Guanidine–Amide-Catalyzed Aza-Henry Reaction of Isatin-Derived Ketimines: Origin of Selectivity and New Catalyst Design

Density functional theory (DFT) calculations were performed to investigate the mechanism and the enantioselectivity of the aza-Henry reaction of isatin-derived ketimine catalyzed by chiral guanidine–amide catalysts at the M06-2X-D3/6-311+G(d,p)//M06-2X-D3/6-31G(d,p) (toluene, SMD) theoretical level. The catalytic reaction occurred via a three-step mechanism: (i) the deprotonation of nitromethane by a chiral guanidine–amide catalyst; (ii) formation of C–C bonds; (iii) H-transfer from guanidine to ketimine, accompanied with the regeneration of the catalyst. A dual activation model was proposed, in which the protonated guanidine activated the nitronate, and the amide moiety simultaneously interacted with the ketimine substrate by intermolecular hydrogen bonding. The repulsion of CPh3 group in guanidine as well as N-Boc group in ketimine raised the Pauli repulsion energy (∆EPauli) and the strain energy (∆Estrain) of reacting species in the unfavorable si-face pathway, contributing to a high level of stereoselectivity. A new catalyst with cyclopropenimine and 1,2-diphenylethylcarbamoyl as well as sulfonamide substituent was designed. The strong basicity of cyclopropenimine moiety accelerated the activation of CH3NO2 by decreasing the energy barrier in the deprotonation step. The repulsion between the N-Boc group in ketimine and cyclohexyl group as well as chiral backbone in the new catalyst raised the energy barrier in C–C bond formation along the si-face attack pathway, leading to the formation of R-configuration product. A possible synthetic route for the new catalyst is also suggested.


Introduction
The aza-Henry reaction (or nitro-Mannich reaction) is one of the most effective methods for the construction of carbon-carbon bonds with concomitant generation of two vicinal stereogenic centers bearing nitro and amino functional groups [1]. The resulting β-nitroamine products can be conveniently converted into a variety of chiral building blocks (e.g., α-amino acids [2][3][4][5][6] and 1,2-diamines [7][8][9][10]); therefore, the development of efficient procedures to promote the reaction in a highly enantioselective way have received wide attention. Since the first example of a catalytic enantioselective aza-Henry reaction was reported by Shibasaki [11], many metal-based [12][13][14][15] and organic catalysts [16,17] have been employed in the nucleophilic addition of aldimine, affording β-nitroamines in high yield and stereoselectivity [18]. Compared to aldimine substrate, the reports using a ketimine as the electrophile in the asymmetric Henry reaction were limited, due to its low reactivity and poor prochiral face control [19].
The aza-Henry reaction of isatin-derived N-Boc ketimine could produce 3-substituted-3-amino-2-oxindoles, which are key structural units in many natural products and phar-obtained. These results are expected to provide useful information for the synthesis of new chiral organocatalysts for aza-Henry reactions of ketimine. Scheme 1. Asymmetric aza-Henry reaction of isatin-derived N-protected ketimines (R1) and nitromethane (R2) catalyzed by guanidine-amide catalysts.

Analysis of Reactivity at N Atoms in G1
It is well known that guanidine can act as a Brønsted base to activate the reactant by hydrogen bonding in organocatalysis [45,46,47,48]. Three types of nitrogen atoms (N2, N3 and N5) exist in the structural unit of guanidine moiety; therefore, we first optimized the geometry of G1 and evaluated the reactivity of nitrogen atoms. As shown in Table S1, Supplementary Materials, the key structural parameters in G1 were similar to those of the corresponding crystal structure obtained in the experiment [44]. Intramolecular hydrogen bonding exists between the guanidine moiety and amide moiety, with an N2···H10 distance of 1.94 Å . The proton affinity of the N2 atom (226.4 kcal·mol −1 ) is higher than those of N3 (196.3 kcal·mol −1 ) and N5 (199.6 kcal·mol −1 ). This indicated that the N2 atom with strong basicity [38,39,40,41,42,43,49] could work as the reacting site for the deprotonation of CH3NO2 in the Henry reaction.

