Affinities of carbocation

According to Eq. (17), AGd° is negative if AG 0 < AG. A value of -50 kJ mol-1 was estimated for AGa° (-70° C) above, so that carbocation salts can only add to olefins to form covalent products if AG > -50 kJ mol-1. As AG depends both on the structure of R+ and on the Lewis acidity of MCI, we can conclude that the thermodynamic driving force for Case d increases with decreasing stabilization of R+ and decreasing chloride-ion affinity of MC1 . Because the magnitude of AG can be estimated from the relative chloride affinities of carbocations and Lewis acidic metal halides in Scheme 7 (Section II.G), one can derive which carbocationic salts might add to alkenes with formation of covalent products. 

Several criteria, including hydride affinities of carbocations (R+—H heterolytic BDE) and adiabatic ionization potentials of the corresponding free radicals (Table 1.30), indicate the order of decreasing stability of fluoromethyl carbocations to be CHF2+ > CH2F+ > CF3+ > CH3+ (Scheme 1.54) [1],... 

Hydride affinity of carbocations (21). Original data from Ref. 22. 

Molecular orbital calculations predict that oxirane forms the cyclic conjugate acid (39), which is 30 kJ moF stabler than the open carbocation (40) and must surmount a barrier of 105kJmoF to isomerize to (40) (78MI50500). The proton affinity of oxirane was calculated (78JA1398) to be 807 kJ mol (cf. the experimental values of 773 kJ moF for oxirane and 777-823 kJ moF for dimethyl ether (80MI50503)). The basicity of cyclic ethers is discussed in (B-67MI50504). 

Table S3. Solution Hydride Affinity of Some Carbocations...

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. 

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. 

As the cation becomes progressively more reluctant to be reduced than [53 ], covalent bond formation is observed instead of electron transfer. Further stabilization of the cation causes formation of an ionic bond, i.e. salt formation. Thus, the course of the reaction is controlled by the electron affinity of the carbocation. However, the change from single-electron transfer to salt formation is not straightforward. As has been discussed in previous sections, steric effects are another important factor in controlling the formation of hydrocarbon salts. The significant difference in the reduction potential at which a covalent bond is switched to an ionic one -around -0.8 V for tropylium ion series and —1.6 V in the case of l-aryl-2,3-dicyclopropylcyclopropenylium ion series - may be attributed to steric factors. 

The proton affinity of a carbene can be derived by means of Eq. 9 (M = RR C ) if AHf of the carbene and of the corresponding carbocation have been estimated independently (Table 7). Appearance potentials (AP) are convenient, although sometimes inaccurate, sources of AHf (RR CH+).129 Adiabatic ionization energies (IEa) of free radicals, in combination with dissociation enthalpies... 

Carbocations have similar electronic structures to carbenes. The P-protonated derivative of phosphinine should also be similar to 23. Indeed, while investigating the proton affinity of 3. the most preferred protonation site was phosphorus and not carbon, whereby the cyclic jt system would be interrupted. ... 

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... 

Free energies of formation, hydride ion affinities, and pKR. Is there an optimum measure of carbocation stability ... 

Perhaps less obviously, the hydrocarbon also provides a reference for the carbocation. It is worthwhile examining the implications of such a reference, by considering briefly thermodynamic measurements of carbocation stabilities in terms of heats (enthalpies) or free energies of formation. Mayr and Ofial contrast our ability to measure the relative energies of tertiary and secondary butyl cations with the significant differences in relative stabilities of secondary butyl and isopropyl cations derived from different equilibrium measurements, namely, hydride, chloride, or hydroxide ion affinities. It is convenient to focus on this example and to assess the effectiveness of hydride affinities for comparing the stabilities of these three ions. 

The group contributions apply only to alkyl cations and are of limited practical value. However, apart from illustrating the application of group additivity contributions to energies of formation of carbocations, they offer a significant insight into comparisons of stability based on hydride ion affinities (HIAs) and pAlR values. 

