Stabilities and Reactivities of Carbocations

Stabilities and Reactivities of Carbocations RORY MORE O’FERRALL School of Chemistry and Chemical Biology, University College Dublin, Belfield, Dublin 4, Ireland 1 Introduction 19 2 Stabilities of carbocations 21 Measures of stability 21 Equilibrium measurements of pKR 28 Kinetic methods for determining pKR 30 Arenonium ions 37 Alkyl cations 46 Vinyl cations 48 The methyl cation: a correlation between solution and the gas phase Oxygen-Substituted carbocations 51 Metal-Coordinated carbocations 64 Carbocations as protonated carbenes 68 Halide and azide ion equilibria 71 3 Reactivity of carbocations 76 Nucleophilic reactions with water 77 Reactions with water as a base 87 Reactions of nucleophiles other than water 90 Reactivity, selectivity, and transition state structure 105 Hard and soft nucleophiles 110 Summary and conclusions 112 Acknowledgments 114 References 114

1

49

Introduction

There have been a number of reviews of carbocation chemistry in the past 10 years,1–11 including a volume of essays marking the 100th anniversary of the subject.1 That volume illustrates the variety of structures and reactions that characterize carbocations. It is this variety which suggests scope for a further study, namely of the stability and reactivity of carbocations in (mainly) aqueous solution. Dedication to AJ Kresge is appropriate. He has pioneered the quantitative characterization of reactive intermediates in water as solvent. If he is best known for his work on enolic species, his steady referencing throughout this chapter reflects the breadth of his influence in physical organic chemistry.

19 ADVANCES IN PHYSICAL ORGANIC CHEMISTRY VOLUME 44 ISSN: 0065-3160 DOI: 10.1016/S0065-3160(08)44002-9


2010 Elsevier Ltd. All rights reserved

20

R. MORE O’FERRALL

Attempts to measure the stabilities of carbocations are not new. Hughes and Ingold established the essential features of solvolysis reactions in the 1930s.12 They identified the SN1 mechanism as involving the formation of a carbocation intermediate and recognized that the rate of solvolysis reflects the stability of that carbocation. For more than 80 years, rate constants of solvolyses have provided measures of stability (with allowance for variations in the stability of reactants).13 Only recently have the stabilities of more than mildly reactive carbocations, accessible by direct equilibrium measurements,14–16 been determined. Indeed the emergence of gas-phase ion chemistry and new techniques of mass spectrometry in the 1980s led to a wider knowledge of the stabilities of carbocations in the gas phase than in solution.2,17 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. 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. The existence of equilibrium measurements today usually implies access to a rate constant for direct reaction of the carbocation with a nucleophile or base. The chapter will also consider reactivity and selectivity for these reactions. This area too has been well studied and reviewed,3–8 especially by Mayr’s group in Munich, who have made extensive recent contributions to the field.27–31 It should be admitted that the author’s own work25,26,32 will be a further focus for the chapter, which in part will be an ‘‘account of research,’’ and indeed an update of an earlier multiauthored review.9 The chapter begins, however, with a digression on the significance of different measures of the stabilities of carbocations. This is followed by a discussion of the use of a solvent free energy relationship to extrapolate equilibrium and kinetic measurements in concentrated solutions of strong acids to a purely aqueous medium. Some readers may

STABILITIES AND REACTIVITIES OF CARBOCATIONS

21

wish to omit these sections. However, throughout the first third of the chapter experimental results are presented in the context of methods used for measurements. The emphasis on methods is followed by discussions of oxygen substituent effects, coordination of metal ions, protonations of carbenes, and equilibria for the reactions of carbocations with halide or azide ions. The discussion of reactivity concludes the chapter.

2

Stabilities of carbocations

MEASURES OF STABILITY

The choice of equilibrium constant for measuring the stability of a carbocation depends partly on experimental accessibility and partly on the choice of solvent. A desire to relate measurements to the majority of existing equilibrium constants implies the use of water as solvent. Water has the advantage and disadvantage that it reacts with carbocations. It follows that the most widely used equilibrium constant is that for the hydration reaction shown in Equation (1), which is denoted KR (or pKR). A simple interpretation of KR is that it measures the ratio of concentrations of unionized alcohol to carbocation in an (ideal) solution of aqueous acid of concentration 1 M. Rþ þ 2H2 O ¼ ROH7 þ H3 Oþ KR ¼

ð1Þ

½R  OH½H3 Oþ  ½Rþ 

Nucleophile affinities As pointed out by Mayr,28 Ritchie,15 and Hine33,34 KR also measures the relative affinities of Rþ and H3Oþ 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 Rþ and H3Oþ as shown in Equations (2) and (3). Such equilibrium constants have been denoted Kc by Hine.33 KR corresponds to the ratio of constants for reactions (2) and (3) and, in so far as Kc for H3Oþ is the inverse of Kw the autoprotolysis constant for water, KR = KcKw Rþþ HO  ¼ ROH Kc ¼

½ROH ½Rþ ½HO  

ð2Þ

22

H3 Oþ þ HO  ¼ 2H2 O

R. MORE O’FERRALL

ð3Þ

A distinction between the reactions of Rþ and H3Oþ is that while Rþ reacts with hydroxide ion in an associative process, H3Oþ reacts by transfer of a proton. The difference corresponds to that between the product-forming step of an SN1 mechanism and an SN2 reaction. Many carbocations are capable of existing in solution independently of a nucleophile, but this is not true of highly reactive electrophiles such as Hþ (or, e.g., CHþ 3 ) reactions of which involve breaking as well as making a bond to a nucleophile. If we focus on Hþ rather than H3Oþ, affinities for nucleophiles (bases) must be expressed relative to a suitable reference. In principle, the familiar equilibrium constants Ka and Kb measure affinities relative to water and hydroxide ion, respectively [Equations (4) and (5)]. AH þ H2 O ¼ A  þ H3 Oþ

ð4Þ

A  þ H2 O ¼ AH þ HO 

ð5Þ

In practice, it is perhaps unfortunate that the complementary character of the KR and Ka scales is somewhat obscured by the formulation of Ka as a measure of acidity, so that the appropriate measure of affinity (in this case basicity) is 1/ K a. For carbocations, an electrophilicity (Lewis acidity) scale can be based on ions other than the hydroxide ion as is shown in general for X in Equation (6), for which the equilibrium constant can be denoted K X R . Scales based on chloride ion, for example, have been used in the gas phase2,17,36 and are also appropriate for nonaqueous solvents. Rþ þ X  ¼ RX

ð6Þ

A further popular scale in the gas phase is hydride ion affinity (HIA)2,37 for which X = H. To avoid dealing explicitly with H, this scale is conveniently referenced to a particular ion such as CHþ 3 as in Equation (7). Commonly HIAs are expressed as free energies rather than pK’s. Rþ þ CH4 ¼ R  H þ CH3þ

ð7Þ

The hydride affinity scale is also applicable to aqueous solution. In analogy with KR we can take H3Oþ as reference as in Equation (8). Rþ þ H2 þ H2 O ¼ RH þ H3 Oþ

ð8Þ

STABILITIES AND REACTIVITIES OF CARBOCATIONS

23


 The two scales are readily interconverted and a ratio of KR values K H R =K R is given by Equation (9). KH ½R  H½H2 O R ¼ ½ROH½H2  KR

ð9Þ

The right-hand side of this equation is evaluated in terms of free energies of formation in aqueous solution at 25C of R–H, R–OH, H2O, and H2.38 Free energies of formation, hydride ion affinities, and pKR: Is there an optimum measure of carbocation stability? The problem arises, which equilibrium constant offers the most effective measure of carbocation stability? A good discussion of this question has been provided by Mayr and Ofial,29 who point out that a rigorous comparison of stabilities is possible only for isomeric cations. Comparisons between nonisomeric cations depend on the equilibrium chosen for the measurements. They argue that the appropriate choice depends on the context and imply that it is not possible to identify a ‘‘best’’ measure of carbocation stability. While this is certainly true it is worthwhile pursuing further the likelihood that some equilibria provide better measures of stability than others, and to assess their effectiveness and limitations. For carbocations possessing a b-hydrogen atom, an alternative to nucleophilic affinities is provided by the pKa for dissociation of a proton to form an alkene. It is rather easy to recognize that a pKa is not always a good measure of carbocation stability. This is evident from an example chosen by Mayr and Ofial, namely, the cyclohexadienyl cation, for which the conjugate base is benzene [Equation (10)]. Thus, if we seek to compare stabilities of the cyclohexadienyl cation and t-butyl cation [Equation (11)] in terms of pKas, the difference will strongly reflect the different stabilities of the carbon–carbon double bonds of their conjugate bases. In this case comparing values of pKR provides a better measure of stability because a contribution from the difference between the corresponding alcohols is smaller. C6 H7 þ ¼ C6 H6 þHþ

ð10Þ

ðCH3 Þ3 Cþ ¼ ðCH3 Þ2 C¼CH2 þ Hþ

ð11Þ

Of course, to speak of the stability of a double bond implies further equilibria or reference structures with which the energy of the unsaturated molecule itself is compared. An obvious reference is the saturated hydrocarbon, with respect to which stability is measured, for example, by a heat of hydrogenation.

24

R. MORE O’FERRALL

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. Extensive measurements of heats of formation of carbocations in the gas phase exist and there have been more limited measurements in solution for nonhydroxylic solvents.39 For comparison with equilibrium measurements in water, however, the most appropriate measurement would appear to be free energies of formation in aqueous solution. It is fortunate therefore that a convenient compilation of values of DGf (aq) at 25C has been provided by Guthrie.38 This allows us for example to derive a value of DGf (aq) for a carbocation from a measurement of its pKR value, provided that the free energy of formation of the corresponding alcohol [R–OH in Equation (1)] is known. Heats or free energies of formation can be used to compare directly the energies of isomeric carbocations. Such a comparison is similar to the more familiar comparisons of energies of isomeric olefins, such as cis- and trans-butene. It depends on the energies of formation of isomeric molecules or ions being based on the same combination of elements. Energies of isomerization can also be measured directly, and Bittener, Arnett, and Saunders have measured the enthalpy of isomerization of secondary to tertiary butyl cations in CH2Cl2 as solvent.39 It is possible to compare direct measurements of relative stabilities of isomeric ions with comparisons of nonisomeric ions by use of a ‘‘group additivity’’ scheme. Group additivity schemes have been developed by Benson for heats of formation (and other thermodynamic properties) of organic molecules in the gas phase,40 and by Guthrie to represent free energies of formation in aqueous solution.38 In both cases, energies of unstrained hydrocarbons accurately correspond to a sum of contributions from primary, secondary, tertiary, and quaternary carbons CH3, CH2, CH, and C. Such a scheme can be extended to carbons bearing functional groups (X) by assigning contributions for CH2X, CHX, and CX. In principle, carbocations can be included, with the positively charged carbon considered as a functional group, with characteristic contributions for primary, secondary, and tertiary cation centers. For strict additivity, a group scheme implies that the influence of a functional group does not extend beyond the carbon atoms adjacent to the functionalized atom, that is, in our case the carbon bearing the positive charge.

STABILITIES AND REACTIVITIES OF CARBOCATIONS

25

This can be tested by drawing on extensive information on carbocation stabilities in the gas phase. Heats of formation of ethyl, isopropyl, sec-butyl and tbutyl cations2 are shown below. From these values it is evident that the t-butyl cation is more stable than the sec-butyl cation by 13 kcal mol1. This corresponds to the direct comparison of (isomeric) ion stabilities noted above by Arnett and Mayr.

DHf (g)

1

(kcal mol )

(CH3)3Cþ

CH3CH2CHþCH3

(CH3)2CHþ

CH3 CH2

170

183

193

215

It can also be seen that the heat of formation of the iso-butyl cation is 10 kcal mol1 less than that of the isopropyl cation. Based on this difference, we may assess the effectiveness of group additivity by comparing the changes in energy for inserting a methylene group into the isopropyl cation to give a sec-butyl cation with the same change in propane to give butane or in propanol to give sec-butyl alcohol. For an effective additivity scheme these changes should be the same because the methylene group is two carbons removed from the charge center of the cation. In practice, whereas converting the isopropyl cation to a sec-butyl cation reduces the heat of formation by 10 kcal mol1, the corresponding conversion for propane and isopropyl alcohol reduces it by 5.0 and 4.8 kcal mol1, respectively. While this implies that to a good approximation an OH functional group is well accommodated by the additivity scheme the carbocation center certainly is not. The situation in solution is quite different. The difficulty of stabilizing charge in the gas phase is well known and in solution smaller differences between structures are expected. There should also be less dependence on the size of the ion, which is a well-recognized feature of gas-phase ion stabilization, but does not appear to be significant in solution.41 Shown in Table 1 are free energies of formation of the same ions in aqueous solution at 25C. The measurements of pKa from which they are derived are described later in the chapter (p. 47). Suffice to say here that the relative values for isopropyl and secondary butyl cations are based on the inference from measurements of equal rate constants for protonation of propene and 1-butene42 that the pKas of the conjugate acids of these alkenes are the same. It can be seen that the differences in energies of formation between the cations are significantly less than in the gas phase. Thus the difference between the t-butyl and ethyl cations is reduced from 45 kcal mol1 to less than 20 kcal mol1. On the other hand, the difference between the t-butyl and sec-butyl cations shows a much smaller reduction, from 13 to 10.2 kcal mol1. Moreover, instead of the energy of the isopropyl cation being 10 kcal mol1 greater than the sec-butyl cation it is now 2.3 kcal mol1 less. In the gas phase the extra CH2

26

R. MORE O’FERRALL

provides important stabilization. In aqueous solution this is overridden by an unfavorable effect on solvation (recall that the standard state remains the gas phase).43 If as above we compare the value of this ‘‘group contribution’’ for CH2 with values based on increases in free energies of formation between propane and butane (2.0 kcal mol1) and isopropyl alcohol and sec-butanol (1.6 kcal mol1), it is apparent that there is a much better cancellation, and thus better prospect that energies of alkyl carbocations can be approximated by an additivity scheme in solution than in the gas phase. Calculated group contributions to free energies of formation for tertiary, secondary, and primary carbocations in aqueous soloution based on the above data are shown below and are compared with Guthrie’s values for hydrocarbons (which were also used for remote methyl groups in deriving the carbocation group contributions). As expected the cations have large positive values. Indeed the values are substantially larger than for alkyne carbons, which fall in the range 27–29 kcal mol1 and currently represent the largest carbon group contributions. CH2þ CHþ Cþ

57.9 50.7 45.7

CH3 CH2 CH C

3.93 2.16 6.43 10.40

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 pKR values. HIAs of the carbocations are listed in Table 1 as differences in values from the t-butyl cation (DHIA in free energies mol1). Returning to the comparison of isopropyl and sec-butyl cations it can be seen that the difference in their

Table 1 Free energies of formation, HIAs, and pKR values for alkyl cations in aqueous solution

DGf (aq) (kcal mol1) DHIAa 1.364pKRb 1.364DpKRc

(CH3)3Cþ

CH3CH2CHþCH3

(CH3)2CHþ

CH3 CH2

33.9 9.8 –22.4

45.6 9.7 –30.6 8.2

43.3 23.3 –30.1 7.7

54.0

HIAs relative to (CH3)3Cþ. pKR converted to free energy mol1. c Relative to (CH3)3Cþ. a

b

–40.8 18.4

STABILITIES AND REACTIVITIES OF CARBOCATIONS

27

HIAs is only 0.1 kcal mol1. This reflects almost complete cancellation of contributions from the extra CH2 group in the butyl structure between the cation and hydrocarbon. It indicates that HIAs provide a good approximation to differences in stability between a carbocation center and the corresponding group contribution from a hydrocarbon, independently of structural variations at carbon atoms not attached to the carbocation center. Moreover, a comparison between two secondary carbocations leads to almost complete cancellation of the contributions from the parent hydrocarbons and from alkyl groups of the carbocations too far removed from the charge center to influence stability. One is very close therefore to a comparison of stabilities comparable to that between isomeric cations. It should be noted that such ‘‘intrinsic’’ stabilities are not expressed in heats of formation of carbocations because they include uncanceled contributions from more remote portions of the structure. Also shown in Table 1 are differences in pKR. These are multiplied by 1.364 to give free energies for easier comparison with HIAs. They correspond to ‘‘intrinsic’’ differences between tertiary, secondary, and primary carbocation centers (CHþ, CH2þ, and CH3þ ) and the corresponding values for the carbon bound to an OH functional group (C–OH, CH–OH, and CH2–OH). In principle, carbocation stabilities may be expressed relative to any functional group, but clearly the convenience and prevalence of measurements of pKR give a special place to the OH group. However, note that the DpKR and DHIA values are not the same. This is because there is a stabilizing geminal interaction between the OH group and methyl groups attached to the a-carbon atom.44–46 These interactions are cumulative so their net contribution depends on the number of methyl groups. They also depend on the nature of the functional group if this differs from OH. As a consequence, stabilities of carbocations defined in terms of affinity for a nucleophile depend on the choice of nucleophile as emphasized by Mayr and Ofial. The magnitudes of the interactions are by no means negligible, particularly between oxygen and another electronegative atom (usually O or N). Nevertheless they are well understood and easily estimated, especially for the OH group,47 which provides the most convenient affinity (pKR) scale. As indicated above, pKR values are readily converted to an HIA scale, which provides a convenient reference for comparisons between scales as well as a better approximation to cation stabilities. However, note that even for HIAs, if cations differ significantly in substitution at their charge center, there may be uncanceled geminal interactions in the reactant hydrocarbon, for example, between methyl groups when comparing secondary and tertiary cations: this will be evident from inspection of the relevant group contributions. Of course, the ‘‘intrinsic’’ stabilities, and the evidence for localization of the influence of carbocation centers, apply only to aliphatic ions. Phenyl or vinyl substitutents lead to extended delocalization of a positive charge. More generally, however, cancellations of ‘‘group’’ contributions between reactants and

28

R. MORE O’FERRALL

products in measurements of pKR or HIAs are subsumed into analyses in terms of substituent effects. This extended discussion brings us then to the conventional conclusion that stabilities of carbocations considered in the context of comparisons of equilibrium constants, benefit from substantial cancellation of effects of noninteracting functional and substituent groups between pairs of reactants and products for structures far removed from those of simple alkyl cations.33,48

EQUILIBRIUM MEASUREMENTS OF pKR

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 pKR or pKa. Considering the instability of most carbocations it is hardly surprising that only unusually stable ions such as the tropylium ion 149 or derivatives of the flavylium ion 250,51 are susceptible to pK measurements in the pH range. +

CH2 +

O

Me

Ph

+

Me

+

+ +

1

2

3

4.75

3.65

–1.70

4 Me

5 Me

–16.3

–11.9

6

~ –7.4

A wider range of structures can be accessed through measurements in strong acid solutions.52–55 Such solutions have the characteristic that pK values vary strongly with acid concentration. This is because H3Oþ has a uniquely high solvation energy and the depletion of water molecules at high acid concentrations leads to increasing protonation of a base (or ionization of an alcohol) if its conjugate acid (or carbocation) is less strongly solvated than H3Oþ. This is illustrated in Equation (12), in which the solvated proton is represented as H9 O 4þ . H9 O4þ þB ¼ BHþ þ 4H2 O

ð12Þ


 What is required is a value of pK extrapolated to water pKH2 O . Fortunately, the dependences of the relevant equilibrium constants on the composition of the acidic medium are well described by free energy relationships. This means that an unknown pKa (or pKR) can be obtained from measurements in concentrated acidic solutions by plotting values against known pKas for the protonation of a reference base.52,53 In practice, medium acidity parameters, Xo ¼ pKa  pKaH2 O , are conveniently defined for a family of structurally

STABILITIES AND REACTIVITIES OF CARBOCATIONS

29

related bases with a large enough range of basicities to span measurements from dilute to concentrated solutions of strong acids. Such a family is provided by primary anilines substituted with nitro and other electron-withdrawing groups. Historically, there has been an uncomfortable period of evolution of the free energy treatment of measurements of pK’s in strongly acidic media from their original formulation as acidity functions. In the context of acidity functions, a pKa was treated as fixed at its value in water, and ‘‘apparent’’ variations in equilibrium constants were assigned to changes in activity coefficient.56,57 It is now well established that plots of pKa against Xo are impressively linear and correspond to the relationship represented by Equation (13), in which m* is the slope of the plot and the pKa in water is the intercept. pKa ¼ m Xo þ pKaH2 O

ð13Þ

The value of m* reflects medium effects on the acid dissociation constant under study, as represented in Equation (14). BHþ þ H2 O ¼ B þ H3 Oþ

ð14Þ

Thus in the case that BHþ is H3Oþ, Equation (14) becomes an ‘‘identity’’ reaction, for which there is no medium effect, and m* = 0. On the other hand, if BHþ is a protonated aniline, m* = 1. These values provide fixed points on a scale of solvation energy changes associated with proton transfer between H3Oþ and the protonated base under study. Our interest in this chapter is in carbocations. In general, these are poorly solvated unless there is an OH or NH group bound to the charge center, and typically m* falls in the range 1.5–2.0. Their equilibria are accessible as pKas for protonation of carbon–carbon double bonds,58–60 or pKR values.61–64 Strictly speaking, free energy treatments of medium acidity apply to pKa rather than pKR. The relationship between these equilibria is shown for the hydration and protonation of styrene in the thermodynamic cycle of Scheme 1 and Equation (15). Thus pKR corresponds to pKa þ pKH2 O where pKH2 O is the equilibrium constant for the hydration reaction. If pKa increases with acidity +

CH CH3 + H2O pK R

pK a

pK H2O H+ + H2O +

CH=CH2

CHCH3 + H+ OH

Scheme 1

30

R. MORE O’FERRALL

in proportion to Xo, the dependence of pKR on Xo will be modified by that of pKH2 O . In practice, KH2 O is likely to increase with increasing acidity because of the premium placed on the availability of solvating water at high acid concentrations. If the variation is not too great, as suggested by data for p-methoxystyrene,65 plots of pKR against Xo should still be close to linear and extrapolate to satisfactory values of pKR in water. KH2 O ¼

KR ½ROH ¼ Ka ½alkene½H2 O

ð15Þ

In practice, extrapolations of pKR in water have usually used the older acidity function based method, for example, for trityl,61,62 benzhydryl,63 or cyclopropenyl (6) cations.66,67 These older data include studies of protonation of aromatic molecules, such as pKa = 1.70 for the azulenium ion 3,59 and Kresge’s extensive measurements of the protonation of hydroxy- and methoxy-substituted benzenes.68 Some of these data have been replotted as pKR or pKa against Xo with only minor changes in values.25,52 However, for more unstable carbocations such as 2,4,6-trimethylbenzyl, there is a long extrapolation from concentrated acid solutions to water and the discrepancy H2 O is greater; use of an acidity function in this case gives pKR ¼ 17:5,61 * compared with 16.3 (and m = 1.8) based on Xo. Indeed because of limitations to the acidity of concentrated solutions of perchloric or sulfuric acid pK’s of more weakly nucleophilic carbocations are not accessible from equilibrium measurements in these media. Care also needs to be taken with the interpretation of UV–visible spectra in concentrated acid solutions. Richard and Amyes have shown that 2O pK H ¼ 16:6 for the 9-methylfluorenyl cation involves an incorrect assignR ment of spectra and that a value based on azide clock measurements (see below) is 11.9.69 In addition to carbocations, extensive measurements of pKas of oxygen and nitrogen protonated bases have been undertaken, including pKas of protonated ketones.65,74 As described below, these lead indirectly to pKR values for a-hydroxycarbocations if the equilibrium constants for hydration of the ketones are known.

KINETIC METHODS FOR DETERMINING pKR

More recent measurements related to carbocation stabilities in strongly acidic media have involved rates of reaction rather than equilibria.52,54,72–75 Application of the Xo function to the correlation of reaction rates as well as equilibria mirrors the use of structure-based free energy relationships. Of interest is the access this gives to rate constants for (a) protonation of weakly basic alkenes and (b) acid-catalyzed ionization of alcohols to relatively unstable

STABILITIES AND REACTIVITIES OF CARBOCATIONS

31

carbocations.73–75 These are kinetic counterparts of equilibrium measurements of pKa and pKR, and allow rate constants of intrinsically slow reactions to be extrapolated to aqueous solution. They are particularly important for the determination of highly negative values of pKa or pKR through combination of the measured values with rate constants for the reverse reactions of the carbocations with water acting as a base or nucleophile. Plots of log k against Xo are consistently linear, facilitating extrapolation of rate constants as small as 1014.72 Combination with the maximum rate constant for reaction of a carbocation with aqueous solvent, which is controlled by the rotational constant for relaxation of water of 1011 s1,24,76 yields a pK of 25, significantly higher than the maximum (negative) value possible from equilibrium studies. The application of kinetic methods to determining pKa and pKR for carbocations, by combining rate constants for their formation from an alcohol or alkene with a rate constant for the reverse reaction of the carbocation with water, has provided the most important development in measurements of these equilibrium constants in recent years. The use of laser flash photolysis to generate carbocations under conditions that rates of their reactions can be monitored by rapid recording of their absorbance in the UV or visible region represents a milestone in studies of carbocations.20,77 Particularly important in this development has been a collaboration between Steenken and McClelland.19,78–84 Their work, and some of the varied photochemistry associated with it, which led to the generation not only of carbocations but of radicals, radical cations, and carbenes, has been reviewed by McClelland.3,4 Detection methods have included conductivity as well as UV–visible spectrophotometry, and the carbocations have been generated by radiolysis79,80 as well as photolysis. These studies ushered in the modern era of stability studies in carbocation chemistry which has extended over the past 20 years. Diffusion-controlled trapping of carbocations: benzylic cations A ‘‘modern era’’ of stability studies can be extended to more than 30 years by taking as its beginning the application of ‘‘clock’’ methods to the determination of rate constants for direct reactions of carbocations with water or other nucleophiles or bases. Young and Jencks used bisulfite ions to trap acetalderived alkoxycarbocations, and assigned equilibrium constants for reaction of the cations with methanol by measuring product ratios for trapping by bisulfite ion. It was assumed that reaction of the bisulfite was diffusion controlled with a rate constant 5109 M1 s1 and that the rate constants for reaction of water and methanol were the same.21 Subsequently, Jencks and Richard used trapping by azide ion to measure pKR values of a-phenethyl cations in 50:50 (v/v) trifluoroethanol (TFE)–H2O mixtures and presented strong arguments for the efficacy of azide ions as a diffusion trap.22 Their conclusions were endorsed by McClelland who measured directly rate constants for reaction of benzhydryl and trityl cations with azide ions and

32

R. MORE O’FERRALL

showed that limiting rate constants were close to 5109 M1 s1.81 Similar measurement were made for a-substituted and unsubstituted p-methoxybenzyl cations.82 It was concluded that the reaction of azide ions with carbocations is diffusion controlled provided that kH2 O , the rate constant for reaction of the carbocation with water, is >105 s1 or pKR is <–5 (cf Fig. 7 on p. 91). Other nucleophiles achieve a diffusion limit only with more reactive cations. Sulfur anions are exceptional in approaching azide ions in efficiency as nucleophilic traps. Flash photolytic generation of carbocations has been achieved through photosolvolysis reactions involving a number of leaving groups. The effectiveness of the leaving group is important in determining competition between formation of carbocations and radicals and does not always correlate with efficiency in thermal reactions. Thus 4-cyanophenoxy is a good leaving group partly because it has an absorption maximum close to the wavelength (248 nm) of the photolyzing laser.17 Carbocations may also be formed from protonation of excited states of double bonds, from photochemically generated carbenes or by fragmentation of radical cations.4 The flash photolytic and ‘‘azide-clock’’ methods are complementary. Trapping a carbocation with azide ion may be applicable where a photolytic method for generating the carbocation is not available. It is a simpler method which can be used by laboratories not equipped for photolysis measurements and depends only on the availability of high-performance liquid chromatography (HPLC) equipment. Even when a sample of azido product is not available for comparison with the chromatogram of trapped products its peak can be identified by (a) its retention time relative to the alcohol, (b) its growth at a rate equal to the disappearance of reactant or appearance of a known product, and (c) the dependence of its intensity on the concentration of azide ion used for trapping.22 Photolytic generation of carbocations and direct measurement of their rates of reaction has been implemented in a limited number of laboratories. This lends special importance to the wide-ranging and thorough investigations carried out by McClelland and Steenken, including an extended plot of logs of rate constants for reaction of azide ions against log kH2 O for trityl and benzhydryl cations.77 This plot is reproduced in a review article by Mayr and Ofial30 and the same data is shown as plots of log k against pKR in Fig. 7 below (p. 91). Carbocation-forming reactions Surprisingly, the kinetic measurements now available for the nucleophilic trapping of carbocations with water are not always matched by measurements of rate constants for formation of the carbocation from the corresponding alcohol required to evaluate the equilibrium constant KR. Although carbocations are reactive intermediates in the acid-catalyzed dehydration of alcohols to form alkenes,85,86 the equilibrium in this reaction usually favors the alcohol and the carbocation forming step is not rate-determining. Rate constants may

