Role of Chiral Skeleton in Chiral Phosphoric Acids Catalyzed Asymmetric Transfer Hydrogenation: A DFT Study

Abstract

Chiral phosphoric acids (CPAs) have received considerable attention due to their high activity for enantioselective transformations. However, the role of various chiral skeletons of CPAs in regulating the mechanism and enantioselectivity of asymmetric transfer hydrogenation has remained unclear. Density functional theory (DFT) calculations are performed to elucidate the role of chiral skeletons on the acidity, mechanism, enantioselectivity, and kinetic stabilities of transition states (TSs) in Asymmetric Transfer Hydrogen (ATH) reaction catalyzed by five CPAs. We found that the acidity of CPAs is strongly dependent on the chiral skeleton. The origin of enantioselectivity of ATH reaction arises from the differential noncovalent interactions between TSs and CPAs. Moreover, the shape and size of the catalyst pocket depending on chiral skeletons play key roles in the stability of TSs and the enantioselectivity of ATH. This study might facilitate to design and computationally screening of CPAs and guide the strategic choice of CPA skeletons to reduce the experimental workload.

1. Introduction

Since the pioneering work in the development of BINOL-derived chiral phosphoric acids by Akiyama and Terada in 2004, chiral phosphoric acids (CPAs) have received considerable attention due to their efficient activity as catalysts for a wide range of enantioselective transformations with potential applications in industry and academia [1,2]. Generally, CPAs catalyze enantioselective transformations in a bifunctional activation by forming dual hydrogen bonds (H-bonds) with both the electrophile and the nucleophile simultaneously [3,4]. The steric bulky bridging groups at the 3,3′-position combined with the chiral skeletons construct a chiral pocket to improve the stereoscopic control ability. Due to this structural motivation, CPAs have been widely applied in asymmetric reactions [5,6,7].

Currently, significant progress in the understanding of CPAs-catalyzed reactions has been achieved. Destiny functional theory (DFT) calculations are a powerful tool for elucidating the mechanisms of a range of reactions catalyzed by CPAs [8,9]. For example, Yamanaka et al. carried out the bifunctional activation model to investigate the reaction mechanism, and the enantioselectivity of chiral BINOL-derived CPA catalyzed benzothiazoline hydrogenation [10]. Terada et al. identified that the multi-point C-H···O H-bonds and the π interactions between the substrates and F₁₀BINOL-derived skeleton were important to determine the stereochemical outcomes [11]. Meanwhile, Grayson and Falcone performed the NBO and NCI analysis to visualize the no-bonding interactions between the substrate and CPAs to explain the origin of the enantioselectivity of aza-Cope rearrangement [12]. In 2020, Yang and Peng et al. elucidated the origin of chirality control by the stacking and staggered intermolecular interactions of CPA and substrates for the allene formation step [13]. Very recently, Champagne showed that the selectivity of N-acyl-azetidine desymmetrization is assigned by the different arrangements of the transition states relative to the CPA structure by using the steric maps [14]. Experimental and theoretical reports found that the enantiomer of CPAs reveals different catalytic performances [15,16]. For example, Ying et al. found that on the (S)-CPA, the enantiomer product ratio is 55:45, while on the (R)-CPA, this ratio is 63:37 in asymmetric selenoetherification [17]. Sunoj also illustrated the relative Gibbs free energies of the TSs on the same skeleton but different in the enantiomer of CPAs are not exactly the same [18]. In addition, Zhang shows based on the SPINOL divided chiral phosphoric acid, the ΔΔG^‡ for transition states on (S)-enantiomer of CPA is 1.3 kcal/mol while this value is 2.0 kcal/mol on (R)-enantiomer of CPA [19].

The asymmetric transfer hydrogenation (ATH) of ketamine (as shown in Scheme 1) is the most powerful approach due to its simple operation and avoiding hydrogen gas as a hydrogen resource [6]. Recently, List et al. increased the steric bulk of the catalyst by adding aromatic substituents at the 3,3′-positions of the binaphthol skeleton, markedly improving catalytic performance (up to 93% ee with 96% yield) [20].

Nowadays, experiments still have been devoted to developing new axially chiral skeletons of CPAs to improve the catalytic performance and extend the substrates of asymmetric reactions. At present, CPAs are derived from the various chiral skeletons (Scheme 2), such as the BINOL [21] (CPA1), H₈-BINOL [22] (CPA2), VAPOL [23] (CPA3), SPINOL [19] (CPA4) and 6,6′-dimethyl-2,2′-biphenyldiol [24] (CPA5), which have been proved to be enabling a broad range of enantioselective reactions. Thus, a deep understanding of how the axially chiral skeletons of CPAs affect the activity and enantioselectivity of asymmetric reactions needs to be discussed in the computational chemistry field. The relative report has not been reported in the literature.

