Prediction of NHC-catalyzed chemoselective functionalizations of carbonyl compounds: a general mechanistic map†

Generally, N-heterocyclic carbene (NHC) complexed with carbonyl compounds would transform into several important active intermediates, i.e., enolates, Breslow intermediates, or acylazolium intermediates, which act as either a nucleophile (Nu) or an electrophile (E) to react with the other E/Nu partner. Hence, the key to predicting the origin of chemoselectivity is to compute the activity (i.e., electrophilic index ω for E and nucleophilic index N for Nu) and stability of the intermediates and products, which are suggested in a general mechanistic map of these reactions. To support this point, we selected and studied different cases of the NHC-catalyzed reactions of carbonyl compounds in the presence of a base and/or an oxidant, in which multiple possible pathways involving acylazolium, enolate, Breslow, and α,β-unsaturated acylazolium intermediates were proposed and a novel index ω + N of the E and Nu partners was employed to exactly predict the energy barrier of the chemoselective step in theory. This work provides a guide for determining the general principle behind organocatalytic reactions with various chemoselectivities, and suggests a general application of the reaction index in predicting the chemoselectivity of the nucleophilic and electrophilic reactions.


Introduction
The combination of a nitrogen atom with a lone pair of electrons and a 6e carbon atom in N-heterocyclic carbenes (NHCs) provides a conjugation between the two atoms, which can signicantly stabilize the unoccupied orbital of the carbon atom to achieve a typical singlet carbene. 1 In this kind of chemistry, NHCs usually act as nucleophiles by using the occupied sp 2 orbital of the carbon atom to activate polarized unsaturated substrates, which can reversibly form a covalent bond with active molecules. 2 Further transformations of the forming intermediates can reverse the electrophilic substrates to nucleophiles by the electron-donation of the conjugative nitrogen atoms. Therefore, NHCs can be used as powerful catalysts in organocatalysis due to the special characteristics of nucleophilicity, 3 good leaving group ability, 4 and tunable electronic 5 and steric properties. 6 As an example (Scheme 1), the reaction of NHCs with aldehydes can generate a formal enol, namely Breslow intermediates, which can be used as a nucleophile to react with electrophilic partners for the synthesis of a variety of functional molecules including biologically active natural products, 7 organic materials, 8 pharmaceuticals, 9 agrochemicals, etc. 10 Indeed, the other electrophiles, such as ketenes, enals, olens, or imines, can also be activated by NHCs according to their nucleophilicity, which signicantly increases the complexity of carbene chemistry. 11 In NHC-mediated transformations, the introduction of an external base or oxidant increases the complication of the Scheme 1 NHC-catalyzed transformation modes of carbonyl compounds. reaction mechanism because the additives can probably reverse the electronic properties of NHC-involved active intermediates. As a contrast, the mechanism for the NHC-catalyzed cycloaddition of ketenes only involves three steps of adsorption, cycloaddition, and dissociation in the absence of external additives. Alternatively, when a Brønsted base participates in the NHC-catalyzed functionalization of aldehydes, 12 enals, 13 or esters, 14 the transformations would involve more steps due to the extra proton transfer in those reactions. Furthermore, the situation becomes much more complex in the presence of an external oxidant, 15 because the key step of hydrogen transfer to oxidants might take place through hydride transfer to oxygen or carbon (HTO/HTC), 16 single electron transfer-hydrogen atom transfer (SET-HAT), 17 or even HAT-SET 18 processes. However, the lack of a universal principle to disclose the mechanism of the NHC-catalyzed carbonyl compound transformations restricts the rational design of both NHC-catalysts and reaction types. Hence, predicting the chemoselectivity and designing a map for the general mechanisms of the NHC-catalyzed transformations of carbonyl compounds in the presence of an external base and/or oxidant are still challenging and highly desirable in this eld.
