A quantitative approach to nucleophilic organocatalysis

The key steps in most organocatalytic cyclizations are the reactions of electrophiles with nucleophiles. Their rates can be calculated by the linear free-energy relationship log k(20 °C) = sN(E + N), where electrophiles are characterized by one parameter (E) and nucleophiles are characterized by the solvent-dependent nucleophilicity (N) and sensitivity (sN) parameters. Electrophilicity parameters in the range –10 < E < –5 were determined for iminium ions derived from cinnamaldehyde and common organocatalysts, such as pyrrolidines and imidazolidinones, by studying the rates of their reactions with reference nucleophiles. Iminium activated reactions of α,β-unsaturated aldehydes can, therefore, be expected to proceed with nucleophiles of 2 < N < 14, because such nucleophiles are strong enough to react with iminium ions but weak enough not to react with their precursor aldehydes. With the N parameters of enamines derived from phenylacetaldehyde and MacMillan’s imidazolidinones one can rationalize why only strong electrophiles, such as stabilized carbenium ions (–8 < E < –2) or hexachlorocyclohexadienone (E = –6.75), are suitable electrophiles for enamine activated reactions with imidazolidinones. Several mechanistic controversies concerning iminium and enamine activated reactions could thus be settled by studying the reactivities of independently synthesized intermediates. Kinetic investigations of the reactions of N-heterocyclic carbenes (NHCs) with benzhydrylium ions showed that they have similar nucleophilicities to common organocatalysts (e.g., PPh3, DMAP, DABCO) but are much stronger (100–200 kJ mol–1) Lewis bases. While structurally analogous imidazolylidenes and imidazolidinylidenes have comparable nucleophilicities and Lewis basicities, the corresponding deoxy Breslow intermediates differ dramatically in reactivity. The thousand-fold higher nucleophilicity of 2-benzylidene-imidazoline relative to 2-benzylidene-imidazolidine is explained by the gain of aromaticity during electrophilic additions to the imidazoline derivatives. O-Methylated Breslow intermediates are a hundred-fold less nucleophilic than deoxy Breslow intermediates.

: Second-order rate constants for reactions of electrophiles with nucleophiles.

Review Introduction
The most comprehensive nucleophilicity and electrophilicity scales presently available, are based on Equation 1, in which electrophiles are characterized by one solvent-independent parameter E, and nucleophiles are characterized by two solventdependent parameters, the nucleophilicity parameter N and the sensitivity parameter s N [1][2][3]. (1) By defining benzhydrylium ions, structurally related quinone methides, and arylidenemalonates as reference electrophiles, which cover a reactivity range of 32 orders of magnitude corresponding to relative reaction times from nanoseconds to 10 15 years, we have been able to compare nucleophiles of widely differing structure and reactivity [4]. As illustrated by Figure 1, this method allows us to characterize strong nucleophiles, such as carbanions and ylides, by their reactivities toward weak electrophiles, and to characterize weak nucleophiles, such as nonactivated alkenes, by their reactivities toward strong electrophiles. Recently we have explicitly outlined the reasons why we prefer Equation 1, a nonconventional version of a linear free-energy relationship, which defines nucleo-philicities as the negative intercepts on the abscissa, over the conventional (mathematically equivalent) linear free-energy relationship depicted in the red frame at the top of Figure 1 [5].

Iminium activated reactions
A key step of the commonly accepted catalytic cycle for iminium activated reactions ( Figure 2) is the attack of a nucleophile 4 on the intermediate iminium ion (3), which can be treated by Equation 1 as indicated in the bottom right of Figure 2 [23][24][25][26][27][28].
In order to predict which nucleophiles 4 are suitable reagents for such transformations because they are strong enough to react with iminium ions 3, but weak enough not to react with  the precursor carbonyl compounds (e.g., 2), it was necessary to determine the reactivity parameters N and s N of potential nucleophilic substrates 4 and the electrophilicity parameters E of iminium ions 3.
Iminium triflates, tetrafluoroborates, or hexafluorophosphates were synthesized as stable salts according to literature procedures [29][30][31][32][33][34][35]. Cinnamaldehyde-derived iminium ions 3 are particularly suitable for kinetic investigations because their reactions with nucleophiles can easily be followed photometrically by monitoring the decay of their absorbance at 370 nm (as exemplified in Figure 3a,b). By using the nucleophiles (for example 7a) in large excess, pseudo-first-order kinetics were achieved, and the first-order rate constants k obs (s -1 ) were derived from the exponential decays of the iminium ions 3 (Figure 3c). Plots of k obs versus the concentrations of the nucleophiles (Figure 3d) were linear, with their slopes giving the second-order rate constants k 2 (M -1 s -1 ) [35,36].