The density functional theory (DFT) calculations are an indispensable tool to provide microscopic insights into the mechanism of ATH catalyzed by CPAs. In this study, we use the DFT calculations to investigate the mechanism of ATH of imine with thiazole, as illustrated in Scheme 1. We aim to reveal the role of the chiral skeleton on the acidity, mechanism and enantioselectivity in the ATH reactions catalyzed by five CPAs, which are derived from various chiral skeletons, as shown in Scheme 2. We first investigated the mechanism and reactivity of ATH reactions on five (R)-/(S)-CPAs. The RE-TS-S and RZ-TS-R are realized to be the relatively stable TSs on CPAs, the enantioselectivity is calculated by the energy barrier difference between these two TSs. Subsequently, we discuss the acidity of various chiral skeletons, which affect the stability of TSs on CPAs through the H-bonds interactions. Through the activation-strain model (ASM) and noncovalent interactions (NCI) index method, we analyze the distortion and interaction energies of TSs, substrates, and CPAs to reveal the origin of enantioselectivity. Finally, a quantitative representation of the shape and size of the pockets of CPAs is performed. We found that the shape and size of the pocket play key roles in the stability of TSs and the enantioselectivity of ATH reactions on CPAs. These DFT results might provide valuable insights for the rational design of an efficient construction strategy for CPAs catalysts.

2. Computational Details

Because of a lack of existing literature on the detailed conformations of TSs on five CPAs, we performed a conformational analysis by using the conformers module in Materials studio software [25]. The initially coarse conformations of TSs on CPAs were generated from DFT calculations. Subsequently, the conformational analysis was performed by varying the four torsion angles of initial TSs as displayed in Figure S1. The systematic grid scan was performed based on the Universal Force Field [26]. We considered the 1296 conformations by rotating four torsion angles on each TS in the range of 0° to 360° within a step size of 60°, simultaneously. Finally, only one lowest energy conformer was carried out in the next DFT calculation. All DFT calculations were carried out within Gaussian 09 software [27]. The geometry optimization of intermediates, transition states, and products within toluene solvent was carried out at M06-2X/6-31G (d) [28] level with a polarizable continuum model (PCM) [29]. The harmonic vibrational frequency was performed at 333 K to testify the energy minima and transition states at the same level. The imaginary frequency of each transition state on each CPA was listed in Tables S4 and S5. The single point energies in toluene solvent were derived from the optimized geometries at M06-2X/6-311G (d, p) level to achieve accurate energy. The intrinsic reaction coordinate (IRC) [30] approach was used to identify the transition states connecting the reactants with products. To better deal with the effects of low-frequency vibrations on the structure, thermodynamic corrections were calculated using the rigid rotor harmonic oscillator (RRHO) model in the Shermo program [31]. The Boltzmann-weight (100%) of TSs on (R)-/(S)-CPAs were obtained by Shermo program. The atomic coordinates for all intermediates, transition states, and products on five CPAs were provided in the Supporting Information section.

The free Gibbs energy (G), activation barrier (ΔG^‡_barrier), and reaction energy (ΔG) on each reaction were calculated from Equations (1)–(3).

G = E^ele + G^therm

(1)

ΔG^‡_barrier = G_TS − G_reactant

(2)

ΔG = G_product − G_reactant

(3)

E^ele and G^therm were the electronic energy and thermal correction. G_TS, G_reactant, and G_product were the free Gibbs energies of the transition state, reactant, and product, respectively. The sum of the Gibbs free energies of the CPA and the two substrates as estimated at 333 K were used as the zero-point reference. Tables S6–S15 list the energies of all the intermediates, transition states and products on CPAs.

Based on the transition-state-theory [32], the rate constants for the (R)- and (S)-enantiomers were calculated from:

$${\mathrm{k}}_{\mathrm{R}}=\frac{{\mathrm{k}}_{\mathrm{B}}\mathrm{T}}{\mathrm{h}}{\mathrm{e}}^{-\Delta G_{\mathrm{R}}^{‡}/\mathrm{RT}}$$

(4)

$${\mathrm{k}}_{\mathrm{S}}=\frac{{\mathrm{k}}_{\mathrm{B}}\mathrm{T}}{\mathrm{h}}{\mathrm{e}}^{-\Delta G_{\mathrm{S}}^{‡}/\mathrm{RT}}$$

(5)

where ΔG^‡_R/S was the reaction barriers for (R)-/(S)-enantiomers, k_B was the Boltzmann constant, h was the Plank’s constant, and T was 333 K. If the enantioselectivity of (R)-/(S)-enantiomers were kinetically controlled, the enantiomeric excess (ee) [33] can be estimated by:

$$\mathit{ee}\%=\left|\frac{\left[{\mathrm{k}}_{\mathrm{S}}\right]-\left[{\mathrm{k}}_{\mathrm{R}}\right]}{\left[{\mathrm{k}}_{\mathrm{S}}\right]+\left[{\mathrm{k}}_{\mathrm{R}}\right]}\right|\times 100\%=\frac{{1-\mathrm{e}}^{-\Delta \Delta G^{‡}/\mathrm{RT}}}{{1+\mathrm{e}}^{-\Delta \Delta G^{‡}/\mathrm{RT}}}\times 100\%$$

(6)

where $\Delta \Delta G^{‡}=\left|\Delta G_{\mathrm{R}}^{‡}-\Delta G_{\mathrm{S}}^{‡}\right|$ was the energy difference in the reaction barriers for the formation of (R)-/(S)-enantiomers.

