Reactive Intermediate Chemistry

42 CROSSING THE BORDERLINE BETWEEN SN1 AND SN2 NUCLEOPHILIC SUBSTITUTION

formation occur as separate events, or by a concerted mechanism in which they take place in a single reaction stage.1 Hughes and Ingold first showed that aliphatic nucleophilic substitution with a zero-order dependence of rate on nucleophile (Nu) concentration (SN1) is favored when the carbocation intermediate is strongly stabilized by electron-donating substituents.2 Conversely, nucleophilic substitution with a first-order dependence on nucleophile concentration (SN2) is favored when this mechanism avoids the formation of the unstable intermediate of the stepwise reaction2 (see Scheme 2.1).

Scheme 2.1

Similar qualitative relationships between reaction mechanism and the stability of the putative reactive intermediates have been observed for a variety of organic reactions, including alkene-forming elimination reactions,3 and nucleophilic substitution at vinylic4 and at carbonyl carbon.5 The nomenclature for reaction mechanisms has evolved through the years and we will adopt the International Union of Pure and Applied Chemistry (IUPAC) nomenclature6 and refer to stepwise substitution (SN1) as DN þ AN (Scheme 2.1A) and concerted bimolecular substitution (SN2) as ANDN (Scheme 2.1B), except when we want to emphasize that the distinction in reaction mechanism is based solely upon the experimentally determined kinetic order of the reaction with respect to the nucleophile.

While the mechanistic imperatives are clear for the ‘‘limiting’’ cases of stepwise nucleophilic substitution through stable carbocation intermediates and concerted bimolecular substitution that avoids the formation of unstable intermediates, a more difficult question is how to model the transition across the borderline between mechanisms where the carbocation intermediate is unstable, but the advantage to a concerted substitution is only beginning to become significant. The term ‘‘borderline’’ implies the existence of a line separating DN þ AN from ANDN nucleophilic substitution reactions, whose position depends, in some sense, on the lifetime of the reaction intermediate. It has been argued that nucleophilic aliphatic substitution generally occurs by a stepwise (DN þ AN) reaction mechanism when the carbocation intermediate exists in an energy well for at least the time of a bond vibration ( 10 13 s); and, that the change to an ANDN mechanism is ‘‘enforced’’ by the disappearance of the energy well for the reaction intermediate (Fig. 2.1). This crossover between mechanisms places the borderline at the point where the lifetime of

the intermediate in the presence of the incoming nucleophile is close to the vibrational limit of 10 13 s.1

This notion that reaction mechanisms are strictly enforced by the intermediate lifetime implies the existence of a narrow borderline region and a sharp change in reaction mechanism with changing lifetime of the carbocation intermediate. However, a narrow borderline region is not observed in all cases. The problem is

INTRODUCTION 43

Figure 2.1. One-dimensional (1D) free energy reaction coordinate profiles that show the DN þ AN reaction mechanism through a carbocation intermediate and the change to an ANDN reaction in which the intermediate is too unstable to exist in an energy well for the time of a bond vibration.

in part semantic. A borderline between reaction mechanisms may be defined with some rigor by the intermediate lifetime, which determines whether its existence in an energy well is possible. On the other hand, the term ‘‘borderline reaction’’ is less rigorous and generally refers to reactions whose observable properties are in some way intermediate between stepwise and concerted. We will define a borderline reaction as one that apparently proceeds through a ‘‘hot’’, unstable, carbocation ‘‘intermediate’’ that shows a small selectivity for reaction with added nucleophiles, so that the yield of the nucleophilic substitution product is very low and it is not possible to determine whether the substitution reaction is kinetically zero-order (SN1) or first-order (SN2) in nucleophile concentration. Such reactions generally show other borderline properties, including internal return of ion pair reaction intermediates,7 and reaction with an excess of inversion or retention of configuration at carbon.8–10 The intermediates of borderline reactions are clearly unstable and their lifetimes may lie close to the vibrational limit ( 10 13 s), which marks the borderline between DN þ AN and ANDN. However, there is no strict requirement that crossing this rigorously defined borderline will result in the appearance of a kinetically significant bimolecular reaction of the nucleophile. Sometimes this is observed, but in other cases it is not, for reasons that will be discussed in this chapter.

