A DFT study of the role of the Lewis acid catalysts in the [3 + 2] cycloaddition reaction of the electrophilic nitrone isomer of methyl glyoxylate oxime with nucleophilic cyclopentene

Abstract

The molecular mechanism and stereoselectivity of the BF₃ Lewis acid catalyzed [3 + 2] cycloaddition (32CA) reaction between C-methoxycarbonyl nitrone and cyclopentene has been theoretically studied using DFT methods at the MPWB1K/6-31G(d) computational level. The BF₃ catalyst accelerates the 32CA reaction by decreasing the activation energy leading to the formation of the trans cycloadduct as the kinetic product, in agreement with the experimental data. Inclusion of solvent effects slightly increases the activation energy and decreases the exothermic character of the 32CA reaction as a consequence of a better solvation of nitrone than the transition state and the cycloadduct. The use of the lithium cation as LA catalyst does not make any remarkable change with respect to the BF₃ catalyzed process. The nature of the mechanism has been also studied using the reactivity indices defined within the conceptual DFT.

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1. Introduction

[3 + 2] cycloaddition (32CA) reactions offer a versatile route for the construction of a variety of complex five-membered heterocycles that are synthetically useful compounds.¹ 32CA reactions of nitrones with alkenes leading to isoxazolidine derivatives have been intensively studied and have found general application in organic synthesis (see Scheme 1).² Oximes and their derivatives as useful synthons are widely utilized in organic synthesis, since they can be easily transformed into nitrones.³ A considerable amount of theoretical and experimental⁴ work devoted to the study of the mechanism and selectivity of 32CA reactions of oximes or nitrones with alkenes can be found in the literature.

Scheme 1 32CA reaction of nitrone 2 with ethylene 3.

Unlike Diels–Alder (DA) reactions, which can be classified as non-polar DA (N-DA) reactions with high activation energies and polar DA (P-DA) reactions with low activation energies,⁵ 32CA reactions lack a clear systematization of their reactivity based on the nucleophilic/electrophilic behavior of the reagents. Recently, the 32CA reactions of a series of twelve three-atom-components (TACs) with ethylene 3 were studied in order to find a structure/reactivity relationship.⁶ A good correlation between the pseudodiradical character, the hardness η, and the nucleophilicity N index of the TAC with the feasibility of these non-polar reaction was established. This study allowed establishing a useful classification of 32CA reactions into pseudodiradical-type (pr-type) reactions involving TACs with a high pseudodiradical character, which take place easily through an earlier TS with non-polar character, and zwitterionic-type (zw-type) reactions involving TACs with a high zwitterionic character, characterized by favorable nucleophilic/electrophilic interactions, taking place through polar TSs.⁶ Thus, the simplest nitrone 2, which has a zwitterionic character, presented a high activation energy towards ethylene 3, 13.0 kcal mol⁻¹, with a very low charge transfer (CT) at the transition state (TS), 0.01e (see Scheme 1).

In order to verify this hypothesis, a series of the most common TACs used in organic synthesis⁷ showing low reactivity in 32CA reactions towards ethylene 3 were recently explored to determine if the electrophilic/nucleophilic activation of both TACs and ethylene derivatives might favor the 32CA reactions via a polar zw-type mechanism.⁸ To this end, a series of seven non-substituted TACs, including the simplest nitrone 2, having a zwitterionic structure were studied analyzing their electrophilic/nucleophilic behavior (see Scheme 2).

Scheme 2 32CA reactions of nitrones and nucleophilic and electrophilic alkenes.

The general characteristic of zwitterionic TACs is their high nucleophilic and low electrophilic behavior. Thus, the simplest nitrone 2 has an electrophilicity index ω = 1.06 eV,⁹ being classified as a moderate electrophile¹⁰ and a nucleophilic index N = 2.92 eV¹¹ being on the borderline of strong nucleophiles.¹² The computed activation energies indicated that non-substituted TACs react quickly toward the electron-deficient 1,1-dicyanoethylene 5, showing their ability to react towards electrophilic ethylenes. Thus, the 32CA reaction of the simplest nitrone 2 with 1,1-dicyanoethylene 5 was 3.7 kcal mol⁻¹, in clear agreement with the CT at the corresponding TS; 0.15e.