NBO (natural bond orbital) [34] analysis was used to display the H-bonds strength for the key transition states on (R)-CPA2. The Non-covalent interactions (NCI) [35] index method was used to reveal the isosurface of non-covalent interactions. The reduced density gradient (RDG) was obtained by Multiwfn [36]. The RDG function was expressed in Equation (7), where ρ (r) was the total electron density. Different types of interactions (attractive and repulsive) were distinguished by multiplying the density with the sign of the second-density Hessian eigenvalue (λ2). The sign of λ2 distinguishes the bonded (λ2 < 0) from nonbonded (λ2 > 0) interactions. The isosurface of RDG was plotted by using VMD software [37].

$$\mathrm{RDG}(r)=\frac{1}{{2(3\mathsf{\pi }}^2{)}^{1/3}} \frac{|\nabla \mathsf{\rho }\left(\mathrm{r}\right)|}{{\mathsf{\rho }\left(\mathrm{r}\right)}^{4/3}}$$

(7)

The origin of enantioselectivity was analyzed by using the activation-strain model (ASM), as reported by Bickelhaupt et al. [38,39] (or the distortion-interaction model of Houk and Ess [40,41]). The potential energy surface was calculated from:

$$\Delta \mathrm{E}\left(\mathsf{\zeta }\right)=\Delta {\mathrm{E}}_{\mathrm{dist}}\left(\mathsf{\zeta }\right)+\Delta {\mathrm{E}}_{\mathrm{int}}\left(\mathsf{\zeta }\right)$$

(8)

where ζ is the reaction coordinate, ΔE_dist (ζ) is the distortion energy, which was associated with the structural deformation that the substrates undergo, ΔE_int (ζ) was the interaction between these increasingly deformed substrates. The activation energy of a reaction $\Delta {\mathrm{E}}^{‡}=\Delta \mathrm{E}\left({\mathsf{\zeta }}^{\mathrm{TS}}\right)$ consists of activation strain $\Delta {\mathrm{E}}^{‡}{}_{\mathrm{dist}}=\Delta {\mathrm{E}}_{\mathrm{dist}}\left({\mathsf{\zeta }}^{\mathrm{TS}}\right)$ plus the TS interaction $\Delta {\mathrm{E}}^{‡}{}_{\mathrm{int}}=\Delta {\mathrm{E}}_{\mathrm{int}}\left({\mathsf{\zeta }}^{\mathrm{TS}}\right)$:

$$\Delta {\mathrm{E}}^{‡}=\Delta {\mathrm{E}}^{‡}{}_{\mathrm{dist}}+\Delta {\mathrm{E}}^{‡}{}_{\mathrm{int}}$$

(9)

The distortion energy was the sum of two components: the energy required to distort substrate from ground-state geometry to transition-state geometry and the energy required to distort catalyst from ground-state to transition-state geometry:

$$\Delta {\mathrm{E}}_{\mathrm{dist}}=\Delta {\mathrm{E}}_{\mathrm{dist}-\mathrm{sub}}+\Delta {\mathrm{E}}_{\mathrm{dist}-\mathrm{cata}}$$

(10)

3. Results and Discussion

3.1. Mechanism and Reactivity

As experimental investigations revealed, (R)-BINOL-derived CPAs are widely used in ATH [42,43]. Assuming the activation bifunctional mode, as previously reported by Yamanaka [10] and co-workers, we first investigate the mechanism of ATH catalyzed by five (R)-/(S)-CPAs (Scheme 1). Herein, we simplified the catalyst in the experiment by changing the 3,3′-position substituents from 2,4,6-triisopropylphenyl to phenyl [20]. The general mechanism of ATH reaction starts with the formation of a co-adsorption (Co-ads) complex. Imine and thiazole simultaneously interact with CPAs through two H-bonds. Then, ATH reaction proceeds a proton transfer step to generate a TS. During this process, imine serves as the electrophile, while thiazole acts as the nucleophile. Finally, a new enantiomer amine (Pro) is afforded. As assumed, thiazole is a racemic mixture with equal amounts of (R)- and (S)-enantiomer, meanwhile, imine is either in (Z)- or (E)-configuration. Four possible TSs named RE-TS-S, RZ-TS-R, SE-TS-S, and SZ-TS-R can be generated on each (R)/(S)-CPAs. Figures S2–S11 show the optimization geometries, H-bonds distances, and the short noncovalent bond interactions distances of TSs on each CPA. Boltzmann-weight (/%) is calculated and used to demonstrate the distributions of four possible TSs in thermodynamics. The values of Boltzmann-weight and reaction barrier ΔG^‡_barrier (kcal/mol) of four TSs are listed in

Table 1. Boltzmann-weight (/%) and reaction barrier ΔG^‡_barrier (kcal/mol) of four possible TSs on CPAs.

