Understanding the stereoselectivity in Brønsted acid catalysed Povarov reactions generating cis/trans CF₃-substituted tetrahydroquinolines: a DFT study

Abstract

The Brønsted acid (BA) catalysed Povarov reactions of (E)-1-phenyl-N-(4-(trifluoromethyl)phenyl) methanimine with 1-vinylpyrrolidin-2-one (VPO) and with allyltrimethylsilane (ATMS), affording CF₃-substituted cis/trans tetrahydroquinoline (THQ) derivatives, have theoretically been studied using the M06-2X functional together with the standard 6-31G(d) basis set. These BA catalysed Povarov reactions are multistep processes initialised by the nucleophilic attack of the non-substituted carbon atom of the nucleophilic ethylene on the imine carbon atom of the super-electrophilic protonated imine, yielding the corresponding cationic intermediate along the endo/exo stereoisomeric approach mode. Upon the formation of the cationic intermediates, a fast intramolecular Friedel–Crafts reaction converts them into the final THQs and the BA catalyst is recovered as well. For the reaction with VPO, the energetic results indicate that the endo stereoisomeric approach mode is kinetically preferred over the exo one. Interestingly, when the ATMS was experimentally used, the trans THQ resulting from an exo approach mode was the major product. A non-covalent interaction (NCI) analysis of the electron-density of the transition state structures involved in the stereoselective-determining step of these BA catalysed Povarov reactions allows an explanation of the endo/exo stereoselectivity experimentally observed.

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1. Introduction

Tetrahydroquinoline (THQ) derivatives comprising simple and/or complex substituents are widely used as pharmacological agents.¹ Anti-HIV, anti-cancer, anti-malaria and anti-diabetic properties of THQs are some examples making their study greatly attractive and valuable.² THQs IV can be constructed via an aza-Diels–Alder (A-DA) reaction of an electron-rich (ER) ethylene derivative II with an N-aryl-imine I followed by a 1,3-hydrogen (1,3-H) shift process in cycloadduct III (see Scheme 1). This domino process, discovered in 1960,³ is known as the Povarov reaction.⁴

Scheme 1 Povarov reaction of N-aryl imines with ER ethylenes.

Since 2-aza-butadienes display very poor reactivity in polar Diels–Alder (P-DA) reactions,⁵ the use of Lewis acid (LA) or Brønsted acid (BA) catalysts is required in order to activate them electrophilically, thus favouring the reaction through a polar or ionic process,⁶ such that Povarov reaction takes place under mild conditions.

Only very few theoretical studies have been devoted to the study of the mechanism of the Povarov reaction.^7,8 Very recently, the BF₃ LA catalysed Povarov reaction of N-phenyl-C-phenyl imine 1 with methyl vinyl ether (MVE) 2, an ER ethylene derivative, yielding THQ 4 was theoretically studied using DFT methods (see Scheme 2).⁸ This DFT study showed that LA catalysed Povarov reactions are domino processes involving two consecutive reactions: (i) a stepwise LA catalysed A-DA reaction through the formation of a zwitterionic (ZW) intermediate affording a formal [4 + 2] cycloadduct (CA); and (ii) a stepwise 1,3-H shift yielding the final THQ (see Scheme 2). It is noteworthy that the 1,3-H shift reaction must take place through a stepwise mechanism due to the formation of a very strained four-membered transition state (TS) along an intramolecular 1,3-H shift.⁹

Scheme 2 LA catalysed Povarov reaction of N-aryl-imine 1 with MVE 2 affording THQ 4.

On the other hand, very recently, the molecular mechanism of the BA catalysed Povarov reaction of N-phenyl-C-methoxycarbonyl imine 5 with methylenecyclopropane 6 yielding THQ 7 was investigated using DFT methods (see Scheme 3).¹⁰ Unlike the LA catalysed Povarov reaction, the BA catalysed reaction is initialised by the formation of a cationic intermediate which experiences a quick intramolecular Friedel–Crafts (IFC) reaction yielding the final THQ (see Scheme 3).

Scheme 3 BA catalysed Povarov reaction of N-phenyl-C-methoxycarbonyl imine 5 with methylenecyclopropane 6 yielding THQ 7.

It has been well established that the incorporation of fluorinated substituents into biological molecules can considerably affect their bioactivities due to some distinguishing properties of the fluorine atom.¹¹ Owing to the astonishing potential of fluorine-containing biologically active molecules, the synthesis of this kind of compounds, e.g. CF₃-substituted THQs, received much attention a long time ago.