Interestingly, when the electrophilically activated phenyl nitrone 7, ω = 3.13 eV, reacted with the electron-rich ethylene 8, N = 3.64 eV, the computed activation energy, 13.2 kcal mol⁻¹was closer to that found in the 32CA reaction of the simplest nitrone 2 towards ethylene 3. These energy results indicated that the electrophilic activation of the TACs by an electron-withdrawing substitution seems to be insufficient to favor the 32CA reaction toward electron-rich ethylenes. Only the coordination of nitrone 7 with a BF₃ Lewis acid (LA) activated it for a nucleophilic attack; the corresponding TS was found to be 3.2 kcal mol⁻¹ below reagents (see Scheme 3).

Scheme 3 LA-catalyzed 32CA reaction between electrophilic nitrone and nucleophilic alkene.

Recently, Sousa and co-workers¹³ studied experimentally the reaction of methyl glyoxylate oxime 12 with cyclopentene 14, finding that this reaction gives exclusively the trans isoxazolidine 15, originating from the exo approach (Scheme 4). The formation of cycloadduct 15 was explained by the 32CA reaction of the nitrone tautomer 13 of the methyl glyoxylate oxime 12 with cyclopentene 14.

Scheme 4 LA catalyzed reaction between glyoxylate oxime and cyclopentene.

Herein, we present a MPWB1K-/6-31G(d) computational investigation of the role of the BF₃ LA catalyst and solvent effects in the 32CA reactions of electrophilically activated nitrones with electron rich ethylenes. For this purpose, the 32CA reaction between nitrone 13 and cyclopentene 14, experimentally studied by Sousa, is analyzed. A predictive study on lithium metal as a LA catalyst is also performed.

2. Computational method

Several works have shown that the B3LYP functional^14,15 is relatively accurate for kinetic data, although the reaction exothermicities are underestimated.^16–18 Recently, the Truhlar's group has proposed some functionals, such as the MPWB1K¹⁹ hybrid meta functional which improve thermodynamic calculations. DFT calculations were carried out using the MPWB1K¹⁹ functional together with the 6-31G(d) basis set.²⁰ These 13DC reactions were also optimized using the M06-2X²¹ and B3LYP functionals and the corresponding energies were compared with the MPWB1K ones.

The stationary points were characterized by frequency calculations in order to verify that transition states (TSs) had one and only one imaginary frequency. The intrinsic reaction coordinate (IRC)^22,23 have been further performed to check the energy profiles connecting each TS to the two associated minima. The electronic structures of critical points were analyzed by the natural bond orbital (NBO) method.²⁴ Thermodynamic calculations were done with the standard statistical thermodynamics at 298.15 K and 1 atm,²⁰ and harmonic vibrational frequencies were scaled by a factor of 0.96.²⁵ Solvent effects of dichloromethane (DCM) were considered at the same level of theory by single-point calculations of the gas-phase structures using a self-consistent reaction field (SCRF)²⁶ based on the polarizable continuum model (PCM) of Tomasi's group.²⁷ All calculations were carried out with the Gaussian 09 suite of programs.²⁸

The global electrophilicity index, ω, is given by the following expression⁹ ω = (μ²/2η), in terms of 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, as μ ≈ (ε_H + ε_L)/2 and η ≈ (ε_L − ε_H), respectively.¹¹ Recently, Domingo introduced an empirical (relative) nucleophilicity index²⁹ N, based on the HOMO energies obtained within the Kohn–Sham scheme³⁰ and defined as N = E_HOMO(Nu) − E_HOMO(TCE). Nucleophilicity is referred to tetracyanoethylene (TCE). The P⁺_k electrophilic and P⁻_k nucleophilic Parr functions³⁰ which allow for the characterization of the electrophilic and nucleophilic centers of a molecule, were obtained through the analysis of the Mulliken atomic spin density of the radical anion and the radical cation of the studied molecules, respectively.

