Non-classical CH⋯O hydrogen-bond determining the regio- and stereoselectivity in the [3 + 2] cycloaddition reaction of (Z)-C-phenyl-N-methylnitrone with dimethyl 2-benzylidenecyclopropane-1,1-dicarboxylate. A topological electron-density study

Abstract

The role of the ester groups in the regio- and stereoselectivities of the zw-type [3 + 2] cycloaddition (32CA) reaction of C-phenyl-N-methylnitrone with dimethyl 2-benzylidenecyclopropane-1,1-dicarboxylate (BCPC) has been studied using DFT methods at the MPWB1K/6-31G(d) level. The possible ortho/meta regioisomeric channels and the endo/exo stereoselective approach modes were explored and characterized. Analysis of the relative energies associated with the different reaction pathways indicates that the presence of the two CO₂Me groups in the cyclopropane ring has a remarkable effect on selectivities favouring the ortho/endo path, in good agreement with the experimental data. Inclusion of solvent effects increases the activation energy and decreases the exothermic character of both 32CA reactions but does not change gas phase selectivities. The electron localisation function (ELF) topological analysis along the most favourable ortho/endo path allows us to explain the formation of the C–C and O–C bonds through a non-concerted two-stage one-step mechanism. Non-covalent interaction (NCI) analysis of the most favourable ortho/endo transition state structure reveals that the formation of a non-classical CH⋯O hydrogen-bond involving the nitrone C–H hydrogen is responsible for the selectivity experimentally found in this non-polar zw-type 32CA reaction.

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1. Introduction

Cycloadditions are among the most useful organic reactions since they enable the preparation of carbocyclic and heterocyclic compounds of great pharmaceutical and industrial interest.¹ [3 + 2] cycloaddition (32CA) reactions are important processes in organic synthesis and they are widely used to obtain five-membered heterocyclic compounds.² Reactions between nitrones and ethylene derivatives leading to isoxazolidines are well-known processes of this kind.^1,2 Substituted isoxazolidines have found numerous applications as enzyme inhibitors³ and as intermediates for the synthesis of a variety of compounds after cleavage of the N–O bond.⁴ On the other hand, the use of methylenecyclopropane derivatives for the synthesis of heterocyclic compounds has widely spread in recent years due to easily accessible methods and their selective synthetic transformations in cycloaddition reactions without the use of catalysts and added reagents.⁵

A considerable amount of experimental and theoretical studies on the mechanisms and selectivities of cycloaddition reactions of methylenecyclopropane derivatives can be found in the literature. Recently, we studied the Diels–Alder reaction between furan 1 and difluoromethylenecyclopropane 2, finding that the reaction proceeded via a synchronous one-step mechanism with high activation energy and a non-polar character (see Scheme 1). This reaction favoured the formation of the endo cycloadduct due to the favourable interaction along the endo approach mode.⁶

Scheme 1 Diels–Alder reaction of furan 1 with difluoro-2-methylenecyclopropane 2.

Moeinpour et al. studied, using density functional theory (DFT) calculations at the B3LYP/6-31G level, the mechanism and the regioselectivity of the 32CA reaction of C-phenyl carbamoyl-N-phenylnitrone 4 with some dialkyl-substituted 2-benzylidenecyclopropane-1,1-dicarboxylates 5 (see Scheme 2).⁷ The authors found that the change of the substituent in the phenyl ring of 2-benzylidenecyclopropane-1,1-dicarboxylates 5 may change the nature of the mechanism for this reaction. They showed that these reactions occur via an asynchronous one-step mechanism with non-polar character and low activation energies.

Scheme 2 32CA reaction of C-phenyl carbamoyl-N-phenylnitrone 4 with dialkyl-substituted 2-benzylidenecyclopropane-1,1-dicarboxylates 5.

Recently, a useful classification of 32CA reactions into pseudodiradical-type (pr-type) reactions involving three-atom-components (TACs) with a high pseudodiradical character, which take place easily through an earlier transition state structure (TS) with non-polar character, and zwitterionic-type (zw-type) reactions involving TACs with a high zwitterionic character, controlled by favourable nucleophilic/electrophilic interactions taking place at the TSs, was established.⁸ Nitrones, which present a high nucleophilic character, are able to participate in zw-type 32CA reactions towards electrophilically activated ethylenes, via a polar mechanism with low activation energy.⁹

Tran et al. experimentally studied the 32CA reaction between C-phenyl-N-methylnitrone 7 and dimethyl 2-benzylidenecyclopropane-1,1-dicarboxylate (BCPC) 8,¹⁰ finding that this reaction is regio- and stereoselective yielding the corresponding ortho/endo cycloadduct 9 as the single regio- and stereocycloadduct (see Scheme 3).