There have been more equilibrium measurements for reactions of carbocations with azide than halide ions. Regrettably, there is little thermodynamic data on which to base estimates of relative values of pARz and pAR using counterparts of Equations (17) and (18) with N3 replacing Cl. Nevertheless, a number of comparisons in water or TFE-H20 mixtures have been made87,106,226,230 and Ritchie and Virtanen have reported measurements in methanol.195 The measurements recorded below are for TFE-H20 and show that whereas pA" 1 is typically 4 log units more positive than pA R. pA Rz is eight units more negative. The difference should be less in water, perhaps by 2 log units, but it is clear that azide ion has about a 1010-fold greater equilibrium affinity for carbocations than does chloride (or bromide) ion. 

A controversial issue of heteroatom-stabilized cations is the relative stabilization of carbocationic centers adjacent to oxygen and sulfur.541 In solution studies, a-O-substituted carbocations were found to be stabilized more than a-iS -substituted carbocations.677 Gas-phase studies reached an opposite conclusion,678 679 whereas subsequent theoretical studies (high-level ab initio methods) supported the findings of solution chemistry. Recent results, namely, basicities of various vinylic compounds (365-370) measured in the gas phase also support this conclusion.680 Although monoheteroatom-substituted compounds 365 and 366 were found to have similar proton affinities, an additional a-methyl group increased the stability of the carbenium ion derived from 367 more than that of the sulfur counterpart 368. Even larger differences were found between proton affinities of the bis-heteroatom-substituted compounds 369 and 370. 

Hopkinson was hired by York to teach theoretical organic chemistry (the Woodward-Hoffmann rules were then a hot topic) and to carry out experimental chemistry. Despite the limited computing capacity at York at the time, he managed to complete some work on the electrophilic addition to alkenes. He is probably best known, however, for his work on proton affinities, destabilized carbocations,234 organosilicon compounds, silyl anions and cations, and more recently, on the calculation of potential energy surfaces and thermodynamic properties. He has had a particularly fruitful collaboration with Diethard Bohme.235... 

The heats of formation of the carbocations are then combined with the heats of formation of the corresponding hydrocarbons [21] and AH ° of H (139 kJ mol-1) [23] to yield the hydride affinity scale of Scheme 2. Although hydride affinities of larger carbocations (molecular formula a... 

Scheme 2 Hydride affinity scale of carbocations. (data from Ref. 23.) With //r°(H ) = 145 kJ mol-1 [20] the calculated hydride affinities are 6 kJ mol-1 greater than listed in this scheme.

Many synthetic reactions, that proceed via carbocations, produce these intermediates from mixtures of alkyl halides and Lewis acidic metal halides. The concentration of carbocations produced under these conditions depends on the tendency of the alkyl halides to ionize ( carbocation stability ) and the strengths of the Lewis acids in a certain solvent. Because the ionizing abilities of alkyl halides can be derived from the schemes and correlations given in Sections B through F, we shall now concentrate on the relative halide affinities of the Lewis acidic metal halides. For this purpose, we consider Eq. (13) which describes the exchange of a chloride ion between the Lewis acids R+ and MCI,. 

Let us first ignore ion-pairing phenomena. With this assumption, the chloride transfer equilibria (13) correspond to the chloride transfer equilibria between two carbocations which were described in Scheme 5 and thus provide a comparison of the chloride affinities of metal halides and of carbocations. One would expect the right side of this equilibrium to be favored if MCI, is the stronger Lewis acid and the left side when R+ is the stronger Lewis acid. 

The influence of cyclopropyl on the gas phase stability of carbocations as measured by ion cyclotron resonance is shown in Table 14, along with data for some reference compounds. The results are given as gas phase basicities, GB, and proton affinities, PA, defined as AG° and AH°, respectively, for dissociation of the protonated molecule, as in equation 11. In addition hydride affinities D(BH H ) for some cations defined as — AH° for equation 18 are included. For the gas phase basicities and proton affinities the products B are alkenes, amines, nitriles or carbonyl compounds, and thus for these values the stability of the cation is compared to a derivative where the substituent is conjugated with a carbon-carbon or carbon-oxygen double bond, or a nitrogen lone pair, whereas for hydride affinities the products are saturated. 

Trialkylsilyl-substituted carbocations are particularly important reactive intermediates in chemical reactions in polar media. Due to the high affinity of silicon for fluorine and oxygen, the... 

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