Bond Energies of Enamines.

Energetics of reactive intermediates underlies their reactivity. The availability of these data provides a rational basis for understanding and predicting a chemical reaction. We reported here a comprehensive computational study on the energetics of enamine intermediates that are fundamental in carbonyl chemistry. Accurate density functional theory (DFT) calculations were performed to determine the bond energies of enamines and their derived radical intermediates. These efforts led to the compilation of a database of enamine energetics including a thermodynamic index such as free-energy stability, bond dissociation energy (BDE), and acid dissociation constant (pK a) as well as a kinetic index such as nucleophilicity and electrophilicity. These data were validated by relating to experimentally determined parameters and their relevance and utility were discussed in the context of modern enamine catalysis. It was found that pK a values of enamine radical cations correlated well with redox potentials of their parent enamines, the former could be used to rationalize the proton-transfer behavior of enamine radical cations. An analysis of the BDE of enamine radical cations indicated that these species underwent facile β-C-H hydrogen transfer, in line with the known oxidative enamine catalysis. The enamine energetics offers the possibility of a systematic evaluation of the reactivities of enamines and related radicals, which would provide useful guidance in exploring new enamine transformations.

Introduction

Enamine catalysis is one of the most important strategies in the realm of organocatalysis.[1] Typical enamine catalysis involves the asymmetric transformation of carbonyl compounds with electrophiles. Although the structure, spectroscopy, and reaction of simple enamine have been well-studied,[2] the understanding of reactivities and properties of catalytic enamine intermediate is still lagging. In recent years, Mayr developed a nucleophilicity (N) scale for a series of enamine intermediates, which are valuable in comparing the reactivity of different amino catalysts.[3] Seebach and Gschwind have studied the conformations of prolinol and prolinol ether enamines.[4,5] List et al. have reported the crystal structures of proline-derived enamines.[6] Vilarrasa et al. have recently determined the relative trend of carbonyl compounds to form enamines and relative stabilities of enamines by 1H NMR titration and theoretical calculations.[7] Albrecht studied the formation of dienamine and trienamine intermediates by 1H NMR spectroscopy.[8]

In addition to the typical highest occupied molecular orbital (HOMO) activation strategy, the recently developed oxidative enamine catalysis[9] has enabled the functionalization reactions of carbonyls with nucleophiles. In the realm of oxidative enamine catalysis, the properties of related radical intermediates have been much less studied. In 2010, Houk and MacMillan investigated the geometries, spin densities, Mulliken charges, and molecular orbitals of enamine radical cations derived from chiral imidazolinone catalysts.[10] In 2011, Engeser et al. further confirmed the existence of enamine radical cation intermediate in singly occupied molecular orbital (SOMO) catalysis by mass spectrometry.[11] Further investigations of the nature and reactivities of enamine radical cations and related radical intermediates are still highly desirable.

Although the above representative studies are valuable in rationalizing enamine catalysis, the basic bond energies of enamines and related free-radical cations remain virtually unknown. Energetic properties are of great significance in providing a rational basis for explaining the mechanism of catalytic processes and developing new catalytic methodologies. Very recently, we have systematically investigated the redox properties of various enamines.[12] To continue our systematical research on enamine, we herein wish to present our theoretical study on the energies of enamines (Scheme ), including stabilities for enamines’ formation, pKa’s, and bond dissociation energy (BDE) of enamine and enamine radical cations, which are key intermediates in aminocatalysis. In addition, we also systematically predict the reactivities of enamines and related radicals. Taken together, this study formulates a comprehensive picture of energies and reactivities of enamines and related radical intermediates, which will be helpful in developing and understanding enamine catalysis as well as oxidative enamine catalysis.

Scheme 1

Energetics of Enamines Investigated in This Work

The enamines derived from various amines (1–17) and aldehydes or ketones (A–F) were evaluated (Figure ). In addition to those primary amines mentioned above, prevalent chiral amino catalysts (7–8, 11–17) as well as model cyclic amines (9 and 10) were selected for evaluation. For further comparison, some secondary enamines derived from β-ketocarbonyls (G) and primary amines (1–8) were also included.

Figure 1

Enamine’s precursors investigated in density functional theory (DFT) calculations.