44 CROSSING THE BORDERLINE BETWEEN SN1 AND SN2 NUCLEOPHILIC SUBSTITUTION

2. NUCLEOPHILIC SUBSTITUTION OF AZIDE ION AT BENZYLIC CARBON

2.1. Introduction

The benzylic substrates X-1-Y and X-2-Y have provided a useful platform for examining the changes in reaction mechanism for nucleophilic substitution that occur as the lifetime of the carbocation intermediate is decreased systematically by varying the metaand paraaromatic ring substituents. When X is strongly resonance electron-donating, X-1-Y and X-2-Y react by a stepwise DN þ AN mechanism through carbocation intermediates with significant and known lifetimes. The change from a strongly electron-donating (4-Me2N) to an electron-withdrawing (3,5-di-CF3) ring substituent X results in a 30 kcal/mol increase in the thermodynamic barrier to substrate ionization to form the corresponding benzylic carbocation reaction intermediate, through a combination of resonance and polar substituent effects. This series allows for a thorough examination of the changes

in reaction mechanism that occur as the lifetime of the putative carbocation intermediate reaches the limiting value of the time for a bond vibration.11–16

2.1.1. Ring-Substituted 1-Phenylethyl Derivatives. Figure 2.2 (* and *) shows that there is a sharp change from a stepwise to a concerted mechanism for nucleophilic substitution of azide ion at 1-phenylethyl derivatives (X-1-Y) in 50:50 (v/v) water/trifluoroethanol as X is changed from strongly electron donating to electron withdrawing.12,15 This change in mechanism gives rise to a narrow minimum in the V-shaped plot

of the nucleophile selectivity for azide ion and solvent determined from product

analysis [ðkaz=ksÞobsd, M 1, Eq. 1], against the Hammett ring substituent constant for X, sþ, or s (Fig. 2.2).12,15 When X is strongly electron donating (sþ 0:32, *)

the formation of X-1-N3 from reaction of X-1-Y is zero order in [N3 ], and the pro-

duct selectivity ðkaz=ksÞobsd ðM 1Þ is independent of the leaving group Y . By contrast, the product X-1-N3 of the reaction of azide ion with X-1-Cl forms exclusively

by a reaction that is first order in [N3 ] when X is electron withdrawing

Figure 2.2. The change with changing aromatic ring substituent X in the azide (az) ion selectivities ðkaz=ksÞobsd (M 1) determined by analysis of the products of the reactions of ring-substituted 1-phenylethyl derivatives (X-1-Y) and ring-substituted cumyl derivatives (X-2-Y) in 50/50 (v/v) water/trifluoroethanol at 25 C.15,16 The selectivities are plotted against the appropriate Hammett substituent constant sþ or s for the aromatic ring substituent. The lifetimes 1/ks (s) of the carbocations X-1þ, determined either directly using the azide ion clock or estimated by extrapolation of a linear free energy Hammett relationship, are given along the top of this figure. The lifetimes of the carbocations X-2þ are about fourfold longer than those of the corresponding X-1þ. Key: (*) reactions of X-1-Y (Y ¼ Cl or ring-substituted benzoate) that are kinetically zero order with respect to azide ion; (*) reactions of X-1-Cl that are kinetically first order with respect to azide ion; (&) reactions of X-2-Y (Y ¼ Cl or ring-substituted benzoate) that are kinetically zero order with respect to azide ion.