Catalytic Mechanism for R1a
As shown in Scheme 2, the reaction mechanism of asymmetric Henry reactions between ketimine (R1a) and nitromethane (R2) consisted of three consecutive steps, including: (i) the deprotonation of CH3NO2 by guanidine-amide catalyst; (ii) formation of a C-C bond; and (iii) H-transfer from the guanidine to ketimine substrate, accompanied with the regeneration of the catalyst. The step associated with the activation of CH3NO2 was predicted to be the rate-determining step (RDS) [18]. The C-C bond formation step was the chiral-controlling step, affording R-or S-enantiomers along re-or si-face attack pathways, alternatively. Scheme 1. Asymmetric aza-Henry reaction of isatin-derived N-protected ketimines (R1) and nitromethane (R2) catalyzed by guanidine-amide catalysts.

Analysis of Reactivity at N Atoms in G1
It is well known that guanidine can act as a Brønsted base to activate the reactant by hydrogen bonding in organocatalysis [45][46][47][48]. Three types of nitrogen atoms (N2, N3 and N5) exist in the structural unit of guanidine moiety; therefore, we first optimized the geometry of G1 and evaluated the reactivity of nitrogen atoms. As shown in Table S1, Supplementary Materials, the key structural parameters in G1 were similar to those of the corresponding crystal structure obtained in the experiment [44]. Intramolecular hydrogen bonding exists between the guanidine moiety and amide moiety, with an N2· · · H10 distance of 1.94 Å. The proton affinity of the N2 atom (226.4 kcal·mol −1 ) is higher than those of N3 (196.3 kcal·mol −1 ) and N5 (199.6 kcal·mol −1 ). This indicated that the N2 atom with strong basicity [38][39][40][41][42][43]49] could work as the reacting site for the deprotonation of CH 3 NO 2 in the Henry reaction.

Catalytic Mechanism for R1a
As shown in Scheme 2, the reaction mechanism of asymmetric Henry reactions between ketimine (R1a) and nitromethane (R2) consisted of three consecutive steps, including: (i) the deprotonation of CH 3 NO 2 by guanidine-amide catalyst; (ii) formation of a C-C bond; and (iii) H-transfer from the guanidine to ketimine substrate, accompanied with the regeneration of the catalyst. The step associated with the activation of CH 3 NO 2 was predicted to be the rate-determining step (RDS) [18]. The C-C bond formation step was the chiral-controlling step, affording Ror S-enantiomers along reor si-face attack pathways, alternatively.

Activation of CH 3 NO 2
When G1 interacted with CH 3 NO 2 , it underwent a change of conformation, constructing O8· · · H4 intramolecular hydrogen bonding. This new conformation facilitated the N2 atom and amide moiety to interact with CH 3 NO 2 simultaneously by intermolecular hydrogen bonding [50]. For the molecular complex G1-COM, the N2· · · H16 and H10· · · O18 distances were 2.27 Å and 2.24 Å, respectively. AIM analysis indicated that the electronic densities (ρ) at the (3, −1) bond critical points (BCP) (a and b in Figure 1) were 0.017 a.u. and 0.014 a.u., with the corresponding hydrogen bonding energies of E a = −2.99 kcal·mol −1 Molecules 2021, 26, 1965 4 of 19 and E b = −2.27 kcal·mol −1 , respectively [51]. Compared to the free CH 3 NO 2 , the C15-H16 bond in G1-COM enlengthened from 1.09 to 1.10 Å. Meanwhile, the corresponding Wiberg bond index was decreased from 0.921 to 0.875. These results suggested that the C-H bond in CH 3 NO 2 was significantly weakened. The deprotonation of CH 3 NO 2 occurred via transition state G1-TS1, accompanied with the global electron density transfer (GEDT) of 0.23 e from G1 to CH 3 NO 2 . Accordingly, an ion-pair intermediate (G1-IM1) was formed. This step was endergonic by 3.3 kcal·mol −1 , with an energy barrier of 10.6 kcal·mol −1 .

