Chiral phosphoric acid catalyzed atroposelective C–H amination of arenes: mechanisms, origin and influencing factors of enantioselectivity

Abstract

The amination reaction between azonaphthalene and carbazole to achieve the C–H amination of an arene can be effectively accomplished by the usage of a chiral phosphoric acid catalyst, which can generate the important N-arylcarbazole framework compound with high yield and excellent enantioselectivity. To figure out the reaction mechanism, origin and influencing factors of enantioselectivity, quantum mechanical calculations were carried out. The results indicate that two pathways lead to the experimental desired major product while other two pathways lead to the enantiomeric minor product. The theoretical ee value is 90% which is in agreement with the experimental 96% ee value. Quantum theory of atoms in molecules was employed to illustrate the roles of weak intermolecular interactions in the reaction process. A detailed analysis of the types of chiral phosphoric acids was performed to elaborate on what factors affect the enantioselectivity and how they cause the effect, and a statistical analysis of the performances of different types of chiral phosphoric acids in the C–N and C–C bond formation reactions was conducted. It is expected that the present work would be insightful for understanding the chiral phosphoric acid catalyzed C–N cross-coupling reaction and thus can guide the selection of chiral phosphoric acids for the asymmetry reaction.

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1. Introduction

Organic molecules containing N-arylcarbazole skeletons are prevalently found in natural products^1,2 which exhibit significant biological activities and organic light-emitting diodes (OLEDs)^3–15 as well as dye-sensitized solar cells (DSSCs)^16–20 which possess unique electronic properties. Consequently, many efforts have been devoted to exploring these structurally novel molecules in the past decades. Conventionally, transition-metal catalysis has been a powerful method to promote C–N bond formation in the carbazole N-arylation reaction.^21–23 For instance, Wu et al. applied the carbazole N-arylation reaction catalyzed by Pd to synthesize a novel bipolar material which can be used for the enhancement of electrophosphorescence.¹⁴ Chu and co-workers reported that Pd(II)-catalyzed one-pot syntheses of 9-(pyridin-2-yl)-9H-carbazoles can be achieved through a tandem C–H activation and C–N cross-coupling process.²⁴ Hung et al. suggested that biscarbazoles can be obtained through Pd-catalyzed inter- and intramolecular coupling reactions of anilines.^22,25 Fu et al. employed a Cu(I)–carbazolide complex to accomplish a photoinduced Ullmann-type coupling which led to N-arylcarbazole compounds.^23,26 But it is noted that the efficiency of the aforementioned reactions is affected due to the necessary prefunctionalization of the arene substrate and the resultant waste production.²⁷

In recent years, organocatalysis^28–34 has been rapidly developed and has become a very promising field in organic synthesis, especially for the reactions catalyzed by chiral phosphoric acids (CPAs) through hydrogen-bonding (HB) interactions.^33–35 Organocatalytic C–H arylation of arenes with CPAs has been successively accomplished by Tan et al.^36,37 in which the C nucleophile has been applied in the aromatic nucleophilic substitution. Inspired by this intriguing work, a more interesting and challenging idea was proposed by Tan's group, that is, how to use the N nucleophile to realize C–H amination of arenes to synthesize N-arylcarbazole frameworks in an organocatalytic way? Excitingly, for the first time, an efficient organocatalytic strategy has been elegantly developed by Tan and coworkers,²⁷ and they utilized a CPA (i.e., the catalyst (S)-C6) to catalyze the C–H amination of an azonaphthalene derivative with 2-tert-butyl-9H-carbazole via C–N cross-coupling and obtained the N-arylcarbazole compound in good yield with excellent enantiocontrol, as shown in Scheme 1. The reactants azonaphthalene derivative and 2-tert-butyl-9H-carbazole are denoted as R1 and R2, respectively. It can be seen that the axially chiral N-arylcarbazole product (denoted as P) with a high yield of 96% and an excellent enantioselectivity of 96% ee is achieved. The proton-donating and accepting abilities of the CPA enable it to act as an efficient bifunctional catalyst.^38,39 Thereby, the dual HB activation mode^38,40–45 can be expected to be applicable to the reaction system in Scheme 1 in which both R1 and R2 would simultaneously interact with (S)-C6 through HBs and thus would be activated. This significant success in organocatalytic C–C and C–N cross-couplings achieved with CPAs greatly stimulates our interest, because the C–C cross-coupling reaction between an azobenzene derivative and indole has been theoretically investigated by us recently;⁴⁶ thus in the present work we aim at figuring out the reaction mechanism, origin of enantioselectivity and role of the catalyst in the C–N cross-coupling reaction between 2-tert-butyl-9H-carbazole and the azonaphthalene derivative catalyzed by (S)-C6, and meanwhile, a comparison of organocatalytic C–C and C–N cross-couplings achieved by the CPA will be made to explore and elucidate their similarity and difference. It is expected that the results would be insightful for the organocatalytic C–C and C–N cross-couplings.

Scheme 1 (S)-C6 catalyzed C–H amination reaction of an azonaphthalene derivative with 2-tert-butyl-9H-carbazole via C–N cross-coupling.