For the investigations of reactions of the iminium ions on the micro-and nanosecond time scale, laser flash spectroscopy was employed [37]. As tertiary phosphines PR 3 (10) are known to be excellent photonucleofuges [38][39][40][41], the stable iminium salts 3-PF 6 were treated with tertiary phosphines 10 at room temperature to give the enamino-phosphonium ions 11 instantaneously ( Figure 4a). Their irradiation with 7 ns laser pulses (266 nm) regenerated the iminium ions, the decay of which was monitored photometrically in the presence of variable concentrations of nucleophiles ( Figure 4b).
As above, the second-order rate constants for the reactions of the iminium ions with nucleophiles were obtained as the slopes of the plots of the first-order rate constants k obs versus the concentrations of the corresponding nucleophiles ( Figure 4c).
The fair correlations of (log k 2 )/s N versus the nucleophilicity parameters N with slopes of unity in Figure 5 indicate the applicability of Equation 1, and is a further evidence that the reactivity parameters N and s N , which are derived from reactions with benzhydrylium ions, also hold for reactions with iminium ions 3.
Analogous experiments showed that the cinnamaldehydederived iminium ions 3a-i cover a reactivity range of five orders of magnitude; the iminium ion 3b, derived from MacMillan's generation II catalyst, turned out to be by far the most reactive one of this series ( Figure 6) [37,42,43].
When comparing the N parameters of substrates previously employed in iminium activated reactions ( Figure 7) [35,42,[44][45][46][47][48][49][50][51][52], one can see that they are characterized by nucleophilicity parameters in the range 2 < N < 14. As Equation 1 describes only one step of the catalytic cycle in Figure 2, we do not claim that N parameters in the indicated range represent a sufficient criterion for the selection of potential substrates in iminium activated reactions. It will be difficult, however, to find suitable nucleophilic substrates outside this range, as stronger nucleophiles will either react with the carbonyl compounds directly or inhibit the formation of the iminium ions due to their high basicity. Weaker nucleophiles, on the other hand, will not be able to attack iminium ions 3; exceptions may be expected for  substrates which undergo concerted pericyclic reactions with the iminium ions and therefore do not follow Equation 1 [53].
In contrast, the reaction of 3a-X with 3-ethyl-2,4-dimethylpyrrole (kryptopyrrole, 12a) was considerably faster when CF 3 CO 2 − was present than when less basic counterions were employed. The acceleration of the reaction by increasing the concentration of CF 3 CO 2 demonstrated that CF 3 CO 2 acted as a general base to deprotonate the Wheland intermediate 13a + and thus suppresses its retroaddition with regeneration of the pyrrole 12a and the iminium ion 3a. Rate constants observed at variable concentrations of CF 3 CO 2 allowed us to calculate the second-order rate constants k 2 for the attack of the iminium ion 3a at the pyrroles 12a-12f, and Figure 9 shows that the observed rate constants agree, within a factor of five, with those calculated by using Equation 1.
We consider this agreement remarkable, as the E parameter for 3a has been derived from rate constants with a large variety of nucleophiles [37] and the N and s N parameters of the pyrroles 12a-12f have been derived from their reactivities toward benzhydrylium ions [57]. As Equation 1 is employed for calculating absolute rate constants k 2 in a reactivity range of 40 orders of magnitude with only three parameters, N, s N , and E, one generally has to tolerate deviations up to factors of 10 to 100 [2,3,5].
However, an even better agreement between calculated and experimental values was observed for the reactions of 3a with imidazoles 15 ( Figure 10) [58].
These additions are highly reversible, however, and the adducts could only be isolated when the reaction mixtures containing 16 (for R 2 = H) were worked up with dry K 2 CO 3 . Aqueous workup led to regeneration of the reactants. Vicario's report that imidazoles, in contrast to triazoles and tetrazoles, do not readily undergo iminium activated additions to α,βunsaturated aldehydes can thus be explained by the low acidity of imidazolium ions [59]. Unlike triazolium and tetrazolium ions, imidazolium ions are unable to transfer a proton to the enamine unit in 16 (corresponding to 5 in the general Figure 2), which is necessary to close the catalytic cycle shown in Figure 2 [60].