Activation of CH3NO2
When G1 interacted with CH3NO2, it underwent a change of conformation, constructing O8···H4 intramolecular hydrogen bonding. This new conformation facilitated the N2 atom and amide moiety to interact with CH3NO2 simultaneously by intermolecular hydrogen bonding [50]. For the molecular complex G1-COM, the N2···H16 and H10···O18 distances were 2.27 Å and 2.24 Å , respectively. AIM analysis indicated that the electronic densities () at the (3, −1) bond critical points (BCP) (a and b in Figure 1) were 0.017 a.u. and 0.014 a.u., with the corresponding hydrogen bonding energies of Ea = −2.99 kcal·mol −1 and Eb = −2.27 kcal·mol −1 , respectively [51]. Compared to the free CH3NO2, the C15-H16 bond in G1-COM enlengthened from 1.09 to 1.10 Å . Meanwhile, the corresponding Wiberg bond index was decreased from 0.921 to 0.875. These results suggested that the C-H bond in CH3NO2 was significantly weakened. The deprotonation of CH3NO2 occurred via transition state G1-TS1, accompanied with the global electron density transfer (GEDT) of 0.23 e from G1 to CH3NO2. Accordingly, an ion-pair intermediate (G1-IM1) was formed. This step was endergonic by 3.3 kcal·mol −1 , with an energy barrier of 10.6 kcal·mol −1 .

Formation of C-C Bond
Starting from G1-IM1, four molecular complexes (G1-I-re-IM2~G1-II-si-IM2) were formed in models I and II, according to the different orientations of N-Boc ketimine (R1a) and nitronate (Scheme 3). The hydrogen bonding between the protonated guanidine with R1a and nitronate were verified by AIM analysis because the magnitudes of Laplacian of electron densities (∇ 2 ρ) at (3, −1) bond critical points (a and b) were positive ( Figure S1). Electrostatic potential (ESP) analysis ( Figure 2b) for the protonated guanidium fragment in G1-IM1 indicated that the surface global maximum (121.2 kcal·mol −1 ) was from the positively charged H16 atom (not H10 atom in Figure 2a), leading to preferable orientation of the CH 2 NO 2 anion by the H16 atom in the guanidium cation [52]. Accordingly, G1-Ire-IM2 and G1-I-si-IM2 in model I were slightly more stable than those of G1-II-re-IM2 and G1-II-si-IM2 by 0.9~1.7 kcal·mol −1 (Figure 3). In the following step, the C=N bond addition was achieved by nucleophilic attack of the nitronate towards the C13 atom of R1a along four pathways (I-re, I-si, II-re or II-si), followed by easy proton transfer from the N2 atom to N14 atom. The hydrogen bonds between the guanidine cation and N-Boc ketimine (R1a) in four TSs were also proved by AIM analysis ( Figure S2). The relative Gibbs free energy of transition states G1-I-re-TS2 and G1-I-si-TS2 were 1.1 and 2.3 kcal·mol −1 , respectively, which were lower than those of G1-II-re-TS2 and G1-II-si-TS2 (2.4 and 4.0 kcal·mol −1 , respectively; Figures 3 and 4). In addition, the activation barrier in the C-C bond formation step along the I-re path (∆G = = 2.4 kcal·mol −1 ) was lower than that of the I-si path (∆G = = 4.6 kcal·mol −1 ) by 2.2 kcal·mol −1 . For the II-re pathway, ∆G = in the C-C bond formation step was 0.4 kcal·mol −1 higher than that along I-re. Meanwhile, both G1-II-re-IM2 and G1-II-re-TS2 were less stable than the corresponding species in I-re pathway. These results indicated that the predominant R-configuration product observed in the experiment was predominantly produced along the I-re path. According to the Curtin-Hammett principle [53], the theoretical enantioselectivity (ee %) was 85%, which was close to the experimental result (91% ee).     We further analyzed the orbital interactions between N-Boc ketimine (R1a) and nitromethane in the C-C bond formation step. The structures of G1-I-re-TS2 and G1-I-si-TS2 were decomposed into a guanidine-nitromethane ion-pair fragment (G1-R2, Frag. 1) and an N-Boc ketimine fragment (R1a, Frag. 2). The schematic orbital interaction diagrams are shown in Figures S3 and S4. For the highest occupied molecular orbital (HOMO) of G1-I-re-TS2, it was mainly formed by the mixture of the occupied highest occupied fragment orbital (HOFO) of the G1-R2 fragment (Frag. 1, 73.35%) and the unoccupied lowest unoccupied fragment orbital (LUFO) of the R1a fragment (Frag. 2, 16.99%). The electronic density delocalization between BD(π) C15-N17 to the unoccupied BD(π*) C13-N14 (E(2) = 19.2 kcal·mol −1 ) promoted the formation of a C13-C15 bond, contributing to the orbital interaction energy (∆E orb ) of −45.29 kcal·mol −1 . Similar molecular orbital interactions was also observed in G1-I-si-TS2, with less contribution of the HOFO orbital of the G1-R2 fragment (63.59%) in the HOMO. For comparison, we also studied the dual hydrogen bond model proposed by the experiment [44]. Four optimized geometries of transition states (G1-I-re-TS2-a~G1-IIsi-TS2-a) along reand si-pathways in two models were located at the same theriacal level ( Figure S5). The ∆G of transition states in model I were significantly lower than those in model II by 7.2~10.2 kcal·mol −1 . For the TSs in model I, the CH 2 NO 2 anion was Molecules 2021, 26, 1965 8 of 19 positioned by two NH groups in the guanidine moiety of G1 catalyst, with a N-H· · · O distance of 1.95~2.47 Å. It seemed that two Cy groups in the guanidine exerted comparable hindrance effects towards ketimine in the two competing transition states. Moreover, the ∆G of G1-I-re-TS2-a was 0.9 kcal·mol −1 less stable than that of G1-I-si-TS2-a, affording the S-product as a major one (not the R-product observed in experimental observation). Although the relative Gibbs free energy of G1-I-re-TS2-a in C-C bond formation steps were lower than that of G1-I-re-TS2 by 2.6 kcal·mol −1 , the guanidine-amide catalyst had to undergo remarkable conformation changes from G1-IM1 to realize the pre-organized structure in TSs (as shown in Figure S6, the ∆G = to change the orientation of two N-Cy groups in the guanidine cation were about 10~13 kcal·mol −1 ). Thus, unless specified, we just focus on the conformation of the guanidine cation with an intramolecular H4· · · O8 in the following discussions.

