Mechanistic and stereoselectivity study for the reaction of trifluoropyruvates with arylpropenes catalyzed by a cationic Lewis acid rhodium complex

Abstract

The possible reaction mechanisms for a stereoselective carbonyl–ene reaction between trifluoropyruvates and arylpropenes catalyzed by a Lewis acid catalyst (Rh(III)-complex) have been investigated using density functional theory (DFT). Six possible reaction pathways, including four Lewis acid-catalyzed reaction pathways and two non-catalyzed reaction pathways have been studied in this work. The calculated results indicate that the Lewis acid catalyzed reaction pathways are more energetically favorable than the non-catalyzed reaction pathways. For the Lewis acid-catalyzed pathways, there are four steps including complexation of the catalyst with the trifluoropyruvates, C–C bond formation, proton transfer, and decomplexation processes. Our computational outcomes show that the C–C bond formation step is both the rate- and enantioselectivity-determining step, and the reaction pathway leading to the S-configured product is the most favorable pathway among the possible stereoselective pathways. Dication Rh(III)-complexes with different counterions (i.e., OTf⁻, Cl⁻, and BF₄⁻) were considered as active catalysts, and the computed results indicate that the stereoselectivity can be improved with the presence of the counterion OTf⁻. All the calculated outcomes align well with the experimental observations. Moreover, the stereoselectivity associated with the chiral carbon center is attributed to lone pair delocalization and variations in the stronger interaction. Furthermore, analysis of the global reactivity index was also performed to explain the role of the Lewis acid catalyst.

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1. Introduction

The carbonyl–ene reaction, which occurs between a carbonyl compound (the enophile) and an alkene with an allylic hydrogen (the ene), is a group-transfer reaction.¹ Generally, this transformation occurs in a one-step manner and has a high barrier under uncatalyzed conditions,² and therefore it typically requires high temperature.³ Since it features one of the simplest methods for C–C bond formation in synthesis, potentially 100% atom efficiency and a high tolerance for ene and enophile variation, many efforts have been made toward the improvement and development of this kind of reaction.

It is noteworthy that Lewis acid-catalyzed carbonyl–ene reactions, which can afford high yields and stereoselectivities at a significantly lower temperature, have been widely used over the past decades. In 1988, Yamamoto communicated the first asymmetric carbonyl–ene reaction catalyzed by modified Al–BINAP complexes.⁴ Subsequently, Mikami published a series of studies on Ti–BINOL-catalyzed asymmetric glyoxylate/fluoral–ene reactions.⁵ Then, more and more transition metal complexes derived from chiral ligands were employed in the catalysis of ene reactions. For example, Evans et al. reported the enantioselective carbonyl–ene reaction catalyzed by C₂-symmetric Cu(II)-bis(oxazolinyl) complexes.⁶ Zheng and co-authors developed a novel chiral N,N′-dioxide nickel(II) complex to promote an asymmetric carbonyl–ene reaction.⁷ Wang and co-workers discovered that Rh(II)/Rh(III) carboxamidates can catalyze the carbonyl–ene reaction.⁸ These transition-metal complexes can rival or even outperform non-transition-metal Lewis acids in terms of conversion, enantioselectivity, diastereoselectivity, and regioselectivity. Besides, the reactivity, stability and other important properties of the transition-metal catalysts can be controlled by systematic ligand modifications and/or variation of the metal center.

Recently, pincer transition-metal complexes (e.g., M = Pd,⁹ Ni,¹⁰ Ru,¹¹ Pt,¹² Ir,¹³ and Fe¹⁴) have been developed as an important class of organometallic Lewis acid catalysts in asymmetric catalysis. Among them, the Rh–phebox complexes have attracted more attention and exhibited excellent stereoselectivities in various catalytic asymmetric reactions, including reductive aldol reactions, conjugate reductions, β-boration of α,β-unsaturated carbonyl compounds, and alkynylation of α-keto esters. Compared with phebox ligands, phebim ligands have the advantage of further tunability of the electron density and steric bulkiness of the ligands by appropriate choice of the substituent on the additional nitrogen atom. An outstanding example of C₂-symmetric pincer rhodium(III) complexes serving as the Lewis acid to catalyze the asymmetric carbonyl–ene reaction of methyl trifluoropyruvate with 2-arylpropenes was firstly reported by Song’s group (Scheme 1),¹⁵ which deserves particular attention if we note the fact that the stereoselectivity of this reaction remains uninvestigated though carbonyl–ene reactions have been widely reported.

Scheme 1 A Lewis acid Rh(III)-complex catalyzed the title reaction.

