Stabilities of carbocations in the gas phase

The mechanistic involvement of the solvent is quite often an important cause of misunderstanding substituent effects in benzylic solvolyses. An effective approach to overcome this difficulty and a contribution to a general theory of substituent effects in benzylic system, which can be directly compared with theoretical results, is to investigate the behaviour of carbocations in the gas 

The relative stabilities of carbocations can be estimated from the free energy changes of the ion-molecule proton transfer equilibria of the corresponding alkenes (26). 

The substituent effect on the stability of a-cumyl cations [2C ] based on the proton transfer equilibria of a-methylstyrenes [33] (Mishima etal., 1989d) can be correlated directly with the ordinary set of solution cr values (Fig. 24). Unexpectedly, the correlation covering the substituent range from p-NMc2 to 3,5-(CF3)2 is excellent, and there is no difficulty in defining the gas-phase cr scale for r = 1.00 by these gas-phase stabilities of substituted cations 

In (27), o G) is a normal substituent constant and Ao r(g) is a resonance substituent constant defined as (cr - o )g Vq is a resonance demand parameter, and pg is a susceptibility parameter of the system in the gas phase. The gas-phase substituent parameter values are given in Table 15. 

The results of analysis based on the gas-phase Y-T equation (27) using gas-phase substituent constants given in Table 15 are summarized for proton-transfer equilibria of ethylenes and acetylenes in Table 16. As an example, the Y-T plot for a-CF3-a-arylethyl cations [5C ] in Fig. 25 may be compared with the plot for the corresponding solvolysis in Fig. 3. The AAG(cc)h+ for the a-neopentyl-a-t-butyl series [4C ] has been found to correlate linearly with the gas-phase Y-T equation (27) with = 0.81 (Fujio et aL, 1997a). a-t-Butyl-a-methylbenzyl cations [18C ] also showed a reduced Tg value of 0.89 (Mishima et al., 1992b), a value which is close to r = 0.91 

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Important contributors to these developments were McClelland and Richard, who have published reviews of their own and related studies.3 8 The present chapter will focus on recent work therefore and present earlier results mainly for comparison with new measurements. It will consider two further methods for deriving equilibrium constants (a) from kinetic measurements where the reverse reaction of the carbocation is controlled by diffusion or relaxation of solvent molecules23 25 and (b) from a correlation of solution measurements with the more extensive measurements of stabilities of carbocations in the gas phase.26 It will also show that stabilities of highly reactive carbocations can be determined from measurements of protonation and hydration of carbon-carbon double bonds. 

Structure-reactivity relationship in polyarylcarbocation systems 334 Conformations of carbocations 334 Reactivity-conformation relationship 337 Stabilities of carbocations in the gas phase 343 Structural effects 343 Tlie resonance demand parameter 355 Theoretically optimized structures of carbocations 362 Reaction mechanisms and transition-state shifts 365 Extended selectivity-stability relationships 365 Ground-state electrophilic reactivity of carbocations 366 Sn2 reactions of 1-arylethyl and benzyl precursors 372 Concluding remarks 378 Acknowledgements 379 References 379... 

Modern measurements show that the stability of carbocations increases with substitution (p. 137). Table 7.5 shows the heats of formation of carbocations in the gas phase. Remember. The more positive its heat of formation, the less stable a species is (p. 115). We can t make too much of the quantitative data in Table 7.5,... 

The Stability of hydrocarbon ions is discovered intuitively by observing whether the hydrocarbon ion can be isolated as a salt, for example, a sodium salt of the carbanion or a tetrafluoroborate salt of the carbocation. Conversely, a single hydrocarbon ion produced in the gas phase is obviously an unstable and short-lived species. Thus, many of the aliphatic carbocations in the gas phase are merely observable species but are not usable for synthesis. 

Table 3 Relative stabilities" (in kcalmol of substituted bromonium ions and alkyl carbocations in the gas phase.11...

Model computational studies aimed at understanding structure-reactivity relationships and substituent effects on carbocation stability for aza-PAHs derivatives were performed by density functional theory (DFT). Comparisons were made with the biological activity data when available. Protonation of the epoxides and diol epoxides, and subsequent epoxide ring opening reactions were analyzed for several families of compounds. Bay-region carbocations were formed via the O-protonated epoxides in barrierless processes. Relative carbocation stabilities were determined in the gas phase and in water as solvent (by the PCM method). 

Our calculations did predict that a y methyl group should provide a small amount of stabilization for 4 in the gas phase. However, subsequent calculations that included solvation effects did find, in agreement with experiment, that a y methyl group on 4 should slightly depress the rate of carbocation formation." ... 

The large difference between the AAG = 5.7 kcal mol 1 found for the cyclohexene system 190/19181 and the AH = 34 kcal mol 1 for the similar ions 196/19720 point to drastic differences in the mode of stabilization of the transition state for the protonation in solution and the free silyl-substituted carbocation in the gas phase. 

The difficulties encountered in using the analysis of substituent effects in solvolyses as a mechanistic probe mostly arise from the mechanistic involvement of the solvent (Shorter, 1978, 1982 Tsuno and Fujio, 1996). Consequently, the behaviour of benzylic carbocations in the gas phase should be the best model for the behaviour of the solvolysis intermediate in solution (Tsuno and Fujio, 1996). The intrinsic substituent effects on the benzylic cation stabilities in the gas phase have also been analysed by equation (2), and they will be compared here with the substituent effects on the benzylic solvolysis reaction. In our opinion, this provides convincing evidence for the concept of varying resonance demand in solvolysis. Finally, we shall analyse the mechanisms of a series of benzylic solvolysis reactions by using the concept of a continuous spectrum of varying resonance demand. 