2. Computational details

All the reactants, catalyst, complexes, transition states, intermediates and products were fully optimized at the M06-2X⁴⁷/6-31G(d,p) level of theory using the Gaussian 09 software package.⁴⁸ The vibrational frequency calculation was also carried out at this level and the temperature was set to 323 K in terms of the experimental temperature. The solvation effect of CHCl₃ was taken into account by using the SMD continuum solvation model.⁴⁹ There are no imaginary frequencies for the optimized reactants, intermediates and products, while only one imaginary frequency was found for each transition state which was also evaluated by intrinsic reaction coordinate (IRC)^50,51 calculations at the M06-2X/6-31G(d,p) level of theory. Single point calculations were performed at the M06-2X/Def2-TZVP level of theory for each optimized structure to gain more accurate energy because the basis set superposition error (BSSE) is less sensitive to the TZVP basis.⁵² The GaussView (Version 5)⁵³ and CYLview (version 1.0b)⁵⁴ software packages were employed to present the optimized structures.

Based on the optimized structures of the reactants, the global and local reactivity indexes within the framework of conceptual density functional theory (CDFT)^55,56 were applied in assessing the reactivity tendency and the reactive sites. The electronic chemical potential (μ) and chemical hardness (η) can be calculated based on the energies of the highest occupied molecular orbital (E_HOMO) and the lowest unoccupied molecular orbital (E_LUMO) using the equations μ = (E_HOMO + E_LUMO)/2 and η = E_LUMO − E_HOMO. The global electrophilicity index (ω) can be calculated in terms of μ and η using ω = (μ²/2η). The global nucleophilicity index (N) can be calculated according to the definition by Domingo and coworkers,^57–60 which can be defined as the HOMO energy difference between the reactant (R) and tetracyanoethylene (TCE): N = E_HOMO(R) − E_HOMO(TCE). The molecule tetracyanoethylene (TCE) has the lowest E_HOMO compared to a large series of molecules,⁶¹ so it is taken as a reference. Herein, the HOMO energies are obtained within the Kohn–Sham scheme.⁶² Additionally, to evaluate the reactivity of an atom k in each reactant, the local reactivity indexes like the condensed-to-atom versions of the Fukui functions^56,63–67 were employed:

Herein, q_k is the electronic charge of an atom k and N is the number of electrons. When the value of f_k⁺ is positive and large, it means that atom k in a molecule is susceptible to nucleophilic attack (electron-accepting). But when the value of f_k⁻ is positive and large, it indicates that atom k in a molecule is susceptible to electrophilic attack (electron-donating). The negative Fukui function will not be taken into account because it is usually obtained from the inability of a molecule to accommodate orbital relaxation due to a change in the number of electrons and/or improper charge partitioning techniques^68–70 or distorted molecular structures.^67,71–73

The powerful theoretical tools including quantum theory of atoms in molecules (QTAIM)^74–76 analyses were utilized to illustrate the roles of intermolecular interactions formed in the complexes, transition states and intermediates. QTAIM analyses can be used to reveal the topological properties at the bond critical points (BCPs) of HB, van der Waals, and π–π interactions.^61,77–85 Natural bond orbital (NBO)^86,87 analyses were used to obtain the natural atomic charge. The plots were obtained using Multiwfn (Version 3.5⁸⁸) software.

3. Results and discussion

3.1 Evaluating the reactivity of the reactants R1 and R2

For the (S)-C6-catalyzed amination reaction displayed in Scheme 1, it is evident that the bonding reaction occurs between the C1 atom of R1 and N3 atom of R2, which finally leads to the axially chiral N-arylcarbazole product P. To understand the electrophilic and nucleophilic reactivities of the reactants R1 and R2, the global electrophilicity (ω) and nucleophilicity (N) indexes were calculated, as summarized in Table 1. Meanwhile, the bonding site selectivity of R1 and R2 was also assessed based on the condensed-to-atom Fukui functions, as outlined in Table 2. It can be seen that R1 has a larger electrophilicity index than R2, meaning that it will act as an electrophile, while R2 has a larger nucleophilicity index than R1, and hence it will serve as a nucleophile. From Table 2, it can be seen that the C1 atom of R1 has the largest f⁺ value while the N3 atom of R2 has the largest f⁻ value, so the C1 atom of R1 has the most electrophilic characteristic while the N3 atom of R2 has the most nucleophilic characteristic. Accordingly, the bonding sites for the reaction between R1 and R2 should appear between the C1 and N3 atoms, agreeing with the experiment result.

