Thermodynamic stabilities of carbocations

Jose-Luis M. ABBOUD,t Ibon Alkorta, Juan Z. DAVALOS,t Paul Muller and Esther QuiNTANiLLAf 

Quantitative thermodynamic criteria of stability in the gas phase 58 Definitions and experimental techniques 58 The specific case of carbocations 61 Theoretical calculations 64 Uncertainties 65 

Aliphatic carbocations with more than four carbon atoms 75 Cyclic species without formal tt systems 79 Cyclopropyl-substituted carbocations 83 

Secondary and tertiary carbocations derived from cage hydrocarbons 89 Carbenium ions with formal tt systems 98 Two-electron aromatic and homoaromatic ions 101 Six-electron aromatic ions 108 Phenyl-substituted carbocations 110 Solution reactivity 116 

Thermodynamic properties 118 Reaction kinetics 122 Conclusion 126 Acknowledgments 127 References 127 

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The physical organic chemistry of very high-spin polyradicals, 40, 153 Thermodynamic stabilities of carbocations, 37, 57 Topochemical phenomena in solid-slate chemistry, 15, 63 Transition state analysis using multiple kinetic isotope effects, 37, 239 Transition state structure, crystallographic approaches to, 29, 87 Transition state structure, in solution, effective charge and 27, 1... 

Tetrahedral intermediates, derived from carboxylic acids, spectroscopic detection and the investigation of their properties, 21, 37 The physical organic chemistry of very high-spin polyradicals, 40, 153 Thermodynamic stabilities of carbocations, 37, 57 Topochemical phenomena in solid-slate chemistry, 15, 63 Transition state analysis using multiple kinetic isotope effects, 37, 239 Transition state structure, crystallographic approaches to, 29, 87 Transition state structure, in solution, effective charge and 27, 1 Transition stale structure, secondary deuterium isotope effects and, 31, 143 Transition states, structure in solution, cross-interaction constants and, 27, 57 Transition states, the stabilization of by cyclodextrins and other catalysts, 29, 1 Transition states, theory revisited, 28, 139... 

Ionization reactions in solution inevitably involve solvated ions the carbocation and its counter-ion are stabilized by interaction with the solvent. In order to assess the thermodynamic stability of carbocations free of complications by intermolecular solvent-ion forces, one is essentially limited to gas phase studies13-1 s). 

We are concerned here with the thermodynamic stability of carbocations. For the sake of generality, we formally consider that they derive from a neutral molecule R-H, which can either lose a hydride or be protonated in the gas phase, reactions (1) and (2) ... 

Experimental studies on the structures, physical and chemical properties, and thermodynamic stabilities of carbocations are especially difficult because of the inherent instability of these reactive intermediates. Of particular fundamental interest are experimental methods for the determination of the structures and stabilities of carbocations in the gas pha.se. These methods can be used to gather data for direct comparison with the results of ah initio theory, without the need for consideration of solvation effects. In this article, we will show comparisons between theory and experiment for hydrocarbon and carbocation stabilities in order to test the performance of... 

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. 

Schleyer s Lewis acid-catalyzed rearrangement method, which is based on diamondoid thermodynamic stability during carbocation rearrangements, has had little or no success in synthesizing diamondoids beyond triamantane. In recent years, outstanding successes have been achieved in the synthesis of adamantane and other lower molecular weight diamondoids [42 9]. Some new methods have been developed and the yield has been increased to 60%. 

The partitioning of simple tertiary carbocations, ring-substituted 1-phenylethyl carbocations, and cumyl carbocations between deprotonation and nucleophilic addition of solvent strongly favors formation of the solvent adduct. The more favorable partitioning of these carbocations to form the solvent adduct is due, in part, to the greater thermodynamic stability of the solvent... 

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. 

The three alkyl-aluminumsilyl oxonium ions are more stable than the carbocations, with the allylcarbinyl aluminumsilyl oxonium ion lying 4.5 and 4.7 kcal.mor1 lower in energy than cyclobutyl. and cyclopropylcarbinyl aluminumsilyl oxonium ions, respectively. This result is in agreement with the thermodynamic stability of the respective chlorides. 

The most significant conclusion that can be drawn from the data summarized in Table III is that substituent effects do not exert the same overwhelming importance for the thermodynamic stability of the higher homologues of carbenium ions, thus they do not play the dominant role as in carbocation chemistry. This can be traced back on (i) the inherent higher stability of the trivalent cations of the elements Si Pb and (ii) the weakness of the stabilizing interaction (in many cases of ii-type) of the most common substituents with the central element atom. 

Now for the relative proportions of products. Only 3% of the unrearranged product shows just how unfavourable the secondary carbocation is compared with the rearranged tertiary carbocation. The relative proportions of the other two alkenes are explained by the increased thermodynamic stability of the more-substituted alkene, though this is not sufficient to produce just the single product. 

Quantitative estimates of the thermodynamic stabilities of various phenyl and cyclopropyl substituted cyclopropenium ions were carried out by their pATR+ measurements18. The pKg+ values for 1,2,3-tricyclopropylcyclopropenium, l,2-dicyclopropyl-3-phenylcy-clopropenium ion and 1 -cyclopropyl-2,3-diphenylcyclopropenium ion were determined to be 10.0, 7.09 and 5.04, respectively. Thus, replacement of each phenyl group by a cyclopropyl group enhances the stability of the carbocation by two pATR+ units (2.74 kcal mol1). These results were also supported by the isodesmic reaction of equation 72 for which the energies were optimized at the HF/3-21G //HF/3-21G level18. 

The effects of a-Mc2NC(0) and a-Mc2NC(S) on the rate constants for partitioning of a-substitutcd l-(4-methoxyphenyl)ethyl carbocations between nucleophilic addition of 50 50 (v/v) MeOH-H20 (ks, s ) and deprotonation by this solvent (ke, s 1) have been examined.128 These substituents lead to 80-fold and > 30 000-fold decreases, respectively, in ks, but to much smaller changes in ke. Ab initio calculations suggest that the partitioning is strongly controlled by the relative thermodynamic stabilities of the neutral products of the reactions. 

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. 

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. 

Amett and co-workers,75 76 in a series of investigations, have determined heats of ionization (AHi) of secondary and tertiary chlorides and alcohols in SbF5-S02ClF and HS03F-SbF5-S02ClF solutions, respectively, at low temperatures. They have also measured heats of isomerizations of secondary to tertiary carbocations in the superacid media. These measured thermochemical data have been useful to determine the intrinsic thermodynamic stability of secondary and tertiary carbocations. 

In addition to the linear free energy studies discussed, there have been many attempts to estimate the thermodynamic stabilities of electrophilic species, such as carbocations.7 The pKr+ values for carbocations reveal trends in relative stability and is defined as, according to the equilibrium established between the carbinol... 

According to MP2/VDZ+P calculations56, the 71-donor ability of halogen substituents in Hal3M+ and HalH2M+ cations (Hal = F, Cl, Br, I M = C, Si, Ge, Sn, Pb) increases from F to I for all of these cations, the thermodynamic stabilization of the cations by halogen substituents increases in the same order, and for the heavier congeners this stabilization is diminished compared to that in the carbocations. 

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