For instance, the Povarov reactions of (E)-1-phenyl-N-(4-(trifluoromethyl)phenyl)methanimine 8 with the ER ethylenes 1-vinylpyrrolidin-2-one (VPO) 9a and allyltrimethylsilane (ATMS) 9b, in the presence of 1,1,1-trifluoro-N-((trifluoromethyl)sulfonyl)methanesulfonamide, Tf₂NH, as the BA catalyst, yielding THQs 10a and 10b were experimentally studied by Shindoh et al.¹² (see Scheme 4). Interestingly, while the ATMS 9b afforded a mixture in which THQ trans-10b was the major product, 75% trans : 25% cis, the use of VPO 9a gave up THQ cis-10a as only product.¹² Note that cis THQs come from the endo approach mode of the ER ethylenes to protonated imine 8:H, while trans THQs come from the exo approach mode.

Scheme 4 BA catalysed Povarov reaction of (E)-1-phenyl-N-(4-(trifluoromethyl)phenyl)methanimine 8 with VPO 9a and ATMS 9b yielding THQs 10a and 10b, experimentally studied by Shindoh et al.¹²

Herein, the BA catalysed Povarov reaction between imine 8 and VPO 9a yielding THQ cis-10a is theoretically studied at the M06-2X/6-31G(d) level in order to establish the reaction mechanism (see Scheme 4). Then, the TSs involved in the stereo-determining step (SDS) of the BA catalysed Povarov reaction of imine 8 with VPO 9a and ATMS 9b are studied in order to establish the factors controlling the cis/trans stereoselectivity in these BA catalysed Povarov reactions.

2. Computational details

Several works have shown that the B3LYP functional¹³ is relatively accurate for kinetic data, although the reaction exothermicities are underestimated. Recently, Truhlar's group showed that the M06-2X hybrid meta density functional theory (HMDFT) method gives good results for main-group thermochemistry and kinetics.¹⁴ Consequently, in the present study, DFT computations were carried out using the M06-2X exchange–correlation functional, together with the standard 6-31G(d) basis set.¹⁵ Optimisations were performed using the Berny analytical gradient optimisation method.¹⁶ The stationary points were characterised by frequency calculations in order to verify that TSs have one and only one imaginary frequency. The intrinsic reaction coordinate (IRC) paths¹⁷ were traced in order to check the energy profiles connecting each TS to the two associated minima of the proposed mechanism using the second order González–Schlegel integration method.¹⁸ Solvent effects of DCE were taken into account through re-optimisation of the gas phase stationary points using the polarisable continuum model (PCM) developed by Tomasi's group¹⁹ in the framework of the self-consistent reaction field (SCRF).²⁰ The electronic structures of the stationary points were analysed by the natural bond orbital (NBO) method.²¹ Non-covalent interactions (NCI) were computed by evaluating the pro-molecular density and using the methodology previously described.^22,23 All computations were carried out with the Gaussian 09 suite of programs.²⁴

The global electrophilicity index ω (ref. 25) is given by the following expression, ω = μ²/2η, based on the electronic chemical potential, μ, and the chemical hardness, η. Both quantities may be approached in terms of the one-electron energies of the frontier molecular orbitals HOMO and LUMO, ε_H and ε_L, such as μ ≈ (ε_H + ε_L)/2 and η ≈ (ε_L − ε_H), respectively.²⁶ The global nucleophilicity index N,²⁷ based on the HOMO energies obtained within the Kohn–Sham scheme,²⁸ is defined as N = ε_HOMO(Nu) − ε_HOMO(TCE), in which Nu denotes the nucleophile. This relative nucleophilicity index refers to tetracyanoethylene (TCE) as it presents the lowest HOMO energy in a long series of molecules already investigated in the context of polar organic reactions. This choice allows handling conveniently a nucleophilicity scale of positive values. The DFT reactivity indices were computed at the B3LYP/6-31G(d) level.

Recently, Domingo proposed the electrophilic, P_k⁺, and nucleophilic, P_k⁻, Parr functions²⁹ derived from the changes of electron-density reached via the global electron density transfer (GEDT)³⁰ process taking place from the nucleophile to the electrophile in polar processes, as powerful tools in the study of the local reactivity in polar processes. Then, the radical P^°_k functions³¹ were proposed for the study of the local reactivity in radical processes. Electrophilic, P_k⁺, and nucleophilic, P_k⁻, Parr functions allow for the characterisation of the most electrophilic and nucleophilic centers of molecules and thus, permit the establishment of the regio- and chemoselectivity in polar reactions, while radical P^°_k Parr functions allow for the characterisation of the local reactivity in radical and ionic species.³² Electrophilic P_k⁺, nucleophilic P_k⁻, and radical P^°_k Parr functions are obtained through an analysis of the Mulliken atomic spin densities (ASD) achieved by unrestricted single point energy calculations of the radical anion, the radical cation or the neutral radical species over the neutral or radical optimised geometries.