3. Results and discussion

The present study has been divided into five sections: (i) first, a comparison between the energies of the B3LYP, M06-2X and MPWB1K functionals is performed to choose the appropriate functional for this study (ii) in the second part, the non-catalyzed 32CA reaction between nitrone 13 and cyclopentene 14 is studied; (iii) in the third part, the BF₃ LA catalyzed 32CA reaction of nitrone 13 with cyclopentene 14 is analyzed; (iv) in the fourth part, the role of the lithium cation as a LA catalyst in the 32CA reaction is also evaluated; (v) in the last part, a DFT-based reactivity indices analysis is performed to shed light on the effect of the LA catalyst on the reaction mechanism.

3.1 Choice of the computational method

In order to find the appropriate functional to realize this study, we have performed a comparative study between the B3LYP, M06-2X and MPWB1K functionals. Relative energies are summarized in Table 1. Total energies are given in Tables S1 in ESI.† We can notice from Table 1 that the use of the three functionals predicts an exo stereoselectivity, where the activation energies obtained with both B3LYP and MPWB1K are slightly similar (2 and 2.9 respectively), while the value obtained with the use of the M06-2X functional is different to them (−0.2 kcal mol⁻¹) leading to a spontaneous reaction, thus it does not reproduce the experimental data. Thereby, B3LYP and MPWB1K functionals are appropriate for kinetically controlled of these cycloaddition reactions. In the other hand, a comparison between the products energies of the more stable cycloadduct (CAn-B) reveals that the values obtained with both M06-2X and MPWB1K functionals are also slightly similar (−38.9 and −37.0 kcal mol⁻¹, respectively), while the value obtained with B3LYP functional is higher (−22.4 kcal mol⁻¹) leading to a less exothermic reaction. Thus, the B3LYP functional fails in thermodynamic controlled of these cycloaddition reactions. Consequently, the MPWB1K functional is the appropriate functional for both kinetic and thermodynamic controlled the BF₃ LA catalyzed 32CA reaction of nitrone 13 with cyclopentene 14, that we will use it to performed this study.

Table 1 B3LYP/6-31G(d), M06-2X/6-31G(d) and MPWB1K/6-31G(d) relative energies (ΔE in kcal mol⁻¹), in gas phase of the stationary points involved in the 32CA reaction of BF₃:nitrone 15 complex with cyclopentene 14

	ΔE gas phase
	B3LYP	M06-2X	MPWB1K
TSn-c	13.1	6.7	10.5
TSx-c	2.0	−0.2	2.9
CAn-c	−22.4	−38.9	−37.0
CAx-c	−20.5	−37.8	−34.7

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3.2 Study of the non-catalyzed 32CA reaction between nitrone 13 and cyclopentene 14

In order for oximes to undergo a 32CA reaction with alkenes they should be transformed into the corresponding nitrone (see Scheme 5). The nitrone-tautomer is more reactive than the oxime one.³² The 32CA reaction between C-methoxycarbonyl nitrone 13 and cyclopentene 14 can take place along two stereoisomeric pathways; namely, the endo and exo approaches (Scheme 5). Analysis of the stationary points involved along the two stereoisomeric channels indicates that this 32CA reaction takes place along a one-step mechanism. Consequently, two stereoisomeric TSs, TSn and TSx, and the corresponding [3 + 2] CAs, CAn and CAx, were located and characterized. Relative energies of the stationary points (TSs and CAs) involved in the 32CA reaction between nitrone 13 and cyclopentene 14, in the gas phase and in DCM, are given in Table 2. Total energies are given in Table S2 in ESI.†

Scheme 5 The possible stereoisomeric pathways for the 32CA reaction between nitrone 13 and cyclopentene 14.

Table 2 MPWB1K/6-31G(d), relative energies (ΔE in kcal mol⁻¹), in gas phase and in DCM, of the stationary points for the 32CA reaction of nitrone 13 with cyclopentene 14

	ΔE gas phase	ΔE DCM
TSn	15.3	16.7
TSx	11.2	12.7
CAn	−38.0	−36.5
CAx	−39.7	−38.3

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The gas phase activation energies associated with this 32CA reactions are: 15.3 (TSn) and 11.2 (TSx) kcal mol⁻¹, the reaction being exothermic by 38.0 (CAn) and 39.7 (CAx) kcal mol⁻¹. The energy difference between the two stereoisomeric TSs, 4.1 kcal mol⁻¹, indicates that this 32CA reaction is completely exo stereoselective, allowing the formation of trans isoxazolidine CAx (Scheme 5). The unfavorable steric hindrance between the hydrocarbon system of cyclopentene 14 and the methyl group of the ester function present in nitrone 13 may be responsible for this exo selectivity. The high exothermic character of this 32CA reaction makes the cycloaddition irreversible.