In NHC-catalysis, carbonyl compounds are one of the most commonly used electrophiles that can be activated by the adsorption of NHCs. When external additives are added, further deprotonation and/or oxidation greatly increase the complexity of the reaction mechanism. For instance, an aldehyde can be activated by the NHC catalyst to afford the Breslow intermediate, which can be oxidized to the acylazolium intermediate by an oxidant (Scheme 1). The deprotonation of the acylazolium assisted by a base can generate azolium enolate, which can isomerize to an a,b-unsaturated Breslow intermediate through proton transfer. Further oxidation can provide the a,b-unsaturated acylazolium species. Previous experiments have demonstrated that all the above mentioned intermediates can react with specic nucleophiles or electrophiles to achieve the functionalization of carbonyl compounds. 13a-i,14,15 However, the origin of chemoselectivity for the competitive transformation of corresponding intermediates still remains a challenge for synthetic chemists and could be solved by the exploration of reaction mechanisms. In this work, a series of NHC-catalyzed carbonyl compound transformation reactions will be considered theoretically, and we will try to predict the origin of chemoselectivity from a general perspective. We hope that the understanding of the reaction mechanism and origin of chemoselectivity would be helpful for the design of new transformations in NHC catalysis.

Computational details
The Gaussian09 program 19 and M06-2X (ref. 20) functional were employed to perform all the calculations, which have been widely used to study the mechanisms and selectivities 21 of various catalytic reactions. 22 All the geometries were optimized at the 6-31G (d,p) basis set in THF and other solvents such as toluene, in which the solvent effect was simulated by the appropriate integral equation formalism polarizable continuum model (IEF-PCM). 23 The harmonic vibrational frequency calculations were performed at the same computational level as that of the optimization, which ensures no imaginary frequency in the intermediate and only one imaginary frequency in the transition state. The discussed energies of all the optimized geometries were gained by adding the singlepoint energies and the Gibbs free energy corrections at the M06-2X-D3/6-31++G(2df,2pd)/IEF-PCM THF //M06-2X/6-31G(d,p)/IEF-PCM THF computational level (L1).
In addition, the global reactivity index (GRI) analysis was performed on the active intermediates to evaluate their nucleophilic (nucleophilic index N) 24 or electrophilic (electrophilic index u) 25 reactivities on the basis of the equations: 26 while the local reactivity index (electrophilic (P + k ) and nucleophilic (P À k ) Parr functions) 27 analysis was also performed to uncover the nucleophilic or electrophilic sites. To conrm the reliability of the computational level (L1), other density functional theory (DFT) methods (i.e., B3LYP-D3, 28 CAM-B3LYP-D3, 29 uB97X-D, 30 and MP2) at different levels (L2-6) were carried out on the crucial stereoselective step. Furthermore, other congurations of the stereoselective transition states have been additionally considered, to conrm that all the discussed geometries had the lowest energy. More computational results and details can be found in the ESI. †

Results and discussion
General mechanistic map for NHC-catalyzed chemoselective functionalizations of esters As a selected model reaction (Scheme 2), when the NHC precursor Pre-NHC was used as a catalyst, ester R1 can react with imine R2 to afford the [3 + 3] oxidative annulation product P with up to 76% yield and a 60% enantiomeric excess (ee) value in the presence of the base DBU and oxidant 3,3 0 ,5,5 0 -tetra-tertbutyl diphenoquinone (DQ). 31 The Chi group also found that the additive HOBt can signicantly improve the yield (from 76% to 94%) and enantioselectivity (from 60% to 94% ee). 31 According to our proposed transformation model in Scheme 1, when acylazolium intermediate M02 is formed, it can be deprotonated to form an enolate intermediate, M3. Moreover, its Breslow type isomer M4 can be oxidized to an a,b-unsaturated acylazolium species, M05. As shown in Scheme 2, all these intermediates can react with nucleophile R2 À or electrophile R2 to afford the corresponding amidation/ketolation, [2 + 2] cycloaddition, [3 + 2] annulation, and [3 + 3] annulation products. However, only the [3 + 3] oxidative annulation product P was observed experimentally, while the origin of chemoselectivity for this transformation still remains unclear. Moreover, the enantioselectivity for [3 + 3] oxidative annulation with additive effects should also be studied. Therefore, this transformation was selected in our theoretical calculation as a model reaction to reveal the common model for the NHC-catalyzed carbonyl compound transformations.
