Leffler indices

Another example of the use of transition state pKa values has been provided by Pollack (1978). From the rate constants for the decarboxylation of substituted a,a-dimethylbenzoylacetic acids ([37] — [38]) and their anions, he calculated pK for reaction of the acids (Table A6.2). The values vary significantly with the phenyl substituent (p = +1.7), much more so than the p/(a values of the substrate acids (p = +0.2). This difference is consistent with the proton being much closer to the phenyl group in the transition state than in the initial state, and it may even denote a relatively late transition state (Pollack, 1978). However, from the pKa values of the reactant acids (approximately 3.4), the transition states (approximately 4.4), and the enol product (11.8) (Pruszynski et al., 1986), the Leffler index... 

The hydration of simple ketenes (RCH=C=0—> RCH2COOH) also shows relatively constant values of oh w which are quite low (100-1000) (Tidwell, 1990 Allen et al., 1992), implying p/fj = 11 to 12 for the transition state for water attack. Corresponding to this, the Leffler index and the /3nuc are both about 0.25. Whether these low values really indicate an early transition state or arise because water and hydroxide ion react quite differently is not yet clear. However, it appears possible that water attack proceeds through a cyclic mechanism involving two (or more) water molecules (Allen et al., 1992) whereas hydroxide ion probably attacks conventionally as a nucleophile (Tidwell, 1990). Of course, any mechanism for the water reaction which is superior to simple nucleophilic attack will elevate kw and necessarily lead to low kOH/kw ratios. 

The Leffler index Unuc, 0,21 (Scheme 38), indicates that bond formation is only 21% complete in the transition structure (Scheme 39). It is not possible to determine the percentage of bond fission from this data. If, however, the reaction were assumed to be quasi-symmetrical, then the results would indicate that bond fission is well advanced in the transition state. 

A. Williams, Effective Charge and Leffler s Index as Mechanistic Tools for Reactions in Solution, Acc. Chem. Res., 1984,17, 425. 

The parameter is the bond length, y, at any point in the reaction map divided by the bond length in the product (rj,(product)) ( Jrc is the value of ry in the reaction complex. The terms r, (r Jrc nd q, for the bond fission component, x, are similarly defined. Since t can be estimated from Leffler s a parameters (see later) it provides a useful experimental index of tightness in a reaction where substantial change is suffered by two bonds. 

S. Thea and A. Williams, Measurement of Effective Charge in Organic Reactions in Solution, Chem. Soc. Rev., 1986, 15, 125 A. Williams, Effective Charge and Leffler s Index as Mechanistic Tools for Reactions in Solution, Acc. Chem. Res., 1984,17, 465. 

Williams A. Effective charge and Leffler s index as mechanistic tools for reactions in solution. Acc Chem Res. 1984 17 425-430. 

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