Carbocation formation equilibria

In the same way as changes in reactivity reflect the nature of the transition state, a change in equilibrium constant corresponds to a change in the thermodynamic stability of the carbocation intermediate. For example, substituent effects on the basicities of arylcarbonyl derivatives ArCOR provide a reference for the formation of a-hydroxycarbocations (17). 

The substituent effects in various unsymmetrical series of [3C (X,Y,Z)] are schematically shown in Fig. 15, where pXr+ values for various series are plotted against the sum of a with an r value of 0.76, in reference to the linear a plot for the symmetrical (trisaryl) series [3(X = Y = Z)]. All the unsym-metrically substituted series show significantly concave (quadratic) correlations, which intersect with the linear plot of the [3C (X = Y = Z)] series as tangent at the point of X = Y = Z. This implies that the p value of any series based on the tangent at the point (X = Y), where the varying X substituent is the same as the fixed Y substituent, should be identical to the p value for the symmetrical series [3C (X = Y = Z)]. 

The bisaryl-series [3C (X = Y,Z = H)] gives a reasonably good linear correlation with a slightly increased r value. However, the Y-T correlation for the monosubstituted series does not result in a satisfactory fit. 

A Taylor expansion for log values with varying X substituents is shown in (18). The second derivative in this expression plays an important role in the case of a curved correlation concave correlations can be approximated in terms of the regressional power series expansion of ax with an appropriate r scale. 

The coefficient pxx represents the deviation from a simple hnear free energy relationship and is related most obviously to the transition state shift arising from the perturbation by the substituents X (O Brien and More O Ferrall, 1978). Simply from the viewpoint of correlation analysis, the concave plots of the substituent effects of equivalently disubstituted (bisaryl) series [3C (X,Y,Z)] with X = Y Z = H, can be treated using equation (18) in terms of Ox with r = 0.76, to give an excellent correlation with px = 8.29 and Pxx = 0.117 for two X groups R = 0.9999 and SD = 0.141. This gives a 

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Solvolysis of 1-arylethenyl sulphonates forming vinyl cations 303 Highly electron-deficient carbocation systems 304 Carbocation formation equilibria 315 Triarylmethyl cations 315 Benzhydryl cations 319 1,1-Diarylethyl carbocations 322... 

Table 9 Yukawa-Tsuno correlations for carbocation formation equilibria. 

The Y-T equation has been used to analyse the substituent effects on carbocation formation equilibria in the gas phase. These correlations are compared with those for the kinetic substituent effects in the corresponding solution phase solvolyses in Table 17 and substituent effects on thermodynamic basicities of carbonyl groups in both phases are compared in Tables 18 and 19. 

Boruah, R. C. Skibo, E. B. Determination of the pKa values for the mitomycin C redox couple by tritration, pH rate profile, and Nemst-Clark fits. Studies of methanol elimination, carbocation formation, and the carbocation/quinone methide equilibrium. J. Org. Chem. 1995, 60, 2232-2243. 

The determinations of absolute rate constants with values up to ks = 1010 s-1 for the reaction of carbocations with water and other nucleophilic solvents using either the direct method of laser flash photolysis1 or the indirect azide ion clock method.8 These values of ks (s ) have been combined with rate constants for carbocation formation in the microscopic reverse direction to give values of KR (m) for the equilibrium addition of water to a wide range of benzylic carbocations.9 13... 

Turning to experimental measurements, the majority of equilibrium constants measured for carbocation formation refer to ionization of alcohols or alkenes in acidic aqueous solution, and correspond to pAR or pAa. Considering the instability of most carbocations it is hardly surprising that only unusually stable ions such as the tropylium ion l49 or derivatives of the flavylium ion 250,51 are susceptible to pA measurements in the pH range. 