CPAs	Boltzmann-Weight					ΔG‡barrier
	RE-TS-S	RZ-TS-R	SE-TS-S	SZ-TS-R		RE-TS-S	RZ-TS-R	SE-TS-S	SZ-TS-R
(R)-CPA1	4.88	94.26	0.85	0.02		15.0	9.8	15.9	17.8
(R)-CPA2	1.44	98.01	0.54	0.01		14.1	8.0	15.2	16.9
(R)-CPA3	2.74	97.25	0.00	0.00		13.9	9.2	18.3	18.2
(R)-CPA4	0.03	99.24	0.07	0.66		15.0	9.5	15.8	13.3
(R)-CPA5	8.65	91.35	0.00	0.01		14.6	10.2	23.6	16.5
(S)-CPA1	3.96	88.65	7.33	0.06		15.0	12.5	13.1	17.6
(S)-CPA2	31.35	67.73	0.80	0.12		15.4	10.4	16.4	15.0
(S)-CPA3	4.55	3.61	90.74	1.10		21.7	17.8	15.2	18.8
(S)-CPA4	0.00	82.83	16.31	0.86		19.6	10.8	11.2	15.6
(S)-CPA5	10.98	84.81	4.17	0.04		16.2	11.3	13.0	17.1

. Enantioselectivity of ATH reaction on CPAs is listed in Table S1.

On most CPAs, when using (R)-thiazole as substrate, it interacts with either (E)- or (Z)-imine to form RE-TS-S and RZ-TS-R, which have high Boltzmann-weight values (Table 1). If (E)-imine is the substrate, no matter what (R)- or (S)-thiazole, SE-TS-S and RE-TS-S are formed, and they are in low Boltzmann-weight on most CPAs, except (S)-CPA3. Similarly, the ΔG^‡_barrier of RZ-TS-R and RE-TS-S are lower than that of SE-TS-S and SZ-TS-R (Table 1) on most CPAs. These results indicate that among four possible TSs on most CPAs, RZ-TS-R and RE-TS-S are high stability in thermodynamics. We also consider that the imine in (E)- or (Z)-conformation is responsible for the stability in thermodynamics of RZ-TS-R and RE-TS-S in the ATH reaction.

It is remarkable that RZ-TS-R has higher Boltzmann-weight values (>67.73%) and lower barriers (<12.5 kcal/mol) than RE-TS-S (<31.35% and >13.9 kcal/mol), leading to the (R)-enantiomer as the major product on most CPAs. The sums of Boltzmann-weight of RZ-TS-R and RE-TS-S are above 99.14% on all of (R)-CPAs, as well as the values are in the range from 82.83% to 99.08% on most (S)-CPAs except (S)-CPA3. Only on (S)-CPA3, the Boltzmann-weight values of SE-TS-S and SZ-TS-R are 90.74% and 1.10%, resulting (S)-enantiomer as the major product. These results mean that RZ-TS-R and RE-TS-S as the major TSs are formed on most CPAs, while SE-TS-S and SZ-TS-R are less likely on most CPAs, except on (S)-CPA3. Based on these above calculations, in subsequent sections, we will discuss the reaction barrier, acidity, origin of enantioselectivity, and the role of the chiral skeleton on ATH reaction by using the data from RE-TS-S and RZ-TS-R on five (R)-/(S)-CPAs.

The energy barrier difference (ΔΔG^‡_barrier) between RE-TS-S with RZ-TS-R for the formation of (R)-/(S)-enantiomers, and the enantioselectivity (ee) of ATH on CPAs are shown in Figure 1. It can be found that the calculated ee values are over 95% with significantly high enantioselectivity of ATH reactions on CPAs, no matter what chiral skeleton. Indeed, the calculated ee values are slightly higher than that (93% ee) in experimental observations, which was reported by List et al. [20] Our calculation results are still extremely instructive and valuable for predicting and screening CPA catalysts. The purpose of our theoretical work is to reveal the effect of the chiral skeleton of CPAs on asymmetric reactions and relationship between structures with catalysis at molecule level based on DFT method. The calculation results show that ATH reactions prefer to form (R)-enantiomers as the major product on most CPAs. Notably, RZ-TS-R is the favorable TS, which always has the low reaction barrier affording to (R)-enantiomer on CPAs. We believe that the pathway affording to (R)-enantiomer is more advantageous in terms of kinetics on CPAs. These results are consistent with the observation reported by Yamanaka et al. [10]. We also note that on the same skeleton of CPAs, the values of ΔG^‡_barrier of RE-TS-S and RZ-TS-R on (R)-CPAs are always lower than that on (S)-CPAs. Significantly, RZ-TS-R on CPA2 has the lowest ΔG^‡_barrier (8.0 kcal/mol) to be the most kinetically preferable in ATH reaction among CPAs, while the largest value of ΔΔG^‡_barrier (8.8 kcal/mol) appears on (S)-CPA4, which offers the highest enantioselectivity (ee 99.99%) in ATH reaction.