STABILITIES AND REACTIVITIES OF CARBOCATIONS

33

then have to be determined from racemization of a chiral alcohol73 or isotope exchange with 18O-labeled water.78 These methods are not always applicable or convenient. A more general method used by Richard and Jencks utilizes HPLC analysis of carbocation formation in alcohol–water mixtures.22 As shown in Scheme 2 for an a-aryl ethyl cation, formation of the ether product from reaction of the carbocation with the alcohol depends on the rate constant for carbocation formation kH and the partition ratio between product formation and the back reaction to form the alcohol kROH =kH2 O . This ratio may be determined from the ratio of products formed from reaction of the carbocation generated from a suitable solvolytic precursor such as an alkyl halide. Richard has used 50:50 TFE–H2O for measurements of kH by this method and has reported values of pKR determined in this solvent mixture. The solvent mixture has the slight disadvantage that other measurements refer to water and comparisons suggest that the values in water are more negative by amounts of up to 1 log unit depending on the structure of the cation.69,73,87 Richard used an initial rate method to derive kH, but kH can also be obtained by combining the rate constant for approach to equilibrium and the equilibrium ratio of alcohol to ether.88 Richard and Jencks combined the above method with use of the azide clock to determine values of pKR for a-phenethyl carbocations bearing electron-donating substituents in the benzene ring and for the cumyl cation for a wider range of substituents.22,89 They inferred values for the parent

kROH [ROH] kH[H+] ArCH(CH3)+ OH k H2O [H2O]

ArCH(CH3)

k obs

OR

ArCH(CH3)

OH

ArCH(CH3)

OR

kH[H+]

=

(1 + k H2O [H2O]/k ROH[ROH]) H2O

ArCH(CH3)

Cl

ArCH(CH3)+ + Cl – ROH

kH

2O

kROH

Scheme 2

ArCH(CH3)

=

[ArCH(CH3)

OH]/[ArCH(CH3)

[H2O]/[ROH]

OR]

34

R. MORE O’FERRALL CH+CH3

X

X=

pKR TFE H2O pKR H2O

(estimated53)

MeO

Me

H

–8.6

–12.6

–15.4

–8.9

–12.8

–15.7

Carbocation

Ph3C+

Ph2CH+

PhCH2+

PhC+Me2

pK R (H2O)

–6.93

(–12.5)

(–21)

(–12.5)

Scheme 3

a-phenethyl cation and derivatives with electron-withdrawing substituents from a Yukawa–Tsuno correlation of substituent effects.22 Representative measurements are shown in Scheme 3 for 50% TFE–H2O and for estimates of corresponding values in water.73 Shown for comparison are pKR values for trityl, benzhydryl, and benzyl carbocations. For the trityl cation pKR was measured by McClelland and Steenken by combining a rate constant kH2 O measured following flash photolytic generation of the carbocation and kH from acid-catalyzed 18O exchange.78 For the benzhydryl and benzyl cations, kH2 O was measured by Amyes and Richard inTFE–H2O mixtures using the azide clock.69 For the benzhydryl cation, kH was determined by the method summarized in Scheme 2 and gave pKR = –11.7 in TFE–H2O. This value is corrected by 0.8 log units below to give a value of 12.5 in H2O (shown in brackets to indicate that this implies an approximation). For the benzyl cation, no value of kH has been determined, but an upper limit of 21 for pKR was established by Amyes and Richard (also shown in brackets), and it has been suggested that this must be close to the correct value in water.26 These values have been discussed in some detail to indicate that care is required to take account of the differences in solvents for measurements. They illustrate, nevertheless that a good framework of stabilities of benzylrelated carbocations exists. Other (oxygen-substituted) benzylic cations for which pKR measurements have been reported are discussed below (p. 57–63). Cations structurally related to benzhydryl are anthracenyl (7)75,87 and fluorenyl (8).69 There has been some dispute as to whether or not the fivemembered ring of the fluorenyl cation is antiaromatic. Clearly the antiaromatic character is less than for the indenyl or cyclopentadienyl cations, but current opinion favors antiaromaticity also for the fluorenyl cation.90–92 This is supported by the large difference in pKR from the anthracenyl cation, (although an additional reason for this difference will be noted later in the chapter, p. 61). Again, the brackets indicate ‘‘correction’’ of a measurement from TFE–H2O to water.

STABILITIES AND REACTIVITIES OF CARBOCATIONS

+ 7 pK R

–6.0

35

+ 8 (–15.7)

Solvent relaxation, hydration equilibria, and the t-butyl cation Recognition that the rotational relaxation constant of water (1011 s1)24,76 provides a limit to values of kH2 O for reaction of sufficiently reactive carbocations offers an important means of establishing this rate constant. It has been invoked by Richard to evaluate equilibrium constants for protonation by water of highly unstable carbanions23,24 and for deriving a value of pKR for the t-butyl cation.93 Evidence that kH2 O has indeed reached its limiting value includes minimal trapping by azide ions and correlations of kH2 O with pKR which approach this limit for more stable cations (see below, p. 43). For the tbutyl cation, Richard has also pointed to formation of a relatively large amount of alkene compared with that from more stable cations. This is consistent with the rate constant reaching a limiting value for nucleophilic attack on the cation, but not for its reaction with water as a base (for which k = 8.0108 s1).86 The rate constant kH has been measured from the rate of 18 O exchange94 and combination with kH2 O ¼ 1011 s  1 yields pKR = –16.4. In so far as the limit of solvent relaxation can be expected to apply to cations less stable than t-butyl, the task of assigning stabilities in such cases might seem straightforward. However, a difficulty now arises with the measurement of kH. For secondary alkyl or simple benzylic carbocations lacking electron-donating substitutents, it is possible that kH will represent SN2 substitution by water rather than carbocation formation, especially as the alcohol precursors of these cations are less well protected from nucleophilic attack by steric hindrance than t-butyl alcohol. It can be argued that if secondary alkyl halides react by an SN1 mechanism the same should be true of a substrate with a leaving group as good as a protonated alcohol. However, despite extensive study,95 it remains unclear whether 18O exchange for 2-butanol, which has a half-life of 25 h in 0.55 M HClO4 at 100C,96 involves a carbocation intermediate. For such unstable carbocations, an alternative approach to pKR can be developed, by recognizing the relationship that exists between pKR and pKa implied in Equation (15) (p. 30). For carbocations with b-hydrogen atoms, loss of a proton normally yields an alkene. Then, as discussed by Richard, pKR and pKa form two arms of a thermodynamic cycle, of which the third is the equilibrium constant for hydration of the alkene, pKH2 O , as already indicated in Scheme 1. The relationship between these equilibrium constants is shown for the t-butyl cation in Scheme 4. In the scheme the equilibria are

36

R. MORE O’FERRALL (CH3)3C+ + H2O –16.4

–12.5

H2O + H+ + (CH3)2C = CH2

–3.9

(CH3)3C OH + H+

Scheme 4

conveniently represented by single arrows to indicate the direction of reaction and thus signs of the quantities in the implied relationship, pKR ¼ pKa þpKH2 O . For isobutene, the equilibrium constant for hydration has been measured as 9.1103, corresponding to pKH2 O ¼ 3:94.86 It follows that the pKa for the t-butyl cation is 12.5. In so far as values of pKH2 O for the hydration of alkenes are known or can be estimated,47 values of pKR can be derived by combining rate constants for protonation of alkenes with the reverse deprotonation reactions of the carbocations. The protonation reactions seem much less likely to be concerted with attack of water on the alkene than the corresponding substitutions. Indeed arguments have been presented that even protonation of ethylene in strongly acidic media involves the intermediacy of the ethyl carbocation.97,98 The situation for the reverse deprotonation reaction is indicated by the derivation of a rate constant 8.0108 s1 for deprotonation of the t-butyl cation75 by combining Ka with the measured rate constant for the hydration of butene,86 for which protonation of the alkene is rate-determining. This rate constant is only 100-fold less than the relaxation limit for water, which is expected to apply to reactions of water as a base as well as a nucleophile. In principle, a rate constant for deprotonation of the carbocation might be measured from the ratio of alkene to alcohol formed from solvolysis of a secondary alkyl chloride, or other substrate with a good enough leaving group to yield the carbocation without competing SN2 substitution. The ratio of alkene to alcohol formed should correspond to a rate constant ratio to which the rate constant for forming the alcohol can be assigned as 1011 s1 and acts as a ‘‘clock’’ similar to diffusion-based clocks. However, in so far as reaction of the carbocation is likely to occur within an ion pair, the yield of alkene may be enhanced by the leaving group acting as proton acceptor and also by protecting one face of the cation from nucleophilic attack.99 The estimated rate constant for loss of the proton would then represent an upper limit compared with reaction in a fully aqueous environment. In practice, it is also possible to take advantage of the closeness of these rate constants to their relaxation limit and interpolate/extrapolate values from a correlation between deprotonation rate constants and pKas. The rate constants for such a correlation come from measurements for secondary or

STABILITIES AND REACTIVITIES OF CARBOCATIONS

37

tertiary benzylic carbocations (Scheme 3) for which pKR has been determined and pKH2 O has been measured or can be estimated.5,25,73,93 Before attempting to derive values for primary and secondary alkyl cations on the basis of such a correlation, however, it is convenient to consider application of the correlation to measurements of pKa and their combination with pKH2 O to derive values of pKR for arenonium ions.

ARENONIUM IONS

Evaluation of pKR from measurements of rate and equilibrium constants for the protonation of carbon–carbon double bonds of alkenes suggests the possibility of a similar approach for aromatic double bonds. Protonated aromatic molecules are the parent structures of the arenonium ion intermediates of electrophilic aromatic substitution. For these cations the equilibrium constant KR refers to equilibria with the corresponding aromatic hydrates, as is illustrated in Scheme 5 for the benzenonium ion (cyclohexadienyl cation) 9 for which the hydrate is cyclohexadienol 10. Cyclohexadienol was prepared by Rickborn in 1970 from reaction of the epoxide of 1,4-cyclohexadiene with methyl lithium.100 A hydrate of naphthalene, 1-hydroxy-1,2-dihydro-naphthalene was prepared by Bamberger in 1895 by allylic bromination of O-acylated tetralol (1-hydroxy-1,2,3,4tetrahydronaphthalene) followed by reaction with base.101 Hydrates of naphthalene and other polycylic aromatics are also available from oxidative fermentation of dihydroaromatic molecules, which occurs particularly efficiently with a mutant strain (UV4) of Pseudomonas putida.102,103 The hydrates are alcohols and they undergo acid-catalyzed dehydration to form the aromatic molecule by the same mechanism as other alcohols, except that the thermodynamic driving force provided by the aromatic product makes deprotonation of the carbocation (arenonium ion) a fast reaction, so that in contrast to simple alcohols, formation of the carbocation is rate-determining (Scheme 6).104,105 OH

+

+ H+

+ H2O 10

9

Scheme 5 OH2+

OH + H

Scheme 6

+

Slow

+ + H2O

Fast

+ H3O+

38

R. MORE O’FERRALL +

kA

+ H3O+

+ H2O kp

Scheme 7

In principle, a value of Ka for the benzenonium ion may be obtained from the ratio of rate constants for protonation of benzene, kA, and proton loss from the ion, kp, as shown in Scheme 7. A value of kA is available from measurements of hydrogen isotope exchange (kx) corrected for primary and secondary isotope effects. This is illustrated in Scheme 8 for the detritiation of tritiated benzene. In the lower part of the scheme, the reacting isotope of the benzenonium ion intermediate (9-t) is indicated as a superscript on the rate constant kp and a secondary isotope effect is neglected. Rate constants for deuterium or tritium exchange of benzene, naphthalene, and other aromatic molecules have been measured in concentrated solutions of sulfuric or perchloric acid. Conveniently, Cox has extrapolated values to aqueous solution from plots of log kx against Xo and corrected them for 72 T isotope effects (e.g., kH p =kp ) to yield kA. For benzene, it has not been possible to measure directly the rate constant kp for deprotonation of the benzenonium ion in order to complete the determination of Ka (= kp/ka). However, this has been possible for 1-protonated naphthalene,106 9-protonated phenanthrene,25 9-protonated anthracene, and 2-protonated benzofuran.75 In the case of the naphthalene, Thibblin and Pirinccioglu showed that the naphthalene hydrate is sufficiently reactive to form the naphthalenonium ion in aqueous azide buffers (pH 4–5).106 Formation of this ion leads to competition between loss of a proton and trapping by azide ion to form the 2-azido-1,2-dihydronaphthalene. From the trapping ratio kp is determined as 1.61010 s1 by the usual ‘‘clock’’ method. The hydrates of phenanthrene (13), anthracene, and benzofuran are not sufficiently reactive to form carbocations at the mild pH of azide buffers. However, the cation may be generated by solvolysis of their acetate or chloroacetate esters. Trapping of the cation by azide ions then occurs in the normal way.25,75 Moreover, the solvolytically generated cations react in these cases not only through loss of a proton to form the aromatic product but by nucleophilic T

T

H +

kA + H3O+

k pT

+ H2TO+

k pH 9-t

kx = kA/(1 + kpH / kpT)

Scheme 8

kA = kx(1 + kpH / kpT)

STABILITIES AND REACTIVITIES OF CARBOCATIONS

39

trapping with water to regenerate the hydrate, which in the absence of acid does not undergo dehydration. Competing formation of the hydrate reflects the lower aromaticity and reduced thermodynamic driving force for formation of the aromatic product compared with benzene or naphthalene. These reactions are illustrated for solvolysis of the dichloroacetate of 9-hydroxy-9,10-dihydrophenanthrene (9,10-phenanthrene hydrate) 11 in Scheme 9, for which the products of deprotonation and azide trapping of the carbocation 12 are phenanthrene (phen) 13 and azido dihydrophenanthrene 15, respectively. All three products in Scheme 9 can be monitored by HPLC. If the product ratio of azide (15) to phenanthrene, [RN3]/[phen], is plotted against the concentration of the azide ion trap, the slope of the plot corresponds to kAz/kp. Assigning kAz the value of 5109 M1 s1 for diffusion leads to kp = 3.71010 s1. A value of kA (the rate constant for protonation of phenanthrene at the 9-position) has not been determined directly in aqueous solution but can be found by combining a partial rate factor for exchange of tritiumlabeled phenanthrene in trifluoroacetic acid with a rate constant for protonation of benzene and assuming that the ratios of rate constants are unaffected by the change in solvent. This gives kA = 5.0  1011 M1 s1. Combining it with kp gives pKa = –log(kp/kA) = –20.9.25 The value of kp obtained in this way for the phenanthreneonium ion is not far from the limit set by the rotational relaxation of water. For such fast reactions, Richard has pointed out that azide trapping could be influenced by preassociation.6 Preassociation has been well characterized in a number of nucleophilic reactions of reactive carbocations with water6 but its impact on deprotonation has not been fully clarified.5,6 In so far as preassociation

+ H+ 13 Phen

kp

O OCCHCl2

+ Cl2CHCOO–

11

12

=

kp k H2O

[ROH]

kH

2O

14 ROH

k Az[N3–]

[Phen] N3

15 RN3

Scheme 9

[Phen] OH

+

[RN3]

=

kp k N3[N3–]

40

R. MORE O’FERRALL

increases the rate of the reaction with azide ion, the inferred value of kp is underestimated and the pKa may be a little less negative than that assigned. However, kp is so close to its limit that the discrepancy must be small. It might seem surprising that a nucleophilic reaction with water competes with proton loss from the phenanthrenonium ion considering the stability of the aromatic product. As discussed by Richard24 (and considered further below) this reflects a higher intrinsic reactivity of the cations toward nucleophilic attack which compensates for the thermodynamic disadvantage of this reaction. For the phenanthrenonium ion the ratio of for
rate constants  deprotonation and nucleophilic attack on the cation kp =kH2 O is 25;25 for the 1-protonated naphthalene it is 1600,106 for 9-protonated anthracene, 1.8.75 In all these cases it is possible to determine KR directly by combining kH2 O with kH, the rate constant for carbocation formation. The latter constant is readily determined spectrophotometrically by monitoring acid-catalyzed dehydration of the aromatic hydrate to the corresponding aromatic product. In principle, as we have seen, when the dehydration product is aromatic, carbocation formation is the rate-determining step of the reaction. However, the finite values of kp =kH2 O for the phenanthrenonium ion and other arenonium ions leading to moderately stable aromatic products imply a small correction for reversibility of this reaction step. For phenanthrene hydrate the derived value of pKR is 11.6. This is comparable to values for the benzhydryl (–12.5) or p-methylphenethyl (–12.8) cations.22,69,73 The evaluation of pKR as well as pKa allows derivation of pKH2 O ¼ pKR  pKa ¼ 9:3. This equilibrium constant offers a measure of the stability of the 9,10-double bond of phenanthrene and thus the aromaticity of its central benzene ring. Comparison with the double bond of 2-butene, for which pKH2 O ¼ 3:94,86 indicates a 1013-fold greater stability, for the aromatic double bond. It should be noted that the value of pKH2 O does not depend on azide trapping. In the difference between pKR and pKa the rate constant kAz cancels out and KH2 O ¼ kA kH2 O =kH kp . The equilibrium constants Ka, KR, and KH2 O are conveniently summarized in Scheme 10 in the form of a cycle similar to that shown above for the a-phenethyl and t-butyl cations (Schemes 1 and 4). It is worth noting that pKH2 O measures the stability of the double bond relative to the alcohol (hydrate). If pKR was converted to HIA, pKH2 O in the cycle would be replaced by the energy of hydrogenation. The latter provides the conventional measure of double bond stability, save that here free energy in aqueous solution is measured rather than the more usual heat of hydrogenation in the gas phase. We will return to a comparison of values of these equilibrium constants for different carbocations, but first pursue pKa and pKR for the benzenonium ion. In azide buffers this cation reveals no trapping by azide ion. This poses the problems, how do we (a) find a value of kp to combine with kA to obtain pKa and (b) determine pKH2 O to derive pKR? We consider first pKH2 O and then kp.

STABILITIES AND REACTIVITIES OF CARBOCATIONS

41

+ H2O + pK R = –11.6

pK a = –20.9

OH pK H2O = 9.3 H2O + H+ +

+ H+

Scheme 10

Equilibrium constants for hydration As already indicated, a number of values of pKH2 O have been measured experimentally, including those just described. Many more can be evaluated from a combination of free energies of formation of alcohols and the relevant alkenes in aqueous solution [DGf (aq)].47 This is illustrated in Scheme 11 in which 1.364 corresponds to 2.303RT at 25C in kcal mol1 and DGf (aq) is abbreviated as DGf . In cases where DGf (aq) for the alcohol is not known, usually it can be found from DGf (aq) for the corresponding hydrocarbon and an estimate of the change in free energy of formation upon replacing H by OH. The value of the latter quantity (DGf (aq)ROH – DGf (aq)RH), designated DGOH, depends on the molecular environment of the OH group. Scheme 12 shows increments, DGOH, to be added to a reference value of DGOH = –39.5 kcal mol1, chosen for the replacement of H by OH in ethane to give ethanol, for a selection of other alcohols. For cyclohexadienol 10 for example the value of DGf (aq) may be estimated from the corresponding value for cyclohexadiene 39.5 (DGOH for EtOH) 1.2 (the increment DGOH for cyclohexen-3-ol), plus a correction of 1.0 kcal mol1 for the unfavorable inductive interaction between the OH group and the remote double bond of the dienol. In so far as DGf (aq) for benzene is known, pKH2 O for addition of water to benzene [Equation (16)] can now be estimated as 22.2.

Scheme 11

42

R. MORE O’FERRALL MeOH

EtOH

PrOH

t-BuOH

5.5

0

0.2

–4.9

OH

OH

–2.0

–1.2

OH

i-PrOH –2.9

–0.6

Scheme 12

OH

pK H2O = 22.2 + H2O

(16) 10

In the cases of naphthalene, phenanthrene, and anthracene similarly calculated values of pKH2 O are 14.2, 9.2, and 7.4 respectively.47 These values may be compared with experimental values of 13.7, 9.3, and 7.5, determined75 as described above for phenanthrene. The good agreement between calculation and experiment, and the systematic dependence of pKH2 O on the stabilization energy of the aromatic rings, lends credence to the value for benzene. It may be noted that the variation in increments shown in Scheme 12 represents differences in interaction energies between the OH group and the hydrocarbon fragment of the alcohol molecule. When pKR values are compared between different carbocations, they include the effect of the structural change upon the alcohol. Thus the difference in values for t-butyl and isopropyl cations underestimates the relative stabilities of the carbocations as measured by their HIAs by 1.5 log units (2.0/1.364). Rate–equilibrium correlations for the deprotonation of carbocations To complete the evaluation of pKa and pKR for protonated benzene, it is necessary to determine a rate constant kp for deprotonation. In so far as there is a substantially greater thermodynamic driving force for deprotonation of the benzenonium ion than for other ions leading to aromatic products, the rate constant must be greater than the values of 2.91010 s1 for the phenanthrenonium ion or 1.61010 for the naphthalenonium ion, and there can be little error in assigning it as 1011 s1. However, it is of interest to examine the variation in kp more rigorously based on a correlation of values of log kp and pKa which takes account of the limiting value of kp at highly negative values of pKa. This correlation is shown for a range of carbocation structures in Fig. 1, with the arenonium ions shown as filled circles. The correlation includes protonated mesitylene, studied by Marziano,107 and earlier measurements of the protonation of methoxy-substituted benzenes108 and azulenes.109 It also

STABILITIES AND REACTIVITIES OF CARBOCATIONS

43

14 12 10

log kp

8 6 4 2 0 –2 –25

–20

–15

–10 pKa

–5

0

5

Fig. 1 A plot of logs of rate constants for deprotonation of carbocations against pKa in aqueous solution at 25C.

includes secondary benzylic cations, including those in Scheme 3 (and Table 4 on p. 59 below), shown as open circles, and tertiary alkyl or benzylic cations shown as squares. The different groups of compounds in Fig. 1 show some dispersion and the correlation line is based on the arenonium ions only. The equation for the line drawn through the points comes from an analysis by Richard of protonation of carbanions which leads to Equation (18). This equation is based on the reaction shown as Equation (17), in which the rate constant for relaxation of the solvent is denoted kreorg. The structure R+H2O represents the carbocation with a solvent shell as initially formed from the alcohol, and H2O R+ represents the carbocation with a ‘relaxed’ solvation shell, which reacts with the loss of a proton. Solvent relaxation becomes rate determining when deprotonation of the carbocations is sufficiently fast. The rate constant ki is an ‘‘intrinsic’’ (microscopic) rate constant for deprotonation. This is unaffected by solvent relaxation, and except for very reactive cations (i.e., for which ki approaches kreorg) is equal to the experimentally measured rate constant kp [which is expressed in terms of ki and kreorg in Equation (18)]. It is assumed that the dependence of log ki upon pKa is linear. With kreorg = 1011 s1, a best fit to the filled circles in Fig. 1 to Equation (18) is obtained with log ki = –0.41pKa þ 1.51. kreorg

ki

Rþ H2 O Ð H2 O Rþ ! Arene kreorg

ð17Þ

44

kp ¼

R. MORE O’FERRALL

kreorg ki ki þkreorg

ð18Þ

It might seem surprising at first that a rate–equilibrium relationship covering such a wide range of reactivity should be assumed to be linear. Although the origin of such linearity is not fully understood it is commonly observed for free energy relationships and is discussed later in the chapter. Certainly, any curvature in Fig. 1 falls within the limits of scatter of the points over the large range of pKa values encompassed (25 log units). As the pKa becomes sufficiently negative, ki can be expected to reach its own vibrationally controlled limit but at a substantially larger value than 1011 s1. Values of kp and pKa for benzene may be obtained from Fig. 1 by substituting the rate constant for protonation of benzene by H3Oþ, kA =2.6 1015 M1 s1 (extrapolated to aqueous solution from kinetic measurements in concentrated solutions of strong acids),72 into the relationship Ka = kp/kA. Taking logs gives pKa = –log kp – 14.36, a relationship which can be plotted as the dashed straight line in Fig 1, which intercepts the correlation line to give pKa = –24.5 and kp = 91010 for protonated benzene. From this value of pKa, and pKH2 O ¼ 22:2, a value of pKR can be derived as pKa þpKH2 O ¼ 2:3.25 A similar analysis for 2-protonated naphthalene 16 complements Thibblin’s measurements106 for the 1-protonated isomer and gives kp = 6.51010 and pKa = –22.5. Table 2 summarizes pK measurements for the simplest protonated aromatic hydrocarbons. The columns to the right and left of the benzenonium ion correspond to benzoannelation of ions subject to protonation at the 2- and 4-positions of the benzene ring, respectively. In the parent ion the two positions correspond to resonance forms (one of which has been rotated through 120 in the table). The naphthalenonium ion 17 is shown as being formed from the 1,4-water adduct (hydrate) of naphthalene. It may also be formed from the isomeric ‘‘2,1’’ hydrate (1,2-dihydro-2-naphthol) with pKR = –6.7 and pKH2 O ¼ 13:7. Table 2 Values of pKH2 O , pKa, and pKR for arenonium ions +

+

7

pKH2 O pKa pKR

7.5 13.5 –6.0

17

16.9 –20.4 –3.5

+

9

22.2 –24.5 –2.3

+

+

+

16

12

14.5 –22.5 –8.0

9.3 –20.9 –11.6

STABILITIES AND REACTIVITIES OF CARBOCATIONS

45

From the tabulation it is evident that for aromatic molecules pKa and pKR provide very different measures of stability. From our earlier discussion (p. 23–28), it is clear that pKR provides the more appropriate measure of the stability of the carbocations and that pKa strongly reflects the stability of the aromatic molecule, which indeed is directly measured by pKH2 O . Thus the nearly invariant pKa for four of the cations arises from compensation between changes in the stability of the cation and of the aromatic molecule. It is noteworthy that as judged by pKR protonated benzene is a particularly stable carbocation. The value of 2.3 is obtained indirectly, as described above, but is consistent with pKR = –3.5 measured by McClelland for the phenylsubstituted dimethyl analog 18.110 A surprising observation is that benzoannelation is quite strongly destabilizing for the cations. We will return to the significance of this later in the chapter, as well as to the fact that the effect of benzoannelation on the pKas is opposite to that on pKR. The latter behavior implies that the unfavorable effect of benzoannelation on the stability of the reacting double bond of the aromatic molecules is greater than that on the stability of the carbocations.

Ph +

Me

Me

18

Cox’s extrapolation of rate constants for protonation of a number of ringsubstituted benzenes72 can be combined with the correlation of Fig. 1 to derive pKas in the same way as for benzene and naphthalene. The pKas include p-protonated bromobenzene 24.3, toluene, 20.5, and anisole 15.0. Cox noted the activating effect of bromine on hydrogen isotope exchange, which is partially concealed by a statistical factor of six which increases the basicity of benzene. In principle, the pKa for anisole might be considered the least well defined of the pKas as the inferred value of kp = 3.0108 is further removed from its limiting value. On the other hand, there is less uncertainty in the extrapolated value of kA than for the less basic aromatics. The only conjugate acid of a substituted benzene for which pKR can reasonably be estimated is the protonated toluene. A value of DGf (aq) for the corresponding hydrate is readily estimated from the likely effect of methyl substitution on the stability of 1,4-benzene hydrate,47 and this can be used to estimate pKH2 O as described above, while pKR is obtained from pKR = pKH2 O þ pKa. The resulting pK values are compared below with those for the corresponding methyl-substituted naphthalenium 19 and anthracenium 20 ions, for which reactions of the hydrates (or their methyl ethers) have been

46

R. MORE O’FERRALL

studied by Thibblin.111,112 For 1-methylnaphthalene, pKH2 O may be estimated in the same way as for toluene and a pKa may be obtained by combining azide clock measurements of kp with a value of kA derived from a partial rate factor in trifluoroacetic acid.75,113 For the 9-methyl-9-anthracenium ion, Zia and Thibblin’s measurements of rate constants from azide trapping and acidcatalyzed reaction of the hydrate yield pKR directly. Azide trapping also provides kp which when combined with a partial rate factor-based kA114 gives pKa and thence pKH2 O . The results listed below are generally consistent with expectations based on pK values for the parent ions, save that it is noticeable that, in contrast to the situation for the benzenonium and naphthalenonium ions, methyl substitution de-stabilizes the anthracenonium ion. This is plausibly attributed to interaction of the methyl group with the peri-hydrogen atoms of the flanking benzene rings. It is perhaps surprising at first that methyl substitution increases the equilibrium constants for hydration (cf. Table 2). This is at least partly due to a geminal stabilizing interaction (2–3 kcal mol1) between the methyl and OH group of the hydrate.