By contrast, measurement of pATR = 4.7 for the Fe(CO)3-cooordinated cyclo-hexadienyl cation 44 (Scheme 26) indicates a 107-fold more favorable equilibrium constant for carbocation formation than for the uncoordinated cation.197 However, a more dramatic effect of coordination is to render nucleophilic reaction with water more favorable than loss of a proton. A pXa = 9 can be estimated by computing the energy differences between coordinated and uncoordinated benzene and coordinated cyclohexadiene. This compares with the value of —24.5 for the uncoordinated cyclohexadienyl cation. The large difference must reflect the unfavorable effect of Fe(CO)3 coordination on benzene, an effect analogous to that found by Mayr for Fe (CO)3 coordination on the tropylium ion.196 As expected, both the coordinated cyclohexadienyl and tropylium ions are highly stereoselective toward exo attack by water. 

Although the value of the coefficient 1.16 in (20) does not have as direct a physical significance as the a-exponent in the extended Brpnsted equation (19) because the reaction, solvents and temperature are different, there is still a good linear rate-equilibrium relationship for benzhydryl carbocation formation the overall correlation embraces clearly concave partial correlations with varying slopes for the respective Y series. The whole pattern of substituent effects, pXr vs should be essentially identical (with only the ordinate scale being slightly different) to that of log (/ xy/Z hh) vs 2 a for the solvolyses shown in Fig. 8. 

Most of these results have been obtained in methanol but some of them can be extrapolated to other solvents, if the following solvent effects are considered. Bromine bridging has been shown to be hardly solvent-dependent.2 Therefore, the selectivities related to this feature of bromination intermediates do not significantly depend on the solvent. When the intermediates are carbocations, the stereoselectivity can vary (ref. 23) widely with the solvent (ref. 24), insofar as the conformational equilibrium of these cations is solvent-dependent. Nevertheless, this equilibration can be locked in a nucleophilic solvent when it nucleophilically assists the formation of the intermediate. Therefore, as exemplified in methylstyrene bromination, a carbocation can react 100 % stereoselectivity. 

We consider the relatively high pKA values of 6-8 to be typical value for a cation-quinone methide equilibrium. The formation of a resonance-stabilized aromatic carbocation is one reason for these high pKA values. Another reason is the high energy of the quinone methide. The thermodynamic cycle shown in... 

The reaction can, however, be made preparative for (91) by a continuous distillation/siphoning process in a Soxhlet apparatus equilibrium is effected in hot propanone over solid Ba(OH)2 (as base catalyst), the equilibrium mixture [containing 2% (91)] is then siphoned off. This mixture is then distilled back on to the Ba(OH)2, but only propanone (b.p. 56°) will distil out, the 2% of 2-methyl-2-hydroxypentan-4-one ( diacetone alcohol , 91, b.p. 164°) being left behind. A second siphoning will add a further 2% equilibrium s worth of (91) to the first 2%, and more or less total conversion of (90) — (91) can thus ultimately be effected. These poor aldol reactions can, however, be accomplished very much more readily under acid catalysis. The acid promotes the formation of an ambient concentration of the enol form (93) of, for example, propanone (90), and this undergoes attack by the protonated form of a second molecule of carbonyl compound, a carbocation (94) ... 

In this context, it was suggested [53] that the reaction involved a tertiary carbocation intermediate that was in equilibrium with quasiphosphonium salt. The elimination of HC1 from the latter, leads to the formation of 2,5-dihydro-l,2-oxaphosphole derivatives. Macomber [54], however, has shown that bromination of optically pure... 

Table 2 Rate constants, equilibrium constants, and estimated Marcus intrinsic barriers for the formation and reaction of ring-substituted l-phenylethyl carbocations X-[6+] (Scheme 8)°... 

Fig. 5 Logarithmic plots of rate-equilibrium data for the formation and reaction of ring-substituted 1-phenylethyl carbocations X-[6+] in 50/50 (v/v) trifluoroethanol/water at 25°C (data from Table 2). Correlation of first-order rate constants hoh for the addition of water to X-[6+] (Y) and second-order rate constants ( h)so1v for the microscopic reverse specific-acid-catalyzed cleavage of X-[6]-OH to form X-[6+] ( ) with the equilibrium constants KR for nucleophilic addition of water to X-[6+]. Correlation of first-order rate constants kp for deprotonation of X-[6+] ( ) and second-order rate constants ( hW for the microscopic reverse protonation of X-[7] by hydronium ion ( ) with the equilibrium constants Xaik for deprotonation of X-[6+]. The points at which equal rate constants are observed for reaction in the forward and reverse directions (log ATeq = 0) are indicated by arrows.