Scheme 3 32CA reaction of C-phenyl-N-methylnitrone 7 with BCPC 8.

As a continuation of our studies on the selectivities and mechanisms of the 32CA reactions of methylenecyclopropane derivatives,⁶ we decided to undertake a theoretical investigation of the regio- and stereoselectivities of the 32CA reaction experimentally performed by Tran's group.¹⁰ In order to explain the role of the ester groups in the reactivity and selectivity of this reaction, the 32CA reactions of C-phenyl-N-methylnitrone 7 with 2-benzylidenecyclopropane (BCP) 10 and with BCPC 8 were studied.

2. Computational methods

Several works have shown that the B3LYP functional¹¹ is relatively accurate for kinetic data, although the reaction exothermicities are underestimated.¹² Recently, Truhlar's group proposed some functionals, such as the MPWB1K hybrid meta functional,¹³ which improve thermodynamic calculations. Consequently, DFT computations were carried out using the MPWB1K¹³ exchange-correlation functional, together with the standard 6-31G(d) basis set.¹⁴ Single point energy calculations at the MPWB1K/6-31+G(d) level were additionally performed in order to test how the diffuse functions modify the selectivities of this 32CA reaction. The stationary points were characterised by frequency computations in order to verify that TSs have one and only one imaginary frequency. Intrinsic reaction coordinate (IRC)¹⁵ pathways were traced to verify the connectivity between minima and associated TSs. Solvent effects of toluene were taken into account through single point energy calculations using the polarisable continuum model (PCM) developed by Tomasi's group in the framework of the self consistent reaction field.¹⁶ Values of enthalpies, entropies and Gibbs free energies in toluene were calculated with standard statistical thermodynamics at 383.15 K and 1 atm over the optimized gas phase structures¹⁷ and were scaled by 0.96.¹⁸

The electronic structures of critical points were analysed by the natural bond orbital (NBO) method.¹⁹ The electron localisation function (ELF) topological analysis, η(r),²⁰ was performed with the TopMod program²¹ using the corresponding MPWB1K/6-311G(d,p) monodeterminantal wavefunctions of the selected structures of the IRC. Non-covalent interactions (NCI) were computed by evaluating the promolecular 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,²⁵ which measures the stabilisation in energy when the system acquires an additional electronic charge ΔN from the environment, is expressed by the following simple equation,²⁵ 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.²⁶ On the other hand, the nucleophilicity index is defined as N = ε_HOMO − ε_HOMO(TCE),²⁷ where ε_HOMO is the HOMO energy of the nucleophile and ε_HOMO(TCE) corresponds to the HOMO energy of tetracyanoethylene (TCE), taken as a reference. The electrophilic, P_k⁺, and nucleophilic, P_k⁻, Parr functions²⁸ were obtained through the analysis of the Mulliken atomic spin densities of the corresponding radical anion and radical cation by single-point energy calculations over the optimised neutral geometries.

3. Results and discussion

The present study has been divided into six sections: (i) first, the 32CA reaction between C-phenyl-N-methylnitrone 7 and BCP 10 is studied; (ii) in the second part, the 32CA reaction between nitrone 7 and BCPC 8 is theoretically investigated. In each part, energetic aspects, geometrical parameters of the TSs and their electronic structures in terms of natural charges are analysed. Solvent effects on these 32CA reactions are also discussed; (iii) in the third part, an ELF topological analysis of the formation of the C–C and O–C single bonds along the most favorable ortho/endo path associated with the 32CA reaction of nitrone 7 with BCPC 8 is carried out; (iv) in the fourth part, the NCIs of the TS involved in the most favourable ortho/endo path associated with this 32CA reaction are analysed; (v) in the fifth part, a DFT analysis based on the reactivity indices is performed; and finally, (vi) in the last part, the origin of the ortho/endo selectivity in the 32CA reaction of nitrone 7 with BCPC 8 is explained.

The zwitterionic TAC, nitrone 7, and BCPC 8 and BCP 10, are unsymmetrical species, thereby, the interaction TAC/ethylene can take place through four reactive channels corresponding to the endo and exo stereoisomeric approach modes of BCPC 8 and BCP 10 towards nitrone 7, and the two regioisomeric modes: the ortho and meta pathways. Thus, four TSs and four cycloadducts were located for each reaction path (see Scheme 4).

Scheme 4 Competitive regio- and stereoisomeric pathways associated with the 32CA reactions of nitrone 7 with BCPC 8 or BCP 10.