(sþ 0:08, Fig. 2.2, m),13 which shows that there is a single rateand productdetermining step for these reactions (see Eq. 1). The possibility that this rate-deter- mining step involves collapse of an ion pair or triple ion intermediate to product was considered, but was excluded by several lines of experimental evidence that showed that these kinetically bimolecular reactions of X-1-Y proceed by a concerted mechanism.13

The descending product selectivities ðkaz=ksÞobsd (M 1) on the left-hand limb of Figure 2.2 (*) for the stepwise reactions of X-1-Y(Scheme 2.2) are due to the

increase in the value of ks (s 1), with decreasing stability of the carbocation inter-

mediate X-1þ, relative to the constant value of kaz (M 1 s 1) for the diffusionlimited reaction of azide ion.12,15 The lifetimes 1/ks in the top left half of

Figure 2.2 for addition of solvent to X-1þ ðsþ 0:32Þ were calculated from

ðkaz=ksÞobsd (M 1) for partitioning of X-1þ and kaz ¼ 5 109 M 1 s 1 for the diffusion-limited reaction of azide ion.15 There is good agreement between

46 CROSSING THE BORDERLINE BETWEEN SN1 AND SN2 NUCLEOPHILIC SUBSTITUTION

R1

XC6H4C N3

R2

Scheme 2.2

ks (s 1) for (4-MeO)-1þ calculated by the ‘‘azide ion clock’’,15 and the value determined directly by monitoring the disappearance of (4-MeO)-1þ generated by laser flash photolysis.17 The lifetimes of X-1þ in the top right half of Figure 2.2 (sþ 0:08) were estimated by extrapolation of the excellent linear logarithmic correlation of 1/ks with the Hammett substituent constant for X for sþ 0:32.15

The break to the ascending right-hand limb in Figure 2.2 (m, sþ 0:08) marks the appearance of a concerted bimolecular substitution reaction of azide ion with X-1-Y, with a second-order rate constant kNu (Scheme 2.2). There is a very narrow borderline between the kinetically SN1 and SN2 nucleophilic substitution reactions of X-1-Cl ( 0:32 sþ 0:08, Fig. 2.2). The increasing product selectivities ðkaz=ksÞobsd observed as the transition states for nucleophilic substitution of solvent and azide ion at X-1-Cl are destabilized by electron-withdrawing X (sþ 0:08) reflect the partial neutralization by azide ion of the developing positive charge in the transition state for bimolecular nucleophilic substitution, [X-1-N3]z. This results in a 2.7-unit more positive Hammett reaction constant for concerted bimolecular nucleophilic substitution by azide ion, rNu ¼ 2:9, com-

pared with rsolv ¼ 5.6 for the stepwise solvolysis of X-1-Cl.13

In the presence of solvent alone, the lifetime of the intermediate of the stepwise

reaction of X-1-Y in the narrow borderline between the SN1 and SN2 substitution reactions of azide ion ( 0:32 sþ 0:08, Fig. 2.2) is 1=ks ¼ 10 10 s.15

Azide ion is 106–107-fold more reactive than water toward triarylmethyl carbocations and related electrophiles, and this selectivity is independent of carbocation reactivity, so long as the reactions of both azide ion and solvent are limited by

Scheme 2.3

the rate constant for chemical bond formation.18,19 However, an azide ion selectivity of kaz=ks ¼ 106 M 1 cannot be maintained across this sharp borderline, because this would require an impossibly large rate constant of ki 1016 s 1 for collapse of the triple ion complex N3 (4-F)-1þ Cl (sþ ¼ 0:08 for 4-F) to product (Scheme 2.3). In fact, (4-F)-1þ is unlikely to exist for the time of a bond vibration (10 13 s) in the presence of azide ion because this would require a difference in the chemical barriers for the reaction of azide ion and solvent of only 4 kcal/mol, which is smaller than the 6 kcal/mol difference observed for a wide variety of carbocation-azide ion addition reactions. It was concluded that the concerted mechanism for the reaction of azide ion with X-1-Y (sþ 0:08) is probably ‘‘enforced’’ because, in the presence of azide ion, the putative carbocation intermediate X-1þ cannot exist in an energy well.13 We will return to Scheme 2.3 in Section 2.3.1.