Table 1 The frontier molecular orbital energies E_HOMO and E_LUMO (in eV), electronic chemical potential (μ, in eV), chemical hardness (η, in eV), global electrophilicity (ω, in eV) and nucleophilicity (N, in eV) indexes for the reactants R1 and R2

	E HOMO	E LUMO	μ	η	ω	N
R1	−7.449	−1.996	−4.723	5.453	2.045	3.058
R2	−6.911	−0.124	−3.518	6.788	0.911	3.596

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Table 2 The condensed-to-atom Fukui functions for the selected C and N atoms in the reactants R1 and R2^a

Reactant	Atom	f ^+	f ^−
a The atomic numbers of the selected C and N atoms in the reactants R1 and R2 are shown in Scheme 1.
R1	C1	0.133	0.117
	C2	−0.032	0.025
	C3	0.016	0.081
	C4	0.026	0.151
	C5	0.048	−0.040
	C6	0.003	0.156
	C7	0.059	0.031
	C8	0.011	0.073
	C9	0.034	0.136
	C10	−0.017	−0.024
R2	C1	0.087	0.102
	C2	0.000	−0.024
	N3	0.020	0.190
	C4	0.007	−0.004
	C5	0.073	0.093
	C6	0.106	−0.003
	C7	−0.003	0.136
	C8	0.114	0.023
	C9	0.039	0.064
	C10	0.048	0.034
	C11	0.126	0.041
	C12	−0.003	0.105
	C13	0.113	0.000

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3.2 Mechanisms of (S)-C6-catalyzed amination reaction between R1 and R2 which leads to the chiral N-arylcarbazole

For the amination reaction shown in Scheme 1, there are four different orientations for R1 and R2, as displayed in Fig. 1, so the reaction could proceed via four different modes corresponding to four pathways (i.e., paths I–IV). In each pathway, R1 and R2 simultaneously interact with (S)-C6via dual HB activation mode, that is, the O2–H2 group of (S)-C6 serves as one HB donor to interact with the N2 atom in the N1=N2CO₂Me group of R1 (i.e., O2–H2⋯N2 HB) while the O1 atom in the P=O1 group of (S)-C6 acts as one HB acceptor to interact with the N3–H3 group of R2 (i.e., O1⋯H3–N3 HB). As shown in Fig. 1, the reaction paths I and III generate the experimental desired product P with a yield ratio of 96%, while paths II and IV lead to the minor enantiomer of product P (denoted as ent-P) with a yield ratio of 4%, and the enantioselectivity ratio of P1 : ent-P1 is 98 : 2 (Scheme 1).

Fig. 1 Four modes of the reaction between R1 and R2 catalyzed by (S)-C6 and the resultant products P and ent-P.

As depicted in Fig. 2, the Gibbs free energy profile for path I indicates that the overall reaction leading to the product P goes through the dimeric and trimeric complexes (i.e., DI and COMI), two transition states (i.e., TSI-1 and TSI-2) and four intermediates (i.e., IMI-1–IMI-4). The optimized geometries of the reactants, catalyst, complexes, transition states, intermediates and product are shown in Fig. 3. Both the reactants (R1 and R2) can interact with the catalyst (S)-C6 to form the dimeric complex, but the calculation results suggest that the dimeric complex formed between R1 and (S)-C6 (i.e., DI) has a lower Gibbs free energy than that between R2 and (S)-C6 (see Table S1 in the ESI† for details), meaning that the complex DI is more favorable. An energy of 4.2 kcal mol⁻¹ is needed in the formation of DI. In DI, the O2–H2⋯N2 HB forms between the N1=N2R group of R1 and the O2–H2 group of (S)-C6 (see Fig. S2 and Table S2 in the ESI†). The subsequent interaction between DI and R2 forms the trimeric complex COMI in which the O1⋯H3–N3 HB between the N3–H3 group of R2 and the P=O1 group of (S)-C6 (see Fig. S3 and Table S3 in the ESI†), and an energy of 2.1 kcal mol⁻¹ are needed for DI to COMI. The H2⋯N2 distance increases after the formation of COMI (i.e., 1.72 Å in DI and 1.73 Å in COMI). From Table 3, it can be seen that the O2–H2⋯N2 HB in COMI has a shorter H2⋯N2 distance than the O1⋯H3 distance of O1⋯H3–N3 HB, and the O2–H2⋯N2 HB strength is stronger than O1⋯H3–N3 HB strength. The natural atomic charge of the C1 atom in COMI becomes less negative than that in R1, indicating that the C1 atom of R1 is electrophilic, while the natural atomic charge of the N3 atom in COMI becomes more negative than that in R2, suggesting that the N3 atom of R2 is nucleophilic. Then the proton transfer occurs from (S)-C6 to R1 which leads to the conversion of the O2–H2⋯N2 HB into O2⋯H2–N2 HB in TSI-1 (see Fig. S4 and Table S4 in the ESI†). Meanwhile, the nucleophilic attack of the N3 atom on the C1 atom also takes places, as can be seen from the decreased C1⋯N3 distance (i.e., 2.08 Å) relative to that in COMI (i.e., 3.12 Å). The C1–N3 bond with a bond length of 1.55 Å forms in IMI-1 (Fig. 3), and an energy release of 7.0 kcal mol⁻¹ is observed for the process from TSI-1 to IMI-1. Due to the proton transfer of the H3 atom to O1 atom, one new O1–H3⋯N3 HB also forms in IMI-1 (see Fig. S5 and Table S5 in the ESI†). From COMI to IMI-1, the tautomerization of (S)-C6 finishes the conversions of the phosphorus–oxygen bond from a single bond (i.e., P–O2 in COMI) to a double bond (i.e., P=O2 in IMI-1) and from the double bond (i.e., P=O1 in COMI) to a single bond (i.e., P–O1 in IMI-1), and (S)-C6 is converted into its tautomer in IMI-1. But then the O1–H3⋯N3 HB breaks in IMI-2 (see Fig. S6 and Table S6 in the ESI†), and the N3 atom recovers back to the sp² hybridized state. In the process of conversion from IMI-1 to IMI-2, the tendency of the axial chirality along the C1–N3 bond appears. The ionization of the tautomerized (S)-C6 in IMI-2 makes the protonation of the N1 atom possible which leads to the formation of the N1–H3 bond. After this, the left O1⁻ group is able to approach the H1 atom of the H1–C1 group and forms the O1⁻⋯H1 interaction with a distance of 2.03 Å in IMI-3 (see Fig. S7 and Table S7 in the ESI†). The processes from IMI-1 to IMI-3 have a total energy release of 9.8 kcal mol⁻¹. The H1 atom gradually shifts to the O1⁻ anion which goes through the transition state TSI-2, and the O1⁻⋯H1 and C1⋯H1 distances in TSI-2 are 1.38 and 1.29 Å, respectively (Fig. 3 and S8, Table S8†). An energy of 6.2 kcal mol⁻¹ is absorbed (Fig. 2) from IMI-3 to TSI-2. The O2⋯H2 distance of O2⋯H2–N2 HB becomes longer (i.e., 1.96 Å) in TSI-2. The O1–H1 bond finally forms in the intermediate IMI-4 and thus the catalyst (S)-C6 is recovered which releases an energy of 28.1 kcal mol⁻¹ (Fig. 2). In IMI-4, (S)-C6 interacts with the experimental favorable axially chiral product Pvia O2⋯H2–N2 and O1–H1⋯N1 HBs (see Fig. S9 and Table S9 in the ESI†). After the breakage of the O2⋯H2–N2 and O1–H1⋯N1 HBs, the catalyst is separated from IMI-4 and the major product P is finally generated.

