Carbocations, thermodynamic stabilities

As thermodynamic stability indexes for the hydrocarbon ions, pA R+ and pA a values [(4) and (5)] have been widely applied for the carbocation and carbanion, respectively, in solution. Here K + stands for the equilibrium constant for the reaction (6) of a carbocation and a water molecule stands for the equilibrium constant for the reaction (7) of a hydrocarbon with a water molecule to give the conjugate carbanion. The equilibrium constants are given by (8) and (9) for dilute aqueous solutions. Obviously, the reference system for the pKn+ scale is the corresponding alcohol, and... 

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... 

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... 

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. 

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. 

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. 

The acid-catalysed hydrolysis of 5-methoxyacenaphthylene 1,2-oxide was shown to proceed via the carbocation (76).149 This cation reacted with water to give an approximately 3 2 ratio of cis.trans diols, despite the trans-diol being substantially more stable. Hence, transition state effects, and not thermodynamic stability, determine the products. A computational investigation examined carbocations derived from oxidized benzo aJanthraccncs.150 Examples of cations considered are (77), derived by epoxi-dation and ring opening, and (78), derived by methyl oxidation and subsequent C—O bond heterolysis. 

The diagram above refers to thermodynamic stability. When we discuss addition reactions you will see that the most stable alkene when mixed with an electrophile is the most reactive according to this diagram. This paradox is due to the intermediate, usually a carbocation. Since a tertiary carbocation is more stable, the energy of activation is lowered and a reaction with a tertiary intermediate proceeds more quickly in general, to predict the alkene product, use the above diagram as a reference, but to predict the most reactive alkene to an electrophile, the order is based on cation formation and is nearly reversed. 

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. 

---