Results and Discussion

Stability of Enamines

Before calculating the bond energies of enamines, the stabilities of enamines were first investigated. Previous reports by Vilarrasa have shown that solvent polarities have a significant impact on the formation of enamines and polar solvents promote the formation of enamines.[7] In their calculation, M06-2X/6-311+G(d,p) and MP2/6-311+G(d,p) methods were utilized to explore enamine formation reactions.[7c,7d] We tried to compare the stability of various enamines in different skeletons rather than in different solvents. The calculated results of stability of enamines in CH3CN at 298.15 K are shown in Figure (Table S1 in the Supporting Information, SI).

Figure 2

Calculated stabilities of enamines (ΔG: kcal/mol) in CH3CN at 298.15 K.

Steric and conjugation effect play important role in the stability of enamines. Enamines derived from α-branched carbonyls E–F are less stable than those derived from other simple aldehydes and ketones. Also, enamines derived from phenylacetaldehyde B are usually more stable than those derived from propionic aldehyde A. The nature of amines also affects the stabilities of enamines. Enamines derived from primary–tertiary diamines are usually slightly more stable than enamines derived from simple primary amines, which supported the privilege of primary–tertiary diamine skeleton. From the point of view of the steric effect, enamines derived from secondary amines and ketones (C–D) are more unstable than those derived from simple aldehydes (A–B). The formation of enamines from sterically hindered catalysts (14–17) and ketones/α-branched aldehydes are quite unfavorable. Less sterically hindered primary amines are more suitable to react with ketones and α-branched aldehydes to form enamines. However, the formation of enamines derived from α-branched ketones is unfavorable in all cases. That is why the simple α-branched ketones remain a challenging type of substrate in enamine catalysis.

In addition, the stabilities of primary–tertiary diamine 1 and some β-ketocarbonyl-derived enamines were also investigated. These secondary enamines are stabilized by intramolecular hydrogen bonding. As shown in Scheme , the size of the ring and the ester/amide group of β-ketocarbonyls showed a significant effect on the stabilities of enamines. Enamines derived from β-ketocarbonyls containing five-member rings are more stable than those derived from β-ketocarbonyls containing six-member rings. Also, cyclic β-ketocarbonyl-derived enamines are more stable than open-chain β-ketocarbonyl-derived enamines. The β-ketoester-derived enamines are more stable than similar β-ketoamide-derived enamines. These data could be used to rationalize the reactivities of different enamines in our recent report of catalytic asymmetric enamines’ α-arylation.[13] As enamines derived from cyclic β-ketoesters are thermodynamically more stable than those derived from acyclic β-ketoesters according to Scheme , the active concentration of cyclic enamine would be larger, favoring its coupling with the fleeting benzyne. This is probably why acyclic β-ketoesters and β-ketoamide are not applicable in α-arylation.

Scheme 2

Calculated Stabilities of β-Ketocarbonyl-Derived Enamine (kcal/mol) in CH3CN at 298.15 K

pKa of Enamine and Enamine Radical Cation

Enamines have long been recognized as basic/nucleophilic species, and the basicity of enamines has been determined by both experimental and theoretical approaches.[14−16] Experimental studies on the acidity of conjugated acids of tertiary enamines revealed that the basicity of simple enamines is stronger than that of saturated amines (Scheme ),[14] which could be attributed to the effect of p−π conjugation. In a further study, two possible modes of enamine protonation were disclosed, namely, C-protonation and N-protonation. It is generally believed that N-protonation is kinetically favored, while C-protonation is thermodynamically favored (Scheme ).[16] The acidity of enamine is sparsely explored. Mó, Gal, and Guillemin et al. measured the gas-phase acidity of vinylamine (369.6 kcal/mol) and ethylamine (391.7 ± 0.7 kcal/mol) by Fourier transform ion cyclotron resonance (FT-ICR) mass spectrometer[17] and the former was about 22.1 kcal/mol more acidic than the latter.