It has also been found that there is a linear correlation between AG° values for protonation of hydrocarbon alkenes to the carbocations in the gas phase with those in solution, with slope equal to 1.2. This correlation included c-Pr2C=CH2 and Ph2C=CH2 and led to the conclusion that the protonation of the former was more favorable by 4 kcal mol than the latter in either the gas phase or aqueous solution. However, it was further suggested that the constancy of this number derived from an enhanced stabilization of each cation in the gas phase, which arose predominantly by n-donation for c-Pr, and polarization for Ph. Thus the correlation of solution and gas phase results is coincidental. 

The data in Table 5.4 indicate that the AH for heterol)dic dissociation of alkanes in the gas phase varies with the alkyl group as follows methyl > ethyl > isopropyl > t-butyl, which is consistent with the generalization that the ease of formation of carbocations is 3° > 2° > 1° > methyl. What is the source of this increase in stability We can explain some, but not all, of the results by saying that an sp hybrid orbital on carbon has a Pauling electronegativity of 2.5, while an sp hybrid orbital on carbon is about 0.25 imits more... 

Because carbocations are key intermediates in many nucleophilic substitution reactions, it is important to develop a grasp of their structural properties and the effect substituents have on stability. The critical step in the ionization mechanism of nucleophilic substitution is the generation of the tricoordinate carbocation intermediate. For this mechanism to operate, it is essential that this species not be prohibitively high in energy. Carbocations are inherently high-energy species. The ionization of r-butyl chloride is endothermic by 153kcal/mol in the gas phase. ... 

There is an excellent correlation between these data and the gas-phase data, in terms both of the stability order and the energy differences between carbocations. A plot of the gas-phase hydride affinity versus the ionization enthalpy gives a line of slope 1.63 with a correlation coefficient of 0.973. This result is in agreement with the expectation that the gas-phase stability would be somewhat more sensitive to structure than the solution-phase stability. The energy gap between tertiary and secondary ions is about 17kcal/mol in the gas phase and about 9.5 kcal/mole in the SO2CIF solution. 

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. 

The free t-butyl cation [7" ] in the gas phase is nothing more than a species detectable by the electron impact method (Yeo and Williams, 1970). However, it is not only an observable species by nmr studies in SbFs/FSOsH (Olah et al., 1964), but can be isolated from the solution in the form of its SbF or Sb2Ffi salt (Olah and Lukas, 1967a,b Olah et al., 1973 Yannoni et al., 1989). The crystal structure shows that this ion is planar and its carbon-carbon bonds are shortened to 144.2 pm (Hollenstein and Laube, 1993). Its particular electronic stabilization among aliphatic carbocations is attributed by physical organic chemists to the operation of both inductive and hyperconjugative effects in the cr bond system. 

As another example, the tropylium ion [3 ], which is stabilized by virtue of the 67t electrons spread over a heptagonal sp hybridized carbon framework [Hiickel s (4n 4- 2)v rule with = 1], is also unstable in the gas phase. Its formation from toluene or the benzyl cation has been a long-standing problem in organic mass spectrometry, and the reaction mechanism and energetics have recently been exhaustively discussed (Lif-shitz, 1994). It was, however, isolated as the bromide salt by Doering and Knox (1954, 1957), and was the first non-benzenoid aromatic carbocation. 

Estimating stability it is possible to apply criteria commonly used in organic chemistry. Tertiary alkyl carbocation is more stable than the secondary one which is in its turn more stable than the primary one. For the carbon ions of this type the row of the stability is reversed. Allyl and benzyl cations are stable due to the resonance stabilization. The latter having four resonance structures may rearrange to be energetically favorable in the gas phase tropilium cation possessing seven resonance forms (Scheme 5.3). 

Significantly slower rates are found only for compounds that do not exhibit any aromatic ring or carbon-carbon double bond, and for aliphatic compounds with no easily abstractable H-atoms. Such H-atoms include those that are bound to carbon atoms carrying one or several electronegative heteroatoms or groups. (Note that the stabilization of a carbon radical (R ) is similar to that of a carbocation.) We will come back to such structure-reactivity considerations in Section 16.3, when discussing reaction of HO" with organic pollutants in the gas phase (i.e., in the atmosphere). 

P-Fluonne or fluorine further removed from the cation center always inductively destabilizes carbocations [115, 116] No simple P-fluoroalkyl cations have been observed in either the gas phase or solution, and unlike the cases of the other halogens, there is no evidence for formation of alkyl fluoronium ions (5) in solution [117, 118], although (CH3)2F+ is long-lived in the gas phase [7791 The only P-fluonnated cations observed m solution are those that benefit from additional conjugativc stabilization, such as a-trifluoromethylbenzyl cations [772] and per-fluonnated allyl [729], cyclopropenium [772], and tropyliiim [727] ions... 

However, it must be taken into account that the a-phenylvinyl cation 185 is already highly stabilized by the phenyl substituent, leading consequently to a smaller -silicon effect in the vinyl cation 183. Ab initio calculations by Buzek predicted for 184 an additional stabilization of 10 kcalmol-1 by the silyl group7. The thermodynamic stabilization of 183 compared with 185, experimentally determined by Stone and coworkers in the gas phase, is 9 kcalmol 121. Thus, the kinetically determined stabilization of the transition state is only about 6 kcalmol-1 smaller than the /J-silyl effect for stabilization of the ground state carbocation. 

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