Among the proposed pathways, the [3 + 3] annulation pathway was mainly discussed in detail for the NHC-catalyzed reactions, while the other four possible pathways were divorced from the key active intermediates. Both the non-freecarbene pathway and carbene generation pathway were considered, and the computed results indicated that the DBUassisted deprotonation of azolium catalyst Pre-NHC to afford free NHC can be easily happen (Fig. S1 of the ESI †). 32 The [3 + 3] annulation pathway contains nine steps, as shown in Fig. 1 As shown in Fig. 1, the active site C1 of the NHC nucleophilically attacks the carbonyl carbon C2 of ester R1 initially through transition state TS1, forming zwitterionic intermediate M1 with an energy barrier of 16.5 kcal mol À1 . The structural transformation from NHC and aryl ester to the zwitterionic (tetrahedral) intermediate needs to overcome an energy barrier of 16.5 kcal mol À1 , which is close to that reported in ref. 33.
Subsequently, the dissociation of OAr À takes place via a C2-O4 bond cleavage transition state TS2 with an energy barrier of only 0.7 kcal mol À1 , affording intermediate M2 (the complexation of the acylazolium intermediate M02 and OAr À ). Then, an a-C(sp 3 )-H deprotonation of M2 is assisted by anionic OAr À through transition states TS3/TS3E to generate the corresponding enolate intermediates M3/M3E. The relative free energy of transition state TS3 is 4.2 kcal mol À1 lower than that of TS3E; hence, the pathway associated with TS3/M3 is preferred. In addition, the base DBU-assisted a-C(sp 3 )-H deprotonation pathway ( Fig. S2 and S3 of the ESI †) was also considered theoretically; however, much higher activation barriers were observed via transition states TS3 DBU /TS3E DBU .  Aer the a-C(sp 3 )-H deprotonation of M2, intermediate M3 undergoes a DBU and HOBt cooperatively assisted [1,3]-proton transfer process via transition states TS4/TS4Z (DG ‡ ¼ 3.7/ 9.7 kcal mol À1 , Fig. 1), affording the related complexes M4 com / M4Z com . These complexes subsequently dissociate into Breslow intermediates M4/M4Z and DBU + HOBt. The energies of TS4/ M4 com are 6.0/4.0 kcal mol À1 lower than those of TS4Z/M4Z com , implying that the pathway associated with TS4 is energetically preferred. Then, intermediate M4 is oxidized into a complex M5, which consists of the unsaturated acylazolium intermediate M05 and anion [DQH] À . The oxidation occurs via transition state TS5 (DG ‡ ¼ 5.8 kcal mol À1 , Fig. 1) through the most favorable HTO pathway, which is determined aer computing and comparing the four proposed oxidative pathways, namely, HTO, HTC, HAT-SET, and SET-HAT. 34 More information on the natural population analysis (NPA) charge and other possible oxidative pathways can be found in the ESI. † For the Michael addition process, the two reacting parts are generally nucleophilic (Nu) and electrophilic (E). Obviously, intermediates M5 or M05 are the electrophilic parts as their electrophilic indexes (u) equal to 3.093 and 2.979 eV, respectively, so the other reacting part related to R2 should be nucleophilic. Thus, imine R2 must be rst deprotonated by a base (i.e., OAr À , DBU, or [DQH] À ) to afford the nucleophilic R2 À anion. As revealed by the computed results in Fig. S9 of the ESI, † the deprotonation of R2 by base [DQH] À through transition state TS0 DQHÀ (DG ‡ ¼ 12.5 kcal mol À1 , Fig. S9 and S10 of the ESI †) is the most favorable pathway among the three possible deprotonation pathways, affording the stable nucleophilic intermediate R2 ÀHOBt by interacting with HOBt and dissociating DQH 2 . As depicted in Scheme 3, the nucleophilic site C6 (with P À k (C6) ¼ 0.61) of anionic R2 ÀHOBt can attack the Re-/Si-faces of the electrophilic site Cb (with P + k (Cb) ¼ 0.24) of M5 through transition state TS6(R/S) HOBt (DG ‡ ¼ 9.9/ 12.3 kcal mol À1 , Fig. 3) in the process of forming intermediate M6(R/S) HOBt and releasing anion [DQH] À , in which a Cb-C6 bond is formed. The energy difference of 2.4 kcal mol À1 between DG ‡ TS6ðRÞ HOBt and DG ‡ TS6ðSÞ HOBt corresponds to the calculated 96.6% ee value, which is close to the 94% ee value in the presence of HOBt observed in the experiment. 31 The letters "R/ S" in M6(R/S) HOBt represent the chirality of the Cb center. In addition, since the energies of TS6(R) HOBt and M6(R) HOBt locate below those of TS6(S) HOBt and M6(S) HOBt , the processes that follow M6(S) HOBt are unnecessary to discuss in detail.