Scheme 3

Basicity of Enamines and Amines in Water: pKa of Their Conjugated Acids

Scheme 4

Basicity of Enamines

In 1980s, Bordwell and Cheng disclosed a method based on thermodynamic cycle to determine the acidities of radical cations.[18] The acidities of radical cations can be obtained by the acidities and redox potentials of the corresponding neutral compounds and redox potentials of anions, which is known as the Bordwell–Cheng equation (eq ). From their pioneering work, it is clear that the acidities of radical cations are quite stronger than those of neutral specials. Due to the instabilities of enamines and especially enamine radical cations, the determination of their acidities is rather difficult by experimental methods. On the other hand, a theoretical calculation is a convenient and reliable method of the prediction of pKa.[19] In this work, we used the proton-exchange method[20] to determine the acidities of enamines and enamine radical cations (eq ). The acidities of aniline (pKa = 30.6) and its radical cation (pKa = 6.5) in dimethylsulfoxide (DMSO) reported by Bordwell and Cheng were used as reference (Scheme ).[21]

Scheme 5

Experimentally Determined Radical Cations’ pKa in DMSO According to the Bordwell–Cheng Equation

Before an extensive study of enamine’s and enamine radical cation’s pKa, we initially considered the possible deprotonation sites in enamine and enamine radical cation. As shown in Scheme , taking the conjugation effect or spin delocalization into consideration, there are three possible deprotonation sites in secondary enamine and its radical cation. The calculated results of enamine 3D and its radical cation are shown in Scheme . For enamine 3D, the acidity of N–H is stronger than that of α/β-C–H. However, the acidity of N–H is quite weak, even weaker than that of DMSO. Compared with those of neutral species, the acidities of radical cation 3D increased by 23 to nearly 40 pKa units. This result indicated that enamine radical cations have strong acidities. The calculation also indicated that the deprotonation at β-C–H is generally more favored.

Scheme 6

Calculated pKa Values of Enamine 3D and Its Radical Cation in DMSO at 298.15 K

The calculated acidities of enamines in DMSO at 298.15 K are shown in Table S1 (see the Supporting Information). Also, the calculated pKa values of enamine radical cations in DMSO at 298.15 K are shown in Table . From Table S1, except for the N–H of aniline-derived enamines, the acidities of enamines are quite weaker and even weaker than that of DMSO. Except for enamines derived from amines 5, 6, and 11, which have strong acid sites, other enamines mainly display strongly basic intermediates. As shown in Table , enamine radical cations have strong acidities with pKa < 15. The acidities of N–H, α-C–H, and β-C–H in enamine radical cations are all stronger than those of the parent enamines, which also indicates the stabilization of radical species by spin delocalization effect in these three sites. For enamine and its radical cation, the pKa value of carboxyl or protonated tertiary amine shows similar values to those of enamine radical cations. In a diamine skeleton with primary amine catalyst 6, the intramolecular proton-transfer process between two amino moieties is quite facile particularly with radical cations (Scheme ), making the calculation of N–H acidity in these instances unreliable; hence, it is not included in our studies. As shown in Table , almost in all cases, the acidities of β-C–H in enamine radical cations are stronger than those of other sites. The acidities of α’-C–H in enamine radical cation can be stronger or weaker than those of N–H. Compared to those of other enamines, MacMillan catalysts (16–18) derived enamine radical cations have the strongest acidities, and those derived from primary–tertiary diamines have the weakest acidities.

Table 2

Calculated pKa Values of β-Ketocarbonyl-Derived Enamine in DMSO at 298.15 Ka

The reported pKa values in each cell are arranged in the following order: pKa1 (if exist), pKa2, and pKa3.

Table 1

Calculated pKa Values of Enamines Radical Cation in DMSO at 298.15 Ka

Unless otherwise noted, the reported values correspond to enamines’ configurations drawn in the column.

Z-configured enamine.

E-configured enamine.

Scheme 7

Intramolecular Proton Transfer of Imine Radical 6A

The pKa of β-ketocarbonyl-derived enamines and their radical cation in DMSO were also studied. Due to the electron-withdrawing nature of the additional carbonyls, the acidities of N–H and α-C–H in enamine enhanced significantly, which were more acidic than β-C–H (Table ). For enamine radical cation, the electron-withdrawing group could also enhance the acidities of α’-C–H, which became as much or even more acidic than N–H or β-C–H. For radical cations of five-member ring β-ketoester, such as 1G and 2G, acidities of α’-C–H were comparable or higher than those of β-C–H. Enamine radical cations derived from trifluoromethyl-substituted β-ketocarbonyls, such as 2G and 5G, show the most significant enhancement of acidity.

