Carbocations measures

Reaction energies for the formation of each type of adduct with both carbocations (measured as the energy difference between the adduct minus guanine and carbocation total energies) were comparable, and the same observation applied to the AGr values. Inclusion of the solvent caused an increase in the endothermicity of the reactions, presumably due to a better sol vation of the carbocations. The change in the preferred product of the addition... 

Apparently, these results implied an inverse relationship between reactivity and selectivity, with the reactivity of the carbocation measured by the inverse of the rate constant for solvolysis. This indeed was not unexpected in the context of a general perception that highly reactive reagents, especially reactive intermediates such as carbocations, carbanions, or carbenes are unselective in their reactions.257 259 Such a relationship is consistent with a natural inference from the Hammond postulate258 and Bell-Evans-Polanyi relationship,260 and is illustrated experimentally by the dependence of the Bronsted exponent for base catalysis of the enolization of ketones upon the reactivity of the ketone,261,262 and other examples21,263 including Richard s careful study of the hydration of a-methoxystyrenes.229... 

When using a cation source in conjunction with a Friedel-Crafts acid the concentration of growing centers is most often difficult to measure and remains unknown. By the use of stable carbocation salts (for instance trityl and tropyhum hexachloroantimonate) the uncertainty of the concentration of initiating cations is eliminated. Due to the highly reproducible rates, stable carbocation salts have been used in kinetic studies. Their use, however, is limited to cationicaHy fairly reactive monomers (eg, A/-vinylcarbazole, -methoxystyrene, alkyl vinyl ethers) since they are too stable and therefore ineffective initiators of less reactive monomers, such as isobutylene, styrene, and dienes. 

Measurement of (R /R ) can be accomplished by cyclic voltammetry for relatively Stable species and by other methods for less stable cations. The values obtained for AG -range from 83kcal/mol for the aromatic tropylium ion to 130kcal/mol for destabilized betizylic cations. For stable carbocations, the results obtained by this method correlate with cation stabiUty as measured by pKf.+. Some of these data are presented in Table 5.3. 

It has been possible to obtain thermodynamic data for the ionization of alkyl chlorides by reaction with SbFs, a Lewis acid, in the nonnucleophilic solvent S02C1F. It has been foimd that the solvation energies of the carbocations in this medium are small and do not differ much from one another, making comparison of the nonisomeric systems possible. As long as subsequent reactions of the carbocation can be avoided, the thermodynamic characteristics of this reaction provide a measure of the relative ease of carbocation formation in solution. 

A wide range of caibocation stability data has been obtained by measuring the heat of ionization of a series of chlorides and cafbinols in nonnucleophilic solvents in the presence of Lewis acids. Some representative data are given in Table 5.4 These data include the diarylmediyl and triarylmethyl systems for which pX R+ data are available (Table 5.1) and give some basis for comparison of the stabilities of secondary and tertiary alkyl carbocations with those of the more stable aryl-substituted ions. 

Ho, the acidity function introduced by Hammett, is a measure of the ability of the solvent to transfer a proton to a base of neutral charge. In dilute aqueous solution ho becomes equal to t d Hq is equal to pH, but in strongly acid solutions Hq will differ from both pH and — log ch+. The determination of Ho is accomplished with the aid of Eq. (8-89) and a series of neutral indicator bases (the nitroanilines in Table 8-18) whose pA bh+ values have been measured by the overlap method. Table 8-19 lists Ho values for some aqueous solutions of common mineral acids. Analogous acidity functions have been defined for bases of other structural and charge types, such as // for amides and Hf for bases that ionize with the production of a carbocation ... 

The second point to explore involves carbocation stability. 2-Methyl-propene might react with H+ to form a carbocation having three alkyl substituents (a tertiary ion, 3°), or it might react to form a carbocation having one alkyl substituent (a primary ion, 1°). Since the tertiary alkyl chloride, 2-chloro-2-methylpropane, is the only product observed, formation of the tertiary cation is evidently favored over formation of the primary cation. Thermodynamic measurements show that, indeed, the stability of carbocations increases with increasing substitution so that the stability order is tertiary > secondary > primary > methyl. 

One way of determining carbocation stabilities is to measure the amount of energy required to form the carbocation by dissociation of the corresponding alkyl halide, R-X - R+ + X . As shown in Figure 6.10, tertiary alkyl halides dissociate to give carbocations more easily than secondary or primary ones. As a result, trisubstituted carbocations are more stable than disubstituted ones, which are more stable than monosubstituted ones. The data in Figure 6.10 are taken from measurements made in the gas phase, but a similar stability order is found for carbocations in solution. The dissociation enthalpies are much lower in solution because polar solvents can stabilize the ions, but the order of carbocation stability remains the same. 

Proton affinities of ethene (684 121) and 680129) kJ mol-1) measured experimentally correspond with results from ab initio calculations (698 kJ mol-1 130)). MINDO/3 calculations (with AHf(H+) = 1528 kJ mol-1 91)) also deliver a result of comparable value (714 kJ mol 1) when the formation of a classical carbocation during the protonation is assumed. 

An important tool for the investigation of carbocation structure is measurement of... 

This species may be OH , halide ion, or any other negative ion, or it may be a neutral species with a pair to donate, in which case, of course, the immediate product must bear a positive charge (see Chapters 10, 13, 15, 16). These reactions are very fast. A recent study measured (the rate constant for reaction of a simple tertiary carbocation) to be 3.5 x 10 s . ... 