3.1 Study of the 32CA reaction between nitrone 7 and BCP 10

First, the zw-type 32CA reaction between nitrone 7 and BCP 10 was studied (see Scheme 4). The MPWB1K/6-31G(d) total and relative energies are summarized in Table 1. The MPWB1K/6-31G(d) gas phase activation energies associated with the four reactive channels of the 32CA reaction between nitrone 7 and BCP 10 are 16.4 (TS-10-on), 18.9 (TS-10-ox), 14.4 (TS-10-mn) and 15.3 (TS-10-mx) kcal mol⁻¹, the reaction being exothermic by between 36 and 40 kcal mol⁻¹. This 32CA reaction presents a high activation energy, 14.4 kcal mol⁻¹ (TS-10-mn). Note that the activation energy associated with the most favourable TS-10-mn is 1.3 kcal mol⁻¹ higher than that associated with the non-polar 32CA reaction between the simplest nitrone and ethylene.⁹ These energy results indicate that this 32CA reaction is low endo stereoselective, as the most favourable endo TS-10-mn is 0.9 kcal mol⁻¹ below the exo TS-10-mx, and displays a moderate meta regioselectivity as the most favourable meta TS-10-mn is 2.0 kcal mol⁻¹ below the ortho TS-10-on. Consequently, due to the strong exothermic character of the reaction, which makes the formation of the four CAs irreversible, the differences between the activation energies suggest that this reaction would lead to an isomeric mixture.

Table 1 MPWB1K/6-31G(d) total (E, in a.u.) and relative^a energies (ΔE, in kcal mol⁻¹) in gas phase and in toluene of the stationary points involved in the 32CA reaction of C-phenyl-N-methylnitrone 7 with BCP 10

	Gas phase		Toluene
	E	ΔE	E	ΔE
a Relative to 7 and 10.
7	−439.94778		−439.95239
10	−386.81884		−386.82071
TS-10-on	−826.74045	16.4	−826.74489	17.7
TS-10-ox	−826.73645	18.9	−826.74091	20.2
TS-10-mn	−826.74359	14.4	−826.74734	16.2
TS-10-mx	−826.74219	15.3	−826.74594	17.0
11-on	−826.82673	−37.7	−826.83014	−35.8
11-ox	−826.83063	−40.2	−826.83387	−38.1
11-mn	−826.82399	−36.0	−826.82766	−34.2
11-mx	−826.82559	−37.0	−826.82927	−35.2

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In order to compare the MPWB1K energy results with the B3LYP ones, the stationary points were optimised at the B3LYP/6-31G(d) level. The B3LYP/6-31G(d) gas phase total and relative energies are given in Table S1 in ESI.† A comparison of the gas phase relative energies indicates that while the B3LYP activation energies are between 3.9 and 5.5 kcal mol⁻¹ higher than those of the MPWB1K ones, the reaction energies are underestimated by around 18 kcal mol⁻¹. Regardless, both functionals yield low selectivity.

Inclusion of solvent effects stabilises all structures in the gas phase calculations; nitrone 7 is more stabilised than BCP 10, TSs and cycloadducts, as a consequence of a higher solvation of nitrone 7 than other stationary points in polar solvents.²⁹ Consequently, solvent effects increase the activation energies by 1.3 kcal mol⁻¹ for both ortho TS-10-on and TS-10-ox, while for the meta TSs they are increased by 1.8 kcal mol⁻¹ for the endo approach and 1.7 kcal mol⁻¹ for the exo one (see Table 1). Thereby, inclusion of solvent effects slightly increases the activation energies and decreases the exothermic character of this 32CA reaction but does not change the low selectivity obtained in gas phase.

The values of the enthalpies, entropies and Gibbs free energies and the relative ones of the stationary points involved in the 32CA reaction of nitrone 7 with BCP 10 are summarized in Table 2. The Gibbs free energy profile of the 32CA reaction between nitrone 7 and BCP 10 is given in Fig. 1. From Table 2, a comparison between the relative activation enthalpies associated with the four reactive pathways of the 32CA reaction of nitrone 7 with BCP 10 indicates that the most favourable approach mode is now that associated with TS-10-mx (ΔH = 17.6 kcal mol⁻¹). Addition of the entropic contribution to the enthalpy increases the activation Gibbs free energy of this reactive channel to 34.1 kcal mol⁻¹. However, the analysis of the activation Gibbs free energies indicates that although the meta/exo reactive channel becomes the most favourable one as the consequence of the unfavourable negative activation entropy associated with TS-10-mn, ΔS = −53.9 cal mol⁻¹ K⁻¹, this 32CA reaction shows low selectivity as TS-10-mx is only 0.6 kcal mol⁻¹ more favourable than TS-10-on. In addition, this 32CA reaction is exergonic by between 5.8 and 13.3 kcal mol⁻¹. Consequently, it is expected to obtain an isomeric mixture from this 32CA reaction.