In order to exhibit the interactions between RE-TS-S, RZ-TS-R and skeleton of CPAs. Here, in, we take CPA2 as the example to show the optimized geometries of RE-TS-S and RZ-TS-R (see Figure 2). The O···HN H-bonds and the noncovalent interactions including the CH-π and π-π interactions are existed between RE-TS-S and RZ-TS-R and (R)/(S)-CPA2. RZ-TS-R possess shorter H-bond interactions and longer noncovalent interactions as compared with RE-TS-S on CPA2. The reason should be attributed to the steric hindrance of RZ-TS-R, which has the (Z)-imine with a small molecular size as the substrate. Thus, RZ-TS-R can be easily accessed by the P=O group of CPA2 to form H-bonds. Furthermore, we also found that RE-TS-S and RZ-TS-R on (S)-CPA2 have longer H-bond distances than that on (R)-CPA2, as shown in Figure 2. Similar observations are also found on the other CPAs, except CPA4, as listed in NBO analysis of Tables S2 and S3. Based on these results, we speculated that the TSs are stabilized on most (R)-CPAs, except CPA4. In other words, (R)-CPAs might be more favorable catalyst for ATH reaction than (S)-CPAs. Furthermore, the orientation and relative position of TSs are likely to depend on the enantiomer and skeleton of CPA4. Due to the enantiomer and the narrow reaction space inherently, (R)-CPA4 might cause a strong steric hindrance to TSs, leading to long H-bond distances and short noncovalent interactions, while on (S)-CPA4, it represents a contrary result.

3.2. Acidity of CPAs

Experiments have demonstrated that the reaction activity and stereoselectivity catalyzed by CPAs are related to their acidities [44,45]. Here, the acidic strength is quantified by proton affinity (PA) [46], which is evaluated as the energy difference between protonated and deprotonated CPAs. Generally, a smaller PA value corresponds to a stronger acidity [47,48]. CPAs have PA values ranging between 292.0 and 297.3 kcal/mol (

Table 2. Proton affinity (PA in kcal/mol) of CPAs.

CPAs	CPA1	CPA2	CPA3	CPA4	CPA5
	293.5	297.3	292.0	296.8	295.2

). The PA value (kcal/mol) decreases in the order CPA2 (297.3) > CPA4 (296.8) > CPA5 (295.2) > CPA1 (293.5) > CPA3 (292.0). This trend is also consistent with the pKa values of CPAs reported by Cheng et al. [44]. Furthermore, we found that the acidity is strongly dependent on the chiral skeleton of CPAs. PA values reduce as associated with decreasing the electronic conjugation. Hence, CPA2 with the large PA value, exhibits the weakest acidity, while CPA3 becomes the strongest acid among the analogues due to the electronic conjugation effect from the 3,3′ and 4,4′-substituents. In addition, CPA4 with a SPINOL-derived skeleton possesses weaker acidity compared to a BINOL-derived skeleton.

NBO analysis of H-bonds in two key TSs on five CPAs is listed in Tables S2 and S3. We found that the strength of H-bonds of TSs is related to the acidity of CPAs. A higher acidity corresponds to weaker hydrogen bonds in TSs. For example, the second-order perturbation energy of H-bonds in TSs on CPA3 are smaller than the other CPAs. In addition, the H-bonds interactions of RZ-TS-R are stronger than that in RE-TS-S, as identified by the second-order perturbation energy on CPAs (see Tables S2 and S3). Thus, we can conclude that the favorable TS (such as RZ-TS-R on CPA2) possesses higher stability, stronger H-bond interactions, shorter H-bonds distances, and closely linear H-bond angles (see Table S2), as compared with unfavorable TS (RE-TS-S on CPA2). These DFT results agree with the experimental observations that were testified by Steiner—Limbach curve from the NMR spectrum [49]. In summary, the acidity of CPAs plays a crucial role in the stability of TSs in ATH reactions.