3. Results and discussion

The present theoretical study is divided into three parts: (i) first, an analysis of DFT reactivity indices at the ground state of the reagents involved in the BA catalysed Povarov reaction between imine 8 and ER ethylenes 9a and 9b is performed in order to explain the reactivity in these reactions; (ii) in the second part, potential energy surfaces (PESs) associated with the endo and exo reaction paths involved in the BA catalysed Povarov reaction between imine 8 and VPO 9a are studied to clarify the impact of BA catalyst Tf₂NH on the energetic and stereoselectivity of this reaction; and finally (iii) in the third part, the origin of the endo/exo stereoselectivity in the BA catalysed Povarov reactions of imine 8 with ethylenes 9a and 9b is analysed.

3.1. Analysis of the global and local DFT reactivity indices at the ground state of the reagents involved in the BA catalysed Povarov reaction between imine 8 and ER ethylenes 9a and 9b

Global reactivity indices defined within the conceptual DFT³³ are powerful tools to explain the reactivity in cycloaddition reactions. Since the global electrophilicity and nucleophilicity scales are given at the B3LYP/6-31G(d) level, reagents were optimised at this DFT level. The global indices, namely, electronic chemical potential (μ), chemical hardness (η), global electrophilicity (ω) and global nucleophilicity (N) for imine 8, protonated imine 8:H and ER ethylenes 9a and 9b are presented in Table 1.

Table 1 B3LYP/6-31G(d) electronic chemical potential, μ, chemical hardness, η, global electrophilicity, ω, and global nucleophilicity, N, in eV, for the species considered in the present study

Species	μ	η	ω	N
Protonated imine 8:H	−8.77	3.65	10.54	−1.47
Imine 8	−4.09	4.42	1.89	2.82
Imine 1	−3.73	4.35	1.60	3.22
1-Vinylpyrrolidin-2-one 9a	−3.02	5.91	0.77	3.14
Ethylene 11	−3.37	7.77	0.73	1.86
Allyltrimethylsilane 9b	−2.79	7.06	0.55	2.80

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The electronic chemical potentials of ER ethylenes 9a and 9b, −3.00 eV and −2.79 eV, are higher than that of protonated imine 8:H, −8.76 eV. Consequently, along the corresponding ionic reactions the GEDT³⁰ will take place from ER ethylenes 9a or 9b toward imine 8:H.

Polar and ionic reactions require the participation of good electrophiles and good nucleophiles. Ethylene 11 is one of the poorest electrophilic, ω = 0.73 eV, and nucleophilic, N = 1.86 eV, species involved in organic reactions, being classified as a marginal electrophile³⁴ and a marginal nucleophile.³⁵ Therefore, it can not participate in polar or ionic reactions. Substitution of one of the hydrogen atoms by a pyrrolidinone group has no significant effect on the electrophilicity ω index of VPO 9a, ω = 0.77 eV, but causes a strong increase of its nucleophilicity N index, N = 3.13 eV, allowing the classification of VPO 9a as a weak electrophile and a strong nucleophile. Similarly, replacement of one of the hydrogen atoms of ethylene 11 by a trimethylsilane group (TMS) produces a significant decrease of the electrophilicity ω index of ATMS 9b to ω = 0.55 eV, together with a strong, but lesser than at 9a, increase of its nucleophilic character, N = 2.80 eV. Thus, the TMS group causes ATMS 9b to be classified as a marginal electrophile, like VPO 9a, but as a moderate nucleophile.

On the other hand, the global electrophilicity ω and nucleophilicity N indices for imine 1, 1.60 eV and 3.22 eV, allow this compound to be classified as a strong electrophile and a strong nucleophile within the corresponding electrophilicity and nucleophilicity scales. Note that there is no relation between the electrophilic and nucleophilic characters in a given species; i.e. in complex molecules having functional groups with different electronic nature, a strong electrophile may be a strong nucleophile or vice versa. The inclusion of an electron-withdrawing CF₃ group at the para-position of the N-aryl substituent of imine 1 moderately increases the global electrophilicity ω of imine 8 to 1.89 eV and notably decreases its global nucleophilicity N index to 2.82 eV, being classified as a strong electrophile and a moderate nucleophile. Therefore, the presence of the electron-withdrawing CF₃ group slightly enhances the already strong electrophilic character of imine 1.