CH3

CH3

CH3

+

+

+

H

H

H

H 19

pKH2 O pKa pKR

21.6 –20.5 1.1

16.0 –17.0 –1.4

H

H 20

6.1 –12.7 –6.6

ALKYL CATIONS

Having introduced the correlation of Fig. 1, we may return to the stabilities of alkyl cations. Rate constants for the hydration of secondary and primary alkenes have been measured in concentrated solutions of aqueous sulfuric acid by Lucchini and Modena97 and by Tidwell and Kresge42 using proton nuclear magnetic resonance (NMR) or UV to monitor progress of the reactions. It is conceivable that the reactions involve a concerted addition of a proton and water molecule to the alkenyl double bonds. However, the very weak basicity of water under the conditions of reaction makes this unlikely, and the steep acidity dependences of the reactions (e.g., m* = –1.65) is

STABILITIES AND REACTIVITIES OF CARBOCATIONS

47

inconsistent with substantial localization of charge on an oxygen atom. Other arguments in favor of rate-determining protonation of the alkenes to form carbocations as discrete short-lived intermediates have been advanced over a number of years by Lucchini and Modena97 and by Tidwell.98,115 The rate constant for the protonation of ethylene, 8.51015 M1 s1, is even smaller than that for protonation of benzene, and there can be little doubt that deprotonation of the ethyl cation in the absence of high concentrations of acid is at or close to the solvent relaxation limit. Assigning this value gives pKa = –25.1 for the ethyl cation, and combining this pKa with pKH2 O ¼ 4:8 for hydration of ethylene gives pKR = –29.9. For 2-propene, the rate constant is considerably larger, 2.4  109 M1 s1, and a derivation of pKa depends on the assignment of kp using the correlation of Fig. 1. There is sufficient dispersion of points in Fig. 1 to suggest some ambiguity in this assignment. Thus the (four) points for protonation of a double bond with a terminal methylene group fall below the correlation line but show a steeper slope. Since the relevant pKa is close to the point at which the two correlations might coincide we derive the value as before from the measured kA = 2.4109 to obtain 17.9, after correction for the statistical effect of six equivalent hydrogens in the isopropyl cation. Combination with pKH2 O ¼ 4:23, then gives pKR = –22.1. The possible uncertainty in this value is indicated by deriving alternative values of pKa and pKR for the isopropyl cation starting with kA = 4.5109 M1 s1 for protonation of 2-butene (sic).42 Proceeding as before we deduce pKa = –16.8 for the 2-butyl cation forming 2-butene and thence pKa = –15.0 for formation of the 1-butene, based on the equilibrium constant for isomerization of the alkenes. Now the identity of the rate constants for protonation of 1-butene and 1-propene suggests that the pKas of the 2-butyl and 2-propyl cations are the same, barring statistical factors, and combination with values of pKH2 O gives pKR = –20.3 and 20.0 respectively. The value of pKR = –20.0 for the isopropyl cation is 2.1 log units more positive than the value derived from protonation of propene directly. In its favor, protonation of 2-butene occurs at a ‘‘secondary’’ rather than (as for 2-propene) a ‘‘primary’’ vinylic carbon atom, as is also true of formation of the cations correlated in Fig. 1. However, that correlation refers to benzylic rather than alkyl cations and there is no good reason to suppose their behavior is strictly comparable. The more negative pKR is preferred for two reasons. Firstly, as will be clear below, it is correlated better with the gas-phase stability of the isopropyl cation. Secondly, derivation of pKR = –16.5 for the cyclohexyl cation from the rate constant for protonation of cyclohexene98 gives a value which, for a secondary alkyl cation, seems too close to that of the t-butyl cation (pKR = –16.4), even though the difference is increased by 2.1 log units if allowance is made for the more favorable geminal interactions of an OH

48

R. MORE O’FERRALL

bond in a tertiary than a secondary alcohol (i.e., by replacing pKR by its HIA counterpart pKRH). These points have been pursued in detail for two reasons. The first is to indicate the level of uncertainty in deriving pKas when the rate of deprotonation falls significantly short of its relaxation limit and the structure-reactivity correlation for the alkene conjugate base of the cation is insufficiently defined. The second is that the identity of the rate constants for 2-propene and 2-butene still imply a difference of 0.3 log units between 2-propyl and 2-butyl cations. In so far as this difference corresponds with the small difference in geminal interaction of the OH groups, the implication is that as measured by their HIAs the two ions have the same stability (cf. discussion on p. 25). In conclusion, the preferred pKR for the 2-propyl cation is listed below with the more secure values for the t-butyl and ethyl cations.

pKRS

(CH3)3Cþ

(CH3)2CHþ

CH3 CH2þ

–16.4

–22.1

–29.9

VINYL CATIONS

Lucchini and Modena also measured rate constants for the hydration of acetylene and methyl acetylene.97 Accepting that the initial and rate-determining step of this reaction is formation of the corresponding vinyl cations, we may analyze the measured rate constants in the same way as for protonation of the alkenes. The rate constants for the two substrates are similar to those for ethylene and propene and lead to pKa values of 25.2 and 18.3.75 Values of pKR can now be derived by recognizing that hydration of acetylene and methylacetylene yield enols of acetaldehyde and acetone, respectively. Values of pKH2 O are accessible because free energies of formation in aqueous solution of the enols can be obtained from the keto–enol equilibrium constants and free energies of formation of the aldehyde and ketone.38,116 Combining these with those of the acetylenes yields values of pKH2 O and thence pKR. The cycle for acetylene, which includes the unsusbstituted vinyl cation, is shown in Scheme 13, from which it can be seen that pKR = –40.2. The pKR for the a-methyl vinyl cation is estimated as 31.7. H2O + H2C CH+ –40.2

–25.2 H2O + H+ + HC CH

Scheme 13

–15.0

H2C CH OH + H+

STABILITIES AND REACTIVITIES OF CARBOCATIONS

49

The value of pKR = –40.2 makes the vinyl cation the most unstable carbocation for which equilibrium measurements are available. It is remarkable that while the vinyl cation and benzenonium ion have similar pKas, their pKR values differ by 38 log units. This is an indication of the sensitivity of pKa to the stability of the conjugate base of the cation, and specifically to the very different energies of p-bonds in acetylene and benzene. Measurements by Okuyama indicate that while secondary (alkyl substituted) vinyl cations are viable intermediates in the solvolysis of vinylic precursors with sufficiently reactive leaving groups,117 the same is not true of primary vinyl cations even in solvents as highly ionizing and poorly nucleophilic as TFE and hexafluorisopropanol.118 Thus Lucchini and Modena’s access to the parent vinyl cation clearly depends on the high energy of the triple bond of their alkyne reactant. Calculations suggest that the most stable form of the vinyl cation is likely to be that in which the proton is coordinated to a p-bond of acetylene rather than forming a -bond with a terminal carbon atom.10,119,120 An extensive mechanistic chemistry of vinyl cations has been developed120 including studies of the rate and stereochemical course of reactions of cations generated by flash photolysis.84,121–124 Nevertheless, although stabilities of the cations have been measured and calculated in the gas phase120 and stabilities in solution have been assessed from rate constants for solovolysis based on the use of leaving groups as reactive as triflate and iodobenzene,117,118,125 the kinetic measurements do not at present provide access to thermodynamic data. This is partly because of the difficulty of measuring rate constants for the reverse of the reactions of vinyl cations with water or alcohols in competition with tautomerization or hydrolysis of the relevant enol or vinyl ether reactants.

THE METHYL CATION: A CORRELATION BETWEEN SOLUTION AND THE GAS PHASE

There exists a further potential source for assignment of stabilities of carbocations. That is to exploit the wider range of stabilities available in the gas phase than in solution through an appropriate correlation between the two. There have been a number of attempts at such correlations126–128 which in the past have been limited partly by the smaller number of measurements available in solution. For sufficiently homogeneous series of structures, correlations certainly exist. Richard and Mishima compared pKas for protonation of ring-substituted a-methylstyrenes in TFE–H2O mixtures and the gas phase and found the slope of a plot of solution against gas phase values to be 0.70.89 They compared this slope with that of 0.40 for the protonation of pyridines129 and ascribed the lower slope in that case to the importance of hydrogen bonding in solvating the pyridinium ions.127 Undoubtedly, more disparate structures lead to greater dispersion of points. Now that more solution values are available the structure

50

R. MORE O’FERRALL

dependence of these correlations would benefit from closer investigation. Such an analysis is beyond the scope of this review, but Keeffe and the author have explored the possibility of extrapolating a pKR for the methyl cation from a correlation of methyl substituent effects between gas phase and solution.26 Figure 2 shows plots of hydride ion affinities HIA in the gas phase against solution values for (a) ethyl, isopropyl, and t-butyl, (b) methoxymethyl, methoxyethyl, and methoxyisopropyl, and (c) benzyl, aphenyl ethyl, and cumyl cations. Also shown are the vinyl cation and methylvinyl cation. The gas-phase HIAs for the benzyl cations are based on heats of reaction, HIAs for the other cations are based on free energies. Despite deviations of the benzyl and vinyl cations from the other values, the satisfactory correlation of the alkyl and methoxyalkyl cations with slope 1.52 implies a consistent behavior within this limited structural family. The inverse of the slope of the plot is 0.67, which is close to the value for the protonation of the a-methylstyrenes. This level of agreement encourages a speculative extrapolation of pKR = –43 for the methyl cation based on the measured value of its HIA in the gas phase.

60

CH2 = CH+

ΔHIA gas phase

40

CH3CH2+

20

(CH3)2CH+ MeOCH2+ PhCH2+

0

–20

–40 –20

–10

0 10 ΔHIA aqueous solution

20

30

Fig. 2 Plot of hydride affinities (HIA) in the gas phase against values in aqueous solution at 25C. Filled circles, alkyl cations; open circles, methoxyalkyl cations; triangles, vinyl cations.

STABILITIES AND REACTIVITIES OF CARBOCATIONS

51

This concludes the discussion of the stabilities of carbocations with hydrocarbon-based structures and also of different methods for deriving equilibrium constants to express these stabilities. The remainder of the chapter will be concerned mainly with measurements of stabilities for oxygen-substituted and metal ion-coordinated carbocations. Consideration of carbocations as conjugate acids of carbenes and derivations of stabilities based on equilibria for the ionization of alkyl halides and azides will conclude the major part of the chapter and introduce a discussion of recent studies of reactivities.

OXYGEN-SUBSTITUTED CARBOCATIONS

Oxygen substitution has a radical effect on the stability of a carbocation, which is manifested in the chemistry of carbohydrates, benzopyran pigments, and the extensive acid-dependent reactions of carbonyl compounds. The greatest effects are from a-oxygen substituents but effects of substituents in the aromatic ring of benzylic carbocations are also large. As we shall see, there is a surprising influence of b-oxygen substituents upon the stabilities of arenonium ions. a-oxygen substituents For several a-alkoxy carbenium ions rate constants for reaction with water were determined by Jencks and Amyes from the partial reversibility and associated common ion rate depression of hydrolysis of the corresponding azidoacetals, as is illustrated in Scheme 14.130 Jencks and Amyes measurements gave ratios kAz =kH2 O for reactions of the carbocations with water and azide ions from which values of kH2 O could be derived in the usual way by assigning a diffusional rate constant, 5109 M1 s1, to kAz, save in the case of the methoxymethyl cation for which kH2 O was presumed to have achieved it relaxation limit (1011 s1). The reverse of the water trapping reaction is acid-catalyzed conversion of a hemiacetal to the carbocation. The rate constant for this reaction, kH, was assigned on the assumption that it was 0.57 times that for the corresponding ethylacetal or 0.8 times that for the methylacetal.130–132 Values of KR were then derived in the usual way as KR ¼ kH2 O =kH .132

R MeOCH N3

k1

+ MeOCH

k H2O

R RCHO + MeOH

MeOCH OH

k Az kobs =

Scheme 14

R + N3–

k1 ( 1 + k Az[N3–]/k H2O )

52

R. MORE O’FERRALL

For di- and trimethoxy carbocations, for which rate constants for reaction of the cations with water have been measured by McClelland and Steenken,4,133 rate constants for the back reactions of the hemiorthoester and hemiorthocarbonate were assigned in the same way as for the hemiacetals from the corresponding methyl or ethyl ethers.134–136 Estimates of pKR for representative methoxy and dimethoxy carbocations are shown in the first two rows of structures at the bottom of the page. The structures and pKR values shown summarize the influence on carbocation stability of (a) accumulating methoxy substitution, (b) the difference between methoxy and ethoxy substituents and between cyclic and acylic structures (with five-membered ring cyclic structures indicated as (CH2O)2C+R) and (c) the influence of methyl and phenyl substituents. From the first two rows, it is clear that a methoxy group has a very strong stabilizing effect on a carbocation and that this effect is attenuated as the stability of the carbocation increases. As pointed out by Kresge and McClelland, relative to methyl, a phenyl group stabilizes a cyclic but destabilizes an acyclic dialkoxy cation.4 This is plausibly attributed to steric hindrance to conjugation of the alkoxy oxygen atom. Of interest is a comparison of a-methoxy with a-hydroxy substituents. The a-hydroxy carbenium ions correspond to protonated ketones and their pKR values may be derived from a combination of a hydration equilibrium constant and a pKa for protonation of the ketone, as illustrated by the thermodynamic cycle based on acetophenone in Scheme 15.137,138 Corresponding data are available for benzaldehyde138,139 and acetone70,140,141 and lead to the values of MeOCHþ 2

(MeO)2CHþ

–15.9

–5.6 þ

(MeO)3Cþ

(EtO)2CHþ

–1.5 þ

–5.7

(MeO)2C Me (MeO)2C Ph (CH2O)2C Me (CH2O)2CþPh –1.3 þ

PhCH –O 14.7

þ

–3.0 

PhCHOH –2.4

–2.0 þ

–1.0

PhCHþ 2

PhCHOMeþ

(–21)

–7.5

PhC(OH) OMeþ 3.0

OH+ H2O + Ph

C

1.31

–3.87 H2O + H+ + PhCOMe

Scheme 15

CH3

5.18

PhC(OH)2Me + H+

PhCðOHÞþ 2 7.4

STABILITIES AND REACTIVITIES OF CARBOCATIONS

53

pKR below the third row of structures on the previous page. Measurements are also available for methyl benzoate,138,142 for which the protonated ester and hydrate adduct are intermediates in acid-catalyzed ester hydrolysis. Extrapolating from the ester, a value may also be estimated for protonated benzoic acid, for which a pKa143 is combined with a value of DGf (aq) for PhC(OH)3 derived from the corresponding value for PhC(OH)2OMe142 by Guthrie’s method.144 Comparisons of structurally related hydroxy- and methoxy-substituted cations show that hydroxy is more stabilizing by between 4 and 5 log units. This difference was recognized 20 years ago by Toullec who compared pKas for protonation of the enol of acetophenone and its methyl ether145 (–4.6 and 1.3, respectively) based on a cycle similar to that of Scheme 15, but with the enol replacing the hydrate, and a further cycle relating the enol ether to a corresponding dimethyl acetal and methoxycarbocation.146 Toullec concluded, understandably but incorrectly, that there was an error in the pKa of the ketone (over which there had been controversy at the time).147,148 In a related study, Amyes and Jencks noted a difference of 105-fold in reactivity in the nucleophilic reaction with water of protonated and O-methylated acetone and concluded that the protonated acetone lacked a full covalent bond to oxygen.130 It seems clear that the explanation of these differences lies in the advantage in solvation energy conferred by an OH group attached to a charge center. The importance of this solvation is indicated by the low m* values for the protonation of most ketones52,71,138 and the lower m* value and greater basicity of carboxylic acids than their esters, for example, pKa = –4.43 and m* = 0.51 for benzoic acid143 compared with pKa = –7.05 and m* = 0.82 for methyl benzoate.138 Other examples of the superior solvation of OH relative to MeO groups conjugated with a positive charge are mentioned below (p. 56) The value of pKR = 7.4 for protonated benzoic acid (PhCðOHÞ2þ on the previous page) is of interest in that it allows comparison with the corresponding value of pKR = 8.8 for the isoelectronic phenylboronic acid PhB(OH)2149. Considering the presence of the positive charge on the carbon acid and absence of a charge on the boronic acid, the difference in Lewis acidities is remarkably small. Presumably, this reflects the greater stability of boron–oxygen than carbon–oxygen bonds. The last row of structures on the previous page includes the effect of an a–O substituent on the stability of a benzyl cation. This comes from considering an aldehyde or ketone as an O-substituted carbocation. A pKR is then obtained from the equilibrium constant for addition of hydroxide ion to the ketone to form the conjugate base of its hydrate. This can be derived from the cycle including the hydrate shown for benzaldehyde in Scheme 16. The cycle includes the equilibrium constant for hydration of the carbonyl group pKhyd and a pKa for ionization of the hydrate.139 In practice, KR is obtained by measuring the equilibrium constant for addition of hydroxide ion Kc150 [Equation (2) on p. 21] and the relationship KR = KcKw. As expected, O is even more

54

R. MORE O’FERRALL H2O + PhCHO pK hyd = 2.10

pK R = 14.74 12.64

PhCH(OH)2

PhCH(OH)O– + H+

Scheme 16

stabilizing than OH. In general, the relative effects of substituents across the structures shown on p. 52 present a consistent pattern. Acid-catalyzed reactions of aldehydes with nucleophiles offer a further method for determining pKR. This is illustrated by the reaction of 9formylfluorene (FlCHCHO) with hydroxylamine to form the oxime shown in Scheme 17. The kinetic dependence of the reaction on concentrations of acid and hydroxylamine suggests that this reaction proceeds by rate-determining attack of hydroxylamine on the O-protonated aldehyde35. If the attack of hydroxylamine is diffusion controlled, the measured first-order rate corresponds to kobs = (kdiff/Ka)[NH2OH], where kdiff = 3.0109 M1 s1 is the rate constant for diffusion and Ka is the acid dissociation constant of the protonated 9-formylfluorene. Despite the diffusion rate, reaction of the protonated aldehyde with hydroxylamine is relatively slow because of the low concentration of unprotonated hydroxylamine at the prevailing acid concentration. Thus, protonation of the aldehyde is readily reversible. Division of the measured rate constant kobs by the rate constant for diffusion and the concentration of hydroxylamine gave pKa = –4.5 for the protonated formylfluorene. Combination of this equilibrium constant with that for hydration of the carbonyl group then gave pKR = –5.3. In general, diffusion control of the reactions of protonated carbonyl groups with nucleophiles is more likely to apply for reactions of aldehydes than ketones because of the less negative pKR and lower reactivity of the conjugate acids of latter. Thus pKR = –5.3 for the protonated 9-formylfluorene may be compared with pKR = 0 and 1.3 for protonated acetone and acetophenone, respectively. For these ketones protonation equilibria can be measured directly138 and reactions of the protonated ketones with hydroxylamine were shown to occur below their diffusion limits.35 For aliphatic aldehydes, direct determination of pKas is usually not

+

O +

H + FlCH

C

OH

1/K a H

FlCH

C

OH

k diff[NH2OH] H

C

FlCH +

Scheme 17

H

NH2OH

FlCHCH

NOH + H2O + H+

STABILITIES AND REACTIVITIES OF CARBOCATIONS

55

feasible, because of the combination of a lack of strong UV chromophore, low basicity, and extended range of acid concentrations over which protonation occurs, reflected in low m* values. However, as described below (p. 57) the diffusion method has been used to infer a pKa for the protonation of a quinone methide. Oxygen substituent effects on arenonium ions It is also possible to examine the effect of oxygen substituents on the stability of arenonium ions. Wirz has studied keto–enol equilibria for phenol,151 naphthol (Wirz J, Personal communication), and anthrol.152,153 The tautomeric constants may be combined with pKas for protonation of the keto tautomer and ionization of the phenol to provide pKas for protonation of the aromatic ring of phenol and the phenoxide ion. As illustrated in Scheme 18 the unstable keto tautomer of phenol 22 was produced by photolysis of the bicyclooctene dione 21. Except in the case of the anthrone a pKa for protonation of the keto tautomer has not been measured directly. However, values can be estimated from the pKa for protonation of the 4,4-dimethylated analog136 with a correction for the substituent effect of the methyl groups. The pKas for C-protonation of the phenols and phenoxide ions are compared with values for the unsubstituted aromatic molecules in Table 3. The focus on pKa rather than pKR is because the equilibrium constants for hydration of the keto tautomers of the phenols have not been measured or estimated. The values  of DpKOH and DpKO a a show the magnitude of the oxygen substituent effects relative to the parent aromatic molecules. Again the substituent effects are large, and much larger for O (more then 20 log units) than OH (10 log units). At first, it is surprising that the effects are so similar for the benzene, naphthalene, and anthracene. Once more this arises because the pKa reflects the stability of OH+

O

hν –(CH2CO)

O

–13.2

–2.1

OH pK E = –12.73

O 21

22 –2.89

Scheme 18

O– 9.84

56

R. MORE O’FERRALL

Table 3 Acid dissociation constants of arenonium ions and their a-HO and a-O derivativesa + +

+

+ +

+ H

H

H

H

H

pKa a-H a-OH a-O

–24.5 –13.2 –1.1

–20.5 –8.3 3.1

–13.4 –3.2 10.0

DpKa a-OH a-O

11.3 23.4

12.2 23.6

10.2 23.4

a

Me

H H

H

H

H

–22.2

–24.5

2.1

–2.9

–15.7 4.1 19.3

24.3

21.6

19.8 35.0

The oxygen substituents are located at the positions shown with a formal positive charge in the parent cation.

both the protonated and unprotonated aromatic molecule. In practice, the aromatic rings delocalize charge and moderate the influence of the substituents. This is indicated by comparison with the quite different and larger effects of HO and O on the carbon basicity of the enol and enolate anion of acetophenone, which are also shown in Table 3. For phenol one can compare the effects of hydroxy and methoxy substituents. Scheme 19 shows effects of O-methyl substitution on pKas for protonation of a benzene ring containing one, two, and three hydroxy substituents. The pKas for di- and trihydroxy-substituted and methoxy-substituted benzenes were measured directly by Kresge et al.68 Again the stabilities of the hydroxysubstituted cations in water are consistently greater than methoxy. The importance of solvation in controlling these effects is demonstrated by the inversion of relative pKas of trihydroxy and trimethoxy benzene in concentrated solutions of perchloric acid.68 Thus the difference in pKas is matched by a

H

pKa

Scheme 19

R=H R = Me

OR

OR

OR

+

+

+

H

–13.2 –15.0

H

H

–6.3 –7.5

OR

RO

H

H

–3.35 –5.2

OR

STABILITIES AND REACTIVITIES OF CARBOCATIONS

57

corresponding difference in m* values, for example, pKa = –5.2 and m* = 1.65 for trimethoxybenzene and pKa = –3.35 and m* = 0.87 for trihydroxybenzene. Oxygen ring substituents: quinone methides Effects of oxygen substitutents in an aromatic ring upon an exocyclic rather than endocyclic carbocation charge center have also been measured. The possibility of comparing HO, MeO, and O substituent effects for the benzylic cations is provided by recent studies of quinone methides, including the unsubstituted p-quinone methide 23, which may be considered as a resonancestabilized benzylic cation with a p-oxyanion substituent.

CH2

CH2+

O

O– 23

Such structures can be generated by flash photolysis of p-hydroxybenzyl alcohol or its derivatives such as p-hydroxybenzyl acetate.154 Kresge has studied the subsequent reaction of the quinone methide with water to yield the corresponding hydroxy-substituted benzyl alcohol 25, as shown in Scheme 20.155 The hydrolysis shows an acid-independent reaction at neutral pH and an acid-catalyzed reaction at lower pH, consistent with attack of water on the neutral and O-protonated (24) quinone methides, respectively. Other nucleophiles show similar acid-dependent and acid-independent reactions. By assuming that for the acid-catalyzed reaction with thiocyanate anion (to form the trapped product 26) attack of the thiocyanate ion is both rate determining and diffusion controlled with a rate constant 5109 M1 s1,156 Kresge was able to derive a pKa = –2.0 for the initial protonation reaction from the

H2O H+ O

CH2 23

25

CH2+

HO 24

CH2OH + H+

HO

SCN–

HO

CH2SCN 26

Scheme 20

58

R. MORE O’FERRALL

relationship kobs = kd/Ka (cf. the similar determination of a pKa for protonation of 9-formylfluorene, p. 54). This also allowed assignment of rate constants kH2 O ¼ 3:3 s  1 and 5.8106 s1 for reactions of the neutral and protonated quinone methide, respectively. The O-protonated quinone methide corresponds to the p-hydroxybenzyl cation 24. Richard measured the rate constant kH for acid-catalyzed formation of this cation from p-hydroxybenzyl alcohol by monitoring formation of a thiol-trapped product by HPLC.157 Combining this rate constant with kH2 O yields pKR = –9.6 for the cation from the usual relationship KR = kH2 O /kH. This equilibrium constant may be combined with the pKa for the protonated quinone methide and an estimated pKa = 9.9 for p-hydroxybenzyl alcohol to give pKR = 2.3 for the p–O-substituted alcohol based on the cycle of Scheme 21. Combining the above values of pKR with the value for the p-methoxybenzyl cation measured by Toteva and Richard158 allows the effect of the three oxygen substituents on the stability of the benzyl cation to be compared in Scheme 22. The values of pKR may also be compared with effects of similar oxygen substitutions at the a-position of the benzyl cation from Table 3, which are also shown in Scheme 22. As expected, the relative magnitudes of the O, HO, and MeO substituent effects exhibit similar patterns in the a- and pK R = –9.6 H2O + HO

CH2+

CH2OH + H+

HO

pKa = 9.9

pKa = –2.0 pK R = 2.3 H+ + H2O + O

CH2

–

CH2OH + 2H+

O

Scheme 21

CH2+

pKR

(–21) PhCH2+

pKR

(–21)

Scheme 22

CH2+

CH2+

CH2+

OMe

OH

O–

–9.6

2.3

PhCHOH +

PhCH=O

–2.4

14.7

–12.4 PhCHOMe+ –7.5

STABILITIES AND REACTIVITIES OF CARBOCATIONS

59

p-positions but the a-effects are larger. Nevertheless, it is evident that even when separated from the carbocation center by an aromatic ring, the stabilizing effects of oxygen remain very large. Measurements of stabilities of benzylic carbocations with o-oxygen substituents show smaller effects than their p-counterparts. This is apparent from the examples 27–30, for which differences in pKR from replacing MeO by Me (or, in cyclic structures, O by CH2) are shown in Table 4.73 For the o-methoxy substituent, the relatively small increment in pKR (DpKR = 2.3 compared with 3.9 for p-MeO) can be understood in terms of steric hindrance to resonance interaction and to the more favorable accommodation of resonance structures by a benzene ring in the p- than o-case in line with greater stability of p- than o-benzoquinone.159 Perhaps more surprising is that the substituent effect is also small when the oxygen is situated in a fused cyclic ring structure as in 29 and 30 (DpKR = 2.4 and 0.1). Presumably, this represents a conformational restraint of the ring, which is greater for a six- than five-membered ring. It should be mentioned that neutral and acid-catalyzed hydrolyses of the o-quinone methide of benzene have also been studied.155 So far, no value of pKR has been reported. b-Oxygen substituents: hyperaromaticity of arenonium ions Carbocations with b-oxygen substituents have received less attention in the literature than those with a-oxygen substituents. Nevertheless, they have been extensively studied as intermediates in the acid-catalyzed ring opening of epoxides,160 especially, of arene oxides and dihydroarene oxides, which are implicated in the mutagenic metabolism of polycylic aromatic hydrocarbons.161 The structures of deoxy analogs of the carbocations have been investigated under stable ion conditions162 but not the b-hydroxy- or alkoxysubstituted ions themselves. At first sight, there is nothing remarkable in the kinetic or equilibrium effects of b-oxygen substituents. A b-hydroxy group normally decreases the Table 4 Effects of oxygen substituents on stabilities of cyclic benzylic carbocations +

+

27

pKR(H2O) DpKR a b

8.9 3.9

Relative to methyl substituent. Relative to carbocyclic cation.