Solvent effects stabilize the reactants, TSs and CAs relative to gas phase calculations. The most noticeable change with the inclusion of solvent effects is the increase in activation energies; the changes are 1.4 and 1.5 kcal mol⁻¹ for TSn and TSx, respectively. Moreover, solvent effects slightly decrease the exothermic character of the reaction; the changes are 1.4 and 1.5 kcal mol⁻¹ for CAx and CAn, respectively. The increase of the activation energies and the decrease of the exothermic character of this 32CA reaction are a consequence of a higher solvation of nitrone 13 than TSs and CAs in polar solvents.³³

Relative enthalpies, entropies and Gibbs free energies of the TSs and cycloadducts involved in the 32CA reaction of nitrone 13 with cyclopentene 14 are summarized in Table 3. The values of enthalpies, entropies and Gibbs free energies are given in Table S3 in ESI.† Inclusion of thermal corrections to the electronic energies raises the activation entropies by ca. 2 cal mol⁻¹ K⁻¹. Analysis of the activation enthalpies associated with the 32CA reaction of nitrone 13 with cyclopentene 14 indicates that the more favorable approach mode is that associated with the exo TSx (ΔH = 13.8 kcal mol⁻¹). Addition of the unfavorable entropic contribution associated to this bimolecular process to the enthalpies increases the Gibbs activation free energy of this reactive channel to 26.1 kcal mol⁻¹, which remains more favored than the endo approach mode (ΔΔG = 3.9 kcal mol⁻¹). Consequently, formation of the exo CAx is clearly favored over the endo CAn, in good agreement with the experimental outcomes.

Table 3 MPWB1K/6-31G(d) relative enthalpies (ΔH, in kcal mol⁻¹), entropies (ΔS, in cal mol⁻¹ K⁻¹), and Gibbs free energies (ΔG, in kcal mol⁻¹), for the TSs and CAs involved in the 32CA reaction between nitrone 13 and cyclopentene 14

	ΔH	ΔS	ΔG
TSn	17.6	−42.0	30.0
TSx	13.8	−41.8	26.1
CAn	−32.9	−42.1	−20.5
CAx	−34.5	−45.6	−21.0

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The geometries of the TSs associated with the 32CA reaction of nitrone 13 and cyclopentene 14 are given in Fig. 1. The lengths of the O1–C5 and C3–C4 forming bonds at the TSs are 2.090 and 2.181 Å at TSn, and 2.093 and 2.203 Å at TSx.

Fig. 1 Optimized structures of the TSs of the 32CA reaction of nitrone 13 and cyclopentene 14.

The extent of bond formation or bond breaking along a reaction pathway is provided by the concept of bond order (BO). The Wiberg bond indices³⁴ have been computed using NBO analysis. At the TSs associated with the non-catalyzed 32CA reaction the BO values for the O1–C5 and C3–C4 forming bonds are 0.33 and 0.30 at TSn and 0.31 and 0.32 at TSx. These values point to synchronous single bond formation processes of this 32CA reaction.

The CT analyses at the TSs of this non-catalyzed 32CA reaction are done to shed light on the nature of the molecular mechanism. Natural population analysis (NPA) allows evaluating the CT along these 32CA reactions, and thus to establish the polar nature of these reactions. The MPWB1K/6–31G(d) natural atomic charges at the TSs were shared between the nitrone 13 and cyclopentene 14. The CT value at both TSn and TSx is 0.06e, thereby indicating that these TSs have a very low polar character, in clear agreement with the high activation energies.⁶

