The Mayr Equation

4 The Mayr Equation. Mayr and his co-workers have developed Equation (31) which correlates the reactivity of carbocations and related electrophiles with k nucleophiles. 

Equation (31) has an electrophilic ( ) and a nucleophilic (N component and the value, s, is a nucleophile specific parameter. This equation has a close family relationship with the Ritchie and Swain-Scott equations (Chapter 2) and the Edwards equation (29). The equation successfully correlates rate constants for a wide range of disparate structures and 

The relative values of a and b indicate that the oxidation equilibrium (Equation 28) is a good model of the nucleophilic attack indeed a plot of log Nu/ waier against E- indicates a good linear correlation even without the introduction of.  

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Nucleophilicity parameters, N and % for electrophile-nucleophile combination based on the Mayr equation ogk = Sj (N+E), were reported for highly nucleophilic pyridines bearing amino groups at carbons 3, 4, and 5, isothioureas," and thiocarboxylates, dithiocarbamate, and dithiocarbonate." Electrophilicity parameters E were reported for triarylmethyl cations with para and meta fluorine substituents," 1,3-diarylallyl cations," and aldehydes, imines, and enones." Nucleofugality parameters Nf and Sf for ionization based upon the Mayr equation logki = Sf(Ef + Nf) were reported for acetate in aqueous methanol" and chloride in aprotic solvents." The latter study also shows that common solvent parameters do not reliably predict ionization rates in aprotic solvents. Electrofugality parameters Ef were reported for triarylmethyl cations with para and meta fluorine substituents." ... 

Nucleophilicity parameters N and % for electrophile-nucleophile combination based on the Mayr equation log k=+E) were reported for fluorides in protic solvents, enamines derived from imidazolidinones, trimethylsilyl enol ethers with perfluori-nated substituents at the a-carbon, O-methylated Breslow intermediates, anions of nucleobases and their subunits, enamides, symmetrical and unsymmetrical hydrazines, and heteroarylboron compounds. Of note, replacement of CH3 with CF3 and C6H5 with CgF5 in the trimethylsilyl enol ethers reduces the nucleophilicity by 8 and 4.5 orders of magnitude, respectively. Hydrazines have very similar nucle-ophilicities to alkyl amines in other words, there is no evidence of an a-effect. With NH2NMC2, there is a fast reversible reaction corresponding to addition of the tertiary amine, followed by a slow irreversible reaction for addition at the primary amine, with a 3000-fold difference in nucleophilicity between the two sites. ... 

Electrophilicity parameters E were reported for highly reactive benzhydrylium ions. This study shows that correlations of log 2 versus E remain linear even when = 0, showing that a change from activation control to entropy control does not cause a bend in the linear free energy relationship. The correlation lines do flatten when the diffusion limit is approached. Nucleofugality parameters and for 5 1 ionization based on the Mayr equation log kjon = + N ) were reported for fluoride in protic solvents, var-... 

In a series of reports published over the last 10-15 years, Mayr and co-workers obtained second-order rate constants for reactions of carbocations and other electrophiles such as metal-7i complexes with a series of nucleophiles, especially 7t-nucleophiles where a C C bond is formed. An impressive body of reactivity data has been accumulated, and, including data from other groups, correlated by the following equation. 

Mayr and co-workers developed an expression for the prediction of nucleophilic reactivity that considers both the nature of the nucleophile and the nature of the electrophile (equation 8.44). Here k is the rate constant for the... 

Finally, two important papers, a critique of Mayr s log k=s E+N) equation " and a rebuttal defending the original equation, have been published. 