When the nitrogen atom of imine 8 is protonated by the presence of the very strong BA catalyst Tf₂NH to generate protonated imine 8:H, the electrophilicity ω index of 8 experiences a drastic increase by more than five times, ω = 10.54 eV, classifying 8:H as a super-electrophile. Otherwise, the nucleophilicity N index of 8 is considerably reduced even reaching a negative value of −1.47 eV (8:H). Such electrophilic activation in imine 8, arising from the coordination of the BA catalyst to the imine nitrogen atom, leads to an ionic reaction with high GEDT in which the nucleophilic attack of either ER ethylenes 9a or 9b, which are strong and moderate nucleophiles, respectively, on protonated imine 8:H, a super-electrophile, is considerably favoured compared to the non-catalysed reaction between imine 8 and ER ethylenes 9a and 9b,¹⁰ in spite of the already strong electrophilic character of imine 8.

By approaching a non-symmetric electrophilic/nucleophilic pair along a polar or ionic process, the most favourable reactive channel is that associated with the initial two-center interaction between the most electrophilic center of the electrophile and the most nucleophilic center of the nucleophile. Accordingly, the electrophilic P_k⁺ and radical P^°_k Parr functions at the C1 and C4 carbon atoms of imine 8 and protonated imine 8:H, respectively, together with the nucleophilic P_k⁻ Parr functions at the C5 and C6 carbon atoms of ER ethylenes 9a and 9b are calculated and presented in Scheme 5.

Scheme 5 B3LYP/6-31G(d) calculated electrophilic P_k⁺ and radical P^°_k Parr functions at the C1 and C4 carbon atoms of imine 8 and protonated imine 8:H, respectively, as well as the nucleophilic P_k⁻ Parr functions at the C5 and C6 carbon atoms of ER ethylenes 9a and 9b.

The analysis of the calculated electrophilic P_k⁺ Parr functions at the reactive sites of imine 8 clearly shows that the C4 carbon atom, P_k⁺ = 0.29, is about six times more electrophilic than the C1 carbon atom, P_k⁺ = 0.05. After protonation of the nitrogen atom of imine 8, while the radical P^°_k Parr function at the C1 carbon of protonated imine 8:H remains almost unchanged, the radical P^°_k Parr function at carbon C4 experiences a noticeable increase by more than 96%, reaching the value of 0.55. In other words, coordination of the BA catalyst to the nitrogen atom of imine 8 leads to the stronger electrophilic activation of the C4 carbon atom than the C1 one, enhancing the reactivity of the imine C4 carbon towards ethylenes 9a or 9b.

On the other hand, the calculated nucleophilic P_k⁻ Parr functions at the reactive sites of ER ethylenes 9a and 9b indicate that while the C5 carbon atom is nucleophilically deactivated in VPO 9a, P_k⁻ = −0.04, and weakly nucleophilically activated in ATMS 9b, P_k⁻ = 0.11, the C6 carbon atom is the most nucleophilic center in these species, P_k⁻ = 0.55 (9a) and 0.53 (9b).

Therefore, it is predicted that along the ionic BA catalysed Povarov reaction between imine 8 and the ER ethylenes 9a and 9b the nucleophilic attack of the C6 carbon atom of 9a or 9b on the C4 carbon atom of protonated imine 8:H initialises these processes.

3.2. Study of the stereoisomeric reaction paths involved in the BA catalysed Povarov reaction between imine 8 and VPO 9a

Due to the non-symmetry of both protonated imine 8:H and VPO 9a, two competitive reaction channels are feasible for the reaction between them. They are related to the two stereoisomeric approach modes of the pyrrolidinone moiety of VPO 9a relative to the phenyl substitution of protonated imine 8:H, named endo and exo (see Scheme 6).

Scheme 6 Stereoisomeric reaction paths involved in the BA Povarov reaction of protonated imine 8:H with VPO 9a. M06-2X/6-31G(d) relative enthalpies (ΔH, in kcal mol⁻¹), at 25 °C and 1 atm in the presence of DCE, are given in red (relative to the reagents) and green (relative to MC2n and MC2x).