O

OMe

MeO 28

11.7 2.1a

+

+

29

9.3 2.4b

O 30

12.0 0.1b

60

R. MORE O’FERRALL

rate of carbocation formation163 and the stability of the carbocation. A comparison of pKR values is provided by the 9-phenanthrenonium ion (pKR –11.6) and its 10-hydroxy analog 31 (pKR = –14.4). The KR values indicate a103-fold less favorable equilibrium constant for formation of the carbocation from addition of the b-hydroxyl group.88 HO +

31

What is remarkable, however, is the stereochemical influence of a bhydroxyl group. b-hydroxycarbocations such as 31 are formed not only from arene oxide as precursors but from arene dihydrodiols. As shown for the parent benzene dihydrodiols in Scheme 23, arene dihydrodiols exist as cisand trans-isomers. The cis-isomers are obtained as products of the action on the aromatic molecule of dioxygenase enzymes and have been prepared on a large scale by fermentation.92 The trans-isomers are normally accessible by straightforward synthesis, for example, from the arene oxide. Both isomers undergo acid-catalyzed dehydration to the parent aromatic molecule, as is also shown in Scheme 23. It is clear that their reactions should involve a common carbocation intermediate,163,164 and in so far as there is little difference in the stabilities of the isomers,165 their difference in reactivities might have been expected to be small. On the contrary, the cis-benzenedihydrodiol is found to react 4500 times more rapidly in the presence acid than the trans. Moreover, as shown below, this ratio falls to 440 for naphthalene dihydrodiols, to 50 for phenanthrene dihydrodiols, and less than 10 for a nonaromatic analog such as the acenaphthylene or dihydronaphthalene dihydrodiols.164 These rate ratios are shown on the following page and suggest that the effect is linked to the aromaticity of the ultimate product of the reaction. Trapping experiments with the 10-hydroxyphenanthrenonium ion 31 indicate that the ratio of

OH H+ OH

H+

Scheme 23

–H

+

OH OH

OH

OH

+

STABILITIES AND REACTIVITIES OF CARBOCATIONS

61

cis/trans dihydrodiol products formed from nucleophilic trapping with water in the microscopic reverse reaction is >30. This demonstrates the consistency of the forward and back reactions for cation formation. The behavior is little affected if the b-hydroxy group is changed to b-methoxy.88 HO

OH

OH OH

OH

OH

OH

OH

kcis /ktrans

440

4500

7

50

The interpretation offered for this surprising behavior is that the arenonium ions are stabilized by C–H hyperconjugation, the effect of which is enhanced by the contribution of an aromatic structure to the no-bond resonance form shown for the benzenonium ion 32 below.164 The difference between cis- and trans-diols then arises because reaction of the trans-diol leads initially to a carbocation in which a pseudoaxial C–OH rather than C–H bond is orientated for hyperconjugation (34 rather than 33). The difference in energies of the two conformations and its dependence on the aromaticity of the no-bond structures is confirmed by calculations, which show 9 kcal mol1 difference between the two conformations of the 2-hydroxy benzenonium ions and only 0.5 kcal mol1 for the corresponding 6-hydroxycyclohexenyl cations with one less double bond.164 + H+

H 32 OH2+ OH

H cis

OH2+ OH

+

H

+

H

H 33

H

H OH 34

trans

OH

Stabilization conferred by ‘‘aromatic’’ hyperconjugation resolves a puzzle concerning the relative stabilities of arenonium ions. As judged by rates of solvolysis reactions, normally a phenyl group is more effective than vinyl in stabilizing a carbocation center.166 This difference is moderated for cycloalkyl substrates, so that benzoannelation has little effect, for example, on the rate of hydrolysis of 3-chlorocyclohexene (Cagney H, Kudavalli JS, More O’Ferrall

62

R. MORE O’FERRALL

RA, unpublished data). By comparison, the large and unfavorable effect of benzoannelation on the stability of the benzenonium ion as reflected in its small negative pKR value (–2.3) compared with the larger negative values for the 1-naphthalenonium ion (–8.0) and 9-phenanthrenonium ion (–11.6) is surprising (cf. Table 2, p. 44). The order is explained, however, if it reflects the relative magnitudes of the hyperconjugative stabilization of the ions, which in turn depends on the aromaticity of their no-bond resonance structures. That the observed effect of benzoannelation is consistent with the aromatic character of the benzenonium ion is confirmed by comparison with corresponding effects on the stabilities of tropylium49,167 and pyrylium ions168,169 shown in Scheme 24. In both cases the stabilities of the ions are severely reduced by the additional benzene rings. Indeed, the effect may be compared with the effect of benzoannelation on the aromatic stabilization of benzene itself, which is characteristically decreased by conversion to naphthalene and phenanthrene or anthracene. The fact that, in contrast to pKR, the pKa of the benzenonium ion is increased by benzoannelation implies that benzoannelation does not have as large an effect on the ‘‘aromaticity’’ of the benzenonium ion as on benzene itself. A further indication of ‘‘aromatic’’ stability is provided by measurement of pKR for the cycloheptadienyl cation 35. This ion is a homolog of the cyclohexadienyl cation (pKR = –2.3) and might have been expected to have a similar stability. In practice, measurements in aqueous solution using the azide clock show that pKR is 11.6, which corresponds to a decrease in stability of 12.5 kcal mol1.88 It seems unlikely that this difference arises solely from strain in the cycloheptadienyl ring. Moreover, for the dibenzocycloheptadienyl cation, 36, a pKR = –8.7 can be deduced from measurements in aqueous trifluoroacetic acid (Scheme 25).170 Despite the difference in solvents it seems clear that in this case and in contrast to its effect in Scheme 24 dibenzoannelation strongly stabilizes the cation.

+

pK R

4.7

+

+

1.6

–3.7

pK R

Scheme 24

<5

+ O

+ O

+ O

–2.0

–6.0

STABILITIES AND REACTIVITIES OF CARBOCATIONS

pK R

+

+

35

36

–11.6

–8.7

63

Scheme 25

Hyperconjugation was invoked by Koptyug’s group in the 1960s to explain the structures and spectroscopic properties of methylated benzenonium and other arenonium ions under stable ion conditions.171 The X-ray structure of protonated hexamethyl benzene shows that the ring is close to planar with an internal bond angle nearer to trigonal than tetrahedral at the formally sp3 carbon atom.172 The stretching frequency of the hyperconjugating C–H bond increases from benzenonium to naphthalenonium to phenanthrenonium ions.173 A further surprising observation explained by hyperconjugation is the greater reactivity of benzene oxide 37 toward acid-catalyzed ring opening in aqueous solution than dehydration of benzene hydrate 10.105 Both reactions occur with rate-determining carbocation formation, but normally an epoxide reacts 106 times as rapidly as a structurally related alcohol. The anomalous behavior of the oxide and hydrate of benzene can be attributed partly to homoaromatic stabilization of the arene oxide,174 but it is likely that initial formation of an unfavorable conformation of a carbocation with a pseudoaxial hydroxyl group b- to the charge center also plays a significant role. OH H+ 10 k H = 190 M–1 s–1

+

O

+ H2O 37

H+

+ OH

k H = ~20 M–1 s–1

Protonated aromatic molecules are intermediates in aromatic hydrogen isotope exchange. The stabilization they experience presumably applies to other Wheland-type intermediates. From the work of Eaborn in the 1950s and 1960s, it is known that trimethylsilyl and other leaving groups conducive to -bond delocalization are highly reactive toward displacement from an aromatic ring,175,176 and this has been attributed to hyperconjugation.114,177 Taking account of the contribution of an aromatic resonance structure to this enhanced hyperconjugation, it seems appropriate to characterize the phenomenon as ‘‘hyperaromaticity.’’ This term is suggested by an obvious analogy with the more familiar homoaromaticity.178 The analogy is illustrated

64

R. MORE O’FERRALL

by comparison with the homoaromatic norcaradiene 38. Both the benzenonium ion 32 and norcaradiene are characterized by resonance of  and p valence bond structures. For 32 the resonance involves an exocyclic -bond and endocyclic p-bond, whereas for 38 the –p resonance is endocyclic. Use of the prefix ‘‘hyper’’ might seem inappropriate for an effect which is less stabilizing than the normal n- and p-aromatic resonance. However, the term ‘‘hyperconjugation’’ was justified by Mulliken on the grounds that it implied ‘‘conjugation over and above that usually recognized,’’179 which would seem appropriate for hyperaromaticity also. Homo

38

METAL-COORDINATED CARBOCATIONS

The effect of metal coordination on the structure and stability of carbocations is great enough to call into question the characterization of many metal complexes as carbocations.180,181 At least two types of metal coordination are common. In one a sigma bond or pair of electrons on a metal contributes a hyperconjugative or neighboring group interaction with a carbocation center. The other involves direct coordination of the metal to a p-system which includes the formal charge center, usually through an 5 or 7 interaction. In such cations the charge may be located primarily on the metal, with little evidence of carbocation behavior other than proneness to nucleophilic reaction at the formal charge center on carbon. For the Cr(CO)3-coordinated benzylic carbocation 39, for example, Cr(CO)3 exhibits both an 6 interaction with benzene ring and a hyperconjugative (-bond) interaction with the benzylic carbon.

+ CH2 Cr OC

CO CO 39

There have been a limited number of quantitative measurements demonstrating the effects of metal coordination. A communication by Petit in 1961 reported pKR values for Fe, Cr, and Mo tricarbonyls coordinated to tropylium and cyclohexadienyl cations,182 but a full paper was not published and some of

STABILITIES AND REACTIVITIES OF CARBOCATIONS

65

his values appear to be in error. Measurements of pKR prior to 1982 were reviewed by Watts180 and these showed that a ferrocenyl substituent and its ruthenium analog are strongly stabilizing toward an adjacent carbocation center and that a benzylic cation is significantly stabilized by coordination of Cr(CO)3 to the phenyl ring. Values of pKR for these cations are compared with those of benzyl and benzyhydryl cations below and illustrate stabilization by neighboring group interactions. The effect of a ferrocenyl substitutent is characteristically greater than that of a Cr(CO)3-coordinated phenyl ring. Some of the stabilization from ferrocene may be through a p-interaction of the carbocation charge center with the cyclopentadienyl ring. However, crystal structures of the ions reveal geometries consistent with substantial bonding between the metal and the cation center and reactions with nucleophiles show a marked selectivity for the opposite face of the cation from the metal (cf. 39).183   PhCH2 þ Ph2CHþ FeCp2 CH2 þ (FeCp2)2CHþ RuCp2 CH2 þ Ph CrðCOÞ3 CH2 þ (–21)

–12.5

–1.2

4.1

1.2

–11.8

There have been extensive kinetic measurements of reactions of p-coordinated carbocations with nucleophiles. These were reviewed in 1984 by Kane-Maguire and Sweigart who compared reactivities of Fe, Ru, Mn, Os, Cr, Mo, W, and Re coordinated to cyclohexadienyl, tropylium, and other unsaturated cyclic cations with or without carbonyl or triphenylphospine ligands for the metals.184 More recent studies have been carried out by Mayr,185,186 including a comparison between reactivities and pKR values for metal-coordinated and uncoordinated ions.187 Based on that correlation (cf. Fig. 10 on p. 106) substitution of a b-hydrogen atom of the ethyl cation by FeCp(CO)2185 increases pKR from 30 to approximately þ10. It should be noted that the attachment here is through the iron atom, whereas for the cations above the CH2þ moiety is bound to the cyclopentadienyl ring (e.g., in FeCp2 CH2 ). There has been interest in the stabilizing effect of coordination of a dicobalt hexacarbonyl on propargyl cations, for which it can act as a protecting group187,188 in the reaction named after Nicholas.189 This stabilization is significantly greater than that of a Cr(CO)3-coordinated phenyl group190 and values of pKR in the range 6.8 to 7.4 have been reported for the ions (e.g., 40).189 It is noteworthy that substituents (R) at the methylene group are practically without effect, implying complete dispersion of charge from the formal carbocation center.187,191 Jaouen has reported pKR values indicating a much greater stabilization of the propargyl cations by Mo2Cp2(CO)4 than Co2(CO)6,192 and Mayr has shown that replacement of CO by Ph3P is also

66

R. MORE O’FERRALL

strongly stabilizing.187 The structure of the propargyl reactant complex reflects the electron deficiency of the bonding to cobalt.193 CH2OH

Co2(CO)6 R

CH2OH

R (CO)3Co

CH R

Co(CO)3

(CO)3Co

Co(CO)3 +

40

Watts and Bunton examined the effect of Cr(CO)3 coordination on pKR for the tropylium ion.194 Because of a competing reaction at high pH in water, the study was conducted in methanolic solutions in which pKR is decreased by up to 5 log units.195 This allowed determination of pKR = 6.6, in methanol which translates to perhaps 9.5 in water. For the uncoordinated tropylium ion pKR is reported as 2.15 in methanol compared with 4.7 in water.195 The moderate stabilization of the tropylium ion by coordination of Cr(CO)3 is pertinent to Schleyer’s conclusion that coordination of Cr(CO)3 does not impair the aromaticity of benzene.181 A very different pKR applies to tropylium ion coordinated to an Fe(CO)3 group, 41. The value has not been determined experimentally but calculations for an isodesmic reaction relating 41 to the uncomplexed tropylium ion imply a pKR in the region of 5.196 The relative instability of this ion must reflect sacrifice of aromatic stabilization in the 5 coordination imposed by the Fe(CO)3. ΔHcalc = –13 kcal mol–1 +

+

+

Fe(CO)3

+ Fe(CO)3

41

Likewise, a neighboring group interaction from Cr(CO)3 coordinated to a benzene ring of the dibenzotropylium ion 42 is destabilizing toward the ion, whereas the same interaction in the corresponding nonaromatic dibenzocycloheptadienyl cation 43 is stabilizing. Changes in pKR accompanying coordination of Cr(CO)3 are indicated under the structures below.170

+ 42 ΔpKR

–2.4

Cr(CO)3

+ 43 +3.5

Cr(CO)3

STABILITIES AND REACTIVITIES OF CARBOCATIONS

67

OH

pK R = 4.7

(CO)3Fe

+ H+

+

(CO)3Fe 44

(CO)3Fe

+ H+

pK a = ~9 (computed)

Scheme 26

By contrast, measurement of pKR = 4.7 for the Fe(CO)3-cooordinated cyclohexadienyl 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 pKa = 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. For the corresponding five-membered ring, in which Fe(CO)3 is formally coordinated to a cyclopentadienyl cation,198,199 there are indications that the complex has the character of a cylopentadienyl anion coordinated to iron with oxidation state of þ2. This is suggested by the characteristic X-ray structure (Kudavalli JS, More O’Ferrall RA, Muller-Bunz H, unpublished data) of a Ph3P-substituted derivative200 and by attack of nucleophiles at the carbonyl group of the complex in preference to a ring carbon atom.198,199 Fischer carbenes (e.g., 45) are not obviously analogs of carbocations. However Bernasconi has pointed to a similarity between displacement of a nucleophilic group attached to the carbenic carbon and ester hydrolysis, which implies a comparison between the C=metal and C=O double bonds.201 From this point of view, Fischer carbenes can be considered as carbocations stabilized by a negatively charged metal ion. There is an obvious analogy with a view of C=O as a carbocation stabilized by a negatively charged oxygen (p. 53). As discussed by Bernasconi, pKR is not directly measurable, but equilibrium constants for addition of methoxide ion in methanol indicate that addition is 106 times more favorable than to a comparably substituted C=O group, which implies values of pKR more positive by six units for an otherwise

68

R. MORE O’FERRALL

comparable ester structure. In so far as pKR for methyl benzoate has been estimated as 21.1 by Guthrie and Cullimore144 the value for 45 should be about 15. This implies that an adduct would be formed in fairly concentrated aqueous sodium hydroxide. Again little difference is expected between Cr, Mo, and W. OMe (CO)5Cr Ph 45

CARBOCATIONS AS PROTONATED CARBENES

Proton loss from carbocations normally occurs from a b-carbon atom to form an alkene, and it is to this process that measurements of pKa for carbocations normally refer. However, in principle, loss of a proton can also occur from an a-carbon atom to yield a carbene. The isolation of the first stable cyclic dinitrogen-substituted carbenes sparked numerous studies of related structures but few experimental attempts to measure pKas.202 However, Alder203 and Streitwieser204 measured pKas for protonation of imidazolyl carbenes to give imidazolium ions in DMSO and these measurements have been extended by Chu and coworkers.205 Recently Amyes has reported aqueous pKas in the range 17–24 for carbenes derived from the imidazolium, oxazolium, and thiazolium ions shown below (46–48).206 For the imidazolium ions, rate constants for hydrogen isotope exchange catalyzed by hydroxide ion measured by proton NMR were combined with rate constants at the limit of solvent relaxation (1011 s1) for reaction of the carbenes with water. For the thiazolium and oxazolium ions, exchange rate constants were measured by Jencks and Washabaugh207 and estimated, respectively. H

H

H

H

N+

N+

N+

N+

H N H pK a

23.8

46

H

H

H

O

S

N

47

48

H

16.9

19.5

~24

49

Amyes et al. point out that the difference in pKas for C- and N-protonation of these carbenes provides the difference in stability of the carbene and parent heterocyle as shown by the cycle of Scheme 27 for the imidazolyl carbene 50. Interestingly, Yates and coworkers have calculated similar pKas for the imidazolium ion 46 and its saturated imidazolinium counterpart 49.208 This

STABILITIES AND REACTIVITIES OF CARBOCATIONS

H+ + 50

H N

H N

H N

16.7

69

:

H + H+

:

N H

N

N H 23.8

H N

51

7.1 H

N+ H

Scheme 27

implies that the aromatic stabilization of the imidazolium ion is similar to that of the carbene, although by other criteria the aromatic character of the ion is greater.209 The magnitude of the stabilization of the carbenes is revealed most directly by their hydrogenation energies as shown in Equation (19).210 This has an obvious analogy with the use of hydrogenation energies to measure the stabilities of aliphatic and aromatic p-bonds.211 The heat of hydrogenation of imidazolyl carbene 50 is calculated to be 17.7 kcal mol1 greater than that of the imidazolinyl carbene 51212 which indicates the magnitude of the aromatic stabilization of the former carbene206,209,210 (although whether the stabilization is solely aromatic has been a subject of discussion). R2 C : þ H2 ¼ R2 CH2

ð19Þ

A variation on Scheme 27 and Equation (19) has been utilized by Keeffe and the author to evaluate pKas of alkyl, aryl and alkoxy carbenes.26 For carbocations for which the pKa for loss of a proton from a b-carbon atom is known, combination of this pKa with the experimental or calculated energy difference between alkene and carbene conjugate bases leads to the pKa for protonation of the carbene, provided it can be assumed that the energy difference between alkene and carbene is insensitive to solvent. Where a pKa for loss of a b-hydrogen of the carbocation is not accessible, for example, for carbenes lacking a b-hydrogen, pKR can be used instead. Thus the cycle of Scheme 28 relates a pKa for protonation of the carbene to an experimentally measured

pK a

R2CH+

R2CHOH + H+

H+ + R2C pK H2O

Scheme 28

pK R

70

R. MORE O’FERRALL

value of pKR and calculated value of pKH2 O for conversion of the carbene to the corresponding alcohol. The value of pKH2 O for the hydration of the carbene provides a measure of carbene stability comparable to the heat of hydrogenation. As already noted both have analogies with the similar measures of stabilization of p-bonds. Keeffe and the author calculated energies of a number of carbenes for which pKR measurements for the corresponding cations are available.26 By assuming that the solvation energy of the carbene was the same as for its alkene isomer, or a related structure, it was possible to derive the desired value of pKH2 O , and thence a pKa for loss of an a-proton from the cation. These values of pKa are listed in Table 5 together with values of pKR for the carbocations derived by protonation of methyl-, phenyl-, and methoxy-substituted carbenes. Also shown are values of pKH2 O for hydration and DH for hydrogenation of the carbene. It is noteworthy that the stabilizing effects of methyl and phenyl substituents are similar for the carbocation and carbene and that pKas for protonation of these carbenes fall in the narrow range 29–33. The similarity of this stabilization is consistent with the comparable aromatic stabilization of the imidazolium ion and corresponding carbene noted by Amyes.206 A surprising conclusion from Table 2 is that methoxy substituents are more strongly stabilizing for a carbene than a carbocation, and yield smaller than normal pKas, comparable to those for the imidazolium and related ions (46–49). This is consistent with Kirmse’s finding that relative rates of protonation of carbenes fall in the order Ph2C > Ph(MeO)C > R(MeO) C > (MeO)2C. As Kirmse and Steenken pointed out, this does not correspond to the order of stability of the carbocation products.213 In principle, the effects of oxygen substituents are consistent with CF2 being a relatively stable carbene despite the corresponding carbocation being quite unstable. This is understandable if the dipolar structure produced by resonance interaction in the carbene (52) is compensated by an inductive ‘‘back donation’’ of electrons in the -bonds. In the cation (53), back donation accentuates rather than compensates charge separation arising from resonance

Table 5 A comparison of stabilities of singlet carbenes (pKH2 O ) and carbocations (pKR) in aqueous solution at 25C Carbocation

pKa

pKR

pKH2 O

DHhydrogen

Carbene

CHþ 3 CH3 CHþ 2 PhCHþ 2 þ Ph2CH MeOCHþ 2 ðMeOÞ2 CHþ

28 30 31 29 19 13a

–42 –29.6 –21 –12.5 –15.9 –5.7

–70 –59.3 –51.8 –41.0 –34.6 –18.6

–119.1 –107.9 –98.9 –84.3 –70.2 –40.8

CH2 CH3CH PhCH Ph2C MeOCH (MeO)2C

a

Value differs from that in Guthrie et al.132,26

STABILITIES AND REACTIVITIES OF CARBOCATIONS

71

interaction with an oxygen atom. Such a -bond interaction would also account for the fact that the resonance appears not to produce a strongly dipolar electron distribution for the carbene. + – MeO CH

MeO CH 52

+ MeO CH2

+ MeO CH2 53

HALIDE AND AZIDE ION EQUILIBRIA

So far we have considered only pKR and (occasionally) HIA as measures of carbocation stability. However, equilibrium constants for the reaction of carbocations with a variety of nucleophiles other than water have been measured. Ritchie especially has measured195 and reviewed15 values for reactions of relatively stable cations, such as trityl ions with electron-donating substituents or aryl tropylium ions, with alcohols, amines, and oxygen or sulfur anions. More recently, there has been interest in less stable cations which can be formed from solvolysis of precursors possessing good leaving groups such as chloride or azide ions. When written in the associative direction, equilibrium constants for these reactions measure the relative stabilities of the carbocations in terms of chloride or azide ion affinities. This is shown in Equation (20) in X which X is Cl or N 3 and KR is the equilibrium constant for the association reaction. RX ¼ Rþ þX  ;

KX R¼

½RX ½Rþ ½X  

ð20Þ

Chloride ions Values of KCl R for chloride ions have been determined by combining a rate constant for solvolysis ksolv (for reactions for which the ionization step is ratedetermining) with a rate constant for the reverse reaction corresponding to recombination of cation and nucleophile. The latter constant may be found (a) by generating the cation by photolysis and measuring directly rate constants for reactions with nucleophiles or (b) from common ion rate depression of the solvolysis reaction coupled with diffusion-controlled trapping by a competing nucleophile used as a clock. A further possibility arises where the carbocation intermediate of the solvolysis is so unstable as to react with water at the limiting rate of solvent relaxation with a rate constant of 1011 s1. It is then likely that the reaction with water occurs at the stage of a carbocation anion pair and that the back

72

R. MORE O’FERRALL

reaction of the ion pair to reform the reactant occurs more rapidly than the solvent relaxation, with a rate constant that may be as large as 1013 s1. Provided the back reaction is significantly faster than reaction with the solvent the measured rate constant for solvolysis should correspond to 1 1011/ K X Rs . Quite often values of K X R have been measured for cations for which pKR is not known. Thus combining Equation (20) with Equation (1) for KR (p. 21, with Hþ replacing H3Oþ) gives the ratio of equilibrium constants as Equation (21). Rewriting this ratio as pKR – pKCl R allows the difference in pK’s to be expressed in terms of free energies of formation in aqueous solution at 25 (DGf ) for the relevant alcohol and alkyl chloride as shown in Equation (22).38,43,214 KR ½Hþ ½Cl  ½ROH ¼ ½H2 O½RCl KRCl  pKR  pK RCl ¼

DGf ðHþ ; Cl  ÞþDGf ðROHÞ  DGf ðH2 OÞ  DGf ðRClÞ 1:364

ð21Þ 

ð22Þ

Experimentally, the simplest evaluation of K RCl is based on measurement of a rate constant in water for solvolysis of an alkyl halide for which reaction of the carbocation with water is at its solvent relaxation limit. An example is provided by the solvolysis of t-butyl chloride. A rate constant for solvolysis in water at 25 was measured by Fainberg and Winstein215 as 2.88102 s1. This yields pK RCl = –12.5. Substitution of the appropriate free energies of formation into Equation (22),38,214 together with an estimate of the free energy of transfer from gas to aqueous solution for t-butyl chloride,43 gives pKR – pKCl R = 4.7 and pKR = –17.2. This value is impressively close to pKR = –16.4 determined by Toteva and Richard.158 Indeed, the agreement is improved by recognizing that K RCl refers to the formation of an ion pair. Thus, taking Richard and Jencks’s value of 0.3 M1 for an ion pair association constant in water85 allows correction of pKR to 16.7. The level of agreement between values is probably fortuitous considering possible sources of discrepancy, such as a difference in solvent relaxation for an ion pair and a cation generated without a counter ion by protonation of an alkene by H3Oþ. A similar estimation for isopropyl chloride leads to a value of 17.3, which seems too low compared with 22.1 from the protonation of propene (p. 48). This is consistent with the expected intervention of an SN2 mechanism.216 The method should work better for adamantyl chlorides or norbornyl chloride for which SN2, and, presumably, preassociation processes are precluded. Speculative values of pK RCl and pKR for the relevant carbocations 54–56 are listed below based on a solvolysis rate constant in water for the

STABILITIES AND REACTIVITIES OF CARBOCATIONS

73

1-adamantyl chloride217 and ratios of values in aqueous acetone for the 1- and 2-adamantyl isomers and exo-norbornyl chloride.218 Although DGf (aq) for the alcohols and chlorides in these cases are not available, good estimates of DGf (ROH) – DGf (RCl) can be made by examining the structure dependence of Cl for OH substitutions for representative alcohols and alkyl chlorides for which free energies of formation have been measured.38,43,214

+

+ +

54

K RCl ¼ 1011=ksolv pKR – pK RCl pKR

56

55

1.31013 –4.6 –17.2

2.61016 –4.1 –20.0

2.11012 –4.1 –15.9

From the above results it can be seen that variations in pKR – pK RCl are rather small. The same is true of pK RCl for the ionization of trityl chloride and p-methoxybenzyl chloride, shown in Table 6 below, from which values of pKR – pK RCl are 4.7 and 4.75 log units, respectively.19,78,219 However, this level of uniformity is not expected of all nucleophiles and substrates. An extreme example of variation in DpKXR is provided by comparison of chloride and dimethyl sulfide as nucleophiles reacting, respectively, with the p-methoxybenzyl cation and the structurally very different electrophile, the di-trifluoromethyl quinone methide 57.220 In the case of the p-methoxybenzyl cation the addition of Me2S is more favorable than addition of chloride ion by a factor of 107-fold; for the quinone methide it is 100 times less favorable. Toteva and Richard attribute the difference to the large and unfavorable steric and polar interactions between the positively charged SMe2þ

Table 6 Comparison of pK RCl , pKR Ph3C+

, and pKR + CH2

MeO

O

C(CF3)2 57

pKR pK RCl 2þ pK RSMe

–6.6 –1.85

–13.4 –8.7 –15.7

– 4.4 6.5

74

R. MORE O’FERRALL

Me2Sþ group and the two CF3 groups in the adduct of the quinone methide. This more than balances the greater carbon affinity of the sulfur nucleophile expressed in the reaction with the p-methoxybenzyl cation. This behavior is exceptional. Nevertheless, the assumption that pKR and pK RCl measure equivalent trends in carbocation stability needs to be treated with caution. Richard and coworkers measured values of pK RCl to assess the influence of b-fluoro substituents on the stability of the a-methyl p-methoxybenzyl cation 58 (R = Me). As indicated in Scheme 29, replacement of an a-methyl by an a-trifluoromethyl group decreases the stability of the 221 carbocation by 7 powers of 10 in K Cl R. Cl However, measurements of pK R in this case lead to a lesser dependence of the equilibrium constant upon carbocation stability than pKR. Guthrie has calculated relative values of pK RCl and pKR and shown that an unfavorable geminal interaction between Cl and CF3 reduces the difference between þ Cl ArCHþ 2 and ArCHCF3 on the pK R scale by about 7 log units compared with pKR. This implies that replacing CH3 by CF3 in the p-methoxybenzyl cation decreases pKR by 14 units. Based on the value of pK RCl = –8.7 for the p-methoxybenzyl cation, pKR for the a-CF3 cation should be close to 23.5. However, note that the values of pK RCl in Scheme 29 were measured in 50–50 v:v TFE–water mixtures rather than water. In general, for anionic nucleophiles pK X R is expected to be highly sensitive to solvent. Results of Pham and McClelland222 indicate that pKR – pK RCl increases by 8 log units between water and 2% aqueous acetonitrile. The effect of a change from water to TFE–water will be much less than this, but a comparison for the p-methoxybenzyl cation shows that pK RCl decreases by 1 log unit.223 Thus neglecting any difference between pKR values in the two solvents the estimate of pKR for the a-trifluoromethyl-substituted p-methoxybenzyl cation is increased to 22.5. This value has been considered at some length because equilibrium measurements for the ions summarized as 58 are relevant to the effects of a-trifluoromethyl substituents on reactivity discussed later in the chapter (p. 80).