The N+ relationship, as discussed above, is a systematization of experimental facts. The equation of Scheme 7-4 has been applied to nearly 800 rate constants of over 30 electrophiles with about 80 anionic, neutral, and even cationic nucleophiles covering a range of measured rate constants between 10-8 and 109s 1 (Ritchie, 1978). Only about a dozen rate constants deviated from the predicted values by more than a factor of 10, and about fifty by factors in the range 5-10. It is therefore, very likely that this correlation is not purely accidental. Other workers have shown it to be valid for other systems, e.g., for ferrocenyl-stabilized cations (Bunton et al., 1980), for coordinated cyclic 7r-hydrocarbons (Alovosus and Sweigart, 1985), and for selectivities of diarylcarbenes towards alkenes (Mayr, 1990 Mayr et al., 1990). On the other hand, McClelland et al. (1986) found that the N+ relationship is not applicable to additions of less stable triphenylmethyl cations. 

Mayr has reviewed the nucleophilicity parameters of allylstannanes and related compounds.276 The allyl-tin bond is easily cleaved, and this has been exploited in the preparation of pentafluorophenyltin chlorides and bromides (Equation (98)).277... 

In a review on the addition of carbenium ions to alkenes (equation 19) as a general procedure for carbon-carbon bond formation50, Mayr reported on investigations which also include the reactions of a variety of 1,3-dienes toward electrophilic carbon species generated by Lewis acid-promoted heterolysis of alkyl chlorides. 

As pointed out by Mayr,28 Ritchie,15 and Hine33,34 KR also measures the relative affinities of R+ and H30+ for the hydroxide ion. It can be regarded as providing a general affinity scale applicable to electrophiles other than carbocations.33,35 It can also be factored into independent affinities of R+ and H30+ as shown in Equations (2) and (3). Such equilibrium constants have been denoted If by Hine.33 AR corresponds to the ratio of constants for reactions (2) and (3) and, in so far as Kc for H30+ is the inverse of Kw the autoprotolysis constant for water, KR = KCKW... 

Rappoport and TaShma s work removed a major difficulty for Ritchie s analysis and helped pave the way for Mayr to exploit fully the wide applicability and simplicity of Equation (29) for predicting rates of reactions of electrophiles with nucleophiles. Mayr pointed out that Equation (29) could be rewritten as Equation (30), in which log ka corresponds to the rate constant for reaction of the electrophile under study with a reference nucleophile266 (chosen as water by Ritchie) which, in so far as it is characteristic of the... 

Eiowever, the equation that Mayr adopts is not Equation (32) but Equation... 

In recognition of the excellent correlation that exists between his own and Swain and Scott s (or Kevill s) parameters, Mayr suggests modifying Equation... 

Picosecond absorption spectroscopy was employed to study the dynamics of contact ion pairs produced upon the photolysis of substituted diphenylmethyl acetates in the solvents acetonitrile, dimethyl sulfoxide, and 2,2,2-trifluoroethanol.66 A review appeared of the equation developed by Mayr and co-workers log k = s(N + E), where k is the rate constant at 20 °C, s and N are nucleophile-dependent parameters, and is an electrophilicity parameter 67 This equation, originally developed for benzhydrylium ions and n-nucleophiles, has now been employed for a large number of different types of electrophiles and nucleophiles. The E, N, and s parameters now available can be used to predict the rates of a large number of polar organic reactions. Rate constants for the reactions of benzhydrylium ions with halide ions were obtained... 

Olah and coworkers, ° and Mayr and Striepe discussed the scope and limitations of aliphatic Friedel-Crafts alkylations. In particular, they considered factors that would favor reactions of the type shown in equation (121), where an alkene is alkylated by an alkyl halide. ° They reasoned that formation of the 1 1 addition products (42) can be expected, if (41) reacts faster with the alkene than (42), otherwise higher addition products will be formed. Mayr ° suggested that the relative dissociation rates of (41) and (42) induced by the Lewis acid should reflect their relative rates of addition to a common alkene. Furthermore, it was assumed that the solvolysis rates in 80% ethanol were proportional to the Lewis acid induced dissociation constants. A few examples where good yields of alkylated (addition) products were obtained are shown in equations (122) and (123). 