Differing from the numerous experimental studies, theoretical investigations of the mechanism and stereoselectivity of this kind of reaction are rare. It should be noted that whether this novel reaction proceeds through a one-step reaction or a stepwise mechanism with a zwitterionic intermediate and either C–C bond formation or proton transfer as the rate-determining step is still debatable to date. For example, Zhang et al. adopted a one-step mechanism to disclose the influence of a variety of widely used Lewis acids (such as AlCl₃ and SnCl₄) on carbonyl–ene reactions.¹⁶ Yamanaka and coworkers discovered a very large amount of asynchronicity and a significant amount of zwitterionic character in the one-step transition state structure as they studied the diastereoselectivity in a AlCl₃- and SnCl₄-catalyzed carbonyl–ene reaction.¹⁷ Bickelhaupt et al. theoretically demonstrated that the more polar the enophile is, the more asynchronous the ene reaction will be.¹⁸ While Hang’s group found that carbonyl enophile complexes followed a stepwise route by using kinetic isotope effect (KIE) determination.¹⁹ Hillier et al. studied bis(oxazoline)copper(II) complex-catalyzed carbonyl–ene reactions using DFT and ONIOM methods and found that the reaction proceeds via a facile stepwise mechanism.²⁰ These studies are all concentrated on the mechanism of this novel reaction, but the factors that control the enantioselectivity are still unclear to date. To the best of our knowledge, a computational investigation of the mechanism and enantioselectivity of Lewis acid Rh(III)–phebim complex catalyzed carbonyl–ene reactions has also remained hitherto unperformed. With the complexity and ambiguity that exists, theoretical investigations are desperately needed to make the mechanistic proposals more persuasive.

In this present study, we aim to disclose the mechanism and enantioselectivity process of the Rh(III)-complex catalyzed carbonyl–ene reaction of methyl trifluoropyruvate with 2-arylpropenes as depicted in Scheme 1. As is known, for a multimolecular reaction, it is crucial to make clear which molecules are involved in each elementary step in order to access a complete understanding of the reaction mechanism. Song and co-workers have conducted some research to propose the possible reaction mechanism. Their explorations of this novel reaction are quite instructive but there are also some key issues that need to be settled: (1) for the keto-moiety, the ester carbonyl group not only renders the adjacent CF₃-substituted keto-group electron-deficient but also influences the coordinated conformation that the methyl trifluoropyruvate adopts. Bidentate coordination restricts rotation around the C–C bond that connects the two carbonyls and provides a more stereodefined complex that enhances the stereocontrol. Thus, which coordination mode is favorable for this reaction? (2) What is the real active species? (3) Is this Rh(III) complex catalyzed carbonyl–ene reaction stepwise or concerted? (4) What is the rate-determining step in this reaction? (5) As the design of a new Lewis acid catalyst relies on a detailed understanding of the underlying factors that govern the enantioselectivity of these kinds of reactions, what are the main factors that control the enantioselectivity of this reaction? With these questions as motivation, the present work will pursue a theoretical investigation of the title reaction to not only obtain a preliminary picture of the Lewis acid promoted carbonyl–ene reaction, but also to explore the factors that control the stereoselectivity of this reaction. We believe that this mechanistic information should be important for understanding the reaction and providing novel insights into the process of investigating this kind of reaction in detail.

For the sake of convenience, the reaction between trifluoropyruvate (R1, R = Me, Scheme 1) and phenylpropene (R2, Scheme 1) catalyzed by a Lewis acid Rh(III) complex catalyst (Cat, R¹ = p-tol, R² = t-Bu, Scheme 2) has been chosen as the object of this investigation. In the present study, we will give the computational results for both of the possible reaction mechanisms at the molecular level using density functional theory (DFT), which has been widely used in the study of organic²¹ and biological reaction mechanisms,²² and others.²³

Scheme 2 A possible catalytic cycle for the title reaction.

2. Computational details

The quantum mechanical calculations reported herein were carried out using density functional theory with the Gaussian 09 suite of programs.²⁴ The solution-phase geometry optimization of all species was performed with the gradient-corrected functional of Becke, and Lee, Yang and Parr (B3LYP),²⁵ using a density functional for exchange and correction, along with the 6-31G* basis set for carbon, hydrogen, oxygen, nitrogen, and fluorine atoms. The SDD basis set,²⁶ as an effective core potential basis set, was used for the rhodium atom. The solvent effects of dichloroethane (DCE, ε = 10.125), according to the experiment, were calculated using the SMD continuum solvation model developed by Truhlar and coworkers.²⁷ The harmonic vibrational frequency calculations were performed at the same level of theory as that used for the geometry optimization to provide thermal corrections of the Gibbs free energies and to make sure that the local minima had no imaginary frequencies, while the saddle points had only one imaginary frequency. Intrinsic reaction coordinates (IRCs)²⁸ were calculated to confirm that the transition state structure connects the correct reactant and product on the potential energy surface, and natural bond orbital (NBO)²⁹ analysis was employed to assign the atomic charges. The computed structures were rendered using CYLView software.³⁰