3.3. Origin of Enantioselectivity on CPAs

To understand the origin of enantioselectivity of the ATH reaction on CPAs, we adopted the NCI analysis to visualize the noncovalent interactions between RE-TS-S and RZ-TS-R and (R)-/(S)-CPAs as shown in Figure 3. The activation-strain model (ASM) is used to analyze the relative distortion and interaction energies of TSs and five (R)-/(S)-CPAs by single-point calculations at M06-2X/6-311G (d, p) level in toluene solvent. The relative energy differences (ΔΔE) between RE-TS-S and RZ-TS-R are decomposed into contributions from the distortions of substrates and CPAs into the TSs geometries (ΔΔE_dist) and the difference in noncovalent interactions between the substrates and CPAs (ΔΔE_int), as listed in

Table 3. Relative distortion and interaction energy (kcal/mol) between RE-TS-S and RZ-TS-R on CPAs.

CPAs	ΔΔE	ΔΔEdist	ΔΔEint	ΔΔEdist-cata	ΔΔEdist-sub
(R)-CPA1	3.7	2.8	0.9	0.0	2.8
(R)-CPA2	6.2	3.2	3.0	0.4	2.8
(R)-CPA3	4.7	3.3	1.4	0.1	3.2
(R)-CPA4	5.4	4.7	0.7	3.5	1.2
(R)-CPA5	5.3	2.9	2.4	0.0	2.9
(S)-CPA1	2.7	5.2	−2.5	2.1	3.1
(S)-CPA2	4.5	8.6	−4.1	4.3	4.3
(S)-CPA3	2.3	1.3	1.0	0.4	0.9
(S)-CPA4	8.6	6.9	1.7	4.2	2.7
(S)-CPA5	3.6	4.8	−1.2	2.5	2.3

. Furthermore, ΔΔE_dist also can be decomposed into the energy difference required to distort CPAs (ΔΔE_dist-cata) and substrates (ΔΔE_dist-sub) into the corresponding to TSs geometries.

As shown in Figure 3, NCI plot shows that RE-TS-S has a large green surface than RZ-TS-R on all CPAs, indicating that the high stabilizing π-stacking interactions are present in the benzene rings between (E)-imine and thiazole. Moreover, it can be found that RZ-TS-R within (Z)-conformation has a smaller steric hindrance to be the favored TS, whose substrates are orientated away from the benzyl group of CPAs. The long noncovalent bond distances and the less green surface of RZ-TS-R on CPAs can prove its good stabilization. RE-TS-S has large molecular dimensions, it is suffered the strong steric repulsion interactions from the 3,3′-position substituents of CPAs. Especially, on CPA4, the short CH-π interactions are present in RE-TS-S as compared with RZ-TS-R leading to the large green surface (Figure 3). Among five CPAs, no matter what (R)- or (S)-enantiomer, RE-TS-S and RZ-TS-R have the shortest CH-π interactions on CPA4, and the longest CH-π interactions on CPA3. Obviously, the distance of CH-π interactions is related to the skeleton and shape pocket of CPAs. We speculate that the enantiomer of CPAs might affect the noncovalent interactions, relative orientations and conformations of RE-TS-S and RZ-TS-R. Hence, we adopt the activation-strain model to express the relative distortion and interaction energies between TSs and CPAs.

As listed in Table 3, on all of CPAs, the ΔΔE_int are less significant as compared with the ΔΔE_dist, which is the major contribution for the ΔΔE. On the (R)-CPAs, the largest ΔΔE_dist (4.7 kcal/mol) appears in the narrowest pocket of CPA4. Its ΔΔE_dist-cata (3.5 kcal/mol) indicates the conformational distortion of chiral skeleton of CPA4, which plays a key role in enantioselectivity. Due to the SPINOL-derived skeleton, CPA4 has a small angle of the chiral axial (

Table 4. Initial and changed chiral angle (CA/◦) and pocket dimension (PD/Å) of TSs’ geometry on CPAs.

CPAs	Parameter	Initial	(R)-CPAs		(S)-CPAs
			RE-TS-S	RZ-TS-R	RE-TS-S	RZ-TS-R
CPA1	CA	56.4	1.4	−1.4	2.5	−1.6
	PD	12.0	1.3	−0.3	1.0	0.4
CPA2	CA	56.6	3.7	3.4	3.5	2.1
	PD	11.9	1.4	−0.1	1.0	1.2
CPA3	CA	73.8	−15.3	−18.5	19.5	18.7
	PD	13.3	0.1	−0.4	0.8	0.6
CPA4	CA	28.8	2.7	0.1	−4.8	−0.4
	PD	10.2	1.4	1.4	3.0	1.6
CPA5	CA	57.3	0.3	−0.8	−3.1	−1.7
	PD	11.9	1.3	−0.1	−1.3	−0.9

), which creates an intrinsic narrow pocket for TSs to exhibit the strong steric repulsion interactions (purple lines in Figure 3) with the short CH-π interactions. The direct evidence is that the structural distortion of chiral skeleton is maximized as listed in Table 3.