Fig. 2 Path I for the reaction between R1 and R2 catalyzed by (S)-C6 leading to the product P and the Gibbs free energy profile. The Gibbs free energies of [R1 + R2 + (S)-C6] were set to 0.0 kcal mol⁻¹ as a reference.

Fig. 3 The optimized geometries of the reactants, catalyst, complexes, transition states, intermediates and product in path I. The distances are in Å. Some hydrogen atoms are omitted for clarity.

Table 3 The intermolecular distances (d, in Å) for the HBs, the HB strengths (E_HB, in kcal mol⁻¹) and the natural atomic charges (q, in electrons) in the complexes COMI–IV formed in paths I–IV^a

Complex	HB^b		Natural atomic charge^c
	O1⋯H3–N3	O2–H2⋯N2	q C1	q N3
a The atomic number is shown in Scheme 1. b The HB strength can be calculated using EHB = −0.429GBCP, in which GBCP is the local electronic kinetic energy density at the bond critical point (BCP) of HB. c The natural atomic charge on the C1 atom in R1 (qC1) is −0.1352 electrons, and that on the N3 atom in R2 (qN3) is −0.5261 electrons.
COMI	d (O1⋯H1) = 2.07	d (H2⋯N2) = 1.73	−0.1036	−0.5438
	E HB = −4.2	E HB = −7.9
COMII	d (O1⋯H1) = 1.95	d (H2⋯N2) = 1.68	−0.1041	−0.5459
	E HB = −5.4	E HB = −9.0
COMIII	d (O1⋯H1) = 1.99	d (H2⋯N2) = 1.71	−0.1247	−0.5415
	E HB = −4.6	E HB = −8.5
COMIV	d (O1⋯H1) = 2.06	d (H2⋯N2) = 1.68	−0.0841	−0.5459
	E HB = −4.4	E HB = −9.3