On the basis of the optimized structures at the B3LYP/6-31G*//SDD level in DCE solvent, the energies were then refined using B3LYP/6-311++G(2d,2p)//SDD single point calculations. The zero-point energies (ZPEs) and thermal corrections to free energies calculated at the B3LYP/6-31G*//SDD level were used to approximate the values of the geometries optimized at the B3LYP/6-311++G(2d,2p)//SDD level. It should be noted that we will denote the computational method of geometry optimization at the B3LYP/6-31G*//SDD level as B3LYP/BS1, the single point energy calculated at the B3LYP/6-311+G(2d,2p) level as B3LYP/BS2, and the energy refinement with single-point energy calculated at the B3LYP/BS2 level plus the ZPE or thermal correction calculated at the B3LYP/BS1 level as B3LYP/BS3.

Furthermore, the energies were also refined with single-point calculations using the electronic basis set def2-DZVP³¹ along with B3LYP, B3LYP-D3,³² or M06-L³³ methods (see ESI†). To date, though with the increased availability of other methods, such as ωB97X-D and the Minnesota functionals, the dominance of B3LYP appears to be fading, B3LYP is still one of the most popular and efficient methods. Moreover, the Stuttgart–Dresden (SDD) ECP with or without polarization functions has been confirmed to be reliable as it offers more flexibility in the valence shell, when combined with a Pople style basis set (e.g., 6-31G* or 6-31G**) for main-group atoms.³⁴ As shown in Table S1,† although the differences between the relative free energies of the key transition states computed at other levels would become slightly smaller than those computed at the selected level (B3LYP/6-311++G(2d,2p)//SDD), the same trend still can be obtained by using the other methods. Considering the above, we think the selected computational level should be appropriate and accurate enough for this catalytic system. All Gibbs free energies shown in this article were calculated at 1 atm and 298.15 K. Unless specified otherwise, all Gibbs free energies discussed in this paper were obtained at the B3LYP/BS3 level.

3. Results and discussion

3.1. The mechanism protocol

3.1.1. The Lewis acid catalyzed reaction mechanism. On the basis of the presumptive mechanism proposed by Song, we suggested a possible catalytic cycle for the Lewis acid-catalyzed carbonyl–ene reaction (shown in Scheme 2). There are generally four steps in this catalytic cycle, including (1) the combination of methyl trifluoropyruvate with Cat via transition state TS1 (complexation process), (2) the reaction between the other reactant 2-arylpropene and M1 to give intermediate M2 via transition state TS2 (C–C bond formation process), (3) the intramolecular proton transfer process for the formation of intermediate M3 via transition state TS3 (proton transfer process), and (4) the dissociation of the final product from Cat via transition state TS4 and the regeneration of Cat (decomplexation process).

As stated in the introduction, the complexation modes should be different due to the coordinated conformation that the methyl trifluoropyruvate adopts, thus, there are two complexation modes (endo and exo). It should be noted that we term the mode endo when the C3=O2 points toward the axial position of the catalyst, whereas the C3=O2 pointing toward the equatorial position of the catalyst is named exo. Scheme 3 and Fig. 1 present the elementary steps of the catalytic cycle and the free energy profile of the entire fundamental channels, respectively. Detailed mechanistic discussions are provided step by step.

Scheme 3 Possible reaction mechanisms for each elementary step for the title reaction.

Fig. 1 The Gibbs free energies of the title reaction (units: kcal mol⁻¹).

First step: the complexation process. The first step is the formation of a catalyst–reactant complex between the methyl trifluoropyruvate (R1) and the Lewis acid catalyst (Cat). The different complexation patterns and different prochiral faces of the catalyst–reactant complexes pose a considerable challenge from the computational point of view. The complexation of the Rh(III) center with two carbonyl oxygen atoms of R1 initiates the catalytic reaction. Coordinated intermediates M1_exo and M1_endo are formed, associated with transition states TS1_exo and TS1_endo, through the coordinated conformation that the methyl trifluoropyruvate adopts (Fig. 2).

Fig. 2 Two different coordination modes.

