Reactive Intermediate Chemistry

a Rate constants in bold have been measured using nanosecond LFP. Others require picosecond LFP. (An ¼ 4-methoxyphenyl.)

As a final comment there is the question whether the cation observed with LFP is the same as the one produced in a ground-state reaction. With nanosecond LFP, the time interval from excitation to observation is likely sufficient to ensure that this is the case. Two pieces of evidence can be cited. (1) There is a good correspondence of ultraviolet–visible (UV–vis) spectra for the transient cations with ones obtained for solutions of ground-state cations under strongly acidic solutions. (2) Ratios of rate constant obtained directly by LFP agree with selectivities measured for the ground-state reactions. Diffusional separation of ion pairs is complete within 1– 10 ns,62 so that a transient cation observed with nanosecond LFP is a free ion. At shorter times, that is, in picosecond LFP, ion pairs can be observed and their dynamics studied.62

3.5. Lifetimes of Carbocations in Protic Solvents

Table 1.3 provides rate constants for the decay of selected carbocations and oxocarbocations in H2O, TFE, and HFIP. As a general comment, water, methanol, and ethanol are highly reactive solvents where many carbocations that are written as free cations in standard textbooks have very short lifetimes. The diphenylmethyl cation, with two conjugating phenyl groups, has a lifetime in water of only 1 ns. Cations such as the benzyl cation,63 simple tertiary alkyl cations such as tertbutyl,64 and oxocarbocations derived from aldehydes65 and simple glycosides,66 if they exist at all, have aqueous lifetimes in the picosecond range, and do not form and react in water as free ions. This topic is discussed in more detail in Chapter 2 in this volume.

Lifetimes are longer in the more weakly nucleophilic TFE and HFIP, and cations whose existence is on the borderline in water and simple alkanols can become quite long lived, especially in HFIP. Benzenium ions such as protonated mesitylene can also be observed in HFIP, and there is an estimate for a simple secondary cation 77.60 There is one estimate of the lifetime of an acylium ion (72), based upon the clock approach.67 Even with the powerful electron-donor 4-Me2N on the aromatic ring, this cation appears to be very short lived in water.

The sþ substituent constant scale was developed based upon the solvolysis of substituted cumyl chlorides, where cumyl cations are formed in the rate-determin- ing ionization. For the carbocation-forming reaction of Eq. 20, there is a good correlation of log kH versus the sum of the sþ constants for the substituents directly on the carbon.68 Such a correlation clearly does not exist for the reaction where the

22 CARBOCATIONS

TABLE 1.3. Solvent Reactivities of Selected Carbocations at 20 C

cations react with solvent.69 This finding is dramatically demonstrated by comparing the triphenylmethyl cation 60, sþ ¼ 0:51, with the dialkoxycarbocation 55, which is two orders of magnitude more reactive despite having sþ ¼ 1:6.

Even for a series with varying aromatic substituents, the correlations with sþ deviate significantly from linearity. Typical behavior is illustrated with data for monosubstituted triarylmethyl cations in Figure 1.2. Significant deviations are observed in the points for the para p donors. Moreover, these deviations are in the direction that indicates that these substituents have kinetic stabilizing effects greater than indicated by sþ. In fact, there are good correlations with sCþ, a parameter based on 13C NMR chemical shifts of benzylic-type cations obtained under stable ion conditions.70

This equation was originally introduced for systems where the interactions lie between those of the two reactions that define the s and the sþ scales with the parameter rþ intended to lie between 0 and 1. However, log kw (and pKR) require rþ values significantly >1 (Table 1.4), which is consistent with the idea that sþ underestimates the effect of para p donors on reactions of fully formed cations. The rate constants for the cation-forming reaction of Eq. 1 ðlog kHÞ on the other hand correlate with rþ slightly <1. In other words, these show a reasonable correlation with sþ, which is not surprising since both kH and sþ refer to rate constants of reactions forming carbocations.

TABLE 1.4. Results of Fitting to Two Parameter

Eqs. 21 and 22

The two-parameter equation suggested by Jencks and co-workers47b (Eq. 22) separates substituent effects into a polar or inductive contribution described by rn and a resonance contribution described by rr .

Where both rate and equilibrium constants are known, ‘‘normalized’’ r values

ðrnormÞ are defined as the ratios rnðkwÞ=rnðKRÞ and rrðkwÞ=rrðKRÞ. Since the value of rðKRÞ measures the overall substituent effect on proceeding from reagent to pro-

duct, rnorm measures the fraction that has occurred at the transition state. As seen in Table 1.4, rn(norm) in the direction of cation hydration, is significantly <0.5, whereas rr(norm) is >0.5. The inequality means that there is imbalance in the transition state. When comparing the transition state to starting carbocation, the substituent ‘‘sees’’ a much larger fractional decrease in positive charge in its resonance interaction as compared to the decrease that it ‘‘sees’’ through the polar interaction. This imbalance is shown schematically in Scheme 1.6 where the numbers represent the charges experienced by the substituent normalized to þ1 in the cation and 0 in the alcohol. A simple explanation is that the incoming water nucleophile has pyramidalized the alpha carbon, so that the resonance interaction has considerably diminished by the time the transition state is reached. There is still substantial positive charge at the alpha carbon, however, so that the polar interaction is still quite strong. For the reverse direction where the cation is forming, the transition state is well developed with respect to the polar interaction, but now the resonance interaction lags behind. For the latter reason, it is not surprising that the sþ substituent scale based upon rate constants for carbocation formation considerably underestimate the full conjugative effect of the aryl substituents.