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Path II is the most favorable pathway in generating the product ent-P (Fig. 1). The Gibbs free energy profile for the whole reaction processes of path II is shown in Fig. 4, and the optimized geometries of the complexes, transition states, intermediates and product are shown in Fig. 5. Similar to the reaction processes occurring in path I, the catalyst (S)-C6 firstly interacts with R1 and forms the dimeric complex DIIvia the O2–H2⋯N2 HB (see Fig. S10 and Table S10 in the ESI†) which needs an energy of 4.2 kcal mol⁻¹. Then R2 participates in the interaction and its H3–N3 group interacts with the P=O1 group of (S)-C6via the O1⋯H3–N3 HB (see Fig. S11 and Table S11 in the ESI†), resulting in the trimeric complex COMII. This process is endothermic and needs an energy of 4.8 kcal mol⁻¹. In COMII, the H2⋯N2 distance of the O2–H2⋯N2 HB is 1.68 Å which becomes shorter than that in DII (i.e., 1.72 Å), while the O1⋯H3–N3 HB has an intermolecular O1⋯H3 distance of 1.95 Å (Fig. 5). Also, it can be seen from Table 3 that the H2⋯N2 distance of the O2–H2⋯N2 HB in COMII is shorter and the O2–H2⋯N2 HB is stronger. The variation of the natural atomic charge of the C1 (or N3) atom in COMI relative to that in R1 (or R2) indicates that the C1 atom of R1 is electrophilic, while the N3 atom of R2 is nucleophilic. Then the proton transfer takes place in which the H2 atom in the O2–H2 group of (S)-C6 is shifted to the N2 atom of R1 and forms a new O2⁻⋯H2–N2 HB with an O2⁻⋯H2 distance of 1.76 Å in TSII-1. As shown in Fig. 5, the O1⋯H3 distance of the O1⋯H3–N3 HB in TSII-1 is contracted (i.e., 1.86 Å). The nucleophilic attack of the N3 atom on the C1 atom is observed in TSII-1, and the C1⋯N3 distance is 2.05 Å (Fig. 5 and S12, Table S12†). The process of conversion from COMII to TSII-1 needs to overcome an energy barrier of 19.1 kcal mol⁻¹ (Fig. 4). Due to the tautomerization of (S)-C6 in TSII-1, the original P–O2 single bond is converted into a P=O2 double bond in IMII-1, while the original P=O1 double bond is converted into a P–O1 single bond, and thus (S)-C6 is converted into its tautomer in IMII-1. In IMII-1, the H3 atom is abstracted from the H3–N3 group and is shifted to the O1 atom, leading to the O1–H3 bond. Two intermolecular HBs (i.e., O2⋯H2–N2 and O1–H3⋯N3 HBs) exist in IMII-1 (see Fig. S13 and Table S13 in the ESI†), and the C1–N3 bond forms with a bond length of 1.54 Å. After the breakage of the O1–H3⋯N3 HB (see Fig. S14 and Table S14 in the ESI†), the N3 atom is recovered to the sp² hybridization state and the axial chirality along C1–N3 bond tends to appear in IMII-2. The acidity of IMII-2 enables it to give its proton in the O1–H3 group to the N1 atom leaving the O1⁻ anion which tends to approach the H1 atom in the C1–H1 group in the intermediate IMII-3. QTAIM analyses of IMII-2 and IMII-3 are shown in Fig. S14, S15 and Tables S14, S15.† The process from IMII-1 to IMII-3 is exothermic. Due to the strong attraction between the O1⁻ anion and H1 atom, the H1 atom gradually shifts to the O1⁻ anion in the transition state TSII-2. QTAIM analyses of TSII-2 are shown in Fig. S16 and Table S16.† As shown in Fig. 5, the interaction distance between the O1⁻ anion and H1 atom is 1.33 Å, while the distance between C1 and H1 atoms is 1.31 Å. The energy barrier for the process from IMII-3 to TSII-2 is 5.4 kcal mol⁻¹. The O1–H1 bond forms in IMII-4, in which the O2⋯H2–N2 HB remains (see Fig. S17 and Table S17 in the ESI†). After the breakage of the O2⋯H2–N2 HB, the catalyst (S)-C6 is regenerated and the minor product ent-P is yielded.

Fig. 4 Path II for the reaction between R1 and R2 catalyzed by (S)-C6 leading to the product ent-P and the Gibbs free energy profile. The Gibbs free energies of [R1 + R2 + (S)-C6] were set to 0.0 kcal mol⁻¹ as a reference.

Fig. 5 The optimized geometries of the complexes, transition states and intermediates in path II. The distances are in Å. Some hydrogen atoms are omitted for clarity.

Both the reaction paths I and III result in the experimental desired product P, while both the reaction paths II and IV lead to the minor product as ent-P, so the mechanism of path III (or IV) is similar to that of path I (or II), and therefore, the detailed reaction mechanisms for paths III and IV are presented in the ESI† for simplicity.

A comparison of the energy barriers in paths I–IV suggests that the enantioselectivity-determining steps correspond to the rate-determining steps in which the transition states TSI-1, TSII-1, TSIII-1, and TSIV-1 in paths I–IV with the highest energies determine the enantioselectivity of (S)-C6-catalyzed amination reaction. From Fig. 2, 4, S18 and S19,† we can see that the energies of TSI-1, TSII-1, TSIII-1, and TSIV-1 in paths I–IV follow an order of TSI-1 (26.2 kcal mol⁻¹) < TSII-1 (28.1 kcal mol⁻¹) < TSIV-1 (38.5 kcal mol⁻¹) < TSIII-1 (39.5 kcal mol⁻¹), indicating that path I is the most favorable pathway leading to the experimental desired product P and path II is the most favorable pathway leading to the product ent-P. In addition, we found that the trimeric complex COMI (or COMII) with a lower energy is more favorable than COMIII (or COMIV) in converting into the corresponding transition state.

The calculated ee value (see the ESI† for details) matches well with the experimental one (96% ee, Scheme 1). The results show that the amination reaction between R1 and R2 catalyzed by (S)-C6 proceeds through path I which leads to the major product P, while the minor product ent-P is achieved through path II.