Table 3 The effects of a-carbonyl and a-thiocarbonyl substituents on the rate and equilibrium constants for the formation and reaction of a-methyl 4-methoxybenzyl carbocations R-[14+] (Scheme 1 l)a... 

Table 5. Rate and equilibrium constants for the formation and reaction of cyclic benzylic carbocations [18 + ] and [20+ ] and analogous ring-substituted 1-phenylethyl carbocations (Scheme 15)°... 

These structures were then used to generate the force fields and calculate the secondary /3-deuterium-d6 equilibrium isotope effects (EIEs) for the formation of the isopropyl carbocation (Table 30). Because the transition states for formation of the carbocation will be close to the structure of the carbocation, these KIEs should be excellent approximations of the maximum secondary /3-deuterium KIEs expected for the limiting SN1 solvolytic reaction. 

Carbon atoms in organic molecules are most often neutral. Positively charged carbocations have attracted the interest of synthetic organic chemists, because of their use as intermediates in reactions leading to formation of carbon-carbon bonds. Our work on carbocations has focused on defining the stability of these species as intermediates of solvolysis reactions, through the determination of rate and equilibrium constants for these stepwise reactions (Scheme 1). This has led to the development of experimental methods to characterize these parameters for carbocations that are sufficiently stable to form in aqueous solution. 

Variations in the absolute concentration of the carbocation solutions and temperature had minor effects on chemical shifts. The counter ion effect and the equilibrium could be minimized by going to higher superacidity systems with lower nucleophilicity counter ions. Resonances due to the PAH itself were considerably shielded. Solvation by FSO3H and the formation of ion pair-molecule clusters were suggested as possible reasons. 

A new mechanism, called the methane-formaldehyde mechanism, has been put forward for the transformation of the equilibrium mixture of methanol and dimethyl ether, that is, for the formation of the first C-C bond.643 This, actually, is a modification of the carbocation mechanism that suggested the formation of ethanol by methanol attaching to the incipient carbocation CH3+ from surface methoxy.460,462 This mechanism (Scheme 3.3) is consistent with experimental observations and indicates that methane is not a byproduct and ethanol is the initial product in the first C-C bond formation. Trimethyloxonium ion, proposed to be an intermediate in the formation of ethyl methyl ether,447 was proposed to be excluded as an intermediate for the C-C bond formation.641 The suggested role of impurities in methanol as the reason for ethylene formation is highly speculative and unsubstantiated. 

An important feature of reactions in which 1,2 and 1,4 additions occur in competition with one another is that the ratio of the products can depend on the temperature, the solvent, and also on the total time of reaction. The reason for the dependence on the reaction time is that the formation of the carbocation is reversible, and the ratio of products at equilibrium need not be the same as the ratio of the rates of attack of Cl0 at Cl and C3 of the carbocation. This is another example of a difference in product ratios resulting from kinetic control versus equilibrium control (e.g., see Section 10-4A). 

This reaction is an dehydration acid-catalyzed.12 The hexaaquocop-per cation behaves as a weak cationic acid in copper-salt solution.13 Protonation of the hydroxy group produces an oxonium ion that decomposes unimolecularly into carbocation 21 and water. Water is removed from the reaction equilibrium by means of a water-separating device. Carbocation 21 eliminates an -proton with formation of the energetically favorable conjugated diene 9. 

The extension of equilibrium measurements to normally reactive carbocations in solution followed two experimental developments. One was the stoichiometric generation of cations by flash photolysis or radiolysis under conditions that their subsequent reactions could be monitored by rapid recording spectroscopic techniques.3,4,18 20 The second was the identification of nucleophiles reacting with carbocations under diffusion control, which could be used as clocks for competing reactions in analogy with similar measurements of the lifetimes of radicals.21,22 The combination of rate constants for reactions of carbocations determined by these methods with rate constants for their formation in the reverse solvolytic (or other) reactions furnished the desired equilibrium constants. 

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