3.3 Study of the BF₃ catalyzed 32CA reaction between nitrone 13 and cyclopentene 14

Nitrones are strong nucleophilic TACs that react with electron-deficient alkenes via a zw-type mechanism.⁸ However, coordination of the oxygen atom of nitrone with a LA catalyst notably increases its electrophilicity, allowing its participations in zw-type 32CA reactions towards electron-rich alkenes. Accordingly, the 32CA reaction of the nitrone:BF₃ complex 15 with cyclopentene 14 was studied (see Scheme 6). Relative energies for the stationary points (TSs and cycloadducts) involved in 32CA reactions of nitrone:BF₃ complex 15 with cyclopentene 14, in the gas phase and in DCM are displayed in Table 4. Total energies are given in Table S4 in ESI.† The geometries of the TSs involved in the BF₃ catalyzed 32CA reaction are given in Fig. 2.

Scheme 6 The possible stereoselective pathways for the BF₃ catalyzed 32CA reaction between C-methoxycarbonylnitrone 15 and cyclopentene 14.

Table 4 MPWB1K/6-31G(d) relative energies (ΔE in kcal mol⁻¹), in gas phase and in DCM, of the stationary points for the 32CA reaction of the BF₃:nitrone complex 15 with cyclopentene 14

	ΔE gas phase	ΔE DCM
TSn-B	10.5	11.5
TSx-B	2.9	5.7
CAn-B	−37.0	−31.3
CAx-B	−34.7	−30.3

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Fig. 2 Optimized structures of the TSs of the 32CA reaction of the BF₃:nitrone complex 15 with cyclopentene 14.

The gas phase activation energies associated with this BF₃ catalyzed 32CA reaction are 10.5 (TSn-B) and 2.9 (TSx-B) kcal mol⁻¹, the reaction being exothermic by 34.7 (CAn-B) and 37.0 (CAx-B) kcal mol⁻¹. These energy results clearly indicate that the coordination of the BF₃ catalyst to the oxygen atom of nitrone 13 favors the exo stereoisomeric channel to decrease the corresponding activation energy by 8.3 kcal mol⁻¹. This behavior makes the LA catalyzed 32CA reaction completely exo stereoselective to be TSx-B 7.6 kcal mol⁻¹ below TSn-B. Note that according to the Boltzmann distribution equation,³⁵ when ΔE between two isomers is above 3 kcal mol⁻¹, one isomer will exclusively be obtained.

Solvent effects of DCM stabilize all the structures; the BF₃:nitrone complex 15 being the most stabilized one. Consequently, solvent effects increase the activation energies: 1.0 kcal mol⁻¹ for the endo approach and 2.8 kcal mol⁻¹ for the exo approach. In spite of the larger increase of the activation energy associated with the exo TSx-B, the solvent effect does not modify the exo stereoselectivity found in gas phase.

Relative enthalpies, entropies and Gibbs free energies of the BF₃ catalyzed 32CA reaction are summarized in Table 5. Values of absolute enthalpies, entropies and Gibbs free energies are given in Table S5 in ESI.† Just as in the non-catalyzed reaction, inclusion of the thermal corrections with the electronic energies raises the activation entropies by ca. 2 kcal mol⁻¹; the activation enthalpy associated to the catalyzed reaction being 7.0 kcal mol⁻¹. Addition of the unfavorable entropic contribution associated to this bimolecular process to the enthalpies raises the Gibbs activation free energy of the most favorable exo reactive channel to 20.3 kcal mol⁻¹, the reaction being exergonic by 12.9 kcal mol⁻¹.

Table 5 MPWB1K/6-31G(d) relative enthalpies (ΔH, in kcal mol⁻¹), entropies (ΔS, in cal mol⁻¹ K⁻¹), and Gibbs free energies (ΔG, in kcal mol⁻¹), for the TSs and CAs involved in the 32CA reaction between BF₃:nitrone 15 complex and cyclopentene 14

	ΔH	ΔS	ΔG
TSn-B	12.9	−43.9	25.9
TSx-B	7.0	−45.1	20.3
CAx-B	−27.0	−54.3	−11.0
CAn-B	−27.2	−48.6	−12.9

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The geometries of the TSs associated with the 32CA reaction of BF₃:nitrone 15 complex and cyclopentene 14 are given in Fig. 2. The lengths of the O1–C5 and C3–C4 forming bonds at the TSs are 2.329 and 2.088 Å at TSn-B, and 2.272 and 2.119 Å at TSx-B, respectively. The BO values for the O1–C5 and C3–C4 forming bonds at the TS associated to the BF₃ catalyzed 32CA reaction are 0.18 and 0.37 at TSn-B and 0.20 and 0.36 at TSx-B, respectively, indicating that these TSs correspond to an asynchronous single bond formation process in which the C–C bond formation is more advanced than the C–O one.