In the course of the complexation, the partly filled d-orbitals of the rhodium center accept electrons from the electron-rich carbonyl oxygen. As shown in Fig. 3, the distance of Rh1–O2 is shortened from 2.52/3.13 Å in TS1_exo/TS1_endo to 1.99/2.80 Å in M1_exo/M1_endo, and the distance of Rh1–O5 is shortened from 3.14/2.49 Å in TS1_exo/TS1_endo to 2.94/2.02 Å in M1_exo/M1_endo, respectively, which shows that accompanied with the electron transfer from R1 to Cat, coordination bonds are formed via TS1_exo and TS1_endo. The Gibbs free energy barriers of these two complexation processes via TS1_exo and TS1_endo (13.27 and 13.39 kcal mol⁻¹, Fig. 1) indicate that the reaction can occur under experimental conditions.¹⁵

Fig. 3 The optimized structures involved in the first step (distances in Å). Most of the hydrogen atoms are omitted for sake of clarity. Gray, red, green, blue, white, and purple represent carbon, oxygen, fluorine, nitrogen, hydrogen, and rhodium, respectively. All the figures which follow are presented using the same method.

Second step: the C–C bond formation step. The second step is the addition of another reactant R2 to M1 (M1_exo and M1_endo) for the formation of the zwitterionic intermediate M2 via the C–C bond formation process. As shown in Fig. 2, the bidentate coordination restricts rotation around the C–C bond that connects the two carbonyls and provides a more stereodefined complex that enhances the stereocontrol. There exists four possible reaction routes (Scheme 4) for the C–C bond formation process, because for either M1_exo or M1_endo, R2 can attack from either the Re or Si face to participate in the reaction. As an important note, the chiral center assigned to the C3 atom is formed during the C–C bond formation process, which depends on whether it is the Re or Si face of M1_exo/endo that R2 gets close to. The different attack modes on the prochiral C3 atom by R2 determine the stereochemistry of the chirality of the C3 atom center during the C–C bond formation step. It should be noted that the chiral center assigned to the C3 atom is introduced in this step, which will be denominated as R/S. As can be seen in Scheme 4, attack on the Re-face of M1_exo by R2 affords the zwitterionic intermediate M2S_exo via TS2S_exo, whereas attack on the Si-face of M1_exo by R2 gives the zwitterionic intermediate M2R_exo via TS2R_exo. Similarly, attack on the Si-face of M1_endo by R2 affords M2R_endo via TS2R_endo, whereas attack on the Re-face of M1_endo by R2 affords M2S_endo via TS2S_endo.

Scheme 4 Illustration of the stereochemistry.

In the course of the C3–C6 bond formation, with the approach of R2 to the intermediate M1_exo/M1_endo, the electrostatic attraction between C3 and C6 will lead to complexes in either an S or R configuration, depending on which face of M1_exo/endo that R2 gets close to. Subsequently, the zwitterionic intermediate M2R/S_exo/endo is formed via transition state TS2R/S_exo/endo, respectively. Fig. 4 shows the main geometrical structures for the four transition states and intermediates. The changes in the distance between the C3 atom and C6 atom show that a C3–C6 bond is formed in this step. During the C–C bond forming process, the bond lengths of C8–H9 are 1.09–1.11 Å, which indicates that the ene reaction occurs via a stepwise manner. In the intermediate M2, the proton H9 is oriented toward the O2 atom with the correct relative conformation necessary for the following proton transfer process. The free energy profile mapped in Fig. 1 reveals that the energy barriers of the C–C bond formation process are 16.04 (TS2S_exo) and 17.01 (TS2R_exo) kcal mol⁻¹ with respect to M1_exo for the exo addition, whereas the values for the endo addition are 22.26 (TS2R_endo) and 24.32 (TS2S_endo) kcal mol⁻¹ with respect to M1_endo, respectively. Obviously, the exo addition pathway is more favorable than the endo addition pathway, thus for the following sections, we think that it is unnecessary to discuss the two possible reaction pathways. The formation of M2S_exo has the lowest energy barrier and the energy barrier of TS2S_exo is 0.97 kcal mol⁻¹ lower than that of TS2R_exo, which indicates that the formation of M2S_exo is more energetically favorable and supports the reported preference to form the S-configuration of the product.

Fig. 4 The optimized structures involved in the second step (distances in Å).