3.3 Origin and influencing factors of enantioselectivity

To assess what factors affect the enantioselectivity and how they cause the effect, as a representative, we first analyzed and made a comparison of the transition states TSI-1 and TSII-1. As shown in Fig. 6, in TSI-1 and TSII-1, (S)-C6 provides one proton to R1 and interacts with R1via the O2⋯H2–N2 HB while it interacts with R2via the O1⋯H3–N3 HB simultaneously. It is evident that (S)-C6 anions and R1 cations in TSI-1 and TSII-1 have similar orientations, while R2 in them has the opposite orientation, and the large chiral pocket of the (S)-C6 anion allows it to accommodate the R1 cation and R2. Noticeably, a greater extent of twisting is observed for the phenanthryl group of the (S)-C6 anion in TSII-1 than that in TSI-1. This phenomenon should be attributed to the close contact of the –tBu group of R2 and the phenanthryl group of the (S)-C6 anion in TSII-1 which causes a large steric hindrance. Thereby, in fact, (S)-C6 is flexible in controlling the size of its chiral pocket, and whether the reactants match with the size of the chiral pocket or not will finally determine the enantioselectivity.

Fig. 6 The orientations of the reactants and catalyst in the optimized structures of TSI-1 and TSII-1.

Accordingly, in the following sections, the size of the chiral pocket of the CPA which affects the enantioselectivity will be elaborated in detail. To gain a good understanding of the relationship between the sizes of chiral pockets of CPA catalysts and their enantioselective performance, the amination reactions between 2-(naphthalen-2-yl)diazenecarboxylate (denoted as R1a) and 2-tBu-9H-carbazole (R2) catalyzed by a series of CPA catalysts with different –R and –Ar groups were selected and investigated, as outlined in Table 4. From the previous analysis of the (S)-C6 catalyzed amination reaction between R1 and R2, it can be found that paths I and II are more favorable and they mainly lead to the respective products P and ent-P, while paths III and IV are less favorable and they make a small contribution in leading to the respective products P and ent-P, so the final ee value is determined by paths I and II. Because the transition state with the highest energy determines the enantioselectivity of the amination reaction, the transition states of the two favorable pathways resulting in the main product and its enantiomer for the amination reactions (Table 4) were taken into account to explain the influence of the structures of CPAs on the ee values. As shown in Fig. 7, the theoretical ee value is in agreement with the experimental ee value, and the result indicates that the catalytic performance in the stereocontrol of BINOL-derived CPAs (i.e., (R)-C8, (R)-C10) is inferior to that of SPINOL-derived CPAs (i.e., (S)-C1, (S)-C2, (S)-C3, (S)-C6) in the amination reactions between R1a and R2 (Table 4).

Fig. 7 The relationship between the experimental and theoretical ee values for the amination reactions catalyzed by CPA catalysts.

Table 4 The selected CPA catalysts, reaction conditions (solvent and temperature T, in °C), relative Gibbs free energy (ΔΔG_TS, in kcal mol⁻¹), and experimental (Exper. ee) and theoretical ee (Theor. ee) values in the reaction catalyzed by each CPA catalyst

CPA	Solvent	T	ΔΔGTS ^b	Exper. ee	Theor. ee
a 10 mol% of (S)-C6 was used, and 3 Å molecular sieves (MS) were added, DCE = 1,2-dichlorethane. b ΔΔGTS is the energy difference between the Gibbs free energies of the transition states in the two favorable pathways resulting in the main product and its enantiomer for the amination reactions.
(S)-C1	CH2Cl2	40	1.3	65	78
(S)-C2	CH2Cl2	40	1.6	74	87
(S)-C3	CH2Cl2	40	2.7	87	98
(S)-C6	CH2Cl2	40	3.0	90	98
(R)-C7	CH2Cl2	40	−1.2	−88	−76
(R)-C8	CH2Cl2	40	−0.6	−25	−46
(R)-C10	CH2Cl2	40	−0.4	−24	−31
(S)-C6^a	CHCl3	50	4.1	93	100

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To assess the role of the –Ar group in the CPA catalyst, a comparison was made. Herein, the –Ar group of (S)-C6 is replaced by a H atom to obtain a new catalyst (denoted as (S)-C6H), and then the interactions of (S)-C6H, R1a and R2 were optimized and they are similar to the previous paths I and II. Accordingly, the two transition states TSI_H-1 and TSII_H-1 corresponding to two paths I_H and II_H for the (S)-C6H catalyzed reaction between R1a and R2 can be obtained, and TSI_H-1 has a higher Gibbs free energy than TSII_H-1 by 1.2 kcal mol⁻¹. It can be seen from their optimized geometries displayed in Fig. 8 that the C1⋯N3 distance in TSII_H-1 is longer than that in TSI_H-1 by 0.05 Å (i.e., 2.09 Å in TSI_H-1 and 2.14 Å in TSII_H-1), which can be attributed to the intermolecular repulsion between the –tBu group of R2 and the azo group of R1a. The relatively lower Gibbs free energy of TSII_H-1 compared to that of TSI_H-1 indicates that the smaller chiral pocket of (S)-C6H cannot cause significant steric hindrance for the interaction between R2 and R1a. Similarly, the reaction between R1a and R2 catalyzed by (S)-C6 with the –Ar group also occurs following paths I_Ar and II_Ar, and the C1⋯N3 distance of TSII_Ar-1 is 0.06 Å longer than that in TSI_Ar-1 (i.e., 2.03 Å in TSI_Ar-1 and 2.09 Å in TSII_Ar-1). It can be seen that the protonated R1a interacts with R2 with an appropriate C1⋯N3 distance in TSI_Ar-1, and the –tBu group of R2 is out of the chiral pocket of the (S)-C6 anion, and these arrangements make the complex between the protonated R1a and R2 match well with the chiral pocket of the (S)-C6 anion. In contrast, the interaction between the protonated R1a and R2 in TSII_Ar-1 has a different arrangement in which the –tBu group of R2 is located in the chiral pocket of the (S)-C6 anion, causing a longer C1⋯N3 distance. Clearly, such an arrangement results in a stronger steric repulsion between the aromatic ring of the protonated R1a (or R2) and the –Ar group of the (S)-C6 anion, so a relatively higher Gibbs free energy (ca. 3.0 kcal mol⁻¹) of TSII_Ar-1 compared to that of TSI_Ar-1 is observed.