Mayr and co-workers further extended the method by stud)dng reactions of nucleophiles with the S-methyldibenzothiophenium ion (55, equation 8.45). The investigators plotted values of (log fc)/sw versus N for a series of nucleophiles and solvents reacting with 55 and obtained a linear correlation with slope 0.6. A subset of the experimental data is shown in Table 8.15 and plotted in Figure 8.38. The results indicated that the reaction of 55 with nucleophiles is affected only 60% as much by the nucleophilidty of the nucleophile as is the reaction of 54. 

Mayr and co-workers extended their investigations of nucleophilicity and basicity scales to the development of a scale of nucleofugality as well. They found that kinetic data could be correlated with a relationship in the form of equation 8.52. ... 

Bentley has proposed alternative equations to those of Mayr for nucleophile-electrophile combinations." He suggests that nucieophilicity depends on the reactivity of the electrophile and accounts for this using a Swain-Scott type of response... 

Initiation rate constants (ie, the rate constant of addition of the initiating carbocations to the monomer as shown in the set of equilibria in eq. 7) were determined for a large number of monomers using carbocations derived from the reaction of diaryl and substituted diarylmethyl chlorides with various Lewis acids (21). As indicated by the reaction scheme shown in equation 7, initiation can occur with the participation of solvent-separated ion pairs or tree ions. According to MayRs results, paired and free carbenium ions have identical reactivity and the reaction rates are independent of the nature of the counteranion. Rate constants were found to increase only slightly with increasing solvent polarity... 

Interestingly, the nucleophilicity parameters were shown to apply fairly well for reactions with the four l-halogeno-2,4-dinitrobenzenes in water and in methanol. An exception was for reaction with the azide ion, which showed lower than expected reactivity in the substitution reaction [20]. Inclusion of an extra parameter increases the applicability of the equation so that Mayr [60] has shown that Equation 6.2, where S is a nucleophile specific slope parameter, allows the reactivities of very many nucleophiles... 

Using Mayr s equation, which relates nucleophilicity (N) and electrophilicity ( ) by log A = s( +Af) using kinetic coefficients [68, 85], it may be possible to obtain an electrophilicity order for XDNB derivatives. The empirical electrophilicity numbers obtained are =-14.1 (X=F), -17.6 (X=C1 and Br), and -18.3 (X=I) for the whole family of halides [11, 71]. The theoretical electrophilicity numbers obtained from Equation 7.3 are as follows < = 1.31, 1.33, 1.30, and 1.28 for X = F, Cl, Br, and I, respectively. These results show that the electrophilicity index is not in line with the experimental figure even qualitatively. The explanation for this outcome may be traced to the absence of solvation effects that are incorporated in the solvent sensitivity parameter (s) in... 

A benzhydrilium carbocation series with calibrated electrophilicities, E, has been used to determine the nucleophilicity parameters, N and % for a variety of nucleophile-electrophile reactions. For example, benzhydrilium ions (16 examples, 1.48 > >-10.04) were used to evaluate the Lewis basicities of 2-imidazolines and related A-heterocyclic compounds through Mayr s equation log k = Sj N+E)3 The nucleophilicity parameters N and % of the A-heterocycles were determined by measuring the second-order rate constants for the reactions between the benzhydrilium ions and A-heterocycles. The calculated N and % parameters were shown to be useful in accurately predicting the reaction rates between the same A-heterocycles and another set of electrophiles, Michael acceptors. 

The reactivity of cationic monomers may be evaluated quantitatively by comparing their nucleophilidty parameter, N. Rates of electrophile-nucleophile combinations can be characterized by a simple equation in Mayr s linear free energy relationship ... 

The key-steps in many organocatalytic cycles are electrophile-nucleophile combinations. The reactions of carbocations and Michael acceptors with C, N, O, and P nucleophiles were carefully studied by Mayr, providing an empirical equation able to describe the reaction rates [4]. 

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