Third step: the proton transfer process. The subsequent step is the proton transfer process associated with the H9 atom transferring from the C8 atom to the O2 atom to form the intermediate M3R_exo/M3S_exo via transition state TS3R_exo/M3S_exo. The H9 atom on the C8 atom transfers to the O2 atom through a six-membered ring transition structure TS3R_exo/TS3S_exo, in which the distances of O2–H9 and C8–H9 are 1.26/1.26 Å and 1.38/1.39 Å (Fig. 5), respectively. The length of the newly formed O2–H9 bond is 0.99/0.99 Å in M3R_exo/M3S_exo showing the formation of an O2–H9 bond. Moreover, the distance of Rh1–O2 has lengthened from 2.00/1.99 Å in M2R_exo/M2S_exo to 2.06/2.08 Å in M3R_exo/M3S_exo, which demonstrates that the coordination bond Rh1–O2 is weaker after the intramolecular proton transfer. This should be due to the electronic delocalization between the Rh1 and O2 atoms. The free energy barriers calculated for this step (7.85 and 9.36 kcal mol⁻¹, Fig. 1) indicate that the proton transfer process is a facile process.

Fig. 5 The optimized structures involved in the third step (distances in Å).

Fourth step: the regeneration of the catalyst. Since in the third step the homoallylic alcohol is formed, then the final step is the dissociation of the catalyst from the product, and this leads to the regeneration of the catalyst. The transition state involved in this step is denoted as TS4R_exo/TS4S_exo. As shown in Fig. 5, the bond length of Rh1–O2 is increased from 2.08/2.06 Å in M3R_exo/M3S_exo to 2.57/2.62 Å in TS4R_exo/TS4S_exo, respectively. The energy barriers for this step are 5.35 (TS4R_exo) and 7.98 (TS4S_exo) kcal mol⁻¹, which implies that the dissociation process is a facilitated process and the catalyst is easy to regenerate.

Furthermore, we have also considered the effects of the solvent (DCE) and the counterion (i.e., OTf⁻, Cl⁻, and BF₄⁻), and the results are summarized in Table 1. From Table 1, we found that the most active catalytic species is the dicationic Rh(III)–phebim complex (Cat), which has the lowest energy barrier. This phenomenon indicates that the coordination of counterions or solvent to the vacant orbital of Cat reduces its electrophilic ability and lowers the activity of the catalyst, which is because the Rh(III)–phebim complex is more stable when coordinated with counterions. Though a coordinated Rh(III)–phebim complex promoting the reaction is dynamically less favorable, the possibility of a Rh(III)–phebim complex coordinated with a counterion catalyzing the reaction is also possible. The experimental results¹⁵ show that the stereoselectivity is improved with the presence of OTf⁻ and our computational results also confirm this tendency (ΔΔG^≠(TSR_exo − TSS_exo) = 2.36 kcal mol⁻¹, Table 1).

Table 1 The Gibbs free energy barriers of the C–C bond formation step, catalyzed by different catalysts (units in kcal mol⁻¹)

Catalyst (L = bis(imidazolinyl)phenyl)	Reaction pathway
	Exo addition		Endo addition
	S	R	R	S
RhL	13.64	15.26	18.70	21.51
RhL-OTf	21.55	23.91	24.57	27.31
RhL-BF4	18.90	20.49	24.43	24.60
RhL-Cl	22.74	25.28	27.35	28.08
RhL-DCE	21.20	22.89	24.42	27.63

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3.1.2. The mechanism for the direct reaction. To give a more comprehensive understanding of the Rh(III)–phebim complex catalyst, the un-catalyzed carbonyl–ene reaction channels (channels A and B) were also investigated. The proposed mechanism of the un-catalyzed carbonyl–ene reaction and the Gibbs free energy of the two transition states are depicted in Scheme 5. The calculated results show that the reaction occurs in a one-step fashion, which is remarkably different from the stepwise manner under the catalysis conditions.

Scheme 5 The un-catalyzed carbonyl–ene reaction of trifluoropyruvates with arylpropenes.

During the reaction, the H9 atom transfers from C8 to O2 along with the formation of a C3–C6 bond via the six-membered ring transition states TS1S_A and TS1R_B to form the products PS and PR, respectively. Attack on the alternative faces of R1 by R2 determines the chirality of the C3 atom in the final product. The distance between the C3 atom and C6 atom is shortened from 1.75 Å in TS1S_A/TS1R_B to 1.57 Å in PS/PR, consistent with that the distance of O2–H8 is shortened from 1.20 Å in TS1S_A/TS1R_B to 0.98 Å in PS/PR. The free energy barriers via TS1S_exo and TS1R_exo are both 34.19 kcal mol⁻¹, which reveals that the reaction should have difficultly to occur under the experimental conditions.