Origin of Stereoselectivity
To understand the origin of stereoselectivity in the aza-Henry reaction between ketimine (R1a) and nitromethane (R2) catalyzed by guanidine G1, we analyzed the structures of the two key transition states (i.e., G1-I-re-TS2 and G1-I-si-TS2) in the chiral-controlling step (i.e., C-C bond formation step). As shown in Figure 4, the N-Boc group was placed at the same side as the bulky CPh 3 group of G1 in the G1-I-si-TS2, with a distance of about 2.83 Å. The steric repulsion between them increased the Pauli repulsion energy ∆E pauli (67.8 vs. 83.5 kcal·mol −1 ), as well as the strain energy ∆E strain of the two reacting fragments (9.8 vs. 12.9 kcal·mol −1 ) at TSs along the I-si pathway ( Figure 5). As a result, the activation energy barrier (∆G = ) along the I-si pathway was higher than those along the I-re pathway by 2.2 kcal·mol −1 . In contrast, the unfavorable steric repulsion could be efficiently avoided in G1-I-re-TS2 because the CPh 3 group was far away from the N-Boc group. The stronger interaction between the deformed reactants played the crucial factor in favoring the repathway [54,55]. That is, the more stabilizing electrostatic energy (∆V elstat ) and orbital energy (∆E orb ) efficiently offset the Pauli repulsion of two reacting fragments. Moreover, the Bn group with structural flexibility could weaken the steric hindrance from the CPh 3 group, contributing to the low relative Gibbs free energy of transition state G1-I-re-TS2 (1.1 vs. 2.4 kcal·mol −1 for G1-I-si-TS2). The noncovalent interaction (NCI) plots in Figure S7, Supplementary Materials, also reveal a large green region in G1-I-re-TS2, associated with the stabilizing CH 2 · · · π interaction between the Bn group in ketimine and CPh 3 group in the catalyst. When the ketimine R1b with a small N-COOEt group was used as a reactant in the catalytic aza-Henry reaction, the repulsion between the N-protected group in R1b and CPh 3 group in G1 was significantly decreased. Accordingly, the ∆∆G of the two competing transition states (G1-1b-I-re and G1-1b-I-si in Figure 6 and Figure S8) was decreased to 0.4 kcal·mol −1 , leading to low stereoselectivity. The inferior enantioselectivity for R1b was also observed in the experiment [44]. In contrast to R1a, the charge accumulated on the O12 atom in R1b was slightly low (−0.580 e vs. −0.584 e in R1a). In addition, the H16· · · O12 distances in G1-1b-I-re-IM2 and G1-1b-I-si-IM2 were 1.976 and 1.986 Å, respectively, which were longer than those in the corresponding intermediates for R1a (1.950 and 1.917 Å). Due to weak catalyst-R1b interactions, more energy was required to deform R1b to the TS geometries. Accordingly, the ∆E = strain values of G1-1b-I-re-TS2 and G1-1b-I-si-TS2 (11.3 and 12.7 kcal·mol −1 ) were more destabilizing than that of G1-I-re-TS2 (9.8 kcal·mol −1 ), leading to higher activation barriers. We then removed a phenyl in G1 to obtained guanidine-amide catalyst G2. The optimized geometries of the two key transition states (i.e., G2-1a-I-re-TS2 and G2-1a-Isi-TS2) in the C-C bond formation step were shown in Figure 7 and energy profile was in Figure S9, Supplementary Materials. Similar to G1, the re-face attack pathway was still more favorable than the si-face attack pathway in model I. However, the ∆∆G of the two competing transition states (G2-1a-I-re-TS2 and G2-1a-I-si-TS2) was decreased to 0.8 kcal·mol −1 , associated with low selectivity (ee = 68%). Thus, the bulky CPh 3 substituent was the key structural unit for asymmetric induction in the chiral guanidine-amide catalyst G1. The steric repulsion between N-Boc ketimine and CPh 3 substituent in G1 increased the Pauli repulsion as well as the strain energy of the reacting fragments in the chiralcontrolling step, contributing to the excellent stereochemical outcomes in the asymmetric aza-Henry reaction of N-Boc ketimine.