The values of CT, which takes place from cyclopentene 14 to the electrophilically activated BF₃:nitrone complex 15, are 0.22e (TSn-B) and 0.21e (TSx-B). The CT found in these TSs accounts for the polar character of this LA catalyzed 32CA reaction. This analysis is in agreement with a zw-type mechanism.

3.4 Study of the effects of the lithium cation as LA catalyst in the 32CA reaction between nitrone 13 and cyclopentene 14

In this part, the effects of the lithium cation as a LA catalyst on the molecular mechanism and the reaction rate of the 32CA reactions between nitrone 13 and cyclopentene 14 is analyzed. Two models for nitrone:lithium complexes have been considered: (i) in the first model, the lithium cation is coordinated to the nitrone oxygen and to a chlorine anion (16), having the corresponding complex charge 0 (see Scheme 7); (ii) in the second model the lithium cation is coordinated to the nitrone oxygen and to three ether molecules to complete a four coordination (17),³⁶ this complex presents a charge +1 (Scheme 8). Since both non-catalyzed and BF₃ catalyzed 32CA reactions between nitrone 13 and cyclopentene 14, presented a complete exo selectivity, only the exo approach mode was considered. Analysis of the stationary points involved in the exo channels associated with these 32CA reactions indicates that they also take place through a one-step mechanism. Consequently, the nitrone:lithium complex, one TS and the corresponding CA were located and characterized. Relative energies of the stationery points associated with the 32CA reactions of nitrone 13 with cyclopentene 14 in presence of LiCl and Li⁺(OMe₂)₃ catalysts are given in Table 6. Total energies are given in Table S6 in ESI.†

Scheme 7 The possible stereoselective pathways for the LiCl catalyzed 32CA reaction between C-methoxycarbonylnitrone 16 and cyclopentene 14.

Scheme 8 The possible stereoselective pathways for the Li⁺(OMe₂)₃ catalyzed 32CA reaction between C-methoxycarbonylnitrone 17 and cyclopentene 14.

Table 6 MPWB1K/6-31G(d) relative energies (ΔE in kcal mol⁻¹), in vacuum and in DCM, of the stationary points for the 32CA reactions of nitrone 13 with cyclopentene 14 in presence of LiCl or Li⁺(OMe₂)₃

	ΔE gas phase	ΔE DCM
TSx-LiCl	10.0	13.3
18	−42.9	−39.7
TSx-Li(OMe2)3	10.8	14.3
20	−40.8	−37.4

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The gas phase activation energies associated to these lithium promoted 32CA reactions are 10.0 (TSx-LiCl) and 10.8 (TSx-Li(OMe₂)₃) kcal mol⁻¹, the 32CA reactions being strongly exothermic by 42.9 (10) and 40.8 (12) kcal mol⁻¹. When these activation energies are compared with the non-catalyzed process, it can be observed that the lithium cation produces an unappreciable acceleration of the reaction. These TSs are only 1.1 kcal mol⁻¹ lower in energy than the non-catalyzed TS1x. When solvent effects of DCM are considered, the interaction with the lithium cation becomes unfavorable. Similar to other 32CA reactions, inclusion of solvent effects produces a deceleration of the gas phase 32CA reaction as a consequence of a better solvation of the nitrone:lithium complexes than TSs. In the two analyzed reactions the larger solvation of the two nitrone:lithium complexes provokes the activation energies to be even higher than that of the non-catalyzed process.