+ CH R

MeO 58

Cl pK R

Scheme 29

R

=

(TFE —H2O)

=

H

CH3

–9.5 –6.3

CH2F

CHF2

CF3

–9.4

–12.1

–13.4

STABILITIES AND REACTIVITIES OF CARBOCATIONS

75

Bromide and fluoride ions From the few measurements of bromide ion affinities it appears that pKBr R is similar to pK RCl . E.g. for the p-hydroxybenzyl cation, for which pKR = –9.6, pK RBr = –5.7.156 For the trityl halides on the other hand, chloride has a one log unit advantage, perhaps from a steric effect189,222,224 Probably, for the same reason, fluoride has a 107-fold greater affinity for the trityl cation19 than has the chloride ion (and is similar to that of acetate19), whereas for the p-methoxybenzyl cation the difference is only 4-fold.158 Azide ions 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 pK RAz and pKR using counterparts of Equations (17) and (18) with N3 replacing Cl. Nevertheless, a number of comparisons in water or TFE–H2O mixtures have been made87,106,226,230 and Ritchie and Virtanen have reported measurements in methanol.195 The measurements recorded below are for TFE–H2O and show that whereas pK RCl is typically 4 log units more positive than pKR, pK RAz 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. + + CHMe

MeO

pK RAz pKR

–13.3 –5.1

+ CMe2

MeO

–16.6 –8.6

–14.2 –5.9

A different picture emerges if we extend the comparison to cations with an a-methoxy substituent, as shown below.130 Now the difference between pKR and pKAz R is in the range 3–4.4 log units, which is much smaller than the eight units above. A small part of the difference may be due to a change in solvent from TFE–H2O to water, but the greater part must represent stabilization of the hemiacetal product of the KR equilibrium by the favorable interaction of geminal oxygen atoms.45,47,225 We have noted earlier that favorable interactions between OH and alkyl groups leads to differences between pKR and HIA. The oxygen–oxygen interactions are much larger.13,45

pKAz R pKR

PhCþ(OMe)Me

Me2CþOMe

PhCHþOMe

EtCHþOMe

–7.9 –4.6

–9.8 –5.4

–10.3 –7.3

–13.3 –10.3

76

R. MORE O’FERRALL

Azide equilibrium measurements have also been used to demonstrate that in addition to N3 having a high affinity for carbocations, N3 as an a-substituent is nearly as strongly stabilizing as a methoxy group. The preparation and solvolysis of gem-diazide derivatives of propionaldehyde and substituted benzaldehydes has allowed Richard and Amyes to study the solvolysis and, through studies of common ion rate depression, the reverse reaction of trapping carbocation intermediates by azide ion.226 Combining solvolysis and trapping rate constants then yields equilibrium constants pK RAz = –16.4 for the a-azido propyl cation compared with pK RAz = –13.2 for the a-ethoxy cation, corresponding to only 4 kcal mol1 greater stabilization by the ethoxy than azido substituent. Comparable differences are found for the substituted a-diazobenzylic and a-methoxy benzylic carbocations. Richard points out that the strong stabilizing effect of the a-azido group has implications for the mechanism of the Schmidt reaction. Were it not for their instability, it seems clear that gem diazides would find wider applications in synthesis. This short review of equilibria for reactions with halide and azide ions illustrates the utility of measures of carbocation stability other than pKR. Provided they refer to aqueous or largely aqueous media and the carbocations do not contain b-substituents which interact strongly with the nucleophile in the cation–nucleophile adduct, such as CF3, RO, or N3, values of pK X R can usually be related to pKR with an uncertainty of less than 1 log unit. On the other hand, they clearly demonstrate the specificity of geminal interactions between the bound nucleophile and electronegative a-substituents in determining relative values of pK X R and pKR.

3

Reactivity of carbocations

An important role of equilibrium measurements is in providing a framework for studies of reactivity and, in the present context, particularly reactivities of carbocations toward nucleophiles and bases. The reactivity of carbocations is too large a topic to deal with comprehensively here, but it may be helpful to attempt an overview of selected topics. Again, important areas, including reactions of vinyl cations120–124 and of b-hydroxy-carbocations formed from acid-catalyzed ring opening of epoxides,160,161 will not be covered, partly because of a lack of equilibrium measurements. Particularly extensive data exists for the reaction of carbocations with water and it is convenient to consider this first and to progress then to a wider range of nucleophiles. Thus we make the same division as for equilibria, but whereas the equilibrium data are dominated by reactions with water, a greater proportion of the kinetic data relates to nucleophiles other than water.

STABILITIES AND REACTIVITIES OF CARBOCATIONS

77

NUCLEOPHILIC REACTIONS WITH WATER

The starting point for most discussions of reactivity is a correlation of rate and equilibrium constants. One such correlation is shown in Fig. 1 of this chapter. It applies not to reactions of the carbocation with water as a nucleophile but to water acting as base, that is, the removal of a b-proton from the carbocation to form an alkene or aromatic product. We will consider this reaction below, but here note that for most of the carbocations in Fig. 1 values of kH2 O , the rate constants for reaction of the carbocation with water as a nucleophile are also available.25 Figure 3 shows a plot of values of log kH2 O against pKR for the carbocations of Fig. 1, namely, arenonium ions, cyclic and noncyclic secondary benzylic carbocations, and tertiary alkyl and benzylic cations.25 The plot is very similar to that reported by McClelland for other groups of carbocations including, benzhydryl, trityl, aryltropylium, and dialkoxyalkyl.3,4 One feature of Fig. 3 is that it incorporates the limiting rate constant of 1011 s1 corresponding to the rotational relaxation of water. Another is the grouping of different structural families on distinct correlation lines. Thus the tertiary alkyl cations show a steeper slope than the secondary cations. This is consistent with McClelland’s 12

log kH2O

10

8

6

4

–18

–16

–14

–12

–10

–8

–6

–4

–2

0

pKR

Fig. 3 Plot of log kH2 O against pKR. The main correlation line based on arenonium ions and secondary benzylic carbocations; the dashed line and filled circles are for tertiary cations.

78

R. MORE O’FERRALL

more extensive results for which the slopes range from 0.68 to 0.54. The slopes of the lines in Fig. 3 are 0.55 and 0.44. A further characteristic of Fig. 3, and of McClelland’s data, is that within structurally related reaction families the plots are quite linear, even where some of the rate constants closely approach their limiting values. This is contrary to a simplistic view that selectivity (represented by the slope of the plot) should depend on reactivity. The linearity of such plots has been analyzed in detail by Richard8 who attributes it to compensation between effects on reactivity of changes in thermodynamic driving force and changes in an intrinsic kinetic barrier to reaction. Much of this section will be devoted to explaining this proposal. Marcus analysis The idea of an intrinsic energy barrier for a reaction, or family of reactions, is embodied in Marcus’s treatment of the relationship between reaction rates and equilibria.227–229 For a family of reactions within which it remains constant an ‘‘intrinsic’’ barrier corresponds to the activation energy of a thermoneutral reaction (DG = 0). For other reactions ‘‘within the family’’ the experimental activation energy is sensitive to the thermodynamic driving force. This is represented schematically in Fig. 4, in which a change in equilibrium constant arises from a structural change (substituent effect) stabilizing the product of the reaction (by free energy DG). The effect of this change diminishes steadily along the reaction coordinate so that it has no effect on the reactant. A consequence is that the barrier to reaction is reduced and its energy maximum

Λ

x=0

x = 0.5

x = 1.0

ΔG °

Fig. 4 Marcus potential energy barrier G = 4x(1 – x)L perturbed by a substituent stabilizing the product by DG.

STABILITIES AND REACTIVITIES OF CARBOCATIONS

79

(transition state) is moved closer to the reactants. For simple analytical representations of the barrier, it is easy to show that the position of the maximum is reflected in the slope  of a plot of activation energy DG6¼ against energy of reaction DG, which is the same as the slope of a rate–equilibrium relationship in which logs of rate constants are plotted against logs of equilibrium constants. Equations (23) and (24) summarize the relationships between DG6¼ and DG and between the slope  = dDG6¼/dDG and DG for the linear perturbation of the inverted parabola shown in Fig. 4. The parabola is represented analytically by G = 4x(1 – x)L, where L is the usual mnemonic symbol for the intrinsic barrier (DG6¼ when DG = 0) and x represents the position along the reaction coordinate between 0 for reactants and 1.0 for products. For the perturbed parabola G = 4x(1 – x)L – xDG, and DG6¼ is G when dG/dx = 0. It should be noted that, in principle, G represents free energy (which is the quantity measured experimentally) but that it is treated as if it were potential energy. It is not difficult to see that if the intrinsic barrier L remains constant Equations (23) and (24) imply that a plot of DG6¼ against DG (or log k against log K) is curved, and that the curvature, which is given by d/dDG = 1/8L, depends (inversely) on the magnitude of the intrinsic barrier. In other words log k versus log K plots for reaction families with common intrinsic barriers should be strongly curved for fast reactions and show little curvature for slow reactions. On the other hand, it can also be seen that if an increase in intrinsic barrier compensates the decrease in barrier arising from the contribution of DG2/16L as the energy of reaction (and thermodynamic driving force) becomes more favorable, then the value of  in Equation (24) and hence the slope of the correlation could remain nearly constant, or at least not decrease as much as expected. ðDG  Þ2 16L

ð23Þ

dDG6¼ DG ¼ 0:5þ 8L dDG

ð24Þ

D G6¼ ¼Lþ 0:5DGþ

ð¼xÞ ¼

Intrinsic barriers for carbocation reactions The origin of intrinsic barriers to reactions of carbocations has been discussed by Richard.8 He suggests that reaction of water with a carbocation possessing a strongly localized positive charge such as CH3 þ will not only be favorable thermodynamically but possess a very low intrinsic barrier. By contrast, a high intrinsic barrier is associated characteristically with an SN2 reaction, in which

80

R. MORE O’FERRALL

H2O

CH3

H2O

CH2

+ Me O H + OMe

Scheme 30

there is strong coupling between making and breaking of bonds to an incoming nucleophile and departing leaving group. Richard points to an analogy between bond breaking to the leaving group in an SN2 reaction and the internal displacement of electrons accompanying attack of a nucleophile on a delocalized carbocation (Scheme 30). He suggests that high intrinsic barriers are associated with reactions of carbocations subject to extensive delocalization of carbocationic charge. A striking instance of such delocalization has been provided by Richard in a study of the reactions with water of p-methoxybenzyl carbocations 58 bearing a-substitutents CH3, CH2F, CHF2, and CF3.230–232 Equilibrium measurements described above (p. 54) showed that the stability of the carbocations along this series of substituents decreases by 7 log units as measured by the equilibrium constant for association of the carbocation with chloride ion pK RCl (and double that on a pKR scale). Remarkably, despite this large change in stability, rate constants for attack of water for the same series of carbocations are practically unchanged (Scheme 31). Indeed, addition of a second aCF3 group actually decreases the rate constant. Richard interprets these measurements as implying an increase in delocalization of charge and increase in double bond character at the benzylic carbon atom of the carbocation as the number of electron withdrawing fluorine substituents increases. This is consistent with a changing balance of contributions of the valence bond resonance forms 59 and 60.

+ CH R

MeO 58

R

=

10–7 × kH2O =

Scheme 31

CH3

CH 2F

4.8

10.0

CHF2

10.0

CF3

5.3

ArC+(CF3)2 0.45

STABILITIES AND REACTIVITIES OF CARBOCATIONS

+ CH CX3

MeO 59

+ MeO

CH CX3

81

(X = H or F)

60

The increase in double bond character is assumed to increase the intrinsic barrier for reaction at the a-carbon atom. As this increase is greatest for the thermodynamically least stable (CF3-substituted) carbocation, changes in thermodynamic driving force and intrinsic barrier oppose each other. The constancy of the values of kH2 O thus reflects a change in intrinsic barrier overriding the second and third terms in the Marcus expression of Equation (20). This is a more radical effect than the lesser variation preserving the linearity of the plots for the reaction families in Fig. 3 (p. 77), for which only the third term is overridden. An alternative interpretation of the dependence of intrinsic barrier on charge delocalization has been provided by Bernasconi.233 Bernasconi emphasizes that in the transition state for reaction or formation of a carbocation delocalization of charge is less effective than in the carbocation itself. How this arises has been well explained by Kresge.234 Supposing that a carbocation in Scheme 31 is formed from a benzyl halide precursor and that the carbon– halogen bond is half broken in the transition state, Kresge pointed out that the charge in the transition state must be delocalized less efficiently than in the product. This is because rehybridization of the breaking sp3 C–Cl bond to generate an empty p orbital at the charge center of the carbocation will have progressed only to the extent of 50%. It follows that if (say) a charge is 80% delocalized in the fully formed cation, it will be delocalized only to the extent of 40% in the transition state. Correspondingly, there will be a greater localization of charge at the formal carbocation center in the transition state than in the product (carbocation). This phenomenon is referred to by Bernasconi as an ‘‘imbalance’’ in charge distribution between the transition state and reactants and products. In so far as delocalization is associated with stablization of charge, it is reasonable that its impairment decreases the (intrinsic) energy barrier to reaction. This modified charge distribution in the transition state leads to a mismatch between substituent effects on the rate of reaction and on the equilibrium constant. With respect to the fluorine substituents in Scheme 31, these decrease both the stability of the carbocation and the stability of the transition state. However, while there must be less carbocation character in the transition state than in the carbocation itself the positive charge is located to a greater degree on the benzylic carbon atom and therefore will be more sensitive to stabilization by substituents. If substituent effects at the a-carbon atom in the carbocation and in the transition state are then of comparable magnitude, there will be no net effect on the rate of reaction, as is observed.

82

R. MORE O’FERRALL

On the other hand, because of the poor delocalization of charge, substitutents in the benzene ring will have a small effect on the stability of the transition state. Their dominant effect will be stabilization or destabilization of the delocalized charge of the carbocation itself, leading to large changes in reactivity. Thus Richard reports a relatively large value of þ = –4.8 for reaction of the ring-substituted a-trifluoromethyl benzylic carbocations (e.g. 59, X=F) with water.232 It should also be noted that while an increase in the number of fluorine substituents leaves the rate of reaction of the cation with water unaffected, the reverse reaction is profoundly affected. In the latter direction the full equilibrium effect of the substituent is felt on the rate. This is because now the effects of changes in thermodynamic driving force and intrinsic barrier complement each other. The corresponding relationship between substituent effects in forward, reverse, and equilibrium reactions and transition state ‘‘imbalance’’ in carbanion reactions, of which the nitroalkane anomaly235 is a prime example, has been discussed in detail by Bernasconi.233 Linearity of log kH2 O – pKR plots If we return now to the plot of log kH2 O against pKR of Fig. 3 (p. 77), we find that the structural changes leading to charge delocalization and changes in rate and equilibrium constants are more various than in Richard’s examples (Scheme 31). However, it remains true that delocalization of charge is the main factor affecting the stability of the carbocation and that this again is expected to lead to an imbalance between the charge distribution in the reactants and transition state. The delocalization stabilizes the carbocation and, less effectively, stabilizes the transition state, so that changes in thermodynamic driving force and intrinsic barrier again complement each other. It is perhaps less obvious in this case how the two factors combine to give a linear rather than a curved free energy relationship than when the effects are opposed. However, in the reverse reaction, the changes do oppose each other. Then, in so far as the slopes of the two log k–log K plots sum to unity, and the degrees of (positive and negative) curvature of the two plots must be the same, linearity of the plot in one direction implies linearity in the other. A way in which compensation between changes in intrinsic barrier and thermodynamic driving force can be expressed in terms of Marcus’s equation has been suggested by Bunting. Bunting and Stefanidis showed that if an intrinsic barrier is taken to vary linearly with DG, that is, L = Lo(1 þ mDG), then the curvature of a plot of log k against log K is reduced.236,237 The reduction in curvature is apparent from modifying the expression for the slope of the plot deriving from Marcus’s equation, that is  = 0.5 þ DG/8L in Equation (24), which on combining with Bunting and Stefanidis’s expression for L236 is transformed to Equation (25).

STABILITIES AND REACTIVITIES OF CARBOCATIONS



DG a ¼ 0:5 þ mLo þ 8Lo



1þmDG=2 ð1þmDG  Þ2

83

! ð25Þ

While Equation (25) appears complicated, a straightforward implication is that when DG = 0, a is no longer 0.5 but 0.5 þ mLo. Moreover the term which controls the variation of a in Equation (24), (DG/8L), which increases as DG increases, is moderated in Equation (25) by a factor which reduces as DG increases. It should be noted that m may be positive or negative and that the sign depends on whether L increases or decreases with increasing DG, which in turn depends on the direction of reaction. Values of mLo typically fall in the range () 0.1–0.5. Thus the lack of effect of b-fluorine substituents on the rate of the a-methyl p-methoxybenzyl cations with water (Scheme 31) implies that a = 0 and mLo = –0.5. The sensitivity of a to DG can readily be assessed for different values of m by substituting integral multiples of Lo for DG in Equation (25). In conclusion, it can also be pointed out that in principle a large value of L is itself sufficient to account for an extended linear free energy relationship. However, as Mayr has noted this is only true if the slope of the plot is 0.5.238 Moreover, if the Marcus expression offers a quantitative guide to the degree of curvature of a free energy relationship (and it is by no means clear that it does),228 it is evident that the intrinsic barriers to reactions of carbocations with familiar nucleophiles are insufficiently large to account for the lack of curvature. Mayr has also commented on the need for compensation for Marcus curvature in an extended free energy relationship. In the context of a discussion of the reactions of carbocations with alkenes, he suggests the alternative possibility that this compensation might arise from a log K-dependent change in the relative energies of frontier orbitals on the carbocation and the nucleophile.30

Estimates of intrinsic reaction barriers Notwithstanding the possibility of variation of an intrinsic barrier within a reaction series, for comparisons between different reactions it is often convenient to assume that an unmodified Marcus expression applies. This approximation is justified partly by the high intrinsic barriers and small amounts of curvature characteristic of most reactions at carbon, including reactions of carbocations. The Marcus relationship then provides a common framework for comparisons between reactions based on the measurement of even a single combination of rate and equilibrium constants. Thus, calculation

84

R. MORE O’FERRALL

of an intrinsic barrier using Equation (23) (p. 79) offers greater insight into comparisons between reactions than is provided by the individual measurements. It should be noted, however, that calculation of an intrinsic barrier requires modification of a measured rate constant by kBT/h, where kB is Boltzmann’s constant and derives from Eyring’s expression for DG6¼, that is L = RT ln{ko/(kBT/h)}, where ko is the rate constant for the hypothetical thermoneutral reaction (log K = 0).239 A common practice is to refer to ko as an intrinsic rate constant and to compare values of log ko between reactions in place of L. An example of the use of values of pKR and kH2 O to calculate and compare intrinsic barriers is provided by Richard’s measurements for carbocations 61–64. The objective of Richard’s study was to compare reactions in which oxygen substituents are directly attached to a charge center with similar reactions in which the charge and substituent are separated by an aromatic ring.157 In the case of formaldehyde 64 and the quinone methide 63, the ‘‘carbocation’’ corresponds to the resonance form in which charge separation places a negative charge on the oxygen atom and positive charge on carbon. In estimating these barriers Richard addresses a problem that so far has been avoided. When discussing the correlation of log kH2 O with pKR in Fig. 3, it was implied that the rate and equilibrium constants refer to the same reaction step. That is not strictly true, because attack of water on a carbocation yields initially a protonated alcohol which subsequently loses a proton in a rapid equilibrium step. As we are reminded in Equation (26) the equilibrium constant KR refers to the combination of these two steps. To calculate an intrinsic barrier for reaction of the carbocation with water therefore the equilibrium constant KR should be corrected for the lack of stoichiometric protonation of the alcohol. Fortunately, there have been enough measurements of pKas of protonated alcohols240 (e.g. pKa = –2.05 for CH3 OH2þ ) for the required corrections to be made readily. þ Rþ þ H2 OÐROHþ 2 ÐROH þ H

ð26Þ

With the appropriate equilibrium constants in hand Richard was able to calculate the intrinsic barriers for attack of a water molecule (L, kcal mol1) shown under the carbocation structures below.157 From comparing the values it can be seen that interposing a benzene ring between the oxygen substituent and carbocation center substantially increases the barrier, consistent with the expectation that the height of an intrinsic barrier depends on the extent of delocalization of charge. Interestingly, the increase between neutral oxygen and O as a substituent is rather small, despite the fact that charge delocalization must be substantially greater in the latter case.

STABILITIES AND REACTIVITIES OF CARBOCATIONS

+ MeO

L (kcal mol1)

+ EtO

CH2

CHEt

O

85

O CH2

CH2

61

62

63

64

11.5

6.6

13.2

8.7

Richard has also shown that intrinsic barriers for carbocation reactions depend not only on the extent of charge delocalization but to what atoms the charge is delocalized. In a case where values of pKR for calculation of L were not available, comparisons of rate constants for attack of water kH2 O with equilibrium constants for nucleophilic reaction with azide ion pKAz for 65–67 showed qualitatively that delocalization to an oxygen atom leads to a lower barrier than to an azido group which is in turn lower than to a methoxyphenyl substituent.226 + EtO Order of Λ:

CHEt

65

N

+ N N CHEt

<

+ MeO

CHMe

<

66

67

It is not intended to extend this discussion of reactions of carbocations with water to consideration of the alcoholic solvents trifluoroethanol (TFE) and hexafluoroisopropanol (HFIP), which have been extensively studied and reviewed by McClelland and Steenken.3 However, an important point of interest of these solvents is that their reactivities toward carbocations are greatly reduced compared with water (by up to a factor of 104 in TFE and 108 in HFIP) and that differences in rate constants can be observed between cations which would react indiscriminately at the solvent relaxation limit in water. The following comparisons of rate constants for carbocations with similar pKR values reacting with hexafluoroisopropanol241,242 reinforces the conclusion that structural variations in the cation lead to changes in intrinsic barrier and, for example, that phenyl substitution is probably associated with such an increase in going from benzyl to benzhydryl (although the benzyl cation itself is not shown).

Ph2CH+

pKR

–12.5

log k (HFIP)

0

Me + Me

CH2+

MeO

–12.4

–12.5

2.48

3.95

+

–15.7 4.3

H

+ CH-Me

–15.7 5.78

86

R. MORE O’FERRALL

No barrier calculations It would not be appropriate to conclude this discussion without recognizing Guthrie’s efforts to evaluate intrinsic barriers using ‘‘no barrier theory.’’243 Guthrie supposes that a chemical reaction involves a combination of energy changes that can be described by a quadratic dependence on a reaction coordinate (which for convenience is taken to vary from 0 to 1.0 between reactants and products). The term ‘‘no barrier’’ arises because the quadratic dependence implies the absence of a barrier for any single energy term. A barrier arises, nevertheless, from the combination of two or more such energy changes. Thus for a methoxybenzyl carbocation reacting with a nucleophile one energy change would correspond to bond formation, and two others to (a) rehybridization from sp2 to sp3 at the reacting carbon and (b) a change in geometry corresponding to loss of resonance of the benzene ring and methoxy group with the charge center of the carbocation as it is transformed to the nucleophilic adduct. What is required to evaluate a barrier is to estimate the energy of ‘‘reactants’’ and ‘‘products’’ of these independent transformations. The process is visualized most easily for two coordinates at right angles which define two sides of a square in which the reactants and products are at opposite corners. The energy is represented vertically and with the two geometric coordinates forms a ‘‘box.’’ The energy surface is generated by taking the two geometric coordinates, say bond breaking and rehybridization, and assigning one-dimensional quadratic energy profiles to the sides of the box, by considering both bond breaking followed by rehybridization and rehybridization followed by bond breaking. A further assumption is that for any section through the diagram for which only one of the geometric coordinates varies (i.e., parallel to one of the sides of the box) the energy is a quadratic function of that coordinate, with the minimum at the low-energy end. This suffices to generate an energy surface with a saddle point, as illustrated in Fig. 5. For the reaction of p-methoxybenzyl cations, Guthrie has estimated energies for the six species at the limits of the three geometric changes corresponding to bond breaking, rehybridization, and electron delocalization. Important anchors in the process are the fully reconstituted reactants and products, which means that the equilibrium constant for the reaction is an essential input into the calculation. He is successful in predicting barriers for the methoxybenzylic carbocations 57 within 2 kcal and has done the same with nucleophilic addition to the carbonyl and protonated carbonyl groups which are considered in an analogous manner to the carbocations proper. In principle, the success of the method depends on identifying the factors contributing to the intrinsic barrier and associating energies with their reactant and product-like geometric limits. Whether or not an energy change contributes significantly to the barrier can be assessed by including and then omitting it.

STABILITIES AND REACTIVITIES OF CARBOCATIONS

87

Free energy (kcal / mol–1)

20.

10.

0.

–10.

–20. 0.0

1.0

0.2

0.4

0.6

0.8

1.0 0.0

0.5 tor dis al c i tr me

n

tio

o

Ge

Bond change

Fig. 5

Construction of Guthrie’s ‘‘no barrier’’ plot.

Poor agreement between calculation and experiment implies that an important energetic contribution has been omitted. At the least, Guthrie’s analysis is a useful contribution to analyzing the origin of barriers to reactions. It is also remarkably successful quantitatively.

REACTIONS WITH WATER AS A BASE

Reactions of carbocations with water as a base removing a b-proton to form an alkene or aromatic product have been less studied than nucleophilic reactions with water. Nevertheless, the correlations included in Fig. 1 (p. 43) represent a considerable range of measurements and these can be further extended to include loss of a proton a to a carbonyl group.116 Indeed, if one places these reactions in the wider context of proton transfers, it can be claimed that they constitute the largest of all groups of reactions for which correlations of rate and equilibrium constants have been studied.116,244,245

88

R. MORE O’FERRALL

A notable difference between reactions of carbocations with water as a nucleophile and a base is the significantly higher intrinsic barrier for the latter. This difference has been demonstrated most explicitly by Richard, Williams, and Amyes22,246 for reaction of the a-methoxyphenethyl cation 68 with methanol (rather than water) acting as the base and nucleophile. The two reactions and the intrinsic barriers calculated from their rate and equilibrium constants are shown in Scheme 32. Values of L = 6.8 and 13.8 kcal mol1 are found for the substitution and elimination, respectively. The present author noted that the ratio of alcohol to alkene products formed from reactions of carbocations with water are correlated with the equilibrium constant for hydration of the double bond of the alkene product, KH2 O . This can be seen to arise if there is a rate-equilibrium relationship between log kH2 O and pKR and also between the deprotonation rate constant log kp and the pKa of the carbocation. Combing the two relationships, the log of the product ratio of alkene to alcohol log(kp/kH2 O ) might be expected to correlate with pKR – pKa, which, as we have seen, is equal to pKH2 O . Strictly speaking, the relationship holds only if the slopes of the constituent rateequilibrium plots are the same. However, comparison of Figs. 1 and 3 indicate that this is approximately true, and Fig. 6 shows that there is indeed a good linear dependence of log(kp/ kH2 O ) on pKH2 O .25 As noted above, this correlation and that of Fig. 1 are deficient in not recognizing that the product of the nucleophilic reaction is not the alcohol, as implied by the correlation with pKR, but the protonated alcohol. However, it is reasonable to suppose that variation of the pKas for O-protonation of the alcohols, which are required to correct values of KR, are small compared with variations in pKR itself (and thus pKH2 O ) and would not significantly affect the quality of the correlation. It is also true that the correlation is dominated by the large and variable values of pKH2 O for aromatic products of deprotonation. These tend to obscure variations in product ratios for tertiary alkyl and secondary benzylic cations which are the focus of a previous discussion of this partitioning by Richard.5

Ph

MeO Λ = 6.8 kcal mol + MeOH + MeO 68

C

–1

MeO

+ H+

CH3

Ph C CH3 MeO

Λ = 13.8 kcal mol–1

Scheme 32

CH2 + H+ + MeOH Ph

STABILITIES AND REACTIVITIES OF CARBOCATIONS

89

8 6

2

log kp /kH O

4 2 0 –2 –4 –6 –5

0

5

10 pKH2O

15

20

25

Fig. 6 A plot of log (kp/kH2 O ) for reactions of secondary (O) and tertiary (&) carbocations with water as a nucleophile and base against pKH2 O for hydration of the p-bond of the deprotonation product; (points close to or above the dashed line correspond to reactions for which deprotonation leads to an aromatic product).