Next, M6(R) HOBt conducts the other [1,3]-proton transfer process with the help of the protic media HOBt through transition state TS7(S) HOBt (DG ‡ ¼ 12.0 kcal mol À1 ), generating This journal is © The Royal Society of Chemistry 2020 Chem. Sci., 2020, 11, 7214-7225 | 7217 intermediate M7(S) and dissociating HOBt. It should be noted that the R-chirality of the Cb atom in TS6/M6 is apparently converted to the S-chirality in TS7/M7, since the unsaturated bond is changed from the C2]Ca bond in TS6/M6 to the C6] C8 bond in TS7/M7. Hereaer, M7(S) undergoes a ring closure process via a six-membered ring transition state TS8(S) (DG ‡ ¼ 3.7 kcal mol À1 ) to produce M8(S). Eventually, the catalyst NHC is recycled and a six-membered ring main product of lactam P(S) is produced through transition state TS9(S) (DG ‡ ¼ 3.2 kcal mol À1 ). The energy of P(S) is found to be 23.7 kcal mol À1 below the energy of the reactant, suggesting that the entire reaction is exothermic. In addition, the difference between the [3 + 3] annulation pathways with or without HOBt is only re-ected in steps 6 and 7. Fig. S11 of the ESI † shows that the energy barriers of steps 6 and 7 via transition states TS6(R/S) and TS7(S/R) HOAr are 13.6/14.4 and 13.2/10.4 kcal mol À1 in the [3 + 3] annulation pathway without HOBt, respectively. Apparently, the energy barrier difference between DG TS6(R) ‡ and DG TS6(S) ‡ is only 0.8 kcal mol À1 and can be theoretically converted to a 59% ee value, which is very close to the observed 60% ee value in the experiment, 31 indicating that HOBt is indeed able to advance the stereoselectivity.
According to the recent work reported by Singleton and Plata, the calculated proton transfer barrier might be unreliable and has a large error in the alcohol-mediated Morita-Baylis-Hillman (MBH) reactions using the most popular DFT methods, i.e., B3LYP and M06-2X, 35 which would be due to the absence of explicit solvents in the models. 36 Therefore, to test whether the same problem exists in the NHC-catalyzed reactions, we have additionally constructed the models with 100 explicit THF solvents, and computed the energy barriers of the proton transfer processes (steps 4 and 5) at the ONIOM(B3LYP/6-31G (d,p):UFF) and ONIOM(M06-2X/6-31G(d,p):UFF) levels.