Relative enthalpies, entropies and Gibbs free energies of the lithium catalyzed 32CA reactions of nitrone 13 with cyclopentene 14 are summarized in Table 7. Values of enthalpies, entropies and free energies are given in Table S7, in ESI.† The use of LiCl and Li⁺(OMe₂)₃ as catalysts increases the activation free energy in comparison with the BF₃ catalyst process (ΔΔG_activation = 7.9 and 6.5 kcal mol⁻¹, respectively). Consequently, the Li cation catalyst is not an alternative catalyst, when compared to BF₃.

Table 7 MPWB1K/6-31G(d) relative enthalpies (ΔH, in kcal mol⁻¹), entropies (ΔS, in cal mol⁻¹ K⁻¹), and free energies (ΔG, in kcal mol⁻¹), for the TSs and CA reactions involved in the 32CA reaction between nitrone 13 and cyclopentene 14 in the presence of LiCl or Li⁺(OMe₂)₃ catalyst

	ΔH	ΔS	ΔG
TSx-LiCl	13.5	−49.5	28.2
18	−34.0	−41.6	−23.6
TSx-Li(OMe2)3	15.7	−37.4	26.8
20	−33.1	−43.4	−20.3

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The geometries of the TSs associated with the 32CA reaction of nitrone 13 and cyclopentene 14 in the presence of LiCl and Li⁺(OMe₂)₃ are given in Fig. 3. The lengths of the O1–C5 and C3–C4 forming bonds at the TSs are 2.286 and 2.120 Å at TSx-LiCl, and 2.256 and 2.117 Å at TSx-Li(OMe₂)₃, respectively. The BO values of the C–O and C–C forming bonds are 0.24 and 0.36 at TSx-LiCl and 0.23 and 0.36 at TSx-Li(OMe₂)₃, respectively. Therefore, these TSs are less asynchronous than that of the BF₃ catalyzed process. Thus, the lithium catalyzed 32CA reactions between nitrone 13 and cyclopentene 14 preceded via an asynchronous one-step mechanism in which the formation of the C–C single bond is more advanced than the C–O one.

Fig. 3 Optimized structures of the TSs for the 32CA reactions of nitrone 13 and cyclopentene 14 in the presence of LiCl and Li⁺(OMe₂)₃.

The CT at the TSs associated with the lithium promoted 32CA reactions is 0.16e (TSx-LiCl) and 0.17e (TSx-Li(OMe₂)₃), indicating that these 32CA reactions took place via some polar mechanism. It may be noted that these values are lower than those found in the BF₃ catalyzed process.

4. DFT-based reactivity indices analysis

Previous studies devoted to DA and 32CA reactions have shown that the analysis of the reactivity indices defined within the context of the conceptual DFT³⁷ is a powerful tool to understand the reactivity in polar cycloadditions. DFT reactivity indices, namely, electronic chemical potential, μ, hardness, η, electrophilicity, ω, and nucleophilicity, N, indices of nitrone, cyclopentene and nitrone-BF₃ are given in Table 8.

Table 8 Electronic chemical potential μ, chemical hardness η, global electrophilicity ω and global nucleophilicity N, in eV, for nitrone, nitrone-c and cyclopentene

	μ	η	ω	N
Nitrone:BF3 complex 15	−6.13	7.39	2.54	0.69
Nitrone 13	−4.47	6.84	1.46	2.63
Cyclopentene 14	−2.63	9.42	0.36	3.18

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The electronic chemical potential μ of nitrone 13 and nitrone:BF₃ complex 15, μ = −4.47 eV and −6.13 eV, respectively, is lower than that of pentene 14, −2.63 eV, indicating that along a polar 32CA reaction the CT will take place from cyclopentene towards nitrone, in agreement with the analysis performed at the TSs.

The electrophilicity and nucleophilicity indices of nitrone 13 are 1.46 and 2.63 eV, respectively, allows for its classification as a moderate electrophile and a moderate nucleophile, based on the electrophilicity¹⁰ and nucleophilicity¹² scales. Coordination of the BF₃ LA to nitrone 13 allowing its electrophilicity increases to ω = 2.54 eV, and decreases the nucleophilicity to N = 0.69 eV, of the corresponding nitrone:BF₃ complex 15. Consequently, it becomes a strong electrophile participating in polar reactions. On the other hand, the electrophilicity and nucleophilicity indices of cyclopentene are ω = 0.36 eV and N = 3.18 eV, being classified as a marginal electrophile and strong nucleophile.