General base catalysis appeared also to be essential for iminium activated reactions of α,β-unsaturated aldehydes with enamides 17. By studying the kinetics of the reactions of enamides 17 with benzhydrylium ions 18 ( Figure 11) we determined the reactivity parameters N and s N for these π-nucleophiles, which are listed in Figure 12 [61]. Figure 12 shows that the nucleophilicities N of the enamides 17 are comparable to those of silylated enol ethers, in between those of allylsilanes and enamines. Accordingly, we expected them to react readily with the iminium ions 3 at room temperature. However, when the iminium triflates or hexafluorophosphates 3a and 3b (~ 5 × 10 -5 M) were combined with 25 equivalents of the enamides 17b and 17g in CH 2 Cl 2 or CH 3 CN, no consumption of the iminium ions was observed [61]. These reactions took place in the presence of 2,6-lutidine, however, indicating the need of general base assistance. By studying the kinetics of these reactions in the presence of variable concentrations of 2,6lutidine, we were able to determine k 2 , the rate constant for the attack of the iminium ions 3 at the enamides 17. As shown in Figure 13, the rate constants thus determined, agree within a factor of 3 with those calculated by Equation 1 using the N and s N parameters of enamides 17, which have been derived from their reactions with the benzhydrylium ions 18 ( Figure 11 and Figure 12) [61].
These observations explain why strong acids, such as p-TsOH, proved not to be suitable cocatalysts for iminium activated reactions of α,β-unsaturated aldehydes with enamides [62]. The demonstration of general base catalysis for these reactions furthermore rules out Hayashi's proposal of a concerted ene reaction for the formation of tetrahydropyridines by the diphenylprolinol-catalyzed reaction of α,β-unsaturated aldehydes with enamides [52] and is in line with Wang's stepwise mechanism with initial formation of 19 [62].
In view of the high nucleophilicities of sulfur ylides [63], we were surprised by MacMillan's statement that iminium ions derived from the imidazolidinones 1a and 1b (for structures, see Figure 16) were inert to the ylide 21 [49]. When we combined the pregenerated iminium salts 3a-e with the sulfur ylide 21, the expected cyclopropanes 23 were indeed formed in good yield, although with low diastereo-and enantioselectivity ( Figure 14) [64].
Even the rate constants calculated by Equation 1 agreed, within the general tolerance, with the experimental values; with one exception. The iminium intermediate derived from indole-2carboxylic acid (3g) reacted at least 10 5 times faster with the  sulfur ylide 21 than calculated by Equation 1, which can be explained by electrostatic activation as initially proposed by MacMillan ( Figure 15) [49].
Thus, the failure of the imidazolidinones 1a and 1b to catalyze cyclopropanations with the sulfur ylide 21 is not due to the low reactivities of sulfur ylides toward iminium ions, but is due to the high Brønsted basicity of the sulfur ylides 24, which leads to deprotonation of the imidazolidinium ions 1-H + and inhibition of the formation of the iminium ions 3 (Figure 16) [64].
In order to calculate the rate constant for this step by Equation 1 one needs the reactivity parameters N and s N for the enamines 28 and the electrophilicity parameter E for the electrophiles 29.
As illustrated in Figure 19, the benzhydrylium methodology was again employed for the determination of the nucleophilicities of enamines. Whereas the enamine 32b, which is    derived from the diphenylprolinol silyl ether [81], had previously been synthesized and characterized (X-ray structure) by Seebach et al. [30], neat samples of the imidazolidinone-derived enamines 32c-32e became only recently available by TsOHcatalyzed condensation of phenylacetaldehyde with the corresponding imidazolidinones and column chromatography on silica gel. The presence of triethylamine (5%) in the eluent (ethyl acetate/n-pentane) turned out to be crucial to avoid decomposition of these enamines on the column [82,83].