An analysis of the stationary points involved in the BA catalysed Povarov reaction between imine 8 and VPO 9a indicates that it takes place through a stepwise mechanism. The reaction is initialised by the nucleophilic attack of VPO 9a on protonated imine 8:H yielding a cationic intermediate which experiences a rapid cyclisation reaction affording a new cationic intermediate. A final proton abstraction in this intermediate yields the final THQ. The two last steps of this stepwise mechanism constitute an IFC reaction. A schematic representation of the stationary points involved in the two stereoisomeric approach modes between protonated imine 8:H and VPO 9a is shown in Scheme 6, in which relative enthalpies of the stationary points, in kcal mol⁻¹, are also included. Two molecular complexes (MCs), three TSs, two cationic intermediates and the corresponding THQ were located and characterised on the PES associated with each of the two stereoisomeric reaction channels. Total and relative electronic energies in gas phase and in DCE, as well as complete thermodynamic data, are given in Tables S1 and S2 of ESI.†

When the two reagents approach each other, depending on the endo or exo stereoisomeric approach mode, two MCs, located 6.4 (MC1n) and 4.8 (MC1x) kcal mol⁻¹ below the reagents, are formed in a very early stage of the reaction channels. Further approach of the reagents increases the potential energy reaching TS1n and TS1x, which remain 3.2 and 0.8 kcal mol⁻¹ below the separated reagents. However, considering the formation of MC1n and MC1x, the activation energies become positive; i.e. 3.2 (TS1n) and 5.6 (TS1x) kcal mol⁻¹. Formation of cationic intermediates IN1n and IN1x is exothermic by 14.0 and 9.4 kcal mol⁻¹, respectively. These relative energy values, which are in agreement with the experimental outcomes,¹² clearly indicate that the endo stereoisomeric approach mode is kinetically preferred over the exo one, since TS1n is 2.4 kcal mol⁻¹ below TS1x.

Once cationic intermediates IN1n and IN1x are formed, they undergo a fast IFC reaction to generate the corresponding THQs cis-10a and trans-10a. As shown in Scheme 6, along the most favourable endo reactive channel, the IFC reaction is initialised by the intramolecular electrophilic attack of the carbocationic C5 carbon atom on the aromatic C1 carbon atom of the N-aryl substituent via TS2n, which is found 2.8 kcal mol⁻¹ above IN1n, yielding a new cationic intermediate IN2n. This intramolecular electrophilic attack is strongly exothermic by 17.3 kcal mol⁻¹. In a similar manner, along the exo channel, the intramolecular electrophilic attack in IN1x through TS2x presents an activation barrier of 3.8 kcal mol⁻¹ yielding IN2x, its formation being exothermic by 16.4 kcal mol⁻¹.

After formation of cationic intermediates IN2n and IN2x, two new stable MCs, MC2n and MC2x, are formed by approaching of the basic Tf₂N⁻ anion toward these cationic intermediates; note that the Tf₂N⁻ anion is the conjugate base of the BA catalyst Tf₂NH. Upon formation of MC2n and MC2x, the hydrogen bound to the C1 carbon atom (shown in blue in Scheme 6) is removed by the basic Tf₂N⁻ anion via TS3n or TS3x, presenting a very low activation energy of 4.6 and 7.4 kcal mol⁻¹, respectively. This proton abstraction does not only recover the BA catalyst Tf₂NH, but also affords the final products THQs cis-10a and trans-10a, in which the aromatic ring is regenerated. This last step is exothermic by 8.3 and 15.3 kcal mol⁻¹.

Addition of the entropies to the enthalpies increases the relative Gibbs free energies of the stationary points involved in the nucleophilic attack of VPO 9a on protonated imine 8:H and the first step of the IFC reaction by between 9 and 18 kcal mol⁻¹, due to the unfavourable entropy associated with this bimolecular process. On the contrary, relative Gibbs energies associated with the proton abstraction step of the IFC reaction vary in a slight amount since this process is unimolecular (see Table S2 in ESI†). The Gibbs free energy profile associated with the BA catalysed Povarov reaction between imine 8 and VPO 9a is graphically depicted in Fig. 1. Note that the formation of MC1n and MC1x becomes endergonic, having no significance in the Gibbs free energy profile.

Fig. 1 Gibbs free energy profile (ΔG, in kcal mol⁻¹) of the Povarov reaction between protonated imine 8:H and VPO 9a. The endo and exo stereoisomeric channels are displayed in blue and red, respectively.