The electrophilicity difference Δω between nitrone 13 and nitrone:BF₃ complex 15, Δω = 1.08 eV, accounts for the catalyst role of the BF₃ LA to favor a zw-type reaction via a polar process; in zw-type 32CA reactions the increase of the polar character of the TS goes accompanied by a decrease of the activation energy.

Recently, Domingo and coworkers³¹ proposed electrophilic, P⁺_k, and nucleophilic, P⁻_k, Parr functions, based on the atomic spin density distribution in the radical anion and radical cation of the neutral molecules, to study the regioselectivity in polar reactions. The electrophilic and nucleophilic Parr functions, respectively, obtained through the analysis of the Mulliken atomic spin density of the radical anion and the radical cation. Accordingly, the electrophilic P⁺_k and nucleophilic P⁻_k Parr functions for nitrone 13 and nitrone-BF₃ 15 are shown in Scheme 9.

Scheme 9 MPWB1K/6-31G(d) electrophilic P⁺_k Parr functions in nitrone 13 and nitrone-BF₃ 15.

Analysis of the electrophilic P⁺_k functions at the nitrone 13 indicates that the O1 oxygen atom is the most electrophilic center P⁺_k = 0.28. Thus, the formation of the new C–O single bond will be more advanced than the C–C one. For nitrone:BF₃ complex 15, the electrophilic P⁺_k Parr functions at the C3 carbon and O1 oxygen atoms are 0.28 and 0.08, respectively. Therefore, the C3 carbon atom is now the most electrophilic center of complex 15. Consequently, coordination of the BF₃ LA catalyst to the nitrone O1 oxygen atom makes the C3 carbon atom as the most electrophilicity center of complex 15 and thereby, the change the asynchronicity of the single bond formation along these 32CA reactions.

5. Conclusion

The mechanism and stereoselectivity of the non-catalyzed and BF₃ catalyzed 32CA reactions between the C-methoxycarbonyl nitrone 13 and cyclopentene 14 to yield exclusively the corresponding trans isoxazolidine has been studied using DFT methods at the MPWB1K/6-31G(d) computational level. In the absence of an LA catalyst, this 32CA reaction takes place through a near synchronous mechanism leading to the formation of the exo cycloadduct as the kinetic and thermodynamic product. The low CT found at the corresponding TS points to the low polar character of this 32CA reaction and the relative high activation energy. The inclusion of solvent effects slightly increases the activation energy and decreases the exothermic character of the 32CA reactions as a consequence of a larger solvation of nitrone 2 than TSs and CAs.

Coordination of the BF₃ catalyst to the oxygen atom of nitrone 2 accelerates the 32CA reaction to increase of the polar character of the reaction with lower activation energy for the exo approach leading to formation of a single trans cycloadduct. The BF₃ catalyzed 32CA reaction takes place via an asynchronous mechanism in which the C–C bond formation is more advanced than the O–C one. Inclusion of solvent effects has a similar trend to that observed in the non-catalyzed process. The computed activation Gibbs free energy of the TSs also favored kinetically the formation of the exo cycloadduct, in agreement with the energy analysis and experimental data.

Finally, the effects of the coordination of the lithium cation as a LA catalyst to nitrone 2 has been analyzed. Coordination of the lithium cation to the oxygen atom of nitrone 2 does not make any appreciable change along the exo stereoisomeric channel with respect to the non-catalyzed process. This analysis suggests that the lithium cation is not an effective metal catalyzing 32CA reactions. The computed activation Gibbs free energies of the exo TSs allow establishing that the coordination of the Li cation to the oxygen atom of nitrone does not provoke any appreciable catalytic effect on these 32CA reactions.

These findings are the basis of our future research, which we will try to make a platform for experimental chemists in the field of asymmetric synthesis, who would like to use a facile and an efficient metal catalysts.

Acknowledgements

Prof. L.R.D. is grateful to Ministerio de Ciencia e Innovación of the Spanish Government, for project CTQ2013-45646-P.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c5ra09139j

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