As summarized in Table 1, the calculated results indicate that the free energy barriers DDG tot (with the normal Gibbs free energy correction), DDG 50% (with 50% of the Gibbs free energy correction), and DDG explicit (calculated in the explicit solvents without the implicit model) are close, and the free energy barriers obtained by the two DFT methods have tiny differences, which is remarkably different from the computed results reported in Singleton's work. As mentioned above, the computational errors in this system should not be signicant and the calculated results using the M06-2X method are consistent with the experiment. More details on the intrinsic reaction coordinate (IRC) results of transition states TS4 and TS5, which were calculated by the different DFT methods in both implicit and explicit models, have been provided in Fig. S18 and S19 of the ESI. †

Roles of HOBt and DBU
To explore the roles of the additive HOBt and base DBU, we have provided more evidence in both experiment and theory. As shown in Fig. 4, the DBU and HOBt cooperatively assisted [1,3]proton transfer via transition state TS4 (DG ‡ ¼ 3.7 kcal mol À1 ) is the most energetically favorable pathway among all the possible [1,3]-proton transfer pathways, including DBU and DBU$H + cooperatively assisted [1,3]-proton transfer pathway via TS4 DBU-DH+ (DG ‡ ¼ 15.2 kcal mol À1 ) and DBU or DBU$H + separately  assisted [1,3]-proton transfer pathway via TS4 DBU (DG ‡ ¼ 25.2 kcal mol À1 )/TS4 DH+ (DG ‡ ¼ 24.6 kcal mol À1 ), implying that DBU serves as a base and the participation of HOBt can signicantly lower the energy barrier of the key 1,3-proton transfer (i.e., b-C-H deprotonation for the transformation from the Ca-Cb single bond of saturated ester to the Ca]Cb double bond), which thus causes the reaction to happen faster and improves the yield of the reaction. In order to prove this point, we have collaborated with Chi's group and the experimental results indicate that the yield indeed can be improved from 76% to 94% by adding the HOBt in the reaction (see Scheme 2). 31 In contrast, when unsaturated ester is used as the reactant in the NHC-catalyzed [3 + 3] annulation for the formation of the same product, 14a the DFT calculations in Scheme S6 and Fig. S22 of the ESI † demonstrated that the addition of HOBt or other alcohols should be not necessary for improving reaction rate or yield, since the b-C-H deprotonation is not involved in the reaction, and the experimental observations also conrmed this conclusion. Hence, the participation of HOBt for the reaction is critical in promoting the reaction yield and enantioselectivity.

Origin of chemoselectivity
For the other four proposed pathways divorced from the active intermediates M2, M3, and M4, the detailed discussions of their related energy proles have been provided in the ESI † for the production of SP A /SP B , SP C , and SP D , as conjectured in Scheme 2. To pursue the origin of the chemoselectivity, we just need to compare the energy barriers involved in the several possible pathways: the possible amidation, ketolation, [2 + 2] cycloaddition, [3 + 2] annulation, and [3 + 3] annulation pathways. Both of the amidation and ketolation pathways are divorced from M2, and the energy prole of the ketolation pathway lies below that of the amidation pathway, which is shown in Fig. S12 of the ESI. † Subsequently, we compared the other four possible pathways. As shown in Fig. 5, since M2 (u ¼ 1.548 eV, P + k (C2) ¼ 0.18) and R2 À (N ¼ 4.459 eV, P À k (C6) ¼ 0.64) are separately electrophilic and nucleophilic, the nucleophilic addition of R2 À onto M2 through transition state TS3 B is likely to happen. However, the much higher energy of TS3 B in the ketolation pathway compared to that of TS3 indicates that it is impossible to occur under the experimental conditions. In addition to the isomerization from enolate M3 to Breslow intermediate M4, since enolate M3 (N ¼ 4.116 eV, P À k (Ca) ¼ 0.62) and R2 (u ¼ 1.709 eV, P + k (C8) ¼ 0.40) are nucleophilic and electrophilic, respectively, the [2 + 2] cycloaddition between M3 and R2 via transition state TS4 C (SS) is likely to occur. However, the much higher energy of TS4 C (SS) in the [2 + 2] cycloaddition pathway compared to that of TS4 demonstrates the unfavorability of the corresponding pathway. In contrast to the oxidation of Breslow intermediate M4, since M4 (N ¼ 4.962 eV, P À k (Cb) ¼ 0.62) and R2 (u ¼ 1.709 eV, P + k (C8) ¼ 0.40) are nucleophilic and electrophilic, respectively, we have located a transition state TS5 D (RS) for the nucleophilic addition of M4 onto R2 combined with a proton transfer. The energy barrier of the single-step reaction via TS5 D (RS) in the [3 + 2] annulation pathway is 11.5 kcal mol À1 and not high. However, as summarized in Table S9 of the ESI, † the energy barriers of the four possible reactions (DG ‡ total ) via TS3 B , TS4 C (SS), TS5 D (RS), and TS6(R) HOBt are 31.0, 28.0, 24.5, and 9.9 kcal mol À1 , hence, only the product P can be formed in theory, which is consistent with the experimental observations. 31 As is well accepted by chemists, for the nucleophilic or electrophilic addition processes, if the two reacting partners have much stronger nucleophilicities or electrophilicities, their corresponding transition states would be related to lower energy barriers. Therefore, based on the empirical point, to uncover the origin of this reaction chemoselectivity, we assumed that the larger electrophilic (u) and nucleophilic (N) indexes u + N of the stable nucleophile (Nu) / electrophile (E) partners (R2 À / M2, M4 / R2, and R2 ÀHOBt / M5) would lead to lower energy barriers, DG ‡ , of the nucleophilic or electrophilic addition processes associated with the transition states (TS3 B , TS5 D (RS), and TS6(R) HOBt ) involved in the three pathways. As summarized in Table S9 of the ESI, † the decreasing single-step energy barriers, DG ‡ , are presented a linear relationship with the corresponding increasing u + N indexes as shown in Fig. 6. It should be noted that the energy barrier via a four-membered ring transition state TS4 C (SS) does not completely correspond to the activity of the reaction partners (M3 / R2), which is due to the large ring strain of the fourmembered ring involved in TS4 C (SS); thus we did not consider its data for the linear relationship depicted in Fig. 6.