Some appealing conclusions can be drawn from the Gibbs free energy profile represented in Fig. 1: (i) the first nucleophilic attack of protonated imine 8:H on VPO 9a is the rate-determining step (RDS) of this BA catalysed Povarov reaction; (ii) the first step is endo stereoselective to be TS1n 3.0 kcal mol⁻¹ below TS1x (see Table S2 in ESI†); (iii) although the formation of cationic intermediate IN1n is slightly endergonic, it quickly undergoes a fast IFC reaction to yield THQ cis-10a. Note that the activation Gibbs free energy of the IFC reaction associated with the most favourable endo stereoisomeric pathway via TS2n is 6.2 kcal mol⁻¹ lower than that of the RDS of the reaction via TS1n; (iv) the high exergonic character of the BA catalysed Povarov reaction between imine 8 and VPO 9a makes this process irreversible, THQ cis-10a being the kinetic control product. Consequently, the first step is also the SDS; (v) accordingly, this reaction is kinetically highly endo stereoselective, leading to the formation of THQ cis-10a, in agreement with the experimental outcomes.¹²

The optimised geometries of the TSs involved in the studied BA catalysed Povarov reaction and the distances of the forming bonds are presented in Fig. 2. At the TSs associated with the nucleophilic attack of VPO 9a on 8:H, the length of the C4–C6 forming bond and the distance between the C1 and C5 carbon atoms are 2.199 and 3.192 Å at TS1n and 2.102 and 3.080 Å at TS1x, respectively (see Scheme 6 for atom numbering). At cationic intermediates, the length of the C4–C6 single bond is 1.581 Å at IN1n and 1.605 Å at IN1x, while the distance between the C1 and C5 carbon atoms decreases to 2.782 Å (IN1n) and 2.820 Å (IN1x). At TS2n and TS2x, associated with the ring closure step of the IFM reaction, the length of the C1–C5 forming bond is 2.098 and 2.224 Å, while at the TSs associated with the proton abstraction step of the IFC reaction, the lengths of the C1–H breaking and Tf₂N–H forming bonds are 1.254 and 1.512 Å at TS3n and 1.384 and 1.422 Å at TS3x.

Fig. 2 M06-2X/6-31G(d) optimised geometries of the TSs involved in the Povarov reaction of protonated imine 8:H with VPO 9a including the lengths of the C4–C6 and C1–C5 forming bonds in Å.

The GEDT that fluxes from the ethylene fragment toward the imine one during the nucleophilic attack of VPO 9a on protonated imine 8:H is 0.34e at TS1n and 0.79e at IN1n along the endo stereoisomeric approach mode, and 0.39e at TS1x and 0.78e at IN1x along the exo stereoisomeric approach mode. These values indicate that there is an increase in GEDT along both stereoisomeric approach modes that reaches its maximum value when the first C4–C6 single bond is completely formed at the corresponding intermediate. The high GEDT values at TS1n and TS1x emphasises the ionic nature of the Povarov reaction between protonated imine 8:H and VPO 9a. Interestingly, the GEDT at the endo stereoisomeric TS1n is slightly lower than at exo TS1x, as a consequence of the more advanced character of the latter (see Fig. 2). Note that in polar reactions, the GEDT along the endo approach mode is higher than that along the exo one as a consequence of the more favourable electrostatic interactions appearing between the two counter charged frameworks along the endo approach mode. In addition, while in polar reactions the GEDT gives rise to zwitterionic TSs, in cationic reactions both frameworks are positively charged at the TSs after the GEDT process. The very high GEDT values found at cationic intermediates IN1n and IN1x arise from the high nucleophilic character of VPO 9a (N = 3.13 eV) and the super-electrophilic character of protonated imine 8:H (ω = 10.15 eV).

3.3 Origin of the endo/exo stereoselectivity in the BA catalysed Povarov reactions of imine 8 with ER ethylenes 9a and 9b

As was commented in the introduction part, the Povarov reaction of protonated imine 8:H with VPO 9a yields the THQ cis-10a resulting of an endo approach mode of 9a respect to the phenyl substituent of 8:H. Analysis of the gas phase M06-2X/6-31G(d) relative energies of TS1n and TS1x gives a ΔE^≠ = 2.1 kcal mol⁻¹, in reasonable agreement with the experimental outcomes. On the other hand, when ATMS 9b was used as the ER ethylene, THQ trans-10b resulting from the exo approach mode of the trialkylsilane group was obtained as the major product (75% trans : 25% cis). In order to explain the different stereoselectivity experimentally observed in these cationic reactions, the endo and exo TSs associated with the nucleophilic attack of ATMS 9b on protonated imine 8:H, TS1n-Si and TS1x-Si, were also studied. Relative energies are given in Table 2, while a top view of the two endo/exo pairs of stereoisomeric TSs are given in Fig. 3.