A clear manifestation of the difference in intrinsic barriers for the nucleophilic and deprotonation reactions is apparent in Fig. 6.25 The horizontal dashed line in the figure corresponds to equal rate constants for formation of substitution and deprotonation products. It can be seen that this corresponds to pKH2 O  7, that is, when dehydration of the alcohol to the alkene is favored by 10 kcal mol1. It implies that a greater thermodynamic driving force by 10 kcal mol1 is required for the alkeneforming pathway to overcome the advantage conferred on the substitution reaction by a more favorable intrinsic barrier. Similarly, when KH2 O = 1, deprotonation occurs 104 times more slowly than the rate of formation of the alcohol product. In so far as in aqueous solution dehydration of alcohols to form alkenes is normally disfavored thermodynamically, it is clear why the rate-determining step in the acid-catalyzed dehydration (or hydration of the alkenes) is normally proton transfer. Only when the double bond of the product is strongly stabilized, for example by forming part of an aromatic ring, does deprotonation become faster than carbocation formation. The correlation of Fig. 6 is dominated by carbocations which undergo deprotonation to form aromatic products. The positive deviations of tertiary alkyl cations have already been mentioned (p. 43). As discussed by Richard7 these

90

R. MORE O’FERRALL

may be due partly to the close approach of the rate constant for the nucleophilic reaction with water to its limiting value. This would mean that it no longer increased with increasing instability of the cation, while the rate constant for the elimination reaction, with its higher intrinsic barrier, would continue to increase. If both reactions had reached their limit, the point in Fig. 6 would lie on or close to the dashed line corresponding to log(kp/kH2 O ) = 0. There are other instances, however, where unusually large extents of elimination are encountered which cannot be explained in this way. An example is provided by a study of the nucleophilic and elimination reactions of the dipentamethyl benzhydryl cation 69.247 Comparisons of pKR values (from extrapolations based on the HR acidity function) with those of the unmethylated and partially methylated benzhydryl cations shown below, indicate that methylation cumulatively stabilizes the cation relative to the alcohol (possibly in part because the latter is destabilized by steric congestion). pK a = – 6.0 + H+ + 70

69

(C6H5)2CH+

(2-CH3C6H5)2CH+

(4-CH3C6H5)2CH+

Mes2CH+

–13.3

–12.7

–10.4

–6.8

69 –4.8

Somewhat surprisingly the di-pentamethylbenzhydryl cation undergoes deprotonation at an o-methyl group to give the alkene possessing the xylylene structure 70. From measurement of the alcohol–alkene equilibrium constant ( pKH2 O = 1.2), the pKa of the carbocation is deduced as pKR – pKH2 O = –5.6. The relative stability of the xylylene again must reflect steric congestion in the alcohol. However, the ratio of rate constants for deprotonation to nucleophilic trapping is also 100 times higher than expected from the correlation of Fig. 6, and it is not hard to attribute this to an even greater steric congestion in the transition state for nucleophilic attack of a water molecule than in the product. A similar reason for a higher than expected alkene-to-alcohol product ratio from reaction of the o-dimethyl cumyl carbocation248 has been proposed by Richard.5,249 REACTIONS OF NUCLEOPHILES OTHER THAN WATER

We will deal more briefly with reactions of carbocations with nucleophiles other than water, and then consider correlations in which the nucleophile rather than (as hitherto) the carbocation is varied. Fig. 7 shows a plot of

STABILITIES AND REACTIVITIES OF CARBOCATIONS

91

12

10

Ν3−

log k

8

6

4 H2O 2

0 –12

–10

–8

–6

–4

–2

0

2

pKR

Fig. 7 Plots of log k against pKR for nucleophilic reactions of water, azide ions and chloride ions (D) with benzhydryl and trityl cations.

logs of rate constants for reactions of azide ions with benzhydryl and trityl cations against pKR.77,250 Also shown for comparison are logs of rate constants (s1) for reaction of water with same cations. The plot shows the much greater reactivity of azide ions and the tendency of their reactions to be diffusion controlled over a considerable range of pKR for which, for the water reaction, the chemical step remains rate-determining. As has been discussed elsewhere, Fig. 7 demonstrates the basis for using reactions with azide ion as a clock for determining values of log kH2 O in the range pKR = –5 to 15. However, the discussion above cautions against too narrow an interpretation of this figure. The correlations apply to benzhydryl cations and trityl cations and, as we have seen, other families of cations can lead to less ‘‘ideal’’ dependences of kH2 O and, presumably, kAz on pKR. Choride ion is considerably less reactive than the azide ion. Thus, although values of kCl/ kH2 O have been quite widely available from mass law effects of chloride ion on the solvolysis of aralkyl halides, normally the reaction of the chloride ion cannot be assumed to be diffusion controlled and the value of kH2 O cannot be inferred, except for relatively unstable carbocations (p. 72). Mayr and coworkers251 have measured rate constants for reaction of chloride ion with benzhydryl cations in 80% aqueous acetonitrile and their values of log k are plotted together with a value for the trityl cation19 in Fig. 7. There is some scatter in the points, possibly because of some steric hindrance to reaction of the trityl cations. However, it can be seen that chloride ion is more

92

R. MORE O’FERRALL

reactive than the aqueous solvent. As Mayr points out, this is consistent with the ionization step being rate determining in solvolysis reactions of aralkyl halides in largely aqueous solvents. However, as the proportion of acetonitrile in the solvent increases, or in a less basic solvent such as TFE, carbocation formation becomes reversible (although for more reactive cations the reversibility may be compromised by encroachment of the diffusion limit to reaction of the chloride ion).251 Compared with chloride, the bromide ion is more reactive by rather less than a factor of 10 with respect to the benzhydryl cations and by less than a factor of 2 for the trityl cation. Fluoride and acetate ions are a little less reactive than chloride ion toward the trityl cation (less than a factor of 10) but their equilibrium affinities for the ion are more than 106-fold greater.19,219 Correlations of nucleophilic reactivity We conclude this chapter with a review of attempts to correlate reactivities of nucleophiles toward carbocations. An obvious difficulty is that for any wide variation in the nature of the nucleophile the identity of the reacting atom changes. This brings us to the limit of reasonable attempts to establish structure–reactivity relationships which, for their success, normally depend on structural changes being made away from the reaction site. It is perhaps not surprising therefore that for reactions of a carbocation with a series of nucleophiles, unless the nucleophiles form a structurally homogeneous family sharing a common reacting atom, simple rate–equilibrium relationships fail. The extent of this failure is evident from comparisons of experimental measurements of rate and equilibrium constants. One comparison in the literature is provided by Ritchie and coworkers’ study of the relatively stable cation, pyronin (the 3,6-bis(dimethylamino)xanthylium cation 71) with a series of nucleophiles.252 Another example is McClelland’s measurements of rate and equilibrium constants for the reactions of halide and acetate ions with the trityl cation.19 As already mentioned fluoride and acetate are less reactive than bromide and chloride despite their equilibrium affinities being much greater. This is reflected indeed in the much lower rates of solvolysis of the fluoride and acetate than bromide or chloride as leaving groups Me2N

+ O

NMe2

71

. Rate and equilibrium constants for reactions of the trityl cation are summarized in the first two columns of Table 7 and clearly indicate that no simple rate–equilibrium relationship exists. The mild decrease in rate constants kX for

STABILITIES AND REACTIVITIES OF CARBOCATIONS

93

Table 7 Rate and equilibrium constants and intrinsic barriers for the reaction of the trityl cation with halide and acetate anions in aqueous acetonitrile (2:1) at 20Ca

Br Cl F AcO a

kX

pKRX

L

5.0106 2.2106 8.6105 4.0105

–0.8 –1.8 –8.0 –7.8

8.9 10.0 14.6

Data from McClelland et al.19

nucleophilic attack along the series Br > Cl > F > AcO contrasts with the large change in equilibrium constants pK X R between the first and second pairs of nucleophiles. Comparable results for the reactions of acetate and halide ions with the quinone methide 57 have been reported by Richard and coworkers.219

O

C(CF3)2 57

A similar picture holds for other nucleophiles. As a consequence, there might seem little hope for a nucleophile-based reactivity relationship. Indeed this has been implicitly recognized in the popularity of Pearson’s concept of hard and soft acids and bases, which provides a qualitative rationalization of, for example, the similar orders of reactivities of halide ions as both nucleophiles and leaving groups in (SN2) substitution reactions, without attempting a quantitative analysis. Surprisingly, however, despite the failure of rate–equilibrium relationships, correlations between reactivities of nucleophiles, that is, comparisons of rates of reactions for one carbocation with those of another, are strikingly successful. In other words, correlations exist between rate constants and rate constants where correlations between rate and equilibrium constants fail. Mayr has amusingly described the ebb and flow of optimism and pessimism in a history of attempts to establish correlations based on varying the nature of a nucleophile.253 Initially, it was natural to seek a correlation for SN2 or other nucleophilic reactions of stable organic substrates, because there were few opportunities for measuring rate constants for reactions between nucleophiles and carbocations directly. Thus in 1953 Swain and Scott254 proposed the relationship of Equation (27) in which the parameters s and n refer to substrate (electrophile) and nucleophile, respectively. Methyl bromide was chosen initially as the reference substrate and, perhaps not altogether wisely, water was taken as the reference nucleophile. Subsequently, Pearson and Songstad measured nucleophilicity parameters nCH3 I for a wider range of nucleophiles using methyl iodide in methanol as electrophile and solvent.255

94

R. MORE O’FERRALL

 log

k kH2 O

 ¼ sn

ð27Þ

Swain and Scott found satisfactory correlations with Equation (27) which provided s values for a number of reactants. However, as indicated in Scheme 33, for the limited number of substrates conveniently studied,158,186 variations in s did not show a clearly discernible pattern (and no obvious correlation with reactivity). Moreover, Pearson and Songstad demonstrated that the correlations break down if extended to extremes of ‘‘soft’’ and ‘‘hard’’ electrophilic centers such as platinum, in the substitution of trans-[Pt(pyridine)2Cl2], or hydrogen in proton transfer reactions.255 Despite this, Swain and Scott’s equation has stood the test of time and it is noteworthy that a serious breakdown in the correlations occurs only when the reacting atoms of both nucleophile and electrophile are varied. In this chapter we will restrict ourselves to carbon as an electrophilic center, and particularly, although not exclusively, to carbocations. Although before the mid-1980s reactions of other than highly stabilized carbocations were not accessible to kinetic measurements, it was possible to measure ratios of products from partitioning between nucleophiles of more reactive carbocations generated in solvolysis reactions. Particularly studied was the competition between water and azide ions for carbocation intermediates produced in reactions of alkyl halides in aqueous organic solvents.28 These measurements provided values of kAz/kH2 O , determined from the ratio of azido to alcohol products. The ratios varied from 3 to 600 and showed a striking dependence on the rate constants for the solvolysis reactions, which varied over 13 powers of 10.256 In principle, these measurements represent an application of the Swain– Scott relationship to two nucleophiles only. This is apparent from Equation (28), in which nAz corresponds to n for the azide ion and the electrophilic parameter s is seen to measure the selectivity of the carbocation between azide

OTs

ArCH2 CH Me

0.27

0.34

0.43

O

O

0.77

0.87

EtOTs 0.66

OH

+

PhCH2Cl

Scheme 33

I

ArCH2 CH Me

s=

s=

Br

ArCH2 CH Me

S

0.95

Me-Br

PhSO2Cl

1.0

1.25

PhCOCl 1.43

STABILITIES AND REACTIVITIES OF CARBOCATIONS

95

and water nucleophiles. Thus the substrates for which s was measured in Scheme 33 are replaced by carbocations, including, for example, Ph2CHþ, t-Buþ and 1- and 2-adamantylþ.256  log

 kAz ¼snAz kH2 O

ð28Þ

Apparently, these results implied an inverse relationship between reactivity and selectivity, with the reactivity of the carbocation measured by the inverse of the rate constant for solvolysis. This indeed was not unexpected in the context of a general perception that highly reactive reagents, especially reactive intermediates such as carbocations, carbanions, or carbenes are unselective in their reactions.257–259 Such a relationship is consistent with a natural inference from the Hammond postulate258 and Bell–Evans–Polanyi relationship,260 and is illustrated experimentally by the dependence of the Bronsted exponent for base catalysis of the enolization of ketones upon the reactivity of the ketone,261,262 and other examples21,263 including Richard’s careful study of the hydration of a-methoxystyrenes.229 However, as has again been well summarized by Mayr,253 a striking antithesis was then established between the variation in these values of kAz/ kH2 O and measurements by Ritchie of rate constants for reactions of a wide range of nucleophiles with relatively stable carbocations such as crystal violet 72, pyronin 71, the p-dimethylaminophenyltropylium ion or the p-nitrophenyldiazonium ion. For such stable cations, direct kinetic measurements were possible using conventional spectrophotometric monitoring or, for faster reactions, a preliminary mixing of reagents by stopped flow. NMe2

+

Me2N

72 NMe2

Far from confirming a dependence of nucleophilic selectivity on the reactivity of the carbocations, Ritchie observed that selectivities were unchanged over a 106-fold change in reactivity.15 He enshrined this result in an equation (29) analogous to that of Swain and Scott, but with the nucleophilic parameter n modified to Nþ to indicate its reference (initially) to reactions of cations, and with the selectivity parameter s taken as 1.0, that is, with no dependence of the selectivity of the cation on its reactivity (as measured by the rate constant for the reference nucleophile, kH2 O for water).

96

R. MORE O’FERRALL

 log

k kH2 O

 ¼Nþ

ð29Þ

This lack of variation of selectivity with reactivity was confirmed in an independent study by Kane-Maguire and Sweigart who found that relative reactivities of amine and phosphine nucleophiles toward a range of organometallic cations were also independent of the nature of the electrophile.184,264 The dilemma presented by these conflicting results was resolved by TaShma and Rappoport.265 They pointed out that the apparent dependence of kAz/ kH2 O upon the reactivity of the carbocation arose because even the most stable cation reacting with azide ion did so at the limit of diffusion control. Thus while kH2 O remained dependent on the stability of the cation in the manner illustrated in Fig. 7 the rate constant for the azide ion remained unchanged. Thus the most stable cation formed in the solvolysis reactions was the trityl ion, for which direct measurements of kH2 O = 1.5105 s1 and kAz = 4.1109 now show that even for this ion the reaction with azide ion is diffusion controlled.22 The advent of laser flash photolytic studies, and the correct use of product ratios to assess reactivities of nucleophiles competing with azide ions reacting at the diffusion limit, led to direct measurements of rates of nucleophilic reactions for a much wider range of carbocation stabilities. Much of this work, which was carried out by the research groups of McClelland and Steenken and Richard and Amyes, has already been cited. We will return to these studies in the context of a further discussion of reactivity and selectivity and the failure of rate constants of reactions of nucleophile to correlate with equilibrium constants at the end of this chapter. First, however, we turn to a further investigation of carbocation reactions undertaken by Mayr and his research group in Munich. In a comprehensive series of studies Mayr has extended Ritchie’s observations and placed them in a wider context, including applications to organic synthesis. As will be seen, together with the studies of McClelland and Richard this work leads at least in outline to a coherent view of reactivity, selectivtiy and equilibrium in carbocation reactions. Nucleophile–electrophile reactions and synthesis Rappoport and TaShma’s work removed a major difficulty for Ritchie’s analysis and helped pave the way for Mayr to exploit fully the wide applicability and simplicity of Equation (29) for predicting rates of reactions of electrophiles with nucleophiles. Mayr pointed out that Equation (29) could be rewritten as Equation (30), in which log ko corresponds to the rate constant for reaction of the electrophile under study with a reference nucleophile266 (chosen as water by Ritchie) which, in so far as it is characteristic of the

STABILITIES AND REACTIVITIES OF CARBOCATIONS

97

electrophile, is sensibly denoted E. We can then rewrite Equation (30) as Equation (31), in which the measured rate constant for reaction is expressed as the sum of one parameter for the nucleophile and one for the electrophile. Log k¼log ko þNþ

ð30Þ

Log k¼EþN

ð31Þ

In Equation (31), Ritchie’s parameter Nþ is replaced by N because, as will become clear, there is a difference in the definition of these parameters, including the choice of reference nucleophile. However, the striking simplicity of the relationship in representing reactions in which the nucleophile and electrophile are equal partners is apparent. It implies that reactivity of electrophile–nucleophile combination reactions might be predicted from two parameters. The challenge of presenting this as a practical aid to organic synthesis was taken up by Mayr’s research group.267 The starting point for Mayr’s work in the mid-1980s was very different from Ritchie’s studies of mainly oxygen and nitrogen nucleophiles. Mayr’s initial aim was to measure rate constants for the synthetically important alkylation reactions of alkenes.27,268,269 As representative alkylating agents, he chose p-substituted benzhydryl cations to provide a homogeneous family of electrophiles. These ions could be generated by the addition of the appropriate benzhydryl chloride to dry methylene chloride containing BCl3. The reactions with alkenes were carried out at 70C and monitored spectrophotometrically or conductimetrically under conditions for which the rate-determining step of the reaction was attack of the electrophile on the alkene.270 The temperature dependences of the reactions were studied to extrapolate rate constants at 20C, and rate constants for a fraction of the reactions were measured directly at this temperature, with the carbocations generated from the benzhydryl chlorides by flash photolysis.27,83 Mayr initially defined a set of electrophilic parameters for the benzhydryl cations using a reference nucleophile, which was chosen as 2-methyl-1pentene.268,269 Values of E were then defined as log k/ko, where ko refers to a reference electrophile (E = 0), which was taken as the 4,40 dimethoxybenzhydryl cation. Plots of log k against E for other alkenes are thus analogous to the plots of log k against pKR in Fig. 7 except that the correlation is referenced to kinetic rather than equilibrium measurements. However, they differ from plots based on the Swain–Scott or Ritchie relationships in which log k is normally plotted against a nucleophilic parameter, that is, n or Nþ, rather than E. In practice, rate constants for only a limited range of benzhydryl cations could be measured for 2-methyl-1-pentene itself. However, it became apparent that if reaction of the cation occurred at a methylene group (=CH2) plots of

98

R. MORE O’FERRALL

log k versus E were almost parallel for alkenes of widely differing reactivity. This allowed E values for benzhydryl cations varying in reactivity from p,p0 -dichloro to p,p0 -bis(dimethylamino) to be assigned. When the structure of the p-nucleophile was varied more widely to include nonterminal alkenes, alkenes with O, N, or other b-substituents, alkynes, and aromatic molecules, a greater variation in the slopes of the plots was found. Fig. 8 shows plots of log k versus E for a representative group of alkene structures as well as for arenes.271 To accommodate the more reactive nucleophiles, the electrophilicity range of the benzhydryl carbocations was extended by inclusion of p-amino substituents for which the electron-donating ability of the amino group was amplified by incorporation in a tricyclic ring structure.272 Variations in slope are not large but are sufficient to merit addition of a slope parameter for each nucleophile. The logic of choosing a structurally homogeneous set of electrophiles is now evident. These can be reacted with

O N

N

OSiMe3

8

OSiMe3

O

OSiMe3 OSiMe3

OSiMe3

OPh

with s = 1

6

SiMe2Cl 4

log k

2

N = –E

0

–2

–4 –10

–8 + CH

N

2

–6

–4

+ CH

+ CH

NMe2 2

NPh2 2

–2 + CH

Ph

N

CF3 2

0 + CH

OMe 2

2

4 + CH

6 + CH

Me 2

Cl

2

with E = 0

Electrophilicity(E )

Fig. 8

Plots of log k versus E for the reaction p-nucleophiles with benzhydryl cations.

STABILITIES AND REACTIVITIES OF CARBOCATIONS

99

nucleophiles of very different structure and differences in slope can be assigned to steric or other effects associated exclusively with the nucleophile. One way to modify Equation (31) to allow for the different slopes is to multiply the electrophilicity parameter E by a variable s as shown in Equation (32). Note again that s here differs from s in the Swain–Scott equation which refers to the slope of a plot of log k versus the nucleophilicity parameter n (or N) rather than electrophilicity parameter (E). However, the equation that Mayr adopts is not Equation (32) but Equation (33),269 in which s multiplies not only E but both E and N. This is formally equivalent to Equation (32), because s is still determined by the slope of the plot of log k against N, that is, by the dependence of log k on the nucleophile only. However, multiplication of N by s leads to some subtle changes which suit the original purpose of the study, namely, to develop synthetically useful predictions of rates of reactions of electrophiles with nucleophiles. It is an unusual but interesting and practical manipulation of an otherwise conventional free energy relationship. Log k ¼ sE þ N

ð32Þ

Log k ¼ sðN þ EÞ

ð33Þ

One virtue of Equation (33) is that it avoids long extrapolations of values of N measured for electrophiles with E values far removed from zero. This can be seen from Fig. 8 which includes plots of log k versus E for highly unreactive p-nucleophiles such as toluene and highly reactive ones such as vinyl acetals and enamines. According to Equation (33), the value of N corresponds to the intersection of the plot of log k versus E not with the vertical line (ordinate) for E = 0 but, as shown in the figure, with the horizontal line corresponding to E = –N. This intersection has the physical significance that the rate constant for combination of the relevant nucleophile and electrophile (i.e. at the E value of the intersection) is 1.0 M1 s1. Mayr points out that an advantage of this definition is that it prevents crossover of correlation lines which in some instances occur if the extrapolations are extended beyond the reactivity ranges likely to lead to reaction. Thus the relative magnitudes of N properly reflect relative reactivities of nucleophiles under realistic reaction conditions. Although not well illustrated in Fig. 8 the potential for crossover is implicit in the lack of parallelism of the correlation lines. Of course, if all lines were parallel with unit slope the relative magnitudes of N would be the same whether defined by Equation (32) or (33). In the most recent correlation analysis based on Equation (33) a ‘‘basis set’’ of 23 benzhydryl cations and 39 p-nucleophiles, for which extensive measurements are available, were selected to provide a set of reference parameters which would not require further modification as data was acquired for new

100

R. MORE O’FERRALL

nucleophiles, and indeed new electrophiles.272 As before the p,p0 dimethoxybenzhydryl cation was assigned the value E = 0 and the slope parameter s for 2-methyl-1-pentene was defined as 1.0. One might query the robustness of anchoring the correlation to a single s value, but the effectiveness of this is endorsed by the good overlap of plots for nucleophiles ranging from the most to the least reactive, as is evident in Fig. 8. Moreover, a comparable analysis of slopes and intercepts of plots of pKa against Xo for a ‘‘basis set’’ of weak bases undergoing protonation in strongly acidic media shows little difference from an alternative analysis in which a common slope parameter is assigned to structurally similar bases covering a range of base strengths.52,53,55 The origin of the variation in s values for the different alkenes encompassed by Equation (33) is not entirely clear but steric effects have an obvious influence. Thus, as shown in Scheme 34, alkylation of tetramethyl ethylene gives s greater than 1.0 (1.44) consistent with increased selectivity as a result of hindrance to attack of an electrophile by the methyl substituents.27 Aromatic p-systems also have high s values, especially where reaction occurs at an o-position.271 However, b-oxygen and allylic silicon, germanium, or tin substituents decrease s,269,273 while for phenylacetylene s also appears to be low.269 A tendency for less reactive nucleophiles to have larger s values may imply a mild dependence of selectivity on reactivity, but the variations in s are small and changes in reactivity large. Just as N for a nucleophile can be determined from a plot of log k against E for a series of electrophiles, in principle, the value of E for an electrophile can be determined from the intercept (at E þ N = 0) of a plot of log (k/s) versus N for a series of nucleophiles (or indeed, if need be, from the measurement for a single nucleophile). In this way E values have been determined for many electrophiles other than benzhydryl cations, including metal-coordinated cations,186 BF3-coordinated aldehydes,274 tropylium ions, and many benzylicand heteroatom-substituted carbocations. In the low reactivity range

0.98

0.94 SiMe3

0.94

OSiMe3

1.32

OPh

1.17 1.62 OSiMe3 OMe

SiMe3 1.40

Scheme 34

0.70 0.98

1.17

Ph

STABILITIES AND REACTIVITIES OF CARBOCATIONS

101

electrophiles extend to neutral molecules. These may also be included within the benzhydryl calibration framework by choosing quinone methides such as 73 in which nucleophilic attack is directed to an electrophilic carbon–carbon double bond by bulky substituents flanking the carbonyl group.275 Such quinone methides have been important in establishing N values for reactive nucleophiles such as nitroalkyl276 and other stabilized carbanions275,277 including phosphorus ylids.278 With a further extension of nucleophiles to include organometallic reagents, the range of processes embraced within the nucleophile–electrophile combinations includes Friedel–Crafts alkylations, Wittig and Mannich reactions, Nicholas propargylation, and Mukaiyama aldol cross couplings among other synthetically useful reactions.27

Me2N

O 73

It should be noted that although the core E and N values are defined for CH2Cl2 as solvent, rates of reactions between positively charged and nonhydrogen-bonded neutral reagents are normally only weakly sensitive to solvent27,270,279 so the values should provide a reasonable approximation over a range of solvents. On the other hand, for reactions of carbocations with carbanions, especially where negative charge is delocalized to oxygen, a much greater solvent sensitivity is observed and different N parameters have been determined in water and DMSO as solvents. It should be noted that the effect of solvent is expressed in the N values and that to a good approximation the E values for nonpolar solvents can be retained. The simplest demonstration of the synthetic utility of the E and N parameters follows from the approximation that all the slope parameters s in Equation (33) are 1.0 and that log k = E þ N. It is then possible to plot E parameters against N parameters to give the reactivity box shown in Fig. 9.280 A diagonal of this box corresponds to E þ N = 0 and k = 1 M1 s1. Lines parallel to this diagonal correspond to constant values of log k indicated by the appropriate (constant) value of E þ N. If the E and N values of two reagents are known or can be guessed then a reasonable assessment of the time for reaction can be made. Reactions with E þ N in the upper left of the box (i.e., with large negative values) will be relatively slow, and this area, for which k is predicted to be <106 M1 s1, is partitioned off. Reactions represented in the lower section of the box will be fast, and the right hand diagonal indicates the limit of reaction under diffusion control, with k = 1010 M1 s1. As is also indicated, reactions in the upper right-hand corner represent attack of a carbanion at an (electrophilic) double bond and, at the lower left, attack

102

R. MORE O’FERRALL Cl

CN N

O

N

OSiMe3

CN

O O

NO2 COOEt COOEt

MeO

–20

k < 10 –6 M–1s–1

COOEt

o

No reaction at 20 C

COOEt

O2N Ph + Pd(PPh ) 3 2

E –10

E+N=0

N2+

Me + N CH2 Me

–1 –1

k = 1.0 M s

+

0

+

+

k > 1010 M–1s–1

Co2(CO)6 OMe +

No reaction at 20oC Me3C +

10 –10

0

10

20

N Fig. 9 Semiquantitative model of reactivity in electrophile–nucleophile reactions.

of a carbocation on a relatively unreactive double bond. Ionic polymerizations of vinyl derivatives are further important reactions for which Fig. 9 provides a valuable guide.281 Although for many reagents determining values of E or N may not be feasible, often an approximate value may be interpolated from comparison with the wide range of structures for which values are known. Extensions of Mayr’s work In addition to their reactions with alkenes and carbanions as nucleophiles benzhydryl cations react with hydride donors.282–284 These hydride transfer reactions show the same linear dependence of log k upon E as the reactions with alkenes and the same constant relative selectivity, that is with slopes of plots s close to 1.0, for structures ranging from cycloheptatriene to the

STABILITIES AND REACTIVITIES OF CARBOCATIONS

103

borohydride anion and dihydropyridines and solvents from methylene chloride to DMSO or aqueous acetonitrile. As with the reactions with alkenes the measurements were shown to be rather insensitive to changes in solvent. It might appear that this discussion has departed far from the original consideration of nucleophiles which was focused on anions in hydroxylic solvents. However, a feature of Mayr’s scheme is the wide range of its application. Of obvious interest is its extension to nucleophilic centers other than carbon or hydrogen and to water as a solvent. Reactions of strong nucleophiles in water are not easily observable for the more unstable benzhydryl carbocations, but are readily monitored with highly stabilized aminosubstituted cations such as those shown in Fig. 8, which were developed by Mayr as part of the benzhydryl series of compounds for this purpose. For these ions, reactions with water, hydroxide ion, other oxyanions, amines, amino acids,285 azide ion,286 and a thiolate ion have been studied.266,287 Plots of log k against E are again linear, and confirm that a consistent nucleophilic behavior is observed between p-nucleophiles and n-nucleophiles as different as olefinic hydrocarbons and the hydroxide ion. These measurements allow a comparison with the earlier analyses of reactions of n-nucleophiles in water in terms of Ritchie’s Nþ equation. A significant finding is that although plots of log k against E are linear, the slopes are significantly less than 1.0, falling consistently in the range 0.52–0.71 except for water (0.89) and –OOCCH2S (0.43). The exceptional behavior of water is consistent with difficulties Ritchie encountered in taking this as a reference nucleophile for the Nþ relationship and is in line with values for other hydroxylic solvents.288 On the other hand, the narrow range of s and N values for other nucleophiles becomes compatible with the Nþ relationship if Nþ = 0.6N. We will return to the significance of this, but note that assignment of s and N values to nucleophiles on which the Nþ relationship was based allows, in turn, assignment of E values to cations studied by Ritchie, notably trityl cations and substituted xanthylium ions and tropylium ions. It is remarkable that Mayr’s study, which originated with a very different reaction and solvent, is able to correlate satisfactorily data for nucleophilic reactions of carbocations in aqueous solution. In principle, any carbocation for which a rate constant for reaction with water below the relaxation limit has been measured, either directly by flash photolysis or indirectly by the azide clock, may be assigned an E value based on the values of N = 5.11 and s = 0.89 for water (although where possible E values are better based on reactions with more nucleophiles). On the other hand, it is to be expected that on moving beyond the structural constraints of the benzhydryl cations, the assigned E values will have less generality, if only because of the influence of steric effects. Thus the E values assigned to trityl cations overestimate by several orders of magnitude their reactivities toward alkenes. This is consistent with the known steric demands of the trityl cation289 and the likelihood that steric effects would be qualitatively different for reactions with alkenes and nitrogen or oxygen bases.