Correlation of pKa of Radical Cation and Redox Potential of Enamine

According to the Bordwell–Cheng equation,[18] we tried to relate pKa of radical cation and the redox potential of enamine.then, we will have

The oxidation potential of hydrogen atom E(H•) is a constant. According to eq , if the bond dissociation free energy of A – H (BDFE(A – H)) can be regarded as a constant, there is a linear correlation between pKa (A – H+•) (pKa of enamine radical cation) and E(HA), the oxidation potential of enamine. As BDE and BDFE are usually less sensitive to the distal substituent groups, we propose that BDFE of enamines or their radical cations derived from the same carbonyl compounds varies only slightly as they contain similar enamine core skeleton (vs infra).

To verify our hypothesis, we divided the pKa values of radical cations into several groups based on the carbonyls and different deprotonating sites. The correlation of enamine radical cation’s pKa and enamine’s (1A–17A) redox potential Eox in DMSO is shown in Figure . The correlation of N–H pKa with redox potential is good (Figure a, R2 = 0.77) and the correlation of β-C–H pKa with redox potential is excellent (Figure b, R2 = 0.98). The relatively poorer correlation of N–H pKa with redox potential is probably due to the change in BDFE of N–H with the variation of amines. Other aldehyde- or ketone-derived enamine radical cations also show good correlations between pKa and enamine’s redox potential Eox (see SI, Figures S1–S4). In addition, a very good correlation was found between β-ketocarbonyl-derived enamine radical cation’s pKa and enamine’s redox potential Eox in DMSO (Figure c, R2 = 0.92). However, a moderate correlation between different carbonyl compounds was observed (see SI, Figure S5). These results indicated that the BDFE of C–H bonds in enamine radical cations is more sensitive to variation of carbonyls than those in amines. Based on these correlations, we can readily predict the acidities of enamine radical cations from the redox properties of neutral enamine.

Figure 3

Correlation of enamine radical cation’s pKa and enamine’s redox potential in DMSO. (a) Enamine radical cation’s N–H pKa and enamine’s redox potential (1A–17A); (b) enamine radical cation’s β-C–H pKa and enamine’s redox potential (1A–17A); and (c) β-ketocarbonyl-derived enamine radical cation’s β-C–H pKa and enamine’s redox potential.

BDE of Enamine and Enamine Radical Cation

Bond dissociative energy (BDE) is the key thermodynamic parameter in assessing the free-radical process. We next investigated the BDE of enamines and their oxidized species via SET. As radical species, enamine radical cations might also undergo H-atom transfer (HAT) to form imine, a known process in oxidative enamine catalysis.[9] These BDE data could be instructive in assessing the HAT process (or its equivalent, coupled electron–proton transfer) involving enamine or enamine radical cation. In 1992, Bordwell et al. reported the experimental BDE values of some enamines.[22] To verify the reliability of the theoretical calculation for the prediction of the enamine’s BDEs, we also calculated these BDEs. The BDEs of enamines and enamine radical cations were calculated as

A comparison of the experimental and calculated BDE values of these enamines is shown in Scheme . This result indicates that using M06-2X/6-311G(d,p) level could balance the time and accuracy.

Scheme 8

Comparison of Experimental and Calculated BDE Values of Enamines

However, slightly different from pKa calculation, only α-C–H and β-C–H relative to enamine are considered. The initially results are shown in Scheme . Cyclohexanone is chosen as the core skeleton, of which the BDE of its α-C–H (94.2 kcal/mol) is known.[23] First evaluation of the BDE of α-C–H and β-C–H of cyclohexanone indicates that the dehydrogenation at β-C–H of cyclohexanone is disfavored. Subsequent evaluation of enolization of cyclohexanone shows a lower BDE value at the β-C–H bond. Also, the BDE of enamine at β-C–H is the lowest among the neutral species. For radical cation species, the dehydrogenation at β-C–H of enamine radical cation is favored. The dehydrogenation at α’-C–H of enamine radical cation is quite unfavorable. Not only higher BDE values but also the formation of unstable bicyclo intermediate was observed. For clarity, only the BDE at β-C–H of enamine radical cation is reported below.

