Brpnsted coefficient

The Brpnsted coefficient a represents the sensitivity of the rate to the acid strength of the catalyst. It is a measure of the degree of proton transfer from catalyst to substrate in the transition state. For nearly all reactions where BH+ contains acidic N-H or O-H groups, a is in the range 0-1. 

Solvolysis studies of meta- and para-substituted phenyl phosphates (240) in anhydrous Bu OH and in Am OH have revealed that generally reactions of dianions are much faster in alcohols than in water. For example, the dianion of p-nitrophenyl phosphate (240 X = 4-NO2) reacts 7500- and 8750-fold faster in Bu OH and Am OH, respectively, than in water." The results of a theoretical study of the reactivity of phosphate monoester anions in aqueous solution do not support the generally accepted view that Brpnsted coefficients fhg = —1.23 and jSnuc = 0.13 determined more than 30 years ago for the uncatalysed reaction of water and a monophosphate dianion (241) represent conclusive evidence for the dissociative mechanism. It is suggested that, instead, the observed LFERs could correspond to a late transition state in the associative mechanism." ... 

Nucleophilic addition of phenolic nucleophiles to l,l-dicyano-2-arylethenes in the gas phase and in water has been studied theoretically" using the semiempirical AMI method and the Cramer-Truhlar solvation model SM2.1. The difference between the Brpnsted coefficients (a" = 0.81 and P" =0.65) determined for the gas-phase reaction is indicative of a small positive transition state imbalance of / = 0.16. For reaction in water the estimates (a" = 0.61 and P" = 0.36, giving I = 0.25) are close to the experimental values (a" = 0.55 and P" = 0.35) obtained with amine bases, and the small imbalance is as expected for a reaction involving no hybridization change at the incipient carbanion site. 

The Brpnsted coefficient /3b = 0.52 for deprotonation of 3-phenylcoumaran-2-one (108) by a series of bases in 50% (v/v) water-dioxane, and q bh = 0.48 for reprotonation by the conjugate acid of the buffer, are indicative of a fairly symmetrical transition state for proton transfer, although the primary KE, ku/ku = 3.81, found for proton abstraction by HO is lower than expected. " The moderate intrinsic rate constant for deprotonation of (108) suggests that generation of the charge in the transition state is accompanied by only a small amount of molecular and solvent reorganization. In acidic solution, below pH 5, O-protonation of (110) occurs initially to form (109)... 

It is accepted that the acmal nucleophile in the reactions of oximes with OPs is the oximate anion, Pyr+-CH=N-0 , and the availability of the unshared electrons on the a-N neighboring atom enhances reactions that involve nucleophilic displacements at tetravalent OP compounds (known also as the a-effect). In view of the fact that the concentration of the oximate ion depends on the oxime s pATa and on the reaction pH, and since the pKs also reflects the affinity of the oximate ion for the electrophile, such as tetra valent OP, the theoretical relationship between the pATa and the nucleophilicity parameter was analyzed by Wilson and Froede . They proposed that for each type of OP, at a given pH, there is an optimum pK value of an oxime nucleophile that will provide a maximal reaction rate. The dissociation constants of potent reactivators, such as 38-43 (with pA a values of 7.0-8.5), are close to this optimum pK, and can be calculated, at pH = 7.4, from pKg = — log[l//3 — 1] -h 7.4, where is the OP electrophile susceptibility factor, known as the Brpnsted coefficient. If the above relationship holds also for the reactivation kinetics of the tetravalent OP-AChE conjugate (see equation 20), it would be important to estimate the magnitude of the effect of changes in oxime pX a on the rate of reactivation, and to address two questions (a) How do changes in the dissociation constants of oximes affect the rate of reactivation (b) What is the impact of the /3 value, that ranges from 0.1 to 0.9 for the various OPs, on the relationship between the pKg, and the rate of reactivation To this end, Table 3 summarizes some theoretical calculations for the pK. ... 

In the second mechanism, the first and second steps are concerted. In the case of hydrolysis of 2-(p-nitrophenoxy)tetrahydropyran, general acid catalysis was shown470 demonstrating that the substrate is protonated in the rate-determining step (p. 259). Reactions in which a substrate is protonated in the rate-determining step are called A-Se2 reactions.471 However, if protonation of the substrate were all that happens in the slow step, then the proton in the transition state would be expected to lie closer to the weaker base (p. 259). Because the substrate is a much weaker base than water, the proton should be largely transferred. Since the Brpnsted coefficient was found to be 0.5,the proton was actually transferred only... 

Acknowledgement is made to the Natural Sciences and Engineering Research Council of Canada for support of theoretical work on the problem of variation of a with T which is, in part, reported in this chapter. The author is also grateful to professors J. O M. Bockris, E. Gileadi and M. Weaver, and Dr. J. Appleby, to whom this chapter was circulated prior to publication, for their comments. Thanks are due also to Professor E. B. Yeager for provision of data on O2 reduction in phosphoric acid and for material related to Eq. (24) in this chapter to Dr. R. P. Bell, F.R.S., for helpful discussion in correspondence on the question of temperature dependence of Brpnsted coefficients to Professor D. F. Evans for provision of unpublished data on nitro-compound reduction and to Messrs. D. F. Tessier and D. Wilkinson in our laboratory for helpful discussion on various points. 

The orders of nucleophilic reactivity for alkylation and acylation were found to be quite different (13, 14) and in subsequent work (15) this finding was related to the extent of bond formation in the transition state as given empirically by the Brpnsted coefficient, (3. Previously, this difference was used to predict the position of bond fission in the alkaline hydrolysis of phosphinate, phosphonate, and phosphate esters (12). Jencks and Carriuolo (16) came to similar conclusions around the same time in outstanding work on the acylation of p-nitrophenyl acetate. 

Normalized p values for this reaction catalyzed by three different aryloxide ions are reported in Table 12 while Brpnsted coefficients for this type of catalysis are summarized in Table 13. The rather low values (high a(k )) suggest that the proton transfer from the attacking methanol nucleophile to the buffer base has made much less progress than the C-0 bond formation at the transition state (or that in the reverse direction protonation of the departing MeO by the buffer acid is ahead of C-0 bond cleavage), as shown in 82 on MeO group). 

The Brpnsted relationship (see Section 3.7.1.2 to review the Brpnsted catalysis law) shows a correlation with the identity of the alkoxy group. The alkoxy groups derived from more acidic alcohols have lower Brpnsted coefficients a. 

By determining k A for several different buffer catalysts and each of several alkoxy leaving groups, it was determined that there was a relationship between the Brpnsted coefficient a and the structure of the alkoxy leaving group. The data are given and show that a decreases as the alkoxy group becomes less basic. 

If one considers the Brpnsted coefficient, a =9AGV9AG, given by the theory of Marcus (eq(45)), one gets... 

A related refinement of the picture of the transition-state region is concerned with the question whether the electronic and atomic motions concerned in the bond changes all take place synchronously or whether in the transition state some of them are more advanced than others. The relative extent of individual bond changes in a transition state is called the balance . Clearly any imbalance will affect the electron distribution and therefore the reactivity of the system. Theoretical agrument shows that a measure of the imbalance is the ratio of the Brpnsted coefficient for bond formation to that for bond fission. 

Brpnsted correlations for proton transfer and methyl transfer between pairs of mimicked 4-substituted pyridines have been simulated by means of AMI molecular-orbital calculations.The relationship to the Marcus equation is also considered. It is concluded that the Brpnsted coefficient fi provides an approximate measure of the position of the transition structure along the reaction coordinate between reactant and product encounter complexes. 

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