104

R. MORE O’FERRALL

Likewise, although N values for alkenes and hydride donors are practically independent of the solvent, hydrogen bonding to oxygen and nitrogen nucleophiles renders their N values sensitive to the nature of the solvent. This solvent dependence has been examined in some detail for the reactions of benzhydryl cations with halide ions, for which the cations were generated by flash photolysis.251 As might be expected, a reduction in the solvent ionizing power, as judged by solvent Y values, increases reactivity. More than a 100-fold difference was found between ethanol and TFE as solvent, and intermediate values were found for water and water–acetonitrile mixtures. In a striking application of this data, combination of N and s values for solvent288 and halide ions with E values for carbocations, allows an effective analysis of the detailed course of SN1 solvolyses, especially if allowance is made for encroachment of the diffusion limit for reactions of more reactive carbocations with halide ions.251 These results are by no means unrelated to the synthetic motivation of the earlier studies of alkylation reactions in CH2Cl2 as solvent. Comparisons of N and s values of alkenes and aromatics with those of hydroxylic solvents offer a guide to the conduct of Friedel–Crafts and other electrophilic carbon-carbon bond-making reactions in hydroxylic solvents. Not surprisingly, TFE is a particularly favorable solvent for such reactions and if allowance is made for a minor solvent dependence of N values for arenes and alkenes a good estimate of the likely feasibility of such reactions can be made.290–293 Remarkably, despite earlier suggestions to the contrary294 a good correlation exists between nucleophilic parameters for reactions of carbocations and those for SN2 substitutions. This is true of the Swain–Scott parameters (or Pearson and Sonntag’s nCH3 I values), and a particularly good correlation exists between Mayr’s N values and rate constants for SN2 displacements of neutral dibenzothiophene from the S-methyldibenzothiophenium ion 73, both for a range of hydroxylic solvents studied by Kevill295 and by oxygen, amine, and even phosphorus nucleophiles measured by Mayr and coworkers.253

+ S Me

74

However, the slope of the plot of log k against N for these reactions is not 1.0 but close to 0.6. This implies that increased nucleophilicity is nearly twice as effective in promoting reaction with a carbocation as with an SN2 substrate. Although the mechanisms of these reactions are different, it is perhaps

STABILITIES AND REACTIVITIES OF CARBOCATIONS

105

surprising that a highly reactive carbocation should be less selective than relatively unreactive alkylating agents such as methyl bromide correlated by the Swain equation. This point has been discussed by Richard, Toteva, and Crugeiras, who point to a likely difference in intrinsic reactivity associated with the closed rather than open electron shell of the reaction site for reactions at a saturated carbon center.219 In recognition of the excellent correlation that exists between his own and Swain and Scott’s (or Kevill’s) parameters, Mayr suggests modifying Equation (33) to include a further electrophilic constant distinguishing reactions at sp2 and sp3 carbon atoms.29,253 He denotes this constant sE to indicate that it refers specifically to the electrophile, and introduces the subscript ‘‘N’’ for the parameter s which has so far referred to the nucleophile. Again, instead of adopting the expected conventional form of log k = sNE þ sEN he chooses Equation (34), in which values of E and N correspond to intercepts on the abscissa rather than the ordinate of plots of log k versus E or N. Of course, the original Equation (33) and indeed the Swain–Scott equation (Equation 27) are special cases of Equation (34). log k¼sE sN ðE þ NÞ

ð34Þ

In Equation (34), Mayr has not only provided a simple and comprehensive relationship embracing nucleophilic reactions at carbon, but has tested the relationship with hundreds of examples. The equation and measurements provide a practical basis for semiquantitative prediction of reaction rates embracing a large number of synthetic organic and organometallic reactions, as we have seen. Many incidental problems have also been addressed, including the choice of amine catalysts for organocatalysis,296,297 partitioning of carbocations between solvent and nucleophiles,288 competition between alkylation and hydride abstraction,283 carbocationic and carbanionic polymerizations,298 quantitative free energy profiles for SN1 nucleophilic substitutions,251 and the nature of the borderline between SN1 and SN2 mechanisms.299 An analog of Equation (33) has been applied to estimating rate constants for SN1 solvolyses in terms of parameters representing reactivities of leaving groups and incipient carbocations.300

REACTIVITY, SELECTIVITY, AND TRANSITION STATE STRUCTURE

In addition to the work on carbocation reactions already described Mayr,28 together with Richard and McClelland, has been concerned with problems raised by the lack of dependence of selectivity on reactivity apparent both from the normal constancy and specific variations in values of the slope parameters sN (and sE).28 We conclude this chapter, therefore, with a brief discussion of

106

R. MORE O’FERRALL

this problem and of additional questions raised by the lack of correlation of rate with equilibrium constants when the reacting atom of the nucleophile is varied between anionic or neutral oxygen, nitrogen, sulfur, phosphorus, or halogen atoms. We begin by considering a plot of Mayr’s E parameters against pKR in Fig. 10. For the benzhydryl cations shown as open circles the correlation is excellent. For other cations there is dispersion into structurally related groups such as trityl cations and tropylium ions. This behavior shows a close analogy with plots of log kp and log kH2 O against pKa and pKR in Figs. 1 and 3 (pp. 43 and 77) and may be considered normal for what amounts to a rate–equilibrium relationship. The slope of 0.68 for the plot is also comparable to that for plots of log kH2 O against pKR.4 There is little or no indication of curvature in Fig. 10 and in this respect the plot is again similar to those of Figs. 1 and 3. The behavior may be interpreted in terms of compensation between changes in thermodynamic driving force for the reaction and variations in intrinsic activation barrier, both depending on changes in equilibrium constant for the reaction, as discussed already (pp. 77–90). An important point made by Mayr, is that the constant slope for these relationships by no means implies a static transition state.282 This was

5

E

0

–5

–10

–10

–5

0 pKR

5

10

Fig. 10 Plot of E parameters against pKR: open circles, benzhydryl cations; filled circles, trityl cations; squares, organometallic cations; filled triangles, tropylium ions; open triangles, flavylium, xanthylium and other O-, S-, or N-conjugated cations.

STABILITIES AND REACTIVITIES OF CARBOCATIONS

107

demonstrated in model calculations for hydride transfer between carbocation centers, which showed a systematic dependence of the degree of hydrogen transfer at the transition state upon the energy of reaction. The calculations also demonstrated that changes in intrinsic barrier occurred and were associated with a marked imbalance in charge distributions between reactants and transition state. When calculated values of the activation energy were plotted against the energy of reaction, they furnished slopes  = 0.72 for structural changes leading to changes in energy of the carbocation acting as hydride acceptor and  = 0.28 for corresponding changes in the hydride donor. These values are close to the values of 0.75 and 0.25 one might expect for a symmetrical transition state in which the hydrogen is half transferred and rehybridization of the reacting bonds had occurred to the extent of 50%, as envisaged in Kresge’s idealized model discussed above (p. 81).234 As expected the intrinsic barrier is increased by electron donating substituents (which stabilize the carbocations through delocalization of the charge) in the hydride donor and acceptor. For the carbocation, the effects of substituents on the energy of reaction and intrinsic barrier are complementary and for the donor, they are opposed. Mayr’s calculations are consistent with his experimental demonstrations that for hydride transfer the magnitudes of N and E are independent of each other. It seems likely that the same is true of reactions of carbocations with alkenes, which again yield a carbocation as immediate product of the reaction. In these reactions then, the lack of dependence of selectivity on reactivity can be interpreted in terms of the compensation between thermodynamic driving force and variable intrinsic barrier, as already discussed, which receives substantial reinforcement from Mayr’s calculations. On the other hand, it seems less likely that the relative reactivities of nnucleophiles should be independent of the reactivity of a carbocation. At least when they act as bases, there is little or no evidence that changes in structure of n-nucleophiles lead to changes in intrinsic barrier.301 One might expect therefore that carbocations of different reactivities reacting with a structurally related group of nitrogen or oxygen nucleophiles would show different slopes of plots of log k versus log K. There are some difficulties with testing this experimentally. The first is that it is not easy to match the same set of bases to electrophiles of quite different reactivity. A second is that the most readily available equilibrium constants characterizing the nucleophiles are pKas of the conjugate acids, which do not necessarily correlate reactivities toward carbocations. Thirdly, one should avoid reactions influenced by diffusion control. Finally, care has to be taken with steric and solvent effects. McClelland has studied the reaction of four primary amines with benzhydryl and trityl cations.4,302 Rate constants for reactions of most of the benzhydryl cations were close to their values for diffusion control. However, he was able to measure diffusion free rate constants for substituted trityl cations. There was a further complication, consistent with earlier measurements by Berg and

108

R. MORE O’FERRALL

Jencks303 in so far as there is a significant influence from a preequilibrium desolvation of the amine, which is larger for more basic amines. Nevertheless, based on careful measurements, McClelland was able to correct for this and demonstrate a clear dependence of slopes ( nuc) of plots of log k against the pKa of the ammonium ion upon the stability of the trityl cation as shown in Fig. 11. Interestingly, no leveling of the plot was observed for trityl cations such as crystal violet conforming to Ritchie’s equation. These measurements are consistent with earlier studies by McClelland of the trityl and xanthylium ions for which plots of log k against Nþ for a wide range of nucleophiles were recorded. The correlations showed some scatter, with a strong positive deviation of the azide ion, but it was clear that the slopes of the best straight lines through the points were considerably less than unity, being 0.33 for the trityl cation19 and 0.65 for the xanthylium ion.304 Again, the distinguishing feature of these cations compared with those studied by Ritchie was their much higher reactivity. A further dependence of the selectivity between different nucleophiles on the stability and reactivity of carbocations was found by Richard and Amyes in a study of reactions of alcohols and carboxylate anions with p-substituted a-trifluoromethyl benzyl cations (75, X = Me, OMe, SMe, N(Me)CH2CF3, and NMe2) monitored using the azide clock.305 Apart from the methylsubstituted substrate, for which the reactions approached diffusion control,

0.7

β nuc

0.6

0.5

0.4

0.3

–10

–5

0

5

pKR

Fig. 11 Plot of  nuc against pKR for reaction of primary amines with trityl cations ( values corrected by 0.2 to allow for desolvation of amines).

STABILITIES AND REACTIVITIES OF CARBOCATIONS

109

there was a strong dependence of selectivity upon the stability of the cation. The selectivities were measured from ratios of products of reactions of ethanol and TFE with the carbocations (or Bronsted exponents for reaction of carboxylate anions) and the stability was measured by the rate constant kS for reaction of the carbocation with the aqueous TFE as solvent. The variation in selectivity (kEtOH/kTFE) became saturated for the most stable p-aminosubstituted cations, for which selectivities are practically independent of the nature of the amino group. This behavior is indicated below by the substituent dependence of kEtOH/kTFE product trapping ratios, which vary by a factor of 100 between Me and Me2N. CH+

X

CF3

75

X

Me

kEtOH/kTFE 1

kS (s )

MeO

3.1

MeS

55 10

110

CF3CH2(Me)N

71 7

270 7

510

1.210

210

Me2N 330

4

<800

It seems clear therefore that more reactive cations than those for which Ritchie’s Nþ relationship was developed, show a distinct dependence of selectivity between nucleophiles upon the stability and reactivity of the carbocation. Richard has confirmed that for a very stable benzylic ‘‘carbocation,’’ represented by the bis-trifluoromethyl quinone methide 57, the Nþ regime is restored and that a plot of log k against Nþ for reactions of nucleophiles, including amines, oxygen and sulfur anions, the azide ion, and a-effect nucleophiles, shows a good correlation with Nþ.219 CF3 O

C CF3 57

This is further confirmation that there is scope for constant selectivity regimes. Richard comments that the sharp dependence of selectivity upon reactivity he and McClelland found for relatively reactive cations must be moderated for more strongly stabilized ions if a limiting value of nuc near to 1.0 is not to be exceeded. As Richard points out, the low reactivity and high intrinsic barriers for highly stabilized electrophiles will necessarily be

110

R. MORE O’FERRALL

associated with a weak dependence of selectivity on reactivity and in this respect is consistent with expectations based on the Marcus equation. It should be emphasized that the dependence of selectivity on reactivity established for electrophiles of intermediate reactivity is by no means at odds with Mayr’s assignments of ‘‘constant’’ N values to n-nucleophiles. Thus in Mayr’s study of amines, changes of selectivity between different nucleophiles can be highlighted by log k–log K plots for different electrophiles reacting with a common group of nucleophiles. For two nitrogen-substituted carbocations differing in reactivity by 300-fold the ratio of nuc values was estimated as 0.85 (Mayr and Ofial unpublished data). However, because systematic variations in selectivity with reactivity appear to be quite mild (a) they are likely to be revealed only by large changes in reactivity and (b) N values still provide a reliable basis for semiquantitative assessments of reactivities. Thus the range of reactivities of electrophiles chosen by Mayr for defining N-values for n-nucleophiles fall within experimentally measurable ranges, and these are likely to be of most relevance to predictions of the feasibility of electrophile– nucleophile combination reactions.

HARD AND SOFT NUCLEOPHILES

The nucleophiles discussed so far have been either carbon nucleophiles, or homogenous sets of amine or neutral oxygen nucleophiles. The Nþ relationship embraces a wide variety of anionic nucleophiles with different reacting atoms. As already demonstrated, reactivities of these nucleophiles strikingly fail to correlate with equilibrium constants for their reactions. The interpretation of reactivities here provides a particular challenge, because differences in solvation and bond energies contribute differently to reaction rates and equilibria. Analysis in terms of the Marcus equation, in which effects on reactivity arising from changes in intrinsic barrier and equilibrium constant can be separated, is an undoubted advantage. Only rather recently, however, have equilibrium constants, essential to a Marcus analysis, become available for reactions of halide ions with relatively stable carbocations, such as the trityl cation, the bis-trifluoromethyl quinone methide (49), and the rather less stable benzhydryl cations.19,219 A comparison of reactions of halide and acetate ions with quinone methide 57 has been provided by Richard, Toteva, and Crugeiras.219 The lack of correlation between rate and equilibrium constants is highlighted by the fact that iodide ion is 1400 times more reactive than acetate despite the reaction being thermodynamically less favorable by 6 kcal mol1. This is characteristic of a comparison of soft and hard nucleophiles, of which the former show lower intrinsic barriers306,307 The consistent behavior between different (Nþ)

STABILITIES AND REACTIVITIES OF CARBOCATIONS

111

electrophiles is signaled by differences in intrinsic barrier between the quinone methide 57 and the trityl cation being independent of the nature of the nucleophile. (Intrinsic barriers for the reactions with the trityl cation are shown in Table 7 on p. 93.) Richard points to two factors likely to affect the comparison between acetate and halide ions (F, Cl, and I). One is that the observed differences in intrinsic barriers parallel differences in solvation energy. In Marcus’s original rate–equilibrium relationship a contribution from a preequilibrium step involving desolvation was explicitly included. In practice, however, it is difficult to separate contributions from this step from changes in intrinsic barrier. Where desolvation is not specifically recognized therefore it will be expressed as a contribution to the intrinsic barrier. Correspondingly, any desolvation of the anions that occurs before covalent interaction of the nucleophile with the carbocation will tend to reduce the difference in intrinsic barriers for the bonding-making reaction step. Put another way, differences in intrinsic barriers between the four ions might be expected to be considerably smaller in the gas phase than in solution. The second factor is the dependence of bonding interactions between the nucleophile and carbocation at the transition state upon the distance between the charge centers. The importance of this is suggested by a comparison of rate and equilibrium constants for the reactions of chloride ion and Me2S with the quinone methide 57 and p-methoxybenzyl cation. For the p-methoxybenzyl cation the equilibrium constant for reaction with the sulfur nucleophile is more favorable than that for the chloride ion by a factor of 107. As already discussed on p. 73 (cf. Table 6) this is a normal reflection of the greater carbon basicity of sulfur than chlorine. However in the case of the quinone methide the relative magnitudes of the equilibrium constants is reversed, with KMe2 S /KCl = 0.008. Toteva and Richard attribute this to the unfavorable steric and electrostatic interactions between the CF3 groups of the quinone methide adduct and the positively charged sulfonium ion. The significance of these results for differences in reactivities of nucleophiles is that, despite the unfavorable relative equilibrium constants, Me2S is more reactive toward the quinone methide than chloride ion by a factor of nearly 3000. This mismatch of rate and equilibrium effects is summarized in Scheme 35. It must imply (a) that there is a relatively long partial bond between sulfur and carbon in the transition state so that the unfavorable steric and electrostatic effects are not developed and (b) that the favorable carbon–sulfur bonding interaction is well developed despite the long bonding distance. It is not intended to pursue this discussion to a firmer conclusion. However, it is reasonable to infer that our understanding of reactivity and selectivity in carbocations has been brought to a point where the origins of differences in reactivities of hard and soft nucleophiles and of lack of correlation of rate and equilibrium constants have been greatly clarified. Particularly, in the hands of

112

R. MORE O’FERRALL

–

Me2S

O

CF3

CF3 SMe2+ CF3 K Me2S /K Cl = 0.008

O CF3

Cl–

–

O

CF3 Cl CF3

k Me2S /kCl = 2700

Scheme 35

Richard, the Marcus analysis, allied to the concept ‘‘imbalance’’ of bond making and charge development at the transition state, has provided an effective framework for tackling one of the outstanding problems for a general interpretation of reactivity. A reasonable conclusion might be that further measurements of equilibrium constants will be required to support and test the level of understanding achieved so far, and to probe more deeply the interpretation of ‘‘hard and soft’’ nucleophilicity in its application to reactions of electrophilic carbon atoms.

SUMMARY AND CONCLUSIONS

It seems clear that for reactions of carbocations with nucleophiles or bases in which the structure of the carbocation is varied, we can expect compensating changes in intrinsic barrier and thermodynamic driving force to lead to relationships between rate and equilibrium constants which have the form of extended linear plots of log k against log K. However, this will be strictly true only for structurally homogeneous groups of cations. There is ample evidence that for wider structural variations, for example, between benzyl, benzhydryl, and trityl cations, there are variations in intrinsic barrier particularly reflecting steric effects which lead to dispersion between families of cations. On the other hand, for carbocations reacting with n-nucleophiles such as amines or alcohols a systematic dependence of selectivity on reactivity becomes apparent. As usual, this is not readily detected as curvature of a free energy relationship for a single carbocation reacting with a series of nucleophiles, because it is difficult to find a structurally homogeneous family covering a sufficiently wide range of reactivity. It is apparent, however, from plots of log k against pKa (or other measure of reactivity or stability) for reaction of a more a limited range of nucleophiles with a series of different carbocations. The slopes of the plots show a systematic relationship between the reactivity of the carbocation and its selectivity between different

STABILITIES AND REACTIVITIES OF CARBOCATIONS

113

nucleophiles. Ironically, the measurements of McClelland and Richard reestablish the conclusion incorrectly drawn from measurement of selectivities between water and azide ion for carbocations reacting with azide ions under diffusion control, namely that there is an inverse relationship between reactivity and selectivity. These results have been assessed from different points of view. In an article entitled ‘‘The Reactivity-Selectivity Principle: An Imperishable Myth in Organic Chemistry’’ Mayr and Ofial comment that except where it is an artifact of competition between chemically activated and diffusion-controlled reactions examples of an inverse relationship between reactivity and selectivity are relatively rare, and they cite extensive earlier literature making this point.30 From an alternative point of view, one can consider such relationships as representing ‘‘ideal’’ behavior consistent with the Hammond postulate and Bell–Evans–Polanyi principle,259 from which real relationships depart, because of variations in intrinsic barrier and associated ‘‘imbalance’’ of bond making and bond breaking in transition states. Expositions of the ‘‘imbalance principle’’ and its application to different reactions are contained in articles by Jencks on carbonyl reactions,263 by Richard8 and Bernasconi,233 on carbocation and carbanion reactions and by Gajewski on electrocyclic reactions.308,309 The views of Mayr and Ofial differ from these by less than might at first appear. They invoke variations in frontier orbital interactions to account for departures from Bell–Evans–Polanyi behavior,30 and in an earlier discussion suggest a similar role for variations in intrinsic barrier in hydride transfer reactions.282 Because ‘‘systematic’’ variations in selectivity with reactivity are commonly quite mild for reactions of carbocations with n-nucleophiles, and practically absent for p-nucleophiles or hydride donors, many nucleophiles can be characterized by constant N and s values. These are valuable in correlating and predicting reactivities toward benzhydryl cations, a wide structural variety of other electrophiles and, to a good approximation, substrates reacting by an SN2 mechanism. There are certainly failures in extending these relationships to too wide a variation of carbocation and nucleophile structures, but there is a sufficient framework of regular behavior for the influence of additional factors such as steric effects to be rationally examined as deviations from the norm. Thus comparisons between benzhydryl and trityl cations reveal quite different steric effects for reactions with hydroxylic solvents and alkenes, or even with different halide ions Steric effects provide examples of ‘‘hard cases’’ with respect to predicting reactivities. The same might be said to be true of solvent effects for reactions of n-nucleophiles or carbanions. However, while values of N may vary with solvent the differences can be exploited, for example, in promoting a desired reaction in synthesis. Moreover, in attempting to interpret solvent effects, it is possible that comparing measurements of reaction rates and (preferably)

114

R. MORE O’FERRALL

equilibria in solvents of widely differing ion-solvating characteristics, such as water, DMSO, and HFIP, will be helpful in separating intrinsic differences in reactivity from specific solvation effects. Marcus’s treatment provides a relatively unexploited framework for such an analysis. A particular difficulty arises for the comparison of hard and ‘‘soft’’ nucleophiles. This difficulty indeed is amplified if one goes beyond carbocation reactions to consider softer or harder electrophilic centers, such as transition metals or protons. Interpreting differences between reacting atoms presents an ultimate challenge for attempts to understand reactivity. Richard has gone a considerable way toward offering a rational analysis of the principal factors to be considered in such an endeavor. However, this is one issue likely to attract attention in the next one hundred years of carbocation chemistry and in the wider field of electrophile–nucleophile combination reactions.

Acknowledgments Many helpful comments from Herbert Mayr, Armin Ofial, and Peter Guthrie and support of much of the author’s own work by The Science Foundation Ireland (Grant No. 04/IN3/B581) are gratefully acknowledged.

References 1. Olah GA, Prakash GKS, editors. Carbocation chemistry. New York: Wiley Interscience; 2004. 2. Aboud J-LM, Alkorta I, Davalos JZ, Muller P. Adv Phys Org Chem 2002;37:57–135. 3. McClelland RA. In: Moss RA, Platz MS, Jones M, Jr., editors. Reactive intermediate chemistry. Hoboken, NJ: Wiley-Interscience; 2004. pp. 3–40. 4. McClelland RA. Tetrahedron 1996;52:6823–58. 5. Richard JP, Amyes TL, Lin S-S, O’Donoghue AC, Toteva MM, Tsuji Y, et al. Adv Phys Org Chem 2000;35:67–115. 6. Richard JP. In: Moss RA, Platz MS, Jones M, Jr., editors. Reactive intermediate chemistry. Hoboken, NJ: Wiley-Interscience; 2004. pp. 41–68. 7. Richard JP, Amyes TL, Toteva MM, Tsuji Y. Adv Phys Org Chem 2004;39:67– 115. 8. Richard JP. Tetrahedron 1995;51:1535–73. 9. MacCormack AC, McDonnell CM, O’Donoghue AC, More O’Ferrall RA. Modern problems in organic chemistry, vol. 14. St. Petersburg: St. Petersburg Press; 2003;88–111. 10. Siehl U. Adv Phys Org Chem 2008;42:125–65. 11. Laali KK, editor. Recent developments in carbocation and onium ion chemistry. Washington, DC: American Chemical Society; 2007. 12. Ingold CK. Structure and mechanism in organic chemistry. London: Bell; 1953. 13. Appeloig Y, Biton R, Abu-Freih A. J Am Chem Soc 1993;115:2522–3. 14. Diffenbach RA, Sano K, Taft RW. J Am Chem Soc 1966;94:3536–9. 15. Ritchie CD. Can J Chem 1986;64:2239–50.

STABILITIES AND REACTIVITIES OF CARBOCATIONS

115

16. Bethell D, Gold V. Carbonium ions an introduction. London: Academic Press; 1967. 17. Aue DH, Bowers MT. In: Bowers MT, editor. Gas phase ion chemistry, vol. 2. New York: Academic Press; 1979, Chapter 9. 18. Das PK. Chem Rev 1993;93:119–44. 19. McClelland RA, Banait N, Steenken S. J Am Chem Soc 1986;108:7023–7. 20. Schnabel W, Naito I, Kitamura T, Kobayashi S, Taniguchi H. Tetrahedron 1980;36:3229–31. 21. Young PR, Jencks WP. J Am Chem Soc 1977;99:8238–48. 22. Richard JP, Rothenburg ME, Jencks WP. J Am Chem Soc 1984;106:1361–72. 23. Richard JP, Williams G, O’Donoghue AC, Amyes TL. J Am Chem Soc 2002;124:2957–68. 24. Richard JP, Amyes TL, Toteva MM. Acc Chem Res 2001;34:981–8. 25. Lawlor DA, More O’Ferrall RA, Rao SN. J Am Chem Soc 2008;130:17997–8007. 26. Keeffe JR, More O’Ferrall RA. ARKIVOC 2008; 183–204. 27. Mayr H, Kempf B, Ofial AR. Acc Chem Res 2003;36:66–77. 28. Mayr H, Ofial AR. In: Olah GA, Prakash GKS, editors. Carbocation chemistry. New York: Wiley; 2004. pp. 331–58. 29. Mayr H, Ofial AR. Pure Appl Chem 2005;77:1807–21. 30. Mayr H, Ofial AR. Angew Chem Int Ed 2006;45:1844–54. 31. Mayr H, Ofial AR. J Phys Org Chem 2008;21:584–95. 32. Keeffe JR, Kudavalli JS, Lawlor DA, Rao SN, More O’Ferrall, RA Science, submitted. 33. Hine J. Structural effects on equilibria in organic chemistry. New York, John Wiley, 1975. 34. Hine J. J Am Chem Soc 1971;93:3701–8. 35. More O’Ferrall RA, O’Brien DM, Murphy DG. Can J Chem 2000;78:1594–612. 36. Sharma RB, Sen Sharma DK, Hiraoka K, Kebarle P. J Am Chem Soc 1985;107:3747–57. 37. Kebarle P. Annu Rev Phys Chem 1977;28:445–76. 38. Guthrie JP. Can J Chem 1992;70:1042–54. 39. Bittener EW, Arnett EM, Saunders M. J Am Chem Soc 1976;98:3734–5. 40. Benson SW, Cruickshank FR, Golden DM, Haugen GR, O’Neal HE, Rodgers AS, et al. Chem Rev 1969;69:279–324. 41. Brauman JL. In: Bowers MT, editor. Gas phase ion chemistry, vol. 2. New York: Academic Press; 1979. 42. Allen AD, Chiang Y, Kresge AJ, Tidwell TT. J Org Chem 1982;47:775–9. 43. Hine J, Mookerjee PK. J Org Chem 1975;40:292–8. 44. Salzner U, Schleyer PvR. J Am Chem Soc 1993;115:10231–6. 45. Harcourt MP, More O’Ferrall RA. Bull Soc Chim France 1988; 407–14. 46. Richard JP, Amyes TL, Rice DJ. J Am Chem Soc 1993;115:2523–4. 47. Dey J, O’Donoghue AC, More O’Ferrall RA. J Am Chem Soc 2002;124:8561–74. 48. Grunwald E, Leffler JE. Rates and equilibria of organic reactions. New York: John Wiley; 1963. 49. Doering WvE. J Am Chem Soc 1954;76:3203–6. 50. McClelland RA, Gedge S. J Am Chem Soc 1980;102:5838–48. 51. Devine DB, McClelland RA. J Org Chem 1985;50:5656–60. 52. Bagno A, Scorrano G, More O’Ferrall RA. Rev Chem Intermed 1987;7:313–52. 53. Cox RA. Adv Phys Org Chem 2000;35:1–66. 54. Bentley TW. Can J Chem 2008;86:277–80. 55. Cox RA, Yates K. Can J Chem 1983;61:2225–43. 56. Long FA, Paul MA. Chem Rev 1957;57:935–1010. 57. Rochester CH. Acidity functions. New York: Academic Press; 1970.