Having established the reaction mechanism of the title reaction, we then evaluated the bond order involved in the C–C bond formation step to disclose the differences between the catalytic and direct coupling reaction. The bond orders, P, nicely reflect the alteration of the C3–C6, C8–H9, and O2–H9 bonds. According to the results depicted in Table 2, the bond order P(C8–H9) changes a very small amount during the C–C bond formation process in the catalytic mechanism, which agrees with that the formation of the C–C and O–H bonds occurs via a stepwise manner. The existence of the bond order P(O2–H9) for TS2 and M2 is due to the formation of a C–H⋯O hydrogen bond and thus weakens the C8–H9 σ bond. In contrast, while the bond order P(C8–H9) decreases to 0.64, the bond orders P(O2–H9) and P(C3–C6) increase to 0.21 and 0.73 for the direct coupling reaction pathway respectively, indicating that the formation of O2–H9 and C3–C6 bonds and the breaking of the C8–H9 bond occur simultaneously. The bond orders clearly reveal that the reaction proceeds via different mechanisms under the catalytic and un-catalytic conditions and this analysis is consistent with the above mechanistic studies.

Table 2 The Wiberg bond order P of the key bonds involved in the C–C bond formation step of the reaction at the B3LYP/6-31G*/SDD//SMD(DCE) level

	Bond order
	P(C3–C6)	P(C8–H9)	P(O2–H9)
R2	—	0.99	—
TS2Rexo	0.33	0.91	0.02
TS2Sexo	0.37	0.89	0.01
TS2Rendo	0.54	0.86	0.04
TS2Sendo	0.48	0.88	0.03
M2Rexo	0.91	0.87	0.02
M2Sexo	0.91	0.85	0.02
M2Rendo	0.86	0.85	0.04
M2Sendo	0.85	0.85	0.04
TSRnon	0.73	0.64	0.21
TSSnon	0.73	0.64	0.21

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Taken together, one can conclude that the catalytic mechanism (Scheme 3) is obviously more favorable than the direct one (Scheme 5), and for the catalytic mechanism, the most favorable mechanism among the four steps is the exo addition associated with the S-configured isomer. The second step, i.e. addition of R2, is the rate- and enantioselectivity-determining step for the whole reaction associated with an energy barrier of 16.04 kcal mol⁻¹ with respect to M1_exo. It also determines the enantioselectivity (S is favorable) associated with the chiral carbon C3 atom.

3.2. The origin of the enantioselectivity

As described above, the second step (the C–C bond formation process) of the title reaction under the catalysis conditions was calculated to be the rate- and enantioselectivity-determining step. To obtain a deep insight into the origins of the enantioselectivity of the target reaction, we then applied NBO second-order perturbation analysis on transition states TS2S_exo and TS2R_exo to address this issue, which has been successfully used for organic reactions to explain the stereoselectivity³⁵ and could help us to evaluate the intramolecular interactions. For each (i) donor and (j) acceptor, the second-order perturbation interaction energy can be expressed using the following equation: E(2) = E_ij = q_iF_ij²/ε_iε_j, where F_ij is the off-diagonal element in the NBO Fock matrix, q_i is the donor orbital occupancy, and ε_i and ε_j are the diagonal elements (orbital energies).

Table 3 lists the donor–acceptor interactions involved in forming bonds in TS2S_exo and TS2R_exo. For TS2S_exo, a significant stabilization interaction favors C6 lone pair delocalization as presented in Table 3, i.e. the delocalization of the C6 lone pair with the π*(2) orbital of the O5–C4 bond with E_n→π* = 323.89 kcal mol⁻¹. For the transition state TS2R_exo, the stabilization energies feature the same characteristic. The major contribution to the stabilization of TS2R_exo comes from the delocalization of the C6 lone pair, namely, the n → π* between the lone pair of C6 and the π*(2) orbital of the O5–C4 bond with E_n→π* = 182.28 kcal mol⁻¹. Obviously, the lone pair delocalization energy for TS2R_exo is much lower than that for TS2S_exo, while the other stabilization interactions in TS2S_exo and TS2R_exo do not differ significantly. The results of the NBO analysis reinforce the importance of stereoelectronic effects, which contribute to the lower energy of TS2S_exo relative to TS2R_exo.

Table 3 The second-order perturbation energy E(2) (kcal mol⁻¹) of the donor–acceptor interactions in terms of forming bonds in TS2S_exo and TS2R_exo