Turnover Frequency (TOF) Analysis
To evaluate the efficiency of the catalyst G1 along four pathways in Figure 3, the theoretical turnover frequency (TOF) of the catalytic cycle was calculated [56]. As shown in Table 1, G1-1a-I-re-IM2~G1-1a-II-si-IM2 were predicated to be TOF-determining intermediates, and G1-1a-I-re-TS2~G1-1a-II-si-TS2 were the TOF-determining transition states. The TOF value along the re-face pathway in model I was 2.06 × 10 10 s −1 , which was higher than those of other three pathways. That is, G1 exhibited better catalytic efficiency when the Henry reaction of N-Boc ketimine R1a occurred along the I-re-pathway. Table 1. Turnover frequency (TOF) of the catalytic cycle of aza-Henry reactions of isatin-derived ketimine (R1a) and nitromethane (R2) along four pathways. TDI and TDTS are the TOF-determining intermediates and TOF-determining transition states, respectively.

Path TDI TDTS TOF (s −1 ) Product
I-re G1-1a-I-re-IM2 G1-1a-I-re-TS2 2.06 × 10 10 P-R (major) I-si G1-1a-I-si-IM2 G1-1a-I-si-TS2 2.98 × 10 8 P-S II-re G1-1a-II-re-IM2 G1-1a-II-re-TS2 1.24 × 10 10 P-R II-si G1-1a-II-si-IM2 G1-1a-II-si-TS2 1.03 × 10 10 P-S Based on the results above, a working model was proposed to explain the activation of the reactants as well as the chiral induction effect of the guanidine-amide catalyst in asymmetric aza-Henry reactions. As shown in Figure 8, three factors were important for the high level of stereoselective outcomes in the catalysis, including: (i) intramolecular hydrogen bonding between the amide skeleton and imine unit of guanidine enhanced the stability of catalyst, and fixed the position of the bulky CPh 3 group in the chiral environment; (ii) N-Boc in the ketimine was placed away from the CPh 3 group, avoiding the unfavorable steric repulsion from the CPh 3 group; and (iii) the nitronate was oriented by hydrogen bonding from the imine moiety of guanidine for the favorable re-face attack for predominant R-configuration products.