Considering the above, we suggested a new application of the u + N index from the reacting ability between the Nu and E to simply and quickly predict the energy barrier of the chemoselective step (DG ‡ p ¼ 51.8-5.9(u + N) eV/23.1 kcal mol À1 ), which would be one of the key factors for exploring the origin of chemoselectivity of the possible reactions commonly involved This journal is © The Royal Society of Chemistry 2020 Chem. Sci., 2020, 11, 7214-7225 | 7219 in a large amount of NHC-catalyzed reactions of saturated or unsaturated carbonyl compounds.

General principle for predicting the chemoselectivity of NHCmediated reactions of carbonyl compounds
To ensure that the u + N index of Nu and E partners can be used to generally predict the single-step energy barriers and even the chemoselectivity in these types of reactions based on our proposed general mechanistic map, we selected three additional NHC-mediated reactions of carbonyl compounds presented in Fig. 7-9 as valuable cases for testing. 13j,14b,17a As shown in Fig. 7, the NHC-catalyzed chemoselective [3 + n] (n ¼ 2, 3) annulation of enal with imine was selected as one special case, 13j and two competing pathways including the [3 + 2] and [3 + 3] annulation pathways were considered according to the general mechanistic map suggested in Scheme 1. The relevant u + N indexes of the Nu and E partners are 7.27 and 7.65 eV, which correspond to the predicted energy barriers of 8.9 and 6.7 kcal mol À1 , respectively, based on the correlation DG ‡ p ¼ 51.8-5.9(u + N) eV/23.1 kcal mol À1 depicted in Fig. 6. Apparently, the predicted energy barriers are close to the calculated energy barriers (9.1 and 6.2 kcal mol À1 , Fig. 7) for the Michael addition process in producing products 3a and 4a. Both of the two transformations should be irreversible, so the chemoselectivity mainly be controlled by kinetics. In kinetics, the [3 + 3] annulation pathway for affording 3a is much more energetically favorable than the [3 + 2] annulation pathway for generating 4a, which is in agreement with the experimental results that the ratio of 3a : 4a is 10 : 1. 13j As depicted in Fig. 8, the NHC-catalyzed reactions of saturated carboxylic esters with o-tosylamino enones probably proceed through the following four possible pathways: the amidation, [2 + 4] cycloaddition, [3 + 4], and [3 + 6] annulation pathways. The corresponding u + N indexes of the Nu and E partners in the four pathways are equal to 5.42, 6.28, 6.92, and 6.92 eV, which indicates that the corresponding DG ‡ would be relatively lower in the [3 + 4]/ [3 + 6] annulation pathway. In thermodynamics, the energy of 3b is much lower than those of S1-b, S2-b, and S3-b, and only the transformation to product 3b is irreversible at room temperature. In summary, we can predict that the formation of 3b through the [3 + 6] annulation pathway is more favorable in both kinetics and thermodynamics. Hence, only the product 3b can be formed in theory, which is in agreement with the experimental observations. 14b Fig. 6 The linear relationship between the single-step energy barriers, DG ‡ , (unit: kcal mol À1 ) of chemoselective transition states and their corresponding u + N indexes (unit: eV) of the E and Nu partners. As shown in Fig. 9, the NHC-catalyzed reaction of simple aldehydes with acetylacetones was selected as another case, and ve pathways, including the ketolation/esterication, [2 + 2] cycloaddition, [3 + 2] annulation, and [3 + 3] annulation pathways with LiCl, were proposed based on the general mechanistic map (Scheme 1). The relevant u + N indexes of the Nu and E partners correspond to 5.53, 5.33, 6.10, and 6.60 eV, and the energy of main product 3c was found to be much lower than those of S1-c, S2-c, S3-c, and S4-c. The above analyses imply that the [3 + 3] annulation pathway with LiCl for affording 3c is more energetically favorable than the other four pathways for generating S1-c, S2-c, S3-c, and S4-c in both kinetics and thermodynamics. Hence, the main product should be 3c in theory, which is still in agreement with the results observed in experiments. 