TS2Sexo				TS2Rexo
Donor	Acceptor	Interaction	E(2)	Donor	Acceptor	Interaction	E(2)
LP(1)C6	BD*(2)O5–C4	n–π*	323.89	LP(1)C6	BD*(2)O5–C4	n–π*	182.28
LP*(1)C8	BD*(2)O5–C4	n*–π*	9.23	BD(2)O5–4	LP(1)C6	π–n	5.19
BD(2)O5–C4	LP(1)C6	π–n	6.13	BD(1)C6–H11	BD*(2)O5–C4	σ–π*	3.58
BD(1)C6–H12	BD*(2)O5–C4	σ–π*	3.20	BD(1)C3–C4	LP(1)C6	σ–n	2.57
BD(1)C3–C4	LP(1)C6	σ–n	2.64	LP*(1)C8	BD*(2)O5–C4	n*–π*	2.26
BD(1)C6–H11	BD*(2)O5–C4	σ–π*	1.75	LP(1)C6	BD*(2)O2–C3	n–π*	1.95
BD(1)C8–C6	BD*(2)O5–C4	σ–π*	1.59	BD(1)C6–H12	BD*(2)O5–C4	σ–π*	1.55
BD(1)C4–C10	LP(1)C6	σ–n	1.30	BD(1)C8–6	BD*(2)O5–C4	π–π*	1.29
LP(1)C6	BD*(2)O2–C3	n–π*	1.09	BD(1)C4–C10	LP(1)C6	σ–n	1.23

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In addition to the stereoelectronic effects, we have also performed distortion/interaction reactivity analysis of the transition states TS2S_exo and TS2R_exo. Distortion/interaction analysis is a fragment approach used to understand organic reactions, in which the height of the energy barrier is described in terms of the original reactants. As depicted in Fig. 6, the activation energy of the transition states is decomposed into two main components: the distortion energy (ΔE^≠_dist) and the interaction energy (ΔE^≠_int).³⁶ The distortion energy involves geometric and electronic changes to deform the reactants into their transition state geometry, which involves bond stretching, angle decrease or increase, dihedral changes and so on. The interaction energy encompasses repulsive, exchange-repulsive and stabilizing electrostatic, polarization, and orbital effects in the transition state structure. The interaction energy is uncovered using the relationship: ΔE^≠_int = ΔE^≠ − ΔE^≠_dist.

Fig. 6 The relationship between the activation energy and the distortion and interaction energies of the reactants.

The calculated distortion and interaction energies of the reactants in the transition state geometries are listed in Table 4. For the two transition states TS2S_exo and TS2R_exo, the distortion energies of the ene (R2) and the Rh–trifluoropyruvate complex (M1_exo) in the required geometries are very similar: 5.68–8.26 kcal mol⁻¹ for ΔE^≠_dist(R2) and 11.65–15.49 kcal mol⁻¹ for ΔE^≠_dist(M1_exo). However, the interaction energies (ΔE^≠_int) of the two deformed reactants can be quite different for these two transition states. The ΔE^≠_int of TS2S_exo is −22.76 kcal mol⁻¹, which is much more negative than that of the transition state which leads to the R-configured product (−16.01 kcal mol⁻¹ for TS2R_exo). Apparently, the much stronger interaction energy between the deformed ene (R2) and Rh–trifluoropyruvate complex (M1_exo) for TS2S_exo makes it the most stabilized transition state for the formation of the S-configured product.

Table 4 The distortion/interaction reactivity analysis for the rate-determining step of the title reaction (all values are in kcal mol⁻¹)

TS	ΔE^≠dist(R2)	ΔE^≠dist(M1exo)	ΔE^≠int	ΔE^≠^a
a The ΔE^≠ value is the calculated electronic energy of each transition state relative to the sum of the electronic energies of the two separate reactants.
TS2Sexo	8.26	15.49	−22.76	0.99
TS2Rexo	5.68	11.65	−16.01	1.32

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As mentioned above, both the stereoelectronic effects and the stronger interaction energy between the deformed ene (R2) and Rh–trifluoropyruvate complex (M1_exo) play important roles in determining whether TS2S_exo is more energetically favorable than TS2R_exo. The computed energy difference between TS2S_exo and TS2R_exo was 0.97 kcal mol⁻¹, which corresponds to an enantiomeric excess of 67% in favor of the S isomer. This prediction is in good accordance with the experimentally observed ee of 77%. It should be noted that the energy of R1 + R2 + Cat is the lowest point in both the energy profiles of the two competitive pathways, and the energy barrier of the entire pathway should be the energy difference between the reactants R1 + R2 + Cat and the corresponding highest energy transition state, so the difference between the energy barriers of the two competitive manifolds is still 0.97 kcal mol⁻¹, which is the same as the energy gap (0.97 kcal mol⁻¹) between the two highest energy transition states.