2.1.2. Ring-Substituted Cumyl Derivatives. In contrast with the sharp change in the kinetic order for nucleophilic substitution of azide ion at 1-phenyl- ethyl derivatives with changing aromatic ring substituent X (Fig. 2.2), there is no corresponding change from SN1 to SN2 nucleophilic substitution of azide ion at ring-substituted cumyl derivatives (X-2-Y) (Fig. 2.2, &).16 The product selectiv-

ities ðkaz=ksÞobsd, (M 1, Eq. 1) for reactions of X-2-Y in 50:50 (v/v) water/trifluoroethanol decrease from ðkaz=ksÞobsd ¼ 380 to 0.7 M 1 as the ring substituent X is changed from electron donating (4-MeO, sþ ¼ 0:79) to weakly electron with-

drawing (3-MeO, s ¼ 0:12). This selectivity then remains almost constant as X

is changed to strongly electron withdrawing (3,5-di-CF3, s ¼ 1.08). In all cases, the observed first-order rate constant, kobsd (s 1), for the reaction of X-2-Y is independent of [N3 ]. However, throughout the broad region of minimum selectivity,

where ðkaz=ksÞobsd ¼ 0:7 M 1 (Fig. 2.2, &), it is possible that small increases in kobsd due to concerted nucleophilic substitution by azide ion are masked by com-

pensating decreases due to a specific azide ion salt effect.16 The reaction mechanism in this region is borderline, because it is not known whether the formation of X-2-N3 is kinetically zero-order (SN1) or first-order (SN2) with respect to azide ion.

48 CROSSING THE BORDERLINE BETWEEN SN1 AND SN2 NUCLEOPHILIC SUBSTITUTION

The addition of an a-Me group to X-1þ to give X-2þ results in a threeto four-

times, 1/ks, for X-2þ are only threeto fourfold longer than those of the corresponding 1-phenylethyl carbocations;15–17 and an extrapolation of a good linear relationship between log 1/ks for addition of solvent to X-2þ and sþ for X ðsþ 0:08Þ gives a lifetime of 1=ks 10 13 s for (3,5-di-CF3)-2þ. The lifetimes of X-2þ in the presence of azide ion must be even shorter than the lifetime in the presence of solvent alone, and they should reach the vibrational limit of 10 13 s as X-2þ is destabilized by strongly electron-withdrawing X. However, in this case there is no break to an ascending limb in Figure 2.2 due to the appearance of a concerted bimolecular nucleophilic substitution reaction of azide ion with X-2-Y as is observed for X-1-Y. Rather, a broad borderline region for the reaction of azide ion with X-2-Y is observed.

Students of reaction mechanism will recognize intuitively that the difference between the narrow and broad borderline regions observed for nucleophilic substitution of azide ion at secondary and tertiary carbon (Fig. 2.2) is due to the greater steric hindrance to bimolecular nucleophilic substitution at the tertiary carbon.2 This leads to a large difference in the effects of an a-Me group on ksolv (s 1) for the stepwise solvolysis and kNu (M 1 s 1) for concerted bimolecular nucleophilic substitution reactions of X-2-Y. The barriers to solvolysis and the reaction of 1 M azide ion with (4-F)-1-Cl (sþ ¼ 0:08 for 4-F) are similar, because the addition of 1 M azide ion results in about a doubling of kobsd (s 1) in 50:50 (v/v) water/trifluoroethanol and the reaction gives a 50% yield of (4-F)-1-N3.13 Now, the addition of an a-Me group to (4-F)-1-Cl to give (4-F)-2-Cl will stabilize the cationic transition state for the stepwise solvolysis reaction (ksolv), but will lead to a relative destabilization of the transition state for bimolecular nucleophilic substitution of azide ion (kNu), due to the increased steric crowding. The result is that ksolv kNu½N3 & for the reaction of (4-F)-2-Cl, and the formation of (4-F)-2-N3 occurs mainly by nucleophile trapping of the carbocation intermediate of a stepwise reaction.16 A change to a ring substituent X that is more electron withdrawing than 4-F will further destabilize (4-F)-2þ, and will favor concerted nucleophilic substitution that avoids formation of the unstable putative intermediate X-2þ. However, the resistance of tertiary carbon to formation of the pentavalent transition state for concerted nucleophilic substitution is so great that kNu for the concerted reaction remains much smaller than ksolv, even when X is strongly electron withdrawing and X-2þ is highly unstable.

