaving groups have been derived from the solvolysis rate constants of X,Y-substituted benzhydryl PFBs and TFBs measured in a series of aqueous solvents, by applying the LFER equation: log k = s(f)(E(f) + N(f)). The heterolysis rate constants of dianisylmethyl PFB and TFB, and those determined for 10 more dianisylmethyl benzoates in aqueous ethanol, constitute a set of reference benzoates whose experimental ΔG(‡) have been correlated with the ΔH(‡) (calculated by PCM quantum-chemical method) of the model epoxy ring formation. Because of the excellent correlation (r = 0.997), the method for calculating the nucleofugalities of substituted benzoate LGs have been established, ultimately providing a method for determination of the S(N)1 reactivity for any benzoate in a given solvent. Using the ΔG(‡) vs ΔH(‡) correlation, and taking s(f) based on similarity, the nucleofugality parameters for about 70 benzoates have been determined in 90%, 80%, and 70% aqueous ethanol. The calculated intrinsic barriers for substituted benzoate leaving groups show that substrates producing more stabilized LGs proceed over lower intrinsic barriers. Substituents on the phenyl ring affect the solvolysis rate of benzhydryl benzoates by both field and inductive effects.

Solvolytic Reactivity of Heptafluorobutyrates and Trifluoroacetates

A series of X,Y-substituted benzhydryl heptafluorobutyrates (1-6-HFB) and trifluoroacetates (1-6-TFA) were subjected to solvolysis in various methanol/water, ethanol/water, and acetone/water mixtures at 25 degrees C. The LFER equation log k = s(f)(E(f) + N(f)) was used to derive the nucleofuge-specific parameters (N(f) and s(f)) for S(N)1-type reaction. In comparison with TFA, the HFB leaving group is a better nucleofuge for less than 0.5 unit of N(f). X,Y-Substituted benzhydryl trifluoroacetates solvolyze by way of S(N)1 reactions unless electron-withdrawing groups are attached to aromatic rings. In such cases the substrates solvolyze faster than predicted for the S(N)1 route because of the change in mechanism. X,Y-Substituted benzhydryl heptafluorobutyrates examined here (E(f) > or = -7.7) solvolyze according to the S(N)1 pathway. The almost parallel log k vs. E(f) lines in various solvents for HFBs and TFAs, and the corresponding slope parameters (s(f) are in the range of 0.91 and 0.83), indicate early TS with moderately advanced charge separation. NBO charges of HFB and TFA anions and the affinities obtained, all calculated at the PCM-B3LYP/6-311+G(2d,p)//PCM-B3LYP/6-311+G(2d,p) level, revealed that the HFB anion slightly better delocalizes the developing negative charge than TFA, and that the affinity of the benzhydrylium ion is slightly larger toward TFA than toward the HFB anion, which is in accordance with the greater solvolytic reactivity of HFB.

Effect of the Leaving Group and Solvent Combination on the LFER Reaction Constants

Fine effects that influence the variations of the reaction constants sf in LFER log k = sf(Nf + Ef) have been summarized here. Increasing solvent polarity in the series of binary mixtures increases the solvolysis rates for the same factor for all benzhydryl derivatives in which the solvation of the leaving group moiety in the transition state is substantial, i.e., log k vs. Ef correlation lines are parallel (same sf). For the substrates in which the demand for solvation of the leaving groups moiety is reduced, (e.g., carbonates) sf parameters decrease as the fraction of the water in a given solvent/water mixture increases (log k vs. Ef plots converge), due to decreasing solvation of the electrofuge moiety toward bigger electrofugality. The abscissa of the intersection of the converging plots might indicate the critical electrofugality above which the solvolysis rates should not depend of the water fraction. Larger reaction constant sf indicate later transition state for structurally related substrates only, while sf parameters for structurally different substrates cannot be compared likely due to different intrinsic barriers. Inversion in relative abilities of leaving groups is possible if they have similar reactivities and are characterized with different reaction constants.

Leaving group property of dimethyl sulfide.

The LFER equation log k = s(f)(E(f) + N(f)) was used to derive the nucleofuge specific parameters (N(f) and s(f)) for dimethyl sulfide in the series of aqueous alcohols, using the S(N)1 solvolysis rate constants obtained for X-substituted benzhydryl dimethyl sulfonates 1-5. The slope parameters (s(f)) are practically independent of the solvent used, while N(f) parameters slightly decrease as the polarity of the solvent increases.

Solvolytic Behavior of Aryl and Alkyl Carbonates. Impact of the Intrinsic Barrier on Relative Reactivities of Leaving Groups

The effect of negative hyperconjugation on the solvolytic behavior of carbonate diesters has been investigated kinetically by applying the LFER equation log k = sf(Ef + Nf). The observation that carbonate diesters solvolyze faster than the corresponding carboxylates and that the enhancement of aromatic carbonates is more pronounced indicates that the negative hyperconjugation and π-resonance within the carboxylate moiety is operative in TS. The plots of ΔG‡ vs approximated ΔrG° for solvolysis of benzhydryl aryl/alkyl carbonates and benzhydryl carboxylates reveal that a given carbonate solvolyzes over the higher Marcus intrinsic barrier and over the earlier transition state than carboxylate that produces an anion of similar stability. Due to the lag in development of the electronic effects along the reaction coordinate, the impact of the intrinsic barrier on solvolytic behavior of carbonates is more important than in the case of carboxylates and phenolates. Consequently, the solvolytic reaction constants (sf) are generally lower for carbonates than for carboxylates. Because of considerable lower reaction constants of carbonates, an inversion of relative reactivities between aryl/alkyl carbonate and another leaving group of similar nucleofugality (Nf) may occur if the electrofuge moiety of a substrate is switched.