Design of New Catalysts
In 2012, Lambert et al. developed a chiral 2,3-bis(dialkylamino) cyclopropenimine for the Michael reaction of a glycine imine substrate. The strong basicity of the cyclopropenimine moiety accelerated the deprotonation of glycine imine. In addition, the alcohol moiety of the catalyst activated methyl acrylate via H-bonding, contributing to the high enantioselectivity results [57]. Feng and Liu found that the modified guanidine-amide with 1,2-diphenylethylcarbamoyl and the 2,6-difluorobenzenesulfonamide group was efficient in the asymmetric catalysis [58]. Inspired by the excellent performance of cyclopropenimine in Brønsted base catalysis, we modified the structure of G1 by replacing the guanidine moiety with cyclopropenimine. In addition, the diamine with a 2,6-difluorob-enzenesulfonamide group was introduced into the molecular skeleton of the catalyst. Two new catalysts (G3 and G4) were designed (Scheme 4), and the corresponding optimized structures are shown in Figure 9. The mechanism of aza-Henry reaction between N-Boc ketimine (R1a) and CH 3 NO 2 catalyzed by G3 and G4 in low-energy model I were studied at the same theoretical level to evaluate their catalytic performance as well as chiral induction effect.
Molecules 2021, 26, x 13 of 2 group, with a distance of about 2.51 Å and 2.46 Å , respectively. Suffering from the steri repulsion from the catalyst, the relative Gibbs free energy of transition state G3-re-TS2 i the C-C bond formation along the re-face attack pathway was slightly higher than via th transition state G3-si-TS2 by 0.3 kcal·mol −1 ( Figure 10). Consequently, the product with S configuration was formed with slight predominance.   The calculations indicated that the reaction mechanisms in the presence of G3 or G4 were the same as that of G1. Due to the strong basicity of cyclopropenimine moiety, the energy barriers associated with the activation of CH 3 NO 2 were decreased to 7.9 kcal·mol −1 for G3, and 7.2 kcal·mol −1 for G4. When protonated G3 interacted with N-Boc ketimine R1a, the molecular complexes G3-re-IM2 and G3-si-IM2 were formed, in which the amide moiety activated ketimine by hydrogen bonding. Compared to G3-si-IM2, the N-Boc in G3-re-IM2 was closer to the six-membered ring of the chiral skeleton as well as the CPh 3 group, with a distance of about 2.51 Å and 2.46 Å, respectively. Suffering from the steric repulsion from the catalyst, the relative Gibbs free energy of transition state G3-re-TS2 in the C-C bond formation along the re-face attack pathway was slightly higher than via the transition state G3-si-TS2 by 0.3 kcal·mol −1 (Figure 10). Consequently, the product with S-configuration was formed with slight predominance. When G4 was used as the catalyst, the O9· · · H13 and N3· · · H11 intramolecular hydrogen bonding weakened its structural flexibility (Figure 9). The molecular complexes G4-re-IM2 and G4-si-IM2 were formed, in which the cyclopropenimine activated the CH 2 NO 2 anion, and N10-H11 as well as the N12-H13 moiety interacted with ketimine R1a by double hydrogen-bonding. In the following step, the C-C bond was constructed via transition state G4-re-TS2 or G4-si-TS2, alternatively (Figures 11 and 12). Compared to G4-re-TS2, the N-Boc group of ketimine in G4-si-TS2 was closer to 2,6-difluorobenzenesulfonamide, Ph group in the chiral backbone, as well as Cy group in the guanidine moiety. This unfavorable steric hindrance made G4-si-TS2 less stable than G4-re-TS2 by 6.3 kcal·mol −1 . The activation barrier from G4-si-IM2 to G4-si-IM3 along the si-pathway was 3.1 kcal·mol −1 , which was higher than ∆G = from G4-re-IM2 to G4-re-IM3 along the re-pathway (1.9 kcal·mol −1 ), contributing to the predominant formation of P-R (inconsistent with G1). In addition, because G4-re-IM2 was 5.1 kcal·mol −1 lower than that of G4-si-IM2, the catalyst concentration could be higher in the G4-re-IM2 reaction system. Therefore, the synergistic effects of the stronger Brønsted base (i.e., cyclopropenimine) and dual hydrogen bonding donor accelerated the activation of CH 3 NO 2 and governed the facial selectivity in substrate binding, contributing to good reactivity and selectivity.
According to synthesis investigation on guanidine derivatives with 1,2-diphenylethane-1,2-diamine groups by Feng and Liu [59], and guanidine-cyclopropenimine proton sponges by Dudding [58], we proposed a possible synthesis route for a new catalyst, G4 (Scheme 5). We expected that these results would be helpful for the development for the new catalytic system in the aza-Henry reaction of ketimine.