Unfortunately, it is not easy to measure acid strengths of very weak acids like the conjugate acids of simple unsubstituted carbanions. There is little doubt that these carbanions are very unstable in solution, and in contrast to the situation with carbocations, efforts to prepare solutions in which carbanions such as ethyl or isopropyl exist in a relatively free state have not yet been successful. Nor has it been possible to form these carbanions in the gas phase. Indeed, there is evidence that simple carbanions such as ethyl and isopropyl are unstable toward loss of an electron, which converts them to radicals. Nevertheless, there have been several approaches to the problem. Applequist and O Brien studied the position of equilibrium for the reaction... 

A free radical (often simply called a radical) may be defined as a species that contains one or more unpaired electrons. Note that this definition includes certain stable inorganic molecules such as NO and NO2, as well as many individual atoms, such as Na and Cl. As with carbocations and carbanions, simple alkyl radicals are very reactive. Their lifetimes are extremely short in solution, but they can be kept for relatively long periods frozen within the crystal lattices of other molecules. Many spectral measurements have been made on radicals trapped in this manner. Even under these conditions, the methyl radical decomposes with a half-life of 10-15 min in a methanol lattice at 77 K. Since the lifetime of a radical depends not only on its inherent stabihty, but also on the conditions under which it is generated, the terms persistent and stable are usually used for the different senses. A stable radical is inherently stable a persistent radical has a relatively long lifetime under the conditions at which it is generated, though it may not be very stable. 

This is less common than rearrangement of carbocations, but it does occur (though not when R = alkyl or hydrogen see Chapter 18). Perhaps the best-known rearrangement is that of cyclopropylcarbinyl radicals to a butenyl radical. The rate constant for this rapid ring opening has been measured in... 

The oxidation potential of carbanions, ox> or the reduction potential of carbocations, red> could be a practical scale of stability as defined by (3). These potentials can be measured by voltammetry, although the scale is subject to assumptions regarding elimination of the diffusional potential and solvation effects. 

The electron affinity of the carbocations as measured by red is a useful index for the stability of the carbocations. It is of great interest to correlate the occurrence of three principal reactions between a carbocation and a carbanion, i.e. covalent bond formation (36), single-electron transfer (37) and salt formation (38), with the magnitude of the E ed for the carbocations. 

Fig. 8 Reactions of various carbocations with Kuhn s anion [2 ] as compared with their reduction potentials (peak potentials measured vs. Ag/Ag in acetonitrile by cyclic voltammetry cf. Tables 1 and 8 and Okamoto et al., 1983). SALT, salt formation COV, covalent bond formation ET, single-electron transfer. 

For the alternant PAH that have been studied extensively, bay-region diol epoxides are important metabolically activated forms. Studies of the chemical and biological activity of a variety of diol epoxides have provided insight into the factors related to reactivity and biological activity. Chemical reactivity, as measured by spontaneous hydrolysis, correlated well with calculated quantum chemical parameters that estimate ir-electron stabilization upon conversion of the epoxide to a benzylic carbocation, provided... 

The relative magnitude of the kinetic effects of two substituents, Rt and R2, on the C0 and carbon atoms of the double bond (Scheme 7) is taken as a measure of the symmetry of the charge development and therefore of bromine bridging in the bromocations. It is assumed that in a bromonium ion the effects of Rx and R2 must be similar, whereas for a /J-bromocarbocation, C+, the effect of Rj must be significantly greater than that of R2. Consequently, the substituent effects are analysed in terms of a multipathway scheme (Scheme 7) where open carbocations and the bridged ion are formed via discrete pathways with rate constants kx, kf and kBr respectively (Ruasse and Dubois, 1974). The rate constant k in (4) is therefore the sum of these three... 

Each of these bond enthalpies is an average enthalpy, measured from a series of similar molecules. Values of AH, . for, say, C-H bonds in hydrocarbons are likely to be fairly similar, as shown by the values in Table 3.3. The bond energies of C-H bonds will differ (sometimes quite markedly) in more exceptional molecules, such as those bearing ionic charges, e.g. carbocations. AH, . values differ for the OH bond in an alcohol, in a carboxylic acid and in a phenol. 

The structure of carbocation has been measured by 13C nmr shift of the carbon atom carrying the positive charge. The shift agrees with the electron density on this carbon. 

As a measure of their thermodynamic stability, the pAfR+ values for the carbocation salts were determined spectrophotometrically in a buffer solution prepared in aqueous solution of acetonitrile. The KR+ scale is defined by the equilibrium constant for the reaction of a carbocation with water molecule (/CR+ = [R0H][H30+]/[R+]). Therefore, the larger p/CR+ index indicates higher stability for the carbocation. However, the neutralization of these cations was not completely reversible. This is attributable to instability of the neutralized products. The instability of the neutralized products should arise from production of unstable polyolefinic substructure by attack of the base at the aromatic core. 

Another method for evaluating carbocation stability involves the measurement of solvolysis rates (14,45). Typically, the transition state of the rate-determining step in SN1 reactions is assumed to closely resemble the intermediate ion pair, on the basis of the Hammond postulate (46). Thus, the free energy of activation for this reaction, AG, reflects the relative thermodynamic stabilities of the intermediate carbocations. 

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