Fig. 8 The transition states (a) TSI_H-1 and TSII_H-1 for (S)-C6H catalyzed and (b) TSI_Ar-1 and TSII_Ar-1 for (S)-C6 catalyzed reactions between R1a and R2. The C1⋯N1 distances are in Å.

To further illustrate the effect of the chiral pocket of the CPA catalyst, a comparison between (S)-C6 and (R)-C10 was made, as shown in Fig. 9. The chiral pocket is measured from the distance between the C atoms of –Ar groups connected to the main skeleton of the CPA. Compared to (S)-C6, (R)-C10 provides a similar chiral environment, but the (R)-C10 catalyzed reaction between R1a and R2 offers the opposite axially chiral product with a lower ee value. The reason can be the fact that (R)-C10 provides a larger chiral pocket which can effectively reduce the steric repulsion between the –tBu group of R2 and the –Ar group of the (R)-C10 anion in the transition state which is denoted as TSI_(R)-C10-1 or TSII_(R)-C10-1. Consequently, the Gibbs free energies for the transition states TSI_(R)-C10-1 and TSII_(R)-C10-1 have a few differences (ca. 0.4 kcal mol⁻¹, Table 4), so a lower enantioselectivity (i.e., −24% ee) is observed.

Fig. 9 The sizes of the chiral pockets of (S)-C6 and (R)-C10. The chiral pocket is measured by the distance between the C atoms of –Ar groups connected to the main skeletons of the CPAs. The distances are in Å.

In terms of the above analyses, for the amination reaction in which the C–N bond forms, it appears that the BINOL-derived CPA catalyst possessing the larger size of the chiral pocket like (R)-C10 shows poor performance while the SPINOL-derived CPA catalyst with the smaller size of the chiral pocket like (S)-C6 shows good performance. In the transition states, given that the C–N bond is shorter than the C–C bond, it can be hypothesized and expected that the BINOL-derived CPA catalyst could catalyze the reaction system in which the C–C bond forms because the C⋯C distance in the transition state for C–C bond formation reaction is usually longer than the C⋯N distance in the transition state for C–N bond formation reaction. To verify this, the BINOL-derived CPA (i.e., (R)-C10) catalyzed C–C bond formation reaction between 2-(naphthalen-2-yl)diazenecarboxylate (denoted as R1a) and 2-tBu-indole (R3) was investigated, as shown in Fig. 10a. It can be seen from Fig. 10 that the C⋯C distances in the transition states (i.e., TSI′_(R)-C10-1 and TSII′_(R)-C10-1) for (R)-C10 catalyzed reactions are longer than the C⋯N distances in the transition states (i.e., TSI_Ar-1, TSII_Ar-1) for the (S)-C6 catalyzed reaction between R1a and R2 by about 0.23 or 0.14 Å. Note that the size of the chiral pocket of BINOL-derived CPAs like (R)-C10 (i.e., the C⋯C distance between the C atoms of –Ar groups connected to the main skeletons of (R)-C10 shown in Fig. 9) is larger than that of SPINOL-derived CPAs like (S)-C6 (i.e., the C⋯C distance between the C atoms of –Ar groups connected to the main skeletons of (S)-C6 shown in Fig. 9) by about 0.17 Å. Therefore, the size of the chiral pocket of BINOL-derived CPAs seems to be suitable for catalyzing the C–C bond formation reaction, but actually the catalytic performance of BINOL-derived CPAs is also related to the sizes of substrates.

Fig. 10 (a) The reaction between 2-(naphthalen-2-yl)diazenecarboxylate (denoted as R1a) and 2-tBu-indole (R3) catalyzed by the (R)-C10 catalyst and (b) the two transition states TSI′_(R)-C10-1 and TSII′_(R)-C10-1 in two paths I′ and II′ of this reaction. The C1⋯C1 distances are in Å.