Materials and Methods
All DFT calculations were performed with the Gaussian 09 program [60]. The structures were optimized using the M06-2X [61] -D3 [62] function with 6-31G(d,p) basis set, and characterized by the vibrational frequency analysis at 243 K. The SMD solvation model [63] for toluene was employed in the structure optimization. The intrinsic reaction coordinate (IRC) [64] paths were traced to check the energy profiles connecting each transition state to the associated minima of the proposed mechanism. Single point energy was obtained using the same functional and 6-311+G(d,p) basis set. Natural bond orbital (NBO) [65] and reactivity indices (electrophilicity index ω and nucleophilicity index N) analysis for the reactants and the key intermediates were performed at the M06-2X-D3/6-311+G(d,p)(SMD, toluene) theoretical level. The gas-phase proton affinity (PA) [66], defined as the enthalpy change (∆H) of the deprotonation reaction (Equation (1)), was used to evaluate the reactivity of the nitrogen atoms in guanidine (G): To gain insights into the factors affecting activation barriers in the reaction process, we performed activation strain model (ASM) [67] (or distortion/interaction model [68]) analysis. Accordingly, the energy barrier (∆E) was decomposed into distortion energy (∆E strain ) and interaction energy (∆E int ) (Equation (2)): In addition, the interaction energy (∆E int ) between the strained reactants was further decomposed into electrostatic interactions (∆V elstat ), orbital interactions (∆E oi ), and Pauli repulsions (∆E Pauli ) by energy decomposition analysis (EDA) (Equation (3)) [69]. The EDA and the fragmental orbital interaction analysis were performed with the Amsterdam density functional (ADF) program package [70] at the M06-2X/TZ2P theoretical level.
Atom in molecule (AIM) analysis was carried out using Multiwfn software [71] to reveal the inter-and intramolecular interactions between catalyst and reactant. A positive or negative Laplacian value of the electron density (ρ) at the (3, −1) bond critical point (BCP) indicates that the electron density is divergent or aggregated, respectively [72,73]. Various possible conformations of the protonated guanidine species were generated by Material studio software and optimized with Gaussian 09 program. Two low-energy conformers were studied in the catalytic reaction.

Conclusions
The DFT method was adopted to study the reaction mechanism and the origin of enantioselectivity of the aza-Henry reaction between isatin-derived N-Boc ketimine and nitromethane catalyzed by the guanidine-amide catalyst. The calculations showed that the catalytic reaction occurred via a three-step mechanism. The deprotonation of nitromethane was the rate-determining step (RDS), while the C-C bond formation was the chiral-controlling step. The intramolecular hydrogen bonding formed between the amide skeleton and imine unit of guanidine enhanced the rigidity of catalyst, facilitating the imine and amide moiety to simultaneously interact with CH 3 NO 2 and N-Boc ketimine by hydrogen bonding. The repulsion between the CPh 3 group in guanidine and the N-Boc group in ketimine played an important role in controlling the enantioselectivity of the product. An unfavorable steric arrangement at the si-face attack pathway enhancing the Pauli repulsion energy as well as strain energy of the reacting species, leading to a predominant R-configuration product. The new catalysts with cyclopropenimine and sulfonamide unit were designed. The strong basicity of the cyclopropenimine moiety accelerated the activation of CH 3 NO 2 by decreasing the energy barrier in the deprotonation step. The hydrogen bonding from diamine oriented ketimine well. The repulsion between the N-Boc group in ketimine and 2,6-difluoro-benzenesulfonamide and Cy groups in the catalyst raised the energy of the C-C bond formation transition state along the si-face attack pathway, leading to the formation of a predominant R-configuration product.