17a All the side products were proposed according to the experimental references, 13j,15a,37 and the justications of the side products were provided in Schemes S7-S9 of the ESI. † The reactivity indices could be useful for catalyst screening, but we still suggest that the searching of the transition state should be necessary to explore the origin of chemo-and stereoselectivities. Noteworthy, we have also computed the key transition states involved in the multiple pathways for generating different products in the reaction models depicted in Fig. 8 and  9. As shown in Fig. S23 of the ESI, † the order of the calculated Gibbs free energy barrier (i.e., DG ‡ (TS4b) ¼ 11.2 kcal mol À1 < DG ‡ (S2-TS3b) ¼ 18.3 kcal mol À1 < DG ‡ (S1-TS2b) ¼ 32.6 kcal mol À1 ) is the same with that of their predicted values (i.e., DG ‡ p ( [3 + 4]/ [3 + 6] annulation pathway) ¼ 11.0 kcal mol À1 < DG ‡ p ([2 + 4] cycloaddition pathway) ¼ 14.7 kcal mol À1 < DG ‡ p (amidation pathway) ¼ 19.8 kcal mol À1 ), indicating that the conclusion on the origin of chemoselectivity should be reliable. Meanwhile, a similar conclusion can be obtained from the calculated results in Fig. S24 of the ESI; † the computed energy barriers of the transition states can be used to explain the chemoselectivity well.

Conclusions
In summary, the introduction of an external base or oxidant indeed increases the complication of the reaction mechanism for the four NHC-mediated reactions of carbonyl compounds in theory, as the additives can reverse the electronic properties of NHC-involved active intermediates, i.e., acylazolium intermediate, enolate, Breslow intermediate, or a,b-unsaturated acylazolium intermediate.
As revealed by the DFT calculations of the NHC-mediated transformations, the nucleophilic enolate is obtained from the base-assisted deprotonation of the electrophilic acylazolium intermediate. The nucleophilic Breslow intermediate is generated from a base and protic media cooperatively assisted isomerization of a nucleophilic enolate, while the electrophilic a,b-unsaturated acylazolium intermediate is produced from the oxidation of a nucleophilic Breslow intermediate by an oxidant. These active intermediates could probably undergo multiple competing pathways, including the amidation/ketolation, [2 + n] (n ¼ 2, 4) cycloaddition, and [3 + n] (n ¼ 2, 4, 6) annulation pathways, when they react with other nucleophilic (Nu) or electrophilic (E) partners. This could lead to the generation of chemoselective products and greatly increases the number of theoretical calculations. Hence, we suggested an exact mechanistic map and a simple rule by merely computing the u + N indexes of the stable E and Nu partners and relative energies of intermediates and products to predict the energy barriers via the chemoselective transition states, and even predict the origin of chemoselectivity to signicantly reduce the number of theoretical computations.
Notably, this simple rule has been successfully used in several cases of NHC-mediated reactions of saturated/ unsaturated esters or aldehydes. Finally, we hope that the obtained insights will facilitate rational design according to the prediction of organocatalytic reactions with special chemoselectivities. Therefore, this work provides a theoretical method for searching and identifying the active intermediates, possible pathways, and even main products in NHC chemistry.

Conflicts of interest
There are no conicts to declare.