Furthermore, a statistical analysis of the previous experimental work^37,89–99 was conducted to assess the tendencies of SPINOL- and BINOL-derived CPAs in catalyzing C–C and C–N bond formation reactions. The reactions catalyzed by CPAs including SPINOL- and BINOL-derived catalysts to form the C–N and C–C bonds are summarized in Tables 5 and 6, respectively. As shown in Fig. 11, the C–N bond formation reaction systems catalyzed by the SPINOL-derived CPAs provide higher ee values and better yields than those catalyzed by the BINOL-derived CPAs. In contrast, the C–C bond formation reaction systems catalyzed by the BINOL-derived CPAs lead to higher ee values and better yields than those catalyzed by the SPINOL-derived CPAs. Thereby, it can be concluded that the type of CPA does significantly affect the experimental results in terms of both the ee value and yield, and to a certain extent the SPINOL-derived CPA possessing a moderate chiral pocket functions more efficiently for the C–N bond formation reaction system while the BINOL-derived CPA possessing a larger chiral pocket functions more efficiently for the C–C bond formation reaction system, and the reason is that the sizes of substrates match well with the chiral pocket of these CPAs. Further analyses suggest that the SPINOL-derived CPA can function excellently in catalyzing not only the C–N bond formation reaction but also the C–C bond formation reaction,¹⁰⁰ or even better than the BINOL-derived CPA,¹⁰¹ while the BINOL-derived CPA can also catalyze the C–N bond formation reaction with good performance.¹⁰² Obviously, the good performance of either the SPINOL- or BINOL-derived CPA is significantly dependent upon the precondition that the sizes of substrates should match well with the chiral pocket of CPA. In addition, it should be noted that the chiral pocket of the CPA catalyst is decided not only by the backbone but also by the substituent on the –Ar group. The bigger hindrance the substituent provides, the smaller pocket the CPA catalyst has. The relationship between the substituent on the –Ar group and the size of the chiral pocket of the CPA will be taken into account in future work.

Fig. 11 The experimental yield (%) and ee (%) value for (a) the C–N and (b) C–C bond formation reactions catalyzed by SPINOL- and BINOL-derived CPAs.

Table 5 The C–N bond formation reaction systems catalyzed by SPINOL- and BINOL-derived CPAs, experimental yield (%) and ee (%) value

Reaction	CPA	Yield	ee	Ref.^a
a Ref.: The reaction yield (%) and ee (%) value are taken from the previous experimental work.
	CA1	51	87	89
	CC1	32	28
	CA2	66	60	90
	CC2	22	34
	CA3	94	72	91
	CB1	91	6
	CA4	94	−68
	CC3	92	−9
	CA5	72	97	92
	CB2	61	81
	CA2	55	−88
	CB3	54	40

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Table 6 The C–C bond formation reactions catalyzed by SPINOL- and BINOL-derived CPAs, experimental yield (%) and ee (%) value

Reaction	CPA	Yield	ee	Ref^a
a Ref.: The reaction, yield (%) and ee (%) value are taken from the previous experimental work.
	CA6	33	−90	37
	CB4	99	92
	CA7	88	−41	93
	CB5	90	57
	CA7	75	−86	94
	CB5	91	−89
	CA8	41	12	95
	CB6	99	96
	CA3	17	44	96
	CB1	33	89
	CA7	Traces	—	97
	CB3	18	88
	CA7	47	60	98
	CB5	76	91
	CA9	39	40	99
	CC4	99	48

---

4. Conclusions

Theoretical investigations on the C–N cross-coupling reaction between azonaphthalene (R1) and carbazole (R2) using the chiral phosphoric acid (i.e., (S)-C6) were carried out. The results show that four pathways (I–IV) may exist in which paths I and II dominantly generate the main and minor products, respectively. The amination reaction between R1 and R2 catalyzed by (S)-C6 was promoted by dual HB activation mode. The roles of intermolecular interactions in the complexes, intermediates and transition states in the four pathways were illustrated by QTAIM analysis. It is demonstrated that the types of chiral phosphoric acids significantly affect the enantioselectivity, and the SPINOL-derived CPAs like (S)-C6 are suitable for the asymmetric C–N bond formation reaction systems while the BINOL-derived CPAs like (R)-C10 are suitable for the asymmetric C–C bond formation reaction systems to a certain extent, but it should be emphasized that the performance of either the SPINOL- or BINOL-derived CPA catalyst significantly depends upon the condition whether the sizes of substrates match well with the chiral pocket of CPA or not.

Conflicts of interest

The authors declare that they have no conflict of interest.

Acknowledgements

We acknowledge the financial support from the Natural Science Foundation of Gansu Province, China (No. 20JR5RA289), the Fundamental Research Funds for the Central Universities (lzujbky-2020-kb06) and the Open and Cooperation Innovation Fund from Xi'an Modern Chemistry Research Institute.

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Footnote

† Electronic supplementary information (ESI) available: The optimized geometries of the dimeric complexes in paths I–IV, and their relative Gibbs free energies and intermolecular interaction energies; QTAIM analyses and for the complexes, transition states and intermediates; the mechanisms of paths III and IV for the enantioselective (S)-C6 catalyzed atroposelective C–H amination reaction; and Cartesian coordinates. See DOI: 10.1039/d0qo01160f

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