Table 2 M06-2X/6-31G(d) and B3LYP/6-31G(d) relative energies (relative to the endo TSs, in kcal mol⁻¹) of the stereoisomeric TSs associated with the nucleophilic attack of ER ethylenes 9a and 9b on protonated imine 8:H

	M06-2X	B3LYP
TS1n	0.0	0.0
TS1x	2.1	1.3
TS1n-Si	0.0	0.0
TS1x-Si	0.4	−0.9

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Fig. 3 Top view of the geometries of TS1n, TS1x, TS1n-Si and TS1x-Si.

At the M06-2X/6-31G(d) computational level, TS1x is found 2.1 kcal mol⁻¹ higher in energy than TS1n, in reasonable agreement with the experimental outcomes. When the pyrrolidinone group present in VPO 9a is substituted by the trimethylsilylmethylene one in ATMS 9b, this energy difference decreases to 0.4 kcal mol⁻¹. Although these energy results indicate a lower interaction between the trimethylsilylmethylene group of 9b and the aryl group of protonated imine 8:H, it is not sufficient to reverse the exo selectivity experimentally observed.

A recent study on the oxa-Povarov reaction of a cationic aryl oxonium 12 with cyclopentene 13 and styrene 14 (ref. 32) showed that DFT calculations were not able to reproduce the endo stereoselectivity experimentally observed,³⁶ which was the result of weak interactions non reproduced by the used computational methods. However, in the present BA promoted Povarov reaction, the M06-2X functional appears to overestimate these weak interactions, being not feasible to reproduce the exo selectivity in the reaction with 9b. In order to prove this finding, the four TSs were optimised using the B3LYP functional. At this level, the energy difference between TS1n and TS1x decreases to 1.3 kcal mol⁻¹ (see Table 2), but when this comparison is made for the reaction involving ATMS 9b, TS1x-Si becomes 0.9 kcal mol⁻¹ lower in energy than TS1n-Si. Consequently, the B3LYP functional accounts for that change of stereoselectivity.

In order to explain the high endo/exo stereoselectivity along these ionic Povarov reactions, a detailed analysis of TS1n, TS1x, TS1n-Si and TS1x-Si was performed. Fig. 3 shows the top view of the four structures. While the pyrrolidinone substituent of the ethylene framework in VPO 9a is disposed away from the N-aryl substituent at TS1x, this substituent is precisely above the N-aryl substituent at TS1n (see Fig. 3). Therefore, this geometrical arrangement at TS1n allows generating some type of interactions between the pyrrolidinone and the N-aryl groups which are absent at TS1x, justifying the preference of endo TS1n over exo TS1x. On the other hand, an analysis of the geometries of TS1n-Si and TS1x-Si indicates that the bulky –SiMe₃ group present in ATMS 9b is positioned perpendicularly to the plain of the ethylene (see Fig. S1 in ESI†). Consequently, along the endo and exo approach modes of ATMS 9b towards protonated imine 8:H, the bulky –SiMe₃ group does not produce any hindrance. This finding is in agreement with the experimental observation that the endo/exo stereoselectivity does not depend on the alkyl substituent present on the silicon, either methyl, isopropyl or butyl.¹²

In order to analyse the favourable interactions appearing between the pyrrolidinone and the N-aryl substituents at TS1n, an NCI analysis²⁴ of the electron-density of TS1n and TS1x was performed. In addition, an NCI analysis of the electron-density of TS1n-Si and TS1x-Si was also performed. Fig. 4 displays low-gradient isosurfaces for the four structures.

Fig. 4 NCI gradient isosurfaces of TS1n, TS1x, TS1n-Si and TS1x-Si. Blue indicates strong attractive interactions, green is indicative of weak interactions and red indicates strong non-bonded overlap.