Scheme 1.6

3.7. Reactivity with Added Nucleophiles

Rate constants for the reactions of carbocations with added nucleophiles are obtained in LFP experiments as the slopes of linear plots of first-order rate constants for cation decay against the concentrations of added nucleophile. One of the first detailed studies using LFP showed that rate constants for the parent triphenylmethyl cation did not adhere to the simple Ritchie Nþ relation of Eq. 13, but that the slope of a plot of log kNu versus Nþ was significantly <1.73 This finding has been verified

28 CARBOCATIONS

in HFIP generates 71, observed with LFP at lmax ¼ 325 nm. The cation reacts with the styrene not consumed in the photolysis with kinit ¼ 1 109 M 1s 1. As the absorbance due to 71 decreases at 325 nm, the absorbance of the dimer cation 83, lmax ¼ 345 nm, is observed to grow in at higher wavelengths. This absorbance is considerably more stable, decaying only on the milliseconds time scale. In both reactivity and lmax, the dimer 83 is very similar to the propagating cation 84 observed in stopped-flow experiments, where kprop has been measured as 1 105 M 1s 1.80 Thus, the monomer 71 has a lower lmax and reacts four orders of magnitude more quickly than the dimer and oligomer cations 83 and 84. One possible explanation is that the latter cations are stabilized by a charge-transfer interaction with the nearby phenyl ring, as depicted in Scheme 1.8.

TABLE 1.5. Electrophilicity and Nucleophilicity Parametersa

a Data from Ref. 81c.

b Reacts by hydride transfer.

3.8. Mayr’s Scales of Electrophilicity and Nucleophilicity

In a series of reports published over the last 10–15 years, Mayr and co-workers81 obtained second-order rate constants for reactions of carbocations and other electrophiles such as metal–p complexes with a series of nucleophiles, especially p-nucleophiles where a C C bond is formed. An impressive body of reactivity data has been accumulated, and, including data from other groups, correlated by the following equation,

where k is the second-order rate constant for the electrophile–nucleophile combination, E is the electrophilicity parameter, N is the nucleophilicity parameter, and s is the nucleophile-dependent slope parameter. Values of these parameters for selected electrophiles and nucleophiles are provided in Table 1.5. Equation 24 takes the same form as the Ritchie equation, Eq. 13, with the addition of the s parameter. It can be seen that s lies in a narrow range around unity; a value of 1 converts Eq. 24 into Eq. 13, and indeed many of the systems investigated by the Mayr group display a constant selectivity with changing reactivity. The Mayr correlation now covers a reactivity range of 30 orders of magnitude in both electrophiles and nucleophiles. The equation reproduces rate constants within a factor of 10–100, excluding reagents of steric bulk such as trityl cations. It has the power of predicting with reasonable precision the rate constant for a particular combination of cation and electrophile, and thus is of value in organic synthesis.

4. MISCELLANEOUS TOPICS

4.1. Carbocations with Electron-Withdrawing Substituents

There has been considerable interest in benzylic cations in which the a-carbon bears an electron-withdrawing group such as CN, CF3, or COR. Originally, these cations were investigated in the context of solvolysis reactions. Despite large rate decreases associated with the substitution of the electron-withdrawing group, a cationic intermediate was still proposed.82 This result has been verified by azideclock experiments, which have suggested that the cation has a similar lifetime to analogues without the electron-withdrawing group.83 The LFP studies have provided absolute rate constants.84 Representative values are given in Table 1.6.

Taking the comparison of 67 and its a-CF3 analogue 85 as the example (Eq. 25), a 107–109 difference is observed in the rate constants kfor for formation of the cations, but there is virtually no difference in the rate constants krev for their reactions with nucleophiles. In other words, the a-CF3 cation is considerably less stable

in the thermodynamic sense but of comparable stability in the kinetic sense. This finding has been explained83b,85 by a model separating the substituent effects into

polar and resonance contributions. The polar effect, which substantially destabilizes

30 CARBOCATIONS

TABLE 1.6. Rate Constants for Decay of Cations with

Electron-Withdrawing Substituents

the CF3-substituted cation, dominates the equilibrium and is responsible for the thermodynamic destabilization. The polar effect, however, is partially compensated by a increased resonance stabilization in the CF3-substituted cation due to the greater importance of the quinonoid resonance contributor 85b as the positive charge is moved away from the electron-withdrawing CF3 group. Evidence for the importance of this resonance contributor is the observation that a-CF3-substituted cations show the highly unusual feature of reacting with nucleophiles at the para position of the benzene ring. As has been discussed in Section 3.6, there is an imbalance in the transition state for a cation–nucleophile combination, with a substantial loss of the resonance interaction at the transition state, but less of a change in the polar interaction. With the greater importance of the latter on the overall equilibrium, it is argued that the opposing changes in resonance and polar effects almost cancel, with the result that the effects on krev are small.

In Table 1.6, it can be seen that the relative kinetic stability of the cation substituted with an electron-withdrawing group is also found in comparing cations 89 and 90 where the para position is substituted by a methyl group. Other cations of interest are those substituted with an a-thioamido group such as 88. These exhibit a substantial kinetic stabilization. The reasons for this are not entirely clear at this time. One suggestion is that there is stabilization by a bridging interaction with the C S group.

4.2Silyl Cations

This section provides a discussion of R3Siþ, the silicon analogue of the carbenium ion. While such species do exist in the gas phase, their existence in condensed