Kinetic studies of their reactions with benzhydrylium ions 18 of suitable electrophilicity showed that introduction of the (Me 3 SiO)Ph 2 C-group in the 2-position of the pyrrolidine ring of N-(β-styryl)pyrrolidine caused a reduction of reactivity by a factor of 30 to 60 (32a versus 32b). A reduction of nucleophilicity by three to five orders of magnitude is encountered for the enamines 32c-32e ( Figure 19). The low nucleophilicities of the imidazolidinone derived enamines, which are in line with the larger 13 C NMR chemical shifts of C-2 in 32d (101.9 ppm) and 32e (102.9 ppm) compared to that of C-2 in 32a (97.4 ppm), are not only due to the electron-withdrawing effect of the additional heteroatoms in the heterocyclic rings [83]. An additional factor is shown in Figure 19: While the enamine nitrogen is almost planar in 32b, it becomes pyramidalized in the enamines 32c and 32e and thus has a weaker electrondonating effect because of the reduced overlap between the nitrogen lone-pair and the π C-C -bond.  Combination of the data in Figure 18 and Figure 19 now explains why the Jørgensen-Hayashi diphenylprolinol trimethylsilyl ether [81], the precursor of 32b, and structurally related pyrrolidines have previously been employed for catalyzing the reactions of aldehydes and ketones with weak electrophiles, such as β-nitrostyrene (E = -13.9) [85] or di-tertbutyl azodicarboxylate (E = -12.2) [86]. The less basic imidazolidinones, which yield the less nucleophilic enamines 32d and 32e, are suitable catalysts for reactions with stronger electrophiles, such as the chlorinating agent 2,3,4,5,6,6-hexachlorocyclohexan-2,4-dien-1-one (E = -6.75) [87] and, in particular, stabilized carbocations, which are generated in situ from the corresponding alcohols under weakly acidic conditions [14,88,89]. Suggestions for further promising electrophilic reaction partners in enamine activated reactions [90] can be derived from the electrophilicity scales in [4].
When proline or structurally related bifunctional catalysts are employed, the mechanism depicted in Figure 17 has to be modified. List and Houk explained the high enantioselectivity of proline catalyzed reactions of aldehydes or ketones with electrophiles by the transition state TS-A in Figure 20, in which the electrophile is activated by the proton of the carboxy group [71]. The formation of oxazolidinones, the only observable intermediates of this reaction cascade, was considered to be an unproductive dead end [70]. On the other hand, Seebach and Eschenmoser raised the question of whether oxazolidinones, rather than being "parasitic species", may also play a decisive role in determining the stereochemical course of prolinecatalyzed reactions. In order to account for the observed stereoselectivities, it was suggested that TS-B is favored over the stereoelectronically preferred TS-C, because it yields the more stable oxazolidinone [91]. Figure 21 shows that the enaminocarboxylate 33 − reacts 50 to 60 times faster with benzhydrylium ions than pyrrolidinocyclohexene 36 and even 800 to 900 times faster than the methyl ester 37 [92].
We consider the high rates of the reactions of 33 − with benzhydrylium ions 18 as evidence for anchimeric assistance by the carboxylate group. As only part of the accelerating effect of the CO 2 − group can be due to Coulomb attraction, the formation of the C-O bond of the oxazolidone 34 is concluded to   occur concomitantly with the formation of the C-C bond. The observation that β-nitrostyrene, a neutral electrophile, also reacts 10 2 times faster with 33than with 36 also excludes Coulomb attraction to be the major factor for the high reactivity of 33 − . On the other hand, di-tert-butyl azodicarboxylate Figure 19: Quantification of the nucleophilic reactivities of the enamines 32a-e in acetonitrile (20 °C) [83]; a definition of the Dunitz pyramidalization Δ is given in [84]. reacts only six times faster with 33 − than with 36, showing that the magnitude of the anchimeric assistance depends largely on the nature of the electrophile.
The data in Figure 21 thus suggest that the oxazolidinones 34 are formed in the stereodifferentiating step when enaminecarboxylate anions are the effective nucleophiles. However, our observations do not affect the rationalization of the stereo-selectivities of proline-catalyzed reactions by TS-A when the electrophilic attack occurs at an enaminocarboxylic acid. Blackmond's observation of a change of enantioselectivity by added bases is in line with our interpretations [93].
On the other hand, the equilibrium constant for the formation of the Lewis acid-Lewis base adduct with 18g is 160 times smaller for DABCO (38) than for DMAP (39), i.e., DABCO (38) is a significantly weaker Lewis base than DMAP (39). We have previously discussed that it is the higher reorganization energy   for the reaction of DMAP (39) that is responsible for the higher intrinsic barrier and subsequently the lower nucleophilicity of DMAP (39) [94].
The upper part of Figure 23 compares the relative rates for the reactions of various organocatalysts (in THF) with the benzhydrylium ion 18e and the structurally related quinone methide 18k. This comparison reveals that the nucleophilicities of the NHCs 41-43 do not differ fundamentally from those of other organocatalysts, e.g., triphenylphosphine (10b), DMAP (39), and DABCO (38) [96].