116

R. MORE O’FERRALL

58. 59. 60. 61. 62. 63. 64. 65. 66. 67. 68. 69. 70. 71.

Deno NC, Groves PT, Saines G. J Am Chem Soc 1959;81:5790–5. Reagan MT. J Am Chem Soc 1969;91:5506–10. Schubert WM, Quacchia RH. J Am Chem Soc 1962;84:3778–9. Deno NC, Jaruzelski JJ, Schriesheim A. J Am Chem Soc 1955;77:3044–51. Deno NC, Evans WL. J Am Chem Soc 1957;79:5804–7. Mindl J, Vecera M. Collect Czech Chem Commun 1972;37:1143–????. Deno NC, Evans WL, Peterson HJ. J Am Chem Soc 1959;81:2344–7. Schubert WM, Keeffe JR. J Am Chem Soc 1971;94:559–66. Breslow R, Grace JT. J Am Chem Soc 1970;92:984–7. Breslow R. Honer H, Chang HW. J Am Chem Soc 1962;84:3168–74. Kresge AJ, Mylonakis SG, Sato Y, Vitullo P. J Am Chem Soc 1971;93:6174–81. Amyes TL, Richard JP, Novak M. J Am Chem Soc 1992;114:8032–41. Bagno A, Lucchini V, Scorrano G. Bull Soc Chim France 1987;563–72 Noto A, D’Anna F, Gruttadauria M, Lo Meo P, Spinelli D. J Chem Soc Perkin Trans 2 2001;2043–6. Cox RA. J Phys Org Chem 1991;4:233–41. Fujio M, Keeffe JR, More O’Ferrall RA, O’Donoghue AC. J Am Chem Soc 2004;126:9982–92. Kelly SC, McDonnell CM, More O’Ferrall RA, Rao SN, Boyd DR, Brannigan IN, et al. Gazetta Chim Ital 1996;126:747–54. MacCormack AC, McDonnell CM, More O’Ferrall RA, O’Donoghue AC, Rao SN. J Am Chem Soc 2002;124:8575–83. Kaatze U, Pottel R, Schumacher AJ. J Phys Chem 1992;96:6017–20. McClelland RA, Kanagasabapathy VM, Banait NS, Steenken S. J Am Chem Soc 1989;111:3966–72. Mathivanan N, McClelland RA, Steenken S. J Am Chem Soc 1990;112:8454–57. Steenken S, Buschek J, McClelland RA. J Am Chem Soc 1986;108:2808–13. McClelland RA, Steenken S. J Am Chem Soc 1988;110:5860–66. McClelland RA, Kanagasabapathy VM, Banait NS, Steenken S. J Am Chem Soc 1991;113:1009–14. McClelland RA, Cozens FL, Steenken S, Amyes TL, Richard JP. J Chem Soc Perkin Trans 2 1993;1717–22. Bartl J, Steenken S, Mayr H, McClelland RA. J Am Chem Soc 1990;112:6918–28. McClelland RA, Cozens FL, Steenken S. Tetrahedron Lett 1990;31:2821–4. Richard JP, Jencks WP. J Am Chem Soc 1984;106:1373–83. Gold V, Gruen LC. J Chem Soc B 1966; 600–3. Courtney MC, McCormack AC, More O’Ferrall RA. J Phys Org Chem 2002;15:529–39. Lawlor DA. PhD Thesis, National University of Ireland (Dublin), 2008. Richard JP, Jagannadham V, Amyes TL, Mishima M, Tsuno,Y. J Am Chem Soc 1994;116:6706–12. Herndon WC, Mills NS. J Org Chem 2005;70:8492–6. Jiao H, Scleyer PvR, Mo Y, McAllister MA, Tidwell TT. J Am Chem Soc 1997;119:7075–83. Allen AD, Tidwell TT. In: Olah GA, Prakash GKS, editors. Carbocation chemistry. New York: Wiley Interscience; 2004, pp. 103–23. Toteva MM, Richard JP. J Am Chem Soc 1996;118:11434–45. Dostrovsky I, Klein FS. J Chem Soc 1955;791–6. Dietze PE, Jencks WP. J Am Chem Soc 1987;109:2057–62. Manassen J, Klein FS. J Chem Soc 1960; 4202–13. Lucchini V, Modena G. J Am Chem Soc 1990;112:6291–6. Chwang WJ, Nowlan VJ, Tidwell TT. J Am Chem Soc 1977;99:7233–8.

72. 73. 74. 75. 76. 77. 78. 79. 80. 81. 82. 83. 84. 85. 86. 87. 88. 89. 90. 91. 92. 93. 94. 95. 96. 97. 98.

STABILITIES AND REACTIVITIES OF CARBOCATIONS 99. 100. 101. 102. 103. 104. 105. 106. 107. 108. 109. 110. 111. 112. 113. 114. 115. 116. 117. 118. 119. 120. 121. 122. 123. 124. 125. 126. 127. 128. 129. 130. 131. 132. 133. 134. 135.

117

Bunnett JF, Eck DL. J Org Chem 1971;36:897–901. Stavascik J, Rickborn B. J Am Chem Soc 1971;93:3046–7. Bamberger E, Lodter W. Liebigs Ann Chem 1895;288:74–133. Boyd DR, Bugg TD. Biomol Org Chem 2005;4:181–92. Paralis RE, Resnick SM. In: Ramos J-L, Levesque RC, editors. Pseudomonas vol. 4, molecular biology of emerging issues. New York: Kluwer Academic/ Plenum publishers; 2005. pp. 287–340. Boyd DR, McMordie RAS, Sharma ND, Dalton H, More O’Ferrall RA, et al. J Am Chem Soc 1990;112:7822–3. Rao SN, More O’Ferrall RA, Kelly SC, Boyd DR, Agarwal A. J Am Chem Soc 1993;115:5458–65. Pirinccioglu N, Thibblin A. J Am Chem Soc 1998;120:6512–7. Marziano A, Tortato C, Bertani RJ. J Chem Soc Perkin Trans 2 1992;955–7. Kresge AJ, Chen HJ, Hakka LE, Kouba JE. J Am Chem Soc 1971;93:6181–8. Long FA, Schulze J. J Am Chem Soc 1964;86:322–7, 327–32. McClelland RA, Ren D, Ghobrial D, Gadosy TA. J Chem Soc Perkin Trans 2 1997;451–6. Jia ZS, Thibblin A. J Chem Soc Perkin Trans 2 2001;247–51. Pirinccioglu N, Jia ZS, Thibblin A. J Chem Soc Perkin Trans 2 2001;2271–5. Eaborn C, Golbon P, Spillet RE, Taylor R. J Chem Soc B 1968; 1112–23. Taylor R. Electrophilic aromatic substitution. New York: Wiley; 1990. Nowlan VJ, Tidwell TT. Acc Chem Res 1977;10:252–8. Keeffe JR, Kresge AJ. In: Rappoport Z, editor. The chemistry of enols. Chichester: Wiley; 1990. pp. 399–480. Okuyama T, Takino T, Sueda T, Ochiai M. J Am Chem Soc 1995;117:3360–7. Fujita M, Sakanishi Y, Okuyama T. J Am Chem Soc 2000;122:8787–8. Bagno A, Modena G. Eur J Org Chem 1999; 2893–7. Okuyama T, Lodder G. Adv Phys Org Chem 2002;37:1–56. Kobayashi S, Hori Y, Hasako T, Koga K, Yamataka Y. J Org Chem 1996;61:5274–9. Mishima M, Ariga T, Fujio M, Tsuno Y. Kobayashi S, Taniguchi H. Chem Lett 1992;21:1085–8. Mishima M, Arima K, Inoue H, Usui S, Fujio M, Tsuno Y. Bull Chem Soc Jpn 1995;68:3199–208. Slegt M, Gronheid R, van der Vlugt D, Ochiai M, Okuyama T, Zuilhof H, et al. J Org Chem 2006;71:2227–35. Okuyama T. Acc Chem Res 2005;35:12–8. Wolf JF, Aboud J-LM, Taft RW. J Org Chem 1977;42:3316–3317. Mishima M, Inoue H, Fujio M, Tsuno Y. Tetrahedron Lett 1989;30:2101–4. Aboud J-LM, Herreros M, Notario R, Lomas JS, Mareda J, Muller P, et al. J Org Chem 1999;64:6401–10. Taagapera M, Summerhays KD, Hehre WJ, Topsom RD, Pross A, Radom L, et al. J Org Chem 1981;46:891–903. Amyes TL, Jencks WP. J Am Chem Soc 1989;111:5458–65. Kresge AJ, Weeks DP. J Am Chem Soc 1984;106:7140–3. Guthrie JP, More O’Ferrall RA, O’Donoghue AC, Waghorne WE, Zrinski I. J Phys Org Chem 2003;16:582–7. Steenken S, McClelland RA. J Am Chem Soc 1989;111:4967–73. Ahmed M, Bergstrom RG, Cashen MJ, Chiang Y, Kresge AJ, McClelland RA, et al. J Am Chem Soc 1979;101:2669–77. Bull HG, Koehler K. Plewtcher TC, Ortiz JJ, Cordes EH. J Am Chem Soc 1971;93:3602–011.

118

R. MORE O’FERRALL

136. 137. 138. 139. 140. 141. 142. 143.

More O’Ferrall RA, Peroni D, Zrinski I., in preparation. Sander EG, Jencks WP. J Am Chem Soc 1968;190:6154–62. Bagno A, Lucchini V, Scorrano G. J Phys Chem 1991;95:345–52. McClelland RA, Coe M. J Am Chem Soc 1983;105:2718–25. Brouillard R, Dubois J-E. J Am Chem Soc 1977;99:1359–64. Bell RP. Adv Phys Org Chem 1966;4:1– Guthrie JP, Culliemore PA. Can J Chem 1980;58:1281–94. De Maria P, Fontana A, Spinelli D, Dell’Erba C, Novi M, Perillo G, et al. J Chem Soc Perkin Trans 2 1993;649–54. Guthrie JP, Culliemore JC. Can J Chem 1975;53:898–906. Toullec J. Tetrahedron Lett 1988;29:5541–4. Toullec J, El-Alaoui M. J Org Chem 1986;51:4054–61. Grieg CC, Johnson CD. J Am Chem Soc 1968;90:6453–7. Arnett EM, Quirke RP, Larsen RW. J Am Chem Soc 1970;92:3977–84. Yan J, Springsteen J, Deeter S, Wong B. Tetrahedron 2004;60:11205–9. Bell RP, Sorenson S. J Chem Soc Perkin Trans 2 1976;1594–8. Capponi N, Gut IG, Hellrung B, Persy G, Wirz J. Can J Chem 1999;77:605–13. Freiermuth B, Hellrung B, Peterli MF, Schulz DZ, Wirz J. Helv Chim Acta 2001;84:3796–809. McCann GM, McDonnell CM, Magris L, More O’Ferrall RA. J Chem Soc Perkin Trans 2 2002;784–95. Wan P, Barker B. Diao L, Fischer M, Shi Y, Yang M. Can J Chem 1996;74:465– 75. Chiang Y, Kresge AJ, Zhu Y. J Am Chem Soc 2001;123:8089–94. Chiang Y, Kresge AJ, Zhu Y. J Am Chem Soc 2002;124:6349–56. Toteva MM, Moran M, Amyes TL, Richard JP. J Am Chem Soc 2003;125:8814– 9. Toteva MM, Richard JP. J Am Chem Soc 2002;124:9798–805. Fattahi A, Kass SR, Liebman JF, Matos MAR, Miranda MS, Morais VMF. J Am Chem Soc 2005;127:6116–22. Whalen D. Adv Phys Org Chem 2005;40:247–98. Doan L, Lin B, Yagi H, Jerina DM, Whalen DL. J Am Chem Soc 2001;123:6785– 91. Laali KK. In: Olah GA, Prakash GKS, editors. Carbocation chemistry. New York: Wiley-Interscience; 2004. pp. 237–78. Boyd DR, Blacker DJ, Byrne B, Dalton H, Hand MV, Kelly SC, et al. J Chem Soc Chem Commun 1994;313–4. Boyd DR, Rao SN, Lawlor DA, Keeffe JR, Kudavalli J, More O’Ferrall RA, in preparation. Goronski JK, Kwit M, Boyd DR, Sharma ND, Malone JF, Drake AF. J Am Chem Soc 2005;127:4308–19. Streitwieser A. Solvolysis reactions. New York: McGraw-Hill; 1962. Berti G. J Org Chem 1957;22:230. Bunting JW. Adv Heterocycl Chem 1979;25:1–82. Canalini G, Degani I, Fochi R, Spunta G. Ann Chim (Rome) 1967;57:1045–. Ceccon A, Gambaro A, Romanin A, Venzo A. Angew Chemie Int Ed Engl 1983;22:559–60. Vyacheslav G, Borodkin S, Borodkin GI. In: Olah GA, Prakash GKS, editors. Carbocation chemistry. New York: Wiley; 2004. pp. 125–85. Borodkin GI, Nagy SM, Gantilov Yu. G, Shakirov MM, Rybalova TV, Shubin VG. Zh Org Khim 1992;28:1806–26.

144. 145. 146. 147. 148. 149. 150. 151. 152. 153. 154. 155. 156. 157. 158. 159. 160. 161. 162. 163. 164. 165. 166. 167. 168. 169. 170. 171. 172.

STABILITIES AND REACTIVITIES OF CARBOCATIONS

119

173. Koptyug VA Korobeinicheva IK, Andreeva TP, Bushmelev VA. Zh Obshch Khim 1968;38:1979–. 174. Jia ZS, Brandt P, Thibblin A. J Am Chem Soc 2001;123:10147–52. 175. Eaborn C, Pande KC. J Chem Soc 1960;1566–71. 176. Eaborn C, Emokpae TA, Sidorov VI, Taylor R. J Chem Soc Perkin Trans 2 1974;1454–9. 177. Pitt CG. J Organomet Chem 1973;61:49–70. 178. Williams RV, Kurtz HA. Adv Phys Org Chem 1994;29:273–331. 179. Mullikan RS, Rieke CA, Brown WG. J Am Chem Soc 1941;63:41–56. 180. Watts WE. In: Wilkenson G, Stone FGA, Abel EW, editors. Comprehensive organometallic chemistry, vol. 8. Oxford: Pergamon; 1982. Chapter 9, pp. 1013– 71. 181. Schleyer PvR, Kiran V, Simion DV, Sorenson TS. J Am Chem Soc 2000;122:510– 3. 182. Mahler JE, Jones DAK, Petit R. J Am Chem Soc 1964;86:3589–90. 183. Bunton CA, Carrasco N. J Chem Soc Perkin Trans 2 1979;1267–73. 184. Kane-Maguire LAP, Honig ED, Sweigart DA. Chem Rev 1984;84:525–44. 185. Dulich F, Muller K-H, Ofial AR, Mayr H. Helv Chim Acta 2005;88:1754–68. 186. Mayr H, Muller K-H, Rau D. Angew Chem Int Ed 1993;32:1630–2. 187. Kuhn O, Rau D, Mayr H. J Am Chem Soc 1998;120:900–7. 188. McGlinchey MJ, Girard L, Ruffalo R. Coord Chem Rev 1995;143:331–81. 189. Connor RE, Nicholas KM. J Organomet Chem 1977;125:C46–C51. 190. Netz A, Muller TJJ. Tetrahedron 2000;56:4149–55. 191. Mayr H, Kuhn O, Schlierf C, Ofial AR. Tetrahedron 2000;56:4219–29. 192. Gruselle M, Cordier C, Salamin M, El Amour H, Vaisserman J, Jaouen G. Organometallics 1990;9:2993–7. 193. Crabtree RFH. The organometallic chemistry of the transition metals. 4th ed. Hoboken, NJ: Wiley-Interscience; 2005. 194. Lal K, Leckey NT, Watts WE, Bunton CA, Mhala MM, Moffat JR. J Chem Soc Perkin Trans 2 1988;1091–7. 195. Ritchie CD, Virtanen POI. J Am Chem Soc 1972;94:4963–5. 196. Mayr H, Muller KH, Ofial AR, Buhl M. J Am Chem Soc 1999;121:2418–24. 197. Galvin M, Guthrie JP, McDonnell CM, More O’Ferrall RA, Pelet S. J Am Chem Soc 2009;131:34–5. 198. Busetto L, Angelici RJ. Inorg Chim Acta 1968;2:391–94. 199. Brown DA, Fitzpatrick NJ, Glass WK, Sayal PK. Organometallics 1984;3:1137– 44. 200. Dombek BD, Angelici RJ. Inorg Chim Acta 1973;7:345–7. 201. Bernasconi CF. Adv Phys Org Chem 2002;37:137–237. 202. Arduengo AJ, III. Acc Chem Res 1999;32:913–21. 203. Alder RW, Allen PR, Williams SJJ. J Chem Soc Chem Commun 1995;1267–8. 204. Kim Y.-J, Streitwieser A. J Am Chem Soc 2002;124:5757–61. 205. Chu Y, Deng H, Cheng J-P. J Org Chem 2007;72:7790–3. 206. Amyes TL, Diver ST, Richard JP, Rivas FM, Toth K. J Am Chem Soc. 126:4366– 74. 207. Washabaugh MW, Jencks WP. J Am Chem Soc 1989;111:4761–5. 208. Haake P, Bausher LP, Miller WB. J Am Chem Soc 1969;91:1113–9. 209. Heinemann C, Mueller T, Appeloig Y, Schwarz H. J Am Chem Soc 1996;111:683–92. 210. Boehme C, Frenking G. J Am Chem Soc 1996;118:2039–46. 211. Kirmse W. In: Brinker U, editor. Advances in carbene chemistry. London: JAI Press; 2000. pp. 1–51. 212. Dixon DA, Arduengo AJ, III. J Phys Chem A 2006;110:1968–74.

120

R. MORE O’FERRALL

213. Kirmse W, Kilian J, Steenken S. J Am Chem Soc 1990;112:6399–400. 214. Frekel M, Marsh KN, Wilhoit RC, Kabo GJ, Roganov GN. Themodynamics of organic compounds in the gas phase. College Station, TX: Thermodynamics Research Centre, 1994. 215. Fainberg AH, Winstein S. J Am Chem Soc 1956;78:2770–7. 216. Dfietze PE, Jencks WP. J Am Chem Soc 1986;108:4549–55. 217. Bentley TW, Carter GE. J Am Chem Soc 1982;104:5741–7. 218. Raber DJ, Harris JM, Hall RE. J Am Chem Soc 1971;91:4821–8. 219. Richard JP, Toteva MM, Crugeiras J. J Am Chem Soc 2000;122:1664–74. 220. Toteva MM, Richard JP. J Am Chem Soc 2000;122:11073–83. 221. Richard JP, Amyes TL, Bei L, Stubblefield V. J Am Chem Soc 1990;112:9513–9. 222. Pham TV, McClelland RA. Can J Chem 2001;79:1887–97. 223. Amyes TL, Richard JP. J Am Chem Soc 1990;112:9507–12. 224. Richard JP. J Am Chem Soc 1991;113:4588–95. 225. Jagannadham V, Amyes TL, Richard JP. J Am Chem Soc 1993;115:8465–6. 226. Richard JP, Amyes TL, Jagannadham V, Lee Y-G, Rice DJ. J Am Chem Soc 1995;117:5198–205. 227. Marcus RA. J Phys Chem 1968;72:891–9. 228. Lewis ES, Shen CS, More O’Ferrall RA. J Chem Soc Perkin Trans 2 1981; 1084–8. 229. Richard JP, Williams KB. J Am Chem Soc 2007;129:6952–61. 230. Amyes TL, Stevens IW, Richard JP. J Org Chem 1993;58:6057–66. 231. Richard JP. J Org Chem 1994;59:25–9. 232. Richard JP. J Am Chem Soc 1989;111:1455–65. 233. Bernasconi CF. Adv Phys Org Chem 1992;27:119–238. 234. Kresge AJ. Can J Chem 1974;52:1897–903. 235. Bordwell FG, Boyle WJ, Jr. J Am Chem Soc 1972;94:3907–11. 236. Bunting JW, Stefanidis D. J Am Chem Soc 1989;111:5834–9. 237. Yamataka H, Nagase S. J Org Chem 1988;53:3232–8. 238. Schindele C, Houk KN, Mayr H. J Am Chem Soc 2002;124:11208–14. 239. Glasstone S, Laidler KJ, Eyring H. Theory of rate processes. New York: McGraw Hill; 1941. 240. Perdoncin J, Scorrano G. J Am Chem Soc 1977;99:6983–6. 241. McClelland RA, Mathivanan N, Steenken S. J Am Chem Soc 1990;112:4857–61. 242. McClelland RA, Chan C, Cozens FL, Modro A, Steenken S. Angew Chem Int Ed 1991;30:1337–9. 243. Guthrie JP, Pitchko V. J Phys Org Chem 2004;17:548–59. 244. Caldin EF, Gold V, editors. Proton transfer reactions. London: Chapman & Hall; 1973. 245. Stewart R. The proton: applications to organic chemistry. Orlando, FL: Academic Press; 1985. 246. Richard JP, Williams KB, Amyes TL. J Am Chem Soc 1999;121:8403–4. 247. Hegarty AF, Wolfe VE. ARKIVOC 2008; 161–82. 248. Creary X, Hatoum HN, Barton A, Aldridge TE. J Org Chem 1992;57:1887–97. 249. Amyes TL, Mizersi T, Richard JP. Can J Chem 1999;77:922–33. 250. McClelland RA, Kanagasabapathy VM, Steenken S. J Am Chem Soc 1988;110:6913–4. 251. Minegishi S, Loos R, Kobayashi S, Mayr H. J Am Chem Soc 2005;127:2641–9. 252. Ritchie CD, VanVerth JE, Ting JY. J Am Chem Soc 1983;105:279–84. 253. Phan TB, Breugst M, Mayr H. Angew Chem Int Ed 2006;45:3869–74. 254. Swain CG, Scott BS. J Am Chem Soc 1953;75:846–8. 255. Pearson RG, Sobel H, Songstad J. J Am Chem Soc 1968;90:319–26. 256. Raber DJ, Harris JM, Hall RE, Schleyer PvR. J Am Chem Soc 1971;93:4821–8.

STABILITIES AND REACTIVITIES OF CARBOCATIONS

121

257. Pross A. Adv Phys Org Chem 1977;14:69–132. 258. Hammond GS. J Am Chem Soc 1955;77:334–8. 259. Argile A, Carey ARE, Fukata G, Harcourt M, More O’Ferrall RA, et al. Isr J Chem 1985;26:303–12. 260. Bell RP. The proton in chemistry. 2nd ed. London: Chapman & Hall; 1973. 261. Bell RP, Lidwell OM. Proc Roy Soc A 1940;176:88–113. 262. Kresge AJ. Chem Soc Rev 1973;2:475–504. 263. Jencks WP. Chem Rev 1985;85:511–27. 264. Alavosus TJ, Sweigart DA. J Am Chem Soc 1985;107:985–7. 265. TaShma R, Rappoport Z. J Am Chem Soc 1983;105:6082–95. 266. Minegishi S, Mayr H. J Am Chem Soc 2003;125:286–95. 267. Mayr H, Kuhn O, Gotta MF, Patz M. J Phys Org Chem 1998;11:642–54. 268. Mayr H, Schneider R, Grabis U. J Am Chem Soc 1990;112:4460–67. 269. Mayr H, Patz M. Angew Chem Int Ed 1994;33:938–57. 270. Mayr H, Schneider R, Schade C, Bartl J, Bederke R. J Am Chem Soc 1990;112:4446–54. 271. Mayr H, Bartl J, Hagen G. Angew Chem Int Ed 1992;31:1613–5. 272. Mayr H, Bug T, Gotta MF, Hering N, Irrgang B, Janker B, et al. J Am Chem Soc 2001;123:9500–12. 273. Burfeindt J, Patz M, Muller M, Mayr H. J Am Chem Soc 1998;120:3629–34. 274. Mayr H, Gorath G. J Am Chem Soc 1995;117:7862–8. 275. Lucius R, Mayr H. Angew Chem Int Ed 2000;39:1995–7. 276. Bug T, Lemek T, Mayr H. J Org Chem 2004;69:7565–76. 277. Kaumanns O, Lucius R, Mayr H. Chem Eur J 2008;14:9675–82. 278. Appel R, Loos R, Mayr H. J Am Chem Soc 2009;131:704–14. 279. Richard JP, Szymanski P, Williams KB. J Am Chem Soc 1998;120:10372–8. 280. Lucius R, Loos R, Mayr H. Angew Chem Int Ed 2002;41:92–95. 281. Ofial AR, Mayr H. Macromol Symp 2004;215:353–67. 282. Wurthwein EU, Lang G, Schaple LH, Mayr H. J Am Chem Soc 2002;124:4084– 92. 283. Mayr H, Lang G, Ofial AR. J Am Chem Soc 2002;124:4076–83. 284. Richler D, Mayr H. Angew Chem Int Ed 2003;48:1958–61. 285. Brotzel F, Mayr H. Org Biomol Chem 2007;5:3814–20. 286. Phan TB, Mayr H. J Phys Org Chem 2006;19:706–13. 287. Brotzel F, Chu YC, Mayr H. J Org Chem 2007;72:3679–88. 288. Minegishi S, Kobayashi S, Mayr H. J Am Chem Soc 2004;126:5174–81. 289. Tsuno Y, Fujio M. Adv Phys Org Chem 1999;34:267–385. 290. Hofmann M, Hampel N, Kanzian T, Mayr H. Angew Chem Intl Ed 2004;43:5402–5. 291. Westmaier H, Mayr H. Org Lett 2006;8:4791–9. 292. Westmaier H, Mayr H. Chem Eur J 2008;14:1638–47. 293. McClelland RA, Cozens FL, Li J, Steenken S. J Chem Soc Perkin Trans 2, 1996; 1531–43. 294. Pross A. Theoretical and physical principles of organic reactivity. New York: Wiley; 1995, p. 232. 295. Kevill DN. In: Charton M, editor. Advances in structure-property relationships. Greenwich: JAI; 1996. pp. 81–115. 296. Baidya M, Kobayashi S, Brotzel F, Schmidhammer U, Riedle E, Mayr H. Angew Chem Intl Ed 2007;46:6176–9. 297. Lakhdar S, Tokuyasu T, Mayr H. Angew Chem Int Ed 2008;47:8723–6. 298. Ofial AR, Mayr H. Macromol Symp 2004;215:4076–83. 299. Nolte C, Phan TB, Kobayashi S, Mayr H. J Am Chem Soc 2009;131:11392–401.

122

R. MORE O’FERRALL

300. Denegri B, Ofial AR, Juric S, Streiter A, Kronja O, Mayr H. Chem Eur J 2006;12:1648–56, 1657–66. 301. Marcus RA. J Am Chem Soc 1969;91:7224–5. 302. McClelland RA, Kanagasabapathy VM, Banait NS, Steenken S. J Am Chem Soc 1992;114:1816–23. 303. Berg U, Jencks WP. J Am Chem Soc 1991;113:6997–7002. 304. McClelland RA. J Am Chem Soc 1989;111:2929–35. 305. Richard JP, Amyes TL, Vontor T. J Am Chem Soc 1992;114:5626–34. 306. Bernasconi CF, Killon RB. J Am Chem Soc 1988;110:7506–12. 307. Bernasconi CF, Ketner RJ, Chen X, Rappoport Z. J Am Chem Soc 1998;120:7461–8. 308. Gajewski JJ. J Am Chem Soc 1979;101:4393–4. 309. Gajewski JJ. Acc Chem Res 1980;13:142–8.