2.2. More O’Ferrall Diagrams

Two-dimensional (2D) More O’Ferrall reaction coordinate diagrams (Fig. 2.3) are helpful in rationalizing the differences in the borderline regions for nucleophilic substitution at X-1-Y and X-2-Y that are illustrated by the data in Figure 2.2. These

50 CROSSING THE BORDERLINE BETWEEN SN1 AND SN2 NUCLEOPHILIC SUBSTITUTION

diagrams utilize separate coordinates to show cleavage of the bond to the leaving group Y (x axis, Fig. 2.3) and formation of the bond to the incoming nucleophilic reagent Nu (y axis, Fig. 2.3). Figure 2.3 also includes the microscopic rate and association constants defined in Scheme 2.4. Note that the encounter between Rþ Y and Nu to form a triple ion intermediate (kd, Scheme 2.4) is not shown on this diagram. This reaction is a minor pathway for formation of the nucleophilic substitution product in the polar solvent water,20 because diffusion-controlled trapping ðkd 5 109 M 1 s 1) is unable to compete effectively with the fast diffusional separation of the ion pair to the free ions (k d 1:6 1010 s 1).14

Figure 2.3 may be used to illustrate the following progression in pathways for nucleophilic substitution at X-1-Y and X-2-Y with changes in the lifetime of the respective carbocation reaction intermediates.13,16,20

2.2.1. Stepwise Ionization and Trapping of a Liberated Reaction Intermediate. Nucleophilic substitution of azide ion at X-1-Y and X-2-Y by a stepwise reaction mechanism around the ‘‘wings’’ of Figure 2.3 (k1, k d, kT) is strongly favored over the concerted reaction (kcon) when these reactions give carbocation intermediates that are stabilized by electron-donating ring substituents

kT ¼ kd ¼ 5 109 M 1 s 1 for the diffusion-limited trapping of the carbocation by azide ion.

2.2.2. Stepwise Preassociation Reactions. The selectivity kaz=ks (M 1) for trapping of X-1þ by azide ion and solvent decreases with increasing carbocation reactivity (ks), until ks is so large that the direct addition of solvent to the carboca- tion-leaving group ion pair (k0s) is faster than its diffusional separation to the free ions: ks0 k d 1:6 1010 s 1 (Scheme 2.4).14 [The rate constant ks0 for the addi-

tion of aqueous solvents to ion pairs is similar to ks for the addition of solvent to the free carbocation.21,22] At this point there will be essentially no formation of the

nucleophilic substitution product R Nu by trapping of the free carbocation (kT, Scheme 2.4) because the carbocation-leaving group ion pair intermediate is too short lived to undergo separation to the free ions. The formation of R Nu can occur only when the nucleophile is present in a ‘‘preassociation complex’’ with the substrate R Y at the time of its ionization (Kas, Scheme 2.4). This corresponds

to a stepwise preassociation reaction of the nucleophile that runs through the inner upper right hand corner of the diagram in Figure 2.3 (Kas, k10 , and ki, Scheme 2.4).16,23

The yield of the nucleophilic substitution product from the stepwise preassociation reaction mechanism must be small in water, because association complexes between anions and neutral molecules in this solvent are weak (Kas is small). The dominance of this unfavorable reaction pathway is enforced when the competing formation of the nucleophilic substitution product by trapping of the free carbocation intermediate of the stepwise reaction is prevented by the faster direct