We also found that on (R)-CPA1, CPA2, and CPA5, their ΔΔE_dist-sub is relatively constant (2.8~2.9 kcal/mol), and the ΔΔE_dist-cata is very small (0.0~0.4 kcal/mol). These results imply that the enantioselectivity arises chiefly from the conformational distortion of the substrates (ΔΔE_dist-sub) on these (R)-biphenyldiol derived chiral skeletons. Moreover, on (R)-CPA2 and CPA5, the ΔΔE_dist (3.3 and 2.9 kcal/mol) corresponds closely to ΔΔE_int (3.0 and 2.4 kcal/mol). We should note that the noncovalent interactions between the substrates and these two CPAs (ΔΔE_int), as well as the conformational distortion of substrates, (ΔΔE_dist-sub) are the dominant factors in controlling the stereoselectivity. Compared with (R)-CPA5, (R)-CPA2 has favorable interactions with RE-TS-S and RZ-TS-R as evidenced by the stronger H-bonds interactions, shorter H-bond distances, more linear NH···O angles (Tables S2 and S3). Therefore, the ΔΔE_int on (R)-CPA2 is 3.0 kcal/mol, which is higher than that on (R)-CPA5. Concerning the contribution to the large substituent groups on the chiral skeleton of CPA2, it possesses well flexibility to adjust its geometry to fit TSs. This is reflected in the ΔΔE_dist-cata value of 0.4 kcal/mol. Similarly, (R)-CPA3 can rotate its chiral angle of the skeleton (ΔΔE_dist-cata in 0.1 kcal/mol) and occur the conformational distortion of the substrates (ΔΔE_dist-sub in 3.2 kcal/mol).

Meanwhile, the values of ΔΔE (2.7, 4.5 and 3.6 kcal/mol) on (S)-CPA1, CPA2, and CPA5 are smaller than that (3.7, 6.2 and 5.3 kcal/mol) on (R)-CPAs. The reason should be contributed by the negative value of ΔΔE_int, which compensates for the large values of ΔΔE_dist (5.2, 8.6 and 4.8 kcal/mol) on (S)-CPA1, CPA2, and CPA5. Combined with the NCI plot to analyze, on these three biphenyldiol derived skeletons, there is an empty region (blue region in Figure 3) between RE-TS-S and (R)-CPAs. On the contrary, the similar empty region is not found on (S)-CPAs. This result implies that the (R)-/(S)-enantiomer of CPAs has a crucial influence on the orientations and conformations of RE-TS-S and RZ-TS-R by changing the noncovalent interactions in their pockets. By distorting (S)-CPAs skeleton and substrates, the ΔΔE_dist-cata (2.1, 4.3 and 2.5 kcal/mol) close to ΔΔE_dist-sub (3.1, 4.3 and 2.3 kcal/mol) in TSs on CPA1, CPA2 and CPA5. On (S)-CPA4, the structural distortions of chiral skeleton (ΔΔE_dist-cata in 4.2 kcal/mol) is the dominant factors in controlling the stereoselectivity and the conformational distortion of substrates and catalysts. For the (S)-CPA3, the ΔΔE_dist-cata (0.4 kcal/mol) and ΔΔE_dist-sub (0.9 kcal/mol) are very small, indicating that steric hindrance is a small influence on the TSs in their pocket. Based on the above results, we can conclude that the enantioselectivity of ATH reactions on CPAs is mainly determined by the differential noncovalent interactions between TSs and CPAs, and the conformational distortion of substrates and catalysts. These structural distortions of chiral skeleton provide an inherent driving force for ATH reaction.

3.4. Chiral Skeletons of CPAs

In this work, we conduct a quantitative representation of the shape and size of pocket of CPAs, two key geometries parameters: chiral angles (CA) and pocket dimension (PD) are shown in Figure S13. Table 4 lists the parameters of the empty pocket and the changed parameters (ΔCA and ΔPD) when TSs are in the pocket. Figure 4 displays the superimposition of the axial projections of (R)-/(S)-CPAs (green), RE-TS-S (blue), and RZ-TS-R (pink), respectively. We can find that CPAs are flexible, and they can rotate their chiral angles to regulate the size of pocket dimensions. The shape and size of the pocket play key roles in the determination of the stability of TSs and enantioselectivity of ATH reaction on CPAs. As listed in Table 4, CPA4 with the small CA (28.8°) and PD (10.2 Å) create a narrow pocket among CPAs due to their SPINOL-derived skeleton. In contrast, the 3,3′ and 4,4′-substituents of CPA3 make it to be an electronic conjugation structure resulting in a wide pocket (CA: 73.8° and PD: 13.3 Å).