Fig. 4 reveals the presence of a larger extended green surface between the pyrrolidinone substituent of VPO 9a and the N-aryl group of protonated imine 8:H at TS1n than at TS1x. This extended green surface, which is associated with weak attractive Van der Waals interactions, accounts for a larger stabilisation of endo TS1n with respect to exo TS1x. Consequently, week attractive Van der Waals interactions appearing between the pyrrolidinone substituent of VPO 9a and the N-aryl group of protonated imine 8:H along the endo approach could be responsible for the endo selectivity experimentally found in this BA catalysed Povarov reaction.¹² On the other hand, Fig. 4 reveals the presence of a similar green surface between the methylene carbon of ATMS 9b and the N-aryl group of protonated imine 8:H at TS1n-Si and TS1x-Si. These behaviours emphasise that there are similar weak Van der Waals interactions in both stereoisomeric TSs, in agreement with the low energy difference between them. In a cationic reaction, the nucleophilic species transfer a considerable amount of electron-density to the cationic species. Consequently, while the nucleophile becomes positively charged, the positive charge of the cationic species is decreased, but it remains positively charged. This behaviour causes that along the endo approach mode the electronic repulsions between the two positively charged frameworks will be larger than along the exo one, in which they are reduced, thus justifying the exo selectivity in cationic reactions.

We can conclude that while along the addition of VPO 9a to protonated imine 8:H the favourable weak Van der Waals interactions appearing along the endo approach mode compensate the electronic repulsions appearing in this cationic TS, these unfavourable electronic repulsions appearing along the addition of ATMS 9b to protonated imine 8:H turns the addition exo selective.

4. Conclusions

The BA catalysed Povarov reactions of imine 8 with VPO 9a and ATMS 9b yielding CF₃-substituted THQs cis-10a and trans-10b have been theoretically studied using DFT methods at the M06-2X/6-31G(d) level.

Analysis of the global and local DFT reactivity indices indicates that the protonation of the nitrogen atom of imine 8 by a BA catalyst considerably increases its global electrophilicity ω index making 8:H a super-electrophile. Such strong electrophilic activation in protonated imine 8:H makes its C4 carbon atom the most electrophilic center. On the other hand, the most nucleophilic center in VPO 9a and ATMS 9b is the C6 carbon. These electrophilic and nucleophilic activations accounts for the nucleophilic attack of the C6 carbon atom of 9a or 9b on the C4 carbon atom of protonated imine 8:H.

Exploration of the PESs associated with the endo and exo stereoisomeric reactive channels of the BA catalysed Povarov reaction of imine 8 with VPO 9a indicates that this reaction takes place through a stepwise mechanism. The reaction is initialised by the nucleophilic attack of VPO 9a on protonated imine 8:H yielding a cationic intermediate which experiences a rapid cyclisation reaction affording a new cationic intermediate. A final proton abstraction in this intermediate yields the final THQ. The two last steps of this stepwise mechanism constitute an IFC reaction.

The first nucleophilic attack is the RDS and the SDS of this BA catalysed Povarov reaction. This reaction is highly stereoselective. Although the formation of cationic intermediate IN1n is slightly endergonic, it is quickly converted into THQ cis-10 through an irreversible IFC reaction at this intermediate. Consequently, THQ cis-10 is obtained by a kinetic control.

NCI analysis of the electron-density of the TSs involved in the SDS of these BA catalysed Povarov reactions allows explaining the stereoselectivity experimentally observed. In the reaction with VPO 9a, the geometrical arrangement of the endo TS1n, in which the pyrrolidinone moiety of VPO 9a is positioned above the N-aryl substituent of 8:H, enables weak attractive Van der Waals interactions between both frameworks stabilising the endo TS. However, in the reaction with ATMS 9b, the larger electronic repulsions appearing in the cationic endo TS1n-Si turns the addition exo selective.

Acknowledgements

This work has been supported by the Ministerio de Economía y Competitividad of the Spanish Government; project CTQ2013-45646-P. MRG thanks the Ministerio de Economía y Competitividad for a pre-doctoral contract co-financed by the European Social Fund (BES-2014-068258).

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Footnote

† Electronic supplementary information (ESI) available: M06-2X/6-31G(d) total and relative energies, in gas phase and in DCE, of the stationary points involved in the Povarov reaction between protonated imine 8:H and ER ethylene 9a, as well as M06-2X/6-31G(d) enthalpies, entropies and Gibbs free energies, and the relative ones, computed at 298 K and 1 atm in DCE. M06-2x/6-31G(d) and B3LYP/6-31G(d) total and relative energies of the stereoisomeric TSs associated with the nucleophilic attack of ER ethylenes 9a and 9b on protonated imine 8:H. M06-2X/6-31G(d) and B3LYP/6-31(d) optimised geometries of the TSs involved in the Povarov reaction of protonated imine 8:H with ATMS 9b. Theoretical background of the NCI analysis. See DOI: 10.1039/c5ra27650k

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