Scheme 9

Calculated BDE Values of Enamines and Enamine Radical Cations at 298.15 K

The calculated BDE values of enamines are listed in Table S2. The calculated BDE values of enamine at β-C–H are very close to each other. For the BDE of enamine derived from the same carbonyls, the calculated values are in a rather small range (ca. 3 kcal/mol). These results supported the above assumption that the BDFE of β-C–H could be considered as a constant for similar enamines. In addition, it should be noted that enamines derived from cyclohexanone have relatively smaller BDE values, which may be attributed to the stronger stabilities of this radical species than other terminal free radicals.

The calculated BDE of enamine radical cations are listed in Table . Compared with the BDE values of enamines, the BDE values of enamines radicals are smaller for nearly 30 kcal/mol (Figure ), which indicates the favorable dehydrogenation of enamine radical cation at β-C–H. Also, similar to the results of enamines, enamine radical cations derived from cyclohexanone have relatively lower BDE values, which may be also attributed to the stronger stabilities of the cation species than other terminal cations. In addition, the variation of amines has a small impact on the BDE of enamine radical cation. Compared to pKa, the BDE values are less sensitive to the electronic effect of amines. The calculated BDE values of enamines derived from β-ketocarbonyl compounds and their free-radical cations are shown in Table . The BDE values at β-C–H of enamine radical cations are lower than those of the corresponding enamines for nearly 30–40 kcal/mol.

Table 3

Calculated BDE Values of Enamine Radical Cations at 298.15 K

Figure 4

Comparison of calculated BDE values of enamines and enamine radical cations.

Table 4

Calculated BDE Values of β-Ketocarbonyl-Derived Enamine

Our calculation indicated that dehydrogenation at the β-C–H site is favorable for both enamine and enamine radical cation. This result is consistent with the previous experimental observations that dehydrogenation is favored at β-C–H in the oxidative enamine catalysis process,[9,24] wherein an enamine radical cation mechanism could be applied (Scheme ).

Scheme 10

Possible Mechanism of Oxidative Imine Catalysis

Calculated Nucleophilicity Index of Enamine and Nucleophilicity/Electrophilicity Index of Related Radical

With the thermodynamics data of enamines and enamines radical cations in hand, we next evaluate the kinetics properties of enamines based on the above or previous calculation. The nucleophilicity of enamine has been deeply studied by Mayr.[3] These nucleophilicity parameters are valuable for predictions of absolute rate constants, inter- and intramolecular selectivities, and analyses of reaction mechanisms. To further study and develop the enamine catalysis, the nucleophilicity of secondary enamines or some hindered tertiary enamines are still highly needed. Because of the thermodynamic instabilities of these enamines, the nucleophilicity could not be easily determined by a conventional kinetic method. Therefore, the theoretical prediction of the nucleophilicity of enamine is an alternative choice. In 2009, Fu and Liu reported the first-principles prediction of nucleophilicity parameters for π-nucleophiles and revealed the mechanistic origin of Mayr’s equation.[25,26] However, the direct calculation of nucleophilicity parameters by Mayr’s equation need extensive calculations of the involved transition states, which is time-consuming and laborious. In 2008, Domingo proposed an empirical (relative) nucleophilic index N,[27] for closed-shell organic molecules, based on the HOMO energies and defined it as follows:

Also, tetracyanoethylene (TCE) is used as a reference in the nucleophilicity scale. Several theoretical and experimental studies have proved the reliability of the nucleophilicity index N in predicting the nucleophilic behavior of organic molecules. In addition, Yu reported the quantification of nucleophilicity and electrophilicity using HOMO and the lowest unoccupied molecular orbital (LUMO) energies.[28]

Herein, based on eq and the above results, the nucleophilicity index of enamines was determined, which would be helpful in understanding the reactivity in enamine catalysis. Also, the calculated nucleophilicity index (eV) of enamines in CH3CN is summarized in Table . Compared with the experimental nucleophilicity of enamines and the calculated nucleophilicity index, we found that there was no universal correlation, only a local correlation. As shown in Figure , the nucleophilicity of enamines derived from phenylacetaldehyde and cyclohexanone correlated well with the experimental nucleophilicity. This result indicates that the nucleophilicity index of enamines is more suitable for comparing the reactivity of structure-related enamines especially those derived from the same carbonyls. Based on this hypothesis, we next compared the nucleophilicity of enamines derived from the same carbonyls (Figure ). For secondary enamines, enamines derived from primary–tertiary diamines were more reactive than enamines derived from simple primary amines. Pyrrolidine-derived enamines had the strongest nucleophilicity in the realm of tertiary enamines. Also, enamines derived from MacMillan catalyst are the least reactive tertiary enamines.