CPA1, CPA2 and CPA5 are biphenyldiol-derived chiral skeletons and have close parameters to provide a similar shape and size pocket. These results indicate that the orientation and conformation of TSs are dependent on the CPAs’ pocket shape, which is again related to the chiral skeleton. When TSs are formed in the wide pocket of CPA3, which rotates its chiral angle of the skeleton to meet the requirements of the noncovalent bond interactions for TSs. The small ΔΔE_dist-cata (<0.4 kcal/mol in Table 3) is identified by the small ΔPD values for TSs (from −0.4 to 0.8 Å). However, CPA4 strongly distorts itself, it is still not enough to support space for TSs. Especially on (S)-CPA4, it supports the largest ΔPD (3.0 Å) for RE-TS-S, which is suffered strongly steric repulsion interactions, as evidenced by the shortest CH-π interactions (2.17 and 2.28 Å) as shown in Figure 3. The calculated ΔΔE_dist-cata (4.2 kcal/mol in Table 3) also confirmed this observation. We consider that CPA4 with the SPINOL-derived skeleton has a rigid structure. In the investigation reported by Houk et al., they also found that the SPINOL-derived CPA are more rigid than BINOL-derived CPA [50]. In addition, the similar research was reported by Wheeler et al., they stated that the sterically bulky 3,3′aryl groups of CPAs serve to create a narrow binding groove that restricts the possible binding orientations of the substrate in TS structure in the asymmetric ring openings of meso-epoxides [51]. The largest and smallest values of ΔPD appear in CPA4 and CPA3, which are constructed by SPINOL- and VAPOL- derived skeletons, that result in either too wide or too narrow pockets for TSs. However, the values of ΔPD of CPA1, CPA2, and CPA5 are very close. This result has been attributed to their biphenyldiol axial chirality. Thus, we consider that the chiral skeleton by adjusting the pocket dimension influence the enantioselectivity of the ATH reaction catalyzed by CPAs. We further speculate that the narrow shape and small dimension of pocket CPAs make steric repulsions important to the kinetic stability of TSs in high enantioselectivity.

Furthermore, the ΔCA and ΔPD values of (S)-CPAs are larger than that on (R)-CPAs. Notably, RZ-TS-R always has the smaller ΔCA and ΔPD values than RE-TS-S on (R)-CPAs. It is attributed to the TS in (Z)-conformation with a small steric hindrance, RZ-TS-R has a favorable conformation with low-barrier on (R)-CPAs. In addition, we also found that CPAs rotate their 3,3′-substituents to change the PD values to accommodate TSs, especially on (R)-CPA4 and (S)-CPA2. The effect of steric hindrance of 3.3′-position substituents of CPAs is important in ATH reaction. This observation is in line with the investigation reported by Goodman et al. [18]. Through the above DFT calculations, we consider that this ATH reaction catalyzed by CPAs is controlled and maintained by the axially chiral skeleton, which simultaneously manipulates the kinetic stabilities of TSs in its pocket and enantioselectivity of ATH. Furthermore, we also speculate the ideal catalyst for the ATH reaction might have the following characteristics: (R)-CPAs prefer to (S)-CPAs, TSs possess the short H-bond distances and appropriate non-covalent bond interactions in high stability on (R)-CPAs; the lower acidity of CPAs could result in the high stability TSs with stronger H-bonds; the shape of the TSs’ structure is unique for ATH reaction, and the shape of the CPAs must fit that TSs without being too narrow or wide pocket.

4. Conclusions

DFT calculations have been carried out to investigate the ATH reaction catalyzed by CPAs with various chiral skeletons. The mechanism, reactivity, and enantioselectivity of ATH reaction are calculated based on the dual activation model, in which TSs interact with CPAs through two H-bonds. We find that ATH reaction prefers to form RE-TS-S and RZ-TS-R, affording to (R)-enantiomers on CPAs. The pathway via (R)-enantiomers is more advantageous in the kinetics on CPAs. We reveal that the acidity of CPAs depends on the chiral skeletons. The H₈-BINOL-derived skeleton has weak acidity to offer strong H-bond interactions between TSs and CPAs. The origin of enantioselectivity of ATH reaction arises chiefly from the differential noncovalent interactions between TSs and CPAs, the conformational distortion of the substrates, the structural distortion, and the (R)-/(S)-enantiomer of CPAs. Concerning the contribution to the chiral skeletons of CPAs, they possess well flexibility to adjust their geometry to fit TSs during ATH reaction. Two key quantitative parameters are conducted to describe the shape and size of the pocket of CPAs. The stability of TSs and enantioselectivity of ATH reaction on CPAs are dependent on the CPAs’ pocket shape, which is again related to the chiral skeleton. Based on our results, we speculate that the ideal catalyst for the ATH reaction might have the following characteristics: the chiral skeleton might be in (R)-enantiomer and their pocket should be fit TSs without being too narrow or wide. Our calculations might facilitate design and computationally screening of CPAs, and this approach can guide the strategic choice of CPA skeletons to reduce the experimental workload.