3.3. Role of the Lewis acid catalyst

In order to further understand the role of the catalyst, the Rh(III)–phebim complex (Cat), in depth and compare the reactivity of the dicationic Rh(III) species with the cationic Rh(III)–counterion complex, we performed an analysis of the global reactivity index (GRI) of the reactants before and after absorption by the catalyst. A molecule’s global electrophilicity character is described using the electrophilicity index, ω,³⁷ which is obtained from the following expression, ω = (μ²/2η),^37,38 in terms of the electronic chemical potential μ and the chemical hardness η. Both quantities may be approached in terms of the one-electron energy of the frontier molecular orbital HOMO and LUMO, E_H and E_L, as μ ≈ (E_H + E_L)/2 and η ≈ (E_L − E_H). Moreover, according to the HOMO energies obtained using the Kohn–Sham method,³⁹ Domingo and co-workers presented a nucleophilicity index N in order to produce a nucleophilicity scale.⁴⁰ The nucleophilicity index is defined as N = E_H(SR) − E_H(TCE). For this nucleophilicity scale, tetracyanoethylene (TCE) is taken as the reference. Following the definition of these indices, for this reaction (Table 5), R2 is classified as the nucleophile with a nucleophilicity index of 2.590 eV, and R1 and M1_exo are electrophiles with a value of 2.785 and 8.421 eV, respectively. Obviously, the coordination of catalyst Cat to the carbonyl oxygen atom of R1 noticeably strengthens the electrophilicity of R1, and thus lowers the free energy barrier of the carbonyl–ene reaction. The GRI analysis further revealed that the coordination of counterions (i.e., Cl⁻, BF₄⁻, TfO⁻, DCE, and H₂O) cannot lower the energy barrier of the reaction, which is probably due to the lower acidity of the Lewis acid. These results further support the fact that the dicationic Rh(III)–phebim complex (Cat) is the most active catalyst.

Table 5 Energies of the HOMO (E_H, a.u.) and LUMO (E_L, a.u.), the electronic chemical potential (μ, a.u.), the chemical hardness (η, a.u.), the global electrophilicity (ω, eV), and the global nucleophilicity (N, eV) of some reactants (SR)

SR	EH (a.u.)	EL (a.u.)	μ (a.u.)	η (a.u.)	ω (eV)	N^a (eV)
a EH(TCE) = −0.31657 a.u. (calculated at B3LYP/6-31G(d)/SDD//IEF-PCM (DCE)).
R1	−0.288	−0.102	−0.195	0.186	2.785	0.778
R2	−0.221	−0.023	−0.122	0.198	1.024	2.590
M1exo	−0.243	−0.173	−0.208	0.070	8.421	1.997
M1exo-Cl (with counterion Cl^−)	−0.221	−0.143	−0.182	0.078	5.758	2.593
M1exo-BF4 (with counterion BF4^−)	−0.227	−0.152	−0.190	0.075	6.558	2.437
M1exo-OTf (with counterion TfO^−)	−0.226	−0.148	−0.187	0.078	6.066	2.473
M1exo-DCE (with solvent DCE)	−0.244	−0.162	−0.203	0.082	6.904	1.970

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4. Conclusions

In this present study, we have analyzed the carbonyl–ene reaction between trifluoropyruvates (R1) and arylpropenes (R2) catalyzed by the Lewis acid catalyst Rh(III)–phebim complex using density functional theory. Both the catalyzed and un-catalyzed (channels A and B) reaction mechanisms were considered. On the basis of our calculations, the Lewis acid catalyzed reaction is demonstrated to occur through four steps, and for each step, more than one possible pathway that involved different participating molecules has been investigated. The calculated results reveal that the exo addition pathway associated with the S-configured isomer is the most favorable pathway among the six reaction pathways and the second step (the C–C bond formation step) is the rate- and stereoselectivity-determining step. The enantioselectivity associated with the chiral carbon center (C3 atom) turns out to be determined by the Re or Si face addition of R2 to M1. All the calculations are consistent with the experimental results.

Moreover, both the stereoelectronic effects and the stronger interaction energy between the deformed ene (R2) and Rh–trifluoropyruvate complex (M1_exo) are the key factors that control the stereoselectivity. The analysis of the global reactivity indexes of the reactants before and after the catalyst absorption revealed the role of the catalyst in strengthening the nucleophilicity of the reactant R1 and thus decreasing the energy barrier of the carbonyl–ene reaction. Therefore, this work should be helpful for not only understanding the role of a Lewis acid in this kind of reaction but also for providing valuable clues for the rational design of potent catalysts for synthesizing homoallylic alcohols with high stereoselectivity.

Acknowledgements

We acknowledge financial support from the National Natural Science Foundation of China (No. 21303167), China Postdoctoral Science Foundation (No. 2013M530340 and 2015T80776), and Excellent Doctoral Dissertation Engagement Fund of Zhengzhou University in 2014.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c5ra21074g

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