The considerably lower nucleophilicity of the triazolylidene 43 compared with the imidazolylidene 42 can be explained by the inductive electron withdrawal of the extra nitrogen in the triazol derivative 43. The similar nucleophilicities of the imidazoleand imidazolidine-derived carbenes 42 and 41 are, at first glance, surprising and will be discussed below. The lower part of Figure 23 illustrates that all three NHCs, 41, 42, and 43, react quantitatively with the quinone methide 18k, while none of the other Lewis bases, despite their similar nucleophilicities, gives an adduct. The resulting conclusion, that all NHCs are significantly stronger Lewis bases than PPh 3 (10b), DMAP (39), and DABCO (38), is confirmed by quantum chemical calculations: The methyl cation affinities (MCAs) of the three carbenes 41-43 are 100-200 kJ mol -1 higher than those of the other Lewis bases in Figure 23 [96].
The linear correlations in Figure 24 show that the nucleophilic reactivities of the so-called deoxy Breslow intermediates 45a-f can be described by Equation 1 [107]. In contrast to the situation described for the NHCs in Figure 23, the benzylideneimidazolines 45a,d are now 10 3 times more nucleophilic than the corresponding benzylidene-imidazolidines 45c,f ( Figure 24 and Figure 25a).
A rationalization for the different sequence in the two series can be derived from the nucleus-independent chemical shifts (NICS) [109][110][111], which are considered to be a measure of aromaticity. In agreement with the almost equal lengths of the exocyclic C-C bonds in 45a (136.1 pm) and 45c (135.4 pm), as determined by X-ray crystallography, none of the two heterocyclic rings in 47a and 47c shows aromatic character (NICS (1)). However, while the electrophilic addition to the exocyclic double bond of 47a yields the cyclic conjugated 6π system in 48a, the analogous electrophilic addition to 47c yields the nonaromatic amidinium ion 48c.
The high nucleophilicity of 45a, which is mirrored by the high proton affinity of 47a, can thus be explained by the gain of aromaticity during electrophilic attack. The same line of arguments can be used to rationalize the higher nucleophilicities and basicities of the triazoline derivatives 45b and 47b, respectively [107].
As the unsaturated carbenes 49a and 49b have already a similar aromatic character as the azolium ions 48a and 48b generated by protonation, unsaturated carbenes neither show higher basicity nor higher nucleophilicity than their saturated analogues [107].
Are the properties of the deoxy Breslow intermediates also representative for the real Breslow intermediates? As shown by Berkessel and co-workers [112], Breslow intermediates generally exist as the keto tautomers 51, and attempts to generate their O-silylated derivatives 52 have failed ( Figure 26).
In order to get closer to the actual Breslow intermediates than in Rovis' aza-Breslow intermediates [113], we synthesized and isolated the O-methylated Breslow intermediates 55a-c, 57, and 59 as described in Figure 27 [114]. Some of them were characterized by single-crystal X-ray crystallography.
Kinetic studies of their reactions with benzhydrylium ions provided their reactivity parameters N and s N [114], and Figure 28 compares the relative reactivities of O-methylated and deoxy-Breslow intermediates toward the bis-pyrrolidinosubstituted benzhydrylium ion 18l. Comparison of the left and the central column shows that the O-methylated Breslow intermediates 55b and 59 are 10 2 times less reactive than their deoxy analogues 61 and 45b, respectively. Obviously, the transition state is more affected by the destabilization of the cationic adduct due to the inductive electron-withdrawing effect than by the +M-effect of the methoxy group, which raises the HOMO of the reactants. Replacement of the sulfur atom in the benzothiazole by a NCH 3 group (55b → 55c) shows that imidazole derivatives are approximately four orders of magnitude more reactive than structurally analogous thiazole derivatives, which can, again, be assigned to the different electronegativities of sulfur and nitrogen.

Conclusion
Organocatalytic reactions are complex multicomponent reactions, and a detailed description of the kinetics of the complete catalytic cycles is not yet possible. We have demonstrated, however, that important information can be obtained by specifically synthesizing relevant intermediates and studying the kinetics of their reactions with nucleophiles or electrophiles. By including them in our comprehensive electrophilicity and nucleophilicity scales (Figure 29), it has become possible to settle mechanistic controversies and to explore the scope of substrates suitable for iminium as well as for enamine activated reactions.
Rate and equilibrium studies of the reactions of N-heterocyclic carbenes and the corresponding deoxy Breslow intermediates showed that N-heterocyclic carbenes have similar nucleophilicities as other frequently employed organocatalysts, but are much stronger Lewis bases. The 10 3 times higher nucleophilicities of benzylidene-imidazolines compared with benzylidene-imidazolidines explain why imidazol-2-ylidenes but not imidazolidine-2-ylidenes are commonly used organocatalysts. Figure 29: Reactivity scales for electrophiles and nucleophiles relevant for organocatalytic reactions (references and further reactivity parameters: [4]).