Table 5

Calculated Nucleophilicity Index (eV) of Enamines in CH3CN

Figure 5

Correlation of the experimental and calculated nucleophilicity of enamines in CH3CN.

Figure 6

Comparison of the nucleophilicity index (eV) of enamines.

In 2007, De Proft et al. reported a global electrophilicity and nucleophilicity scale for 35 free radicals.[29] To establish the electrophilicity scale, Parr’s electrophilicity index ω was used[30]where μ is the electronic chemical potential[31] and η is the chemical hardness.[32] These two quantities, which are defined as μ = −(I + A)/2 and η = (I – A), were calculated using the vertical ionization energy I and electron affinity A. According to Koopmans’s theorem, the relationships I = −EHOMO and A = −ELUMO were used. For radicals, the relationships[33]I = −EHOMOα and A = −ELUMOβ were used.

In 2013, Domingo proposed the global nucleophilicity N of free radicals[34] and defined it as

Based on eqs and 8, the nucleophilicity/electrophilicity index of enamine radical species could be obtained.

We first evaluate cyclohexanone-derived enamine to study the nucleophilicity/electrophilicity index of enamine radical cations, α-imino radicals, and enamine radicals. The calculation results are shown in Table , and brief index (eV) scales on electrophilicity/nucleophilicity are shown in Figure . It can be seen from the table that all enamine radical cations have strong electrophilicity. The α-imino radical formed by the deprotonation of the secondary enamine radical cations also has strong electrophilicity. Compared with that of free-radical cations, the electrophilicity of α-imino radical is relatively weak. Both α-enamino radicals and β-enamino radicals have strong nucleophilicity, and β-enamino radicals are more nucleophilic.

Table 6

Electrophilicity/Nucleophilicity Index (eV) of Enamine Radicals

Figure 7

Brief electrophilicity/nucleophilicity index (eV) scales for enamine radicals.

We also evaluate the β-ketocarbonyl-derived enamine radicals (Figure ). To make a comparison, the nucleophilicity/electrophilicity index of carbonyl radicals is also studied. Enamines are electron-rich species. Thus, the enamine radicals are more nucleophilic than carbonyl radicals. In addition, enamine α-radical and α-imino radical are electrophilic radicals. Also, enamine β-radical is a nucleophilic radical. It should be noted that the carbonyl β-radical is an electrophilic radical. The nucleophilicity/electrophilicity nature of enamine can be rationalized in SOMO catalysis. The electrophilicity/nucleophilicity index of radical is in agreement with the fact that electron-rich olefins were used in α-functionalization, while electron-poor olefins were used in β-functionalization.[35]

Figure 8

Electrophilicity/nucleophilicity index of β-ketocarbonyl-G4-derived enamine radicals 1G4.

Conclusions

In summary, accurate DFT calculations were performed to predict the energies and reactivity of enamines and related radical intermediates. Our calculation indicated that enamine radical cations had strong acidities. Also, the correlation of pKa values of enamine radical cations and redox potentials was found, which could be used to predict the acidities of enamine radical cations. Enamine radical cation easily lost a hydrogen atom. The deprotonation and dehydrogenation processes were favored at the β-C–H position, which could be used to rationalize the 5πe activation mode and oxidative imine catalysis. In addition, the reactivity of enamine and related radical are evaluated. These theoretical calculations would provide guidance in exploring oxidation enamine transformations.

Calculation Methods

Since theoretical approaches have been found to give a precise prediction of thermodynamics properties in solution,[19,36] we explored theoretical methods to predict the properties of enamines using Gaussian 09.[37] As Truhlar et al.’s M06-2X hybrid functional was shown to provide accurate predictions of thermodynamic properties of organic molecules,[38] geometry optimizations and frequency computations were performed at the M06-2X/6-311G(d,p) level of theory. An IEF-PCM model was used to account for the solvation effects in acetonitrile and DMSO.[39] Thermal free energy corrections were obtained at 298.15 K to calculate stability, pKa, and BDE. Contributions of low frequencies (<100 cm–1) to vibrational entropy were corrected according to the quasi-harmonic approximation method of Grimme using GoodVibes.[40]