Table 2 MPWB1K/6-31G(d) enthalpies (H, in a.u.), entropies (S, in cal mol⁻¹ K⁻¹) and Gibbs free energies (G, in a.u.), and the relative^a ones (ΔH in kcal mol⁻¹, ΔS in cal mol⁻¹ K⁻¹ and ΔG in cal mol⁻¹ K⁻¹, respectively), computed at 398.15 K and 1 atm in toluene, for the stationary points involved in the 32CA reaction between nitrone 7 and BCP 10

System	H	ΔH	S	ΔS	G	ΔG
a Relative to 7 and 10.
7	−439.78289		103.2		−439.84557
10	−386.63984		98.6		−386.70004
TS-10-on	−826.39365	18.2	158.2	−43.6	−826.49027	34.7
TS-10-ox	−826.38981	20.7	156.4	−45.4	−826.48528	37.9
TS-10-mn	−826.39337	18.4	147.9	−53.9	−826.48366	38.9
TS-10-mx	−826.39473	17.6	158.1	−43.7	−826.49122	34.1
11-on	−826.47549	−33.1	149.6	−52.1	−826.56687	−13.3
11-ox	−826.46494	−26.5	155.2	−46.6	−826.56339	−11.2
11-mn	−826.45873	−22.6	151.6	−50.2	−826.55489	−5.8
11-mx	−826.46032	−23.6	154.9	−46.9	−826.55860	−8.1

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Fig. 1 Gibbs free energy profile (ΔG, in kcal mol⁻¹) of the 32CA reaction between nitrone 7 and BCP 10.

The geometries of the TSs involved in the 32CA reaction between nitrone 7 and BCP 10 are given in Fig. 2. The lengths of the C–C and O–C forming bonds at the TSs are 2.132 and 2.211 Å at TS-10-on, 2.123 and 2.254 Å at TS-10-ox, 2.308 and 1.932 Å at TS-10-mn and 2.429 and 1.918 Å at TS-10-mx. The O–C bond in the TSs associated with the most favourable meta channels is shorter than the C–C one. However, for the ortho channel, the C–C bond is slightly shorter than the O–C one. These geometric parameters suggest an asynchronous bond formation process along the most favourable meta regioisomeric channel but an almost synchronous one along the ortho reactive channel.

Fig. 2 MPWB1K/6-31G(d) optimised structures of the TSs of the 32CA reaction of nitrone 7 with BCP 10. Lengths are given in Angstroms.

The evaluation of the global electron-density transfer (GEDT) along these 32CA reactions is made by a Natural Population Analysis (NPA).³⁰ The MPWB1K/6-31G(d) natural atomic charges at the TSs were shared between nitrone 7 and BCP 10. The values of the GEDT at the TSs, which fluxes from BCP 10 toward nitrone 7, are 0.04 e at TS-10-on, 0.05 e at TS-10-ox, 0.06 e at TS-10-mn and 0.05 e at TS-10-mx. These very low values indicate that this 32CA reaction has a non-polar character, thus explaining the high activation energy found in this zw-type 32CA reaction.⁹

3.2 Study of the 32CA reaction between nitrone 7 and BCPC 8

Next, the 32CA reaction of nitrone 7 with BCPC 8 was studied (see Scheme 4). Total and relative energies for the stationary points (reactants, TSs and cycloadducts) involved in the 32CA reactions of nitrone 7 with BCPC 8, in gas phase and in toluene, are displayed in Table 3. The IRCs from the four isomeric TSs to the separated reagents end in a series of molecular complexes (MCs) formed in an earlier stage of the reaction in which nitrone 7 and BCPC 8 are positioned in a parallel disposition at a distance of ca. 3.3 Å. Only the most favorable MC-8-on among the four isomeric MCs, which is 7.3 kcal mol⁻¹ more stable than the separates reagents, was studied (see later). The gas phase activation energies associated with the four reactive channels of this 32CA reaction are 12.0 (TS-8-on), 18.1 (TS-8-ox), 14.7 (TS-8-mn) and 15.4 (TS-8-mx) kcal mol⁻¹, the reaction being exothermic by 37.2 (9-on), 40.9 (9-ox), 38.1 (9-mn) and 39.6 (9-mx) kcal mol⁻¹. The activation energy associated with the most favourable ortho/endo pathway of this 32CA reaction, 12.0 kcal mol⁻¹ (TS-8-on), is only 2.4 kcal mol⁻¹ lower than that associated with the most favourable meta/endo pathway of the 32CA reaction with BCP 10, this zw-type 32CA being also unfavourable. These energy results indicate that the 32CA reaction between nitrone 7 and BCPC 8 is highly ortho regioselective as the most favourable ortho TS-8-on is 2.7 kcal mol⁻¹ below meta TS-8-mx, and displays high endo stereoselectivity as the most favourable endo TS-8-on is 3.4 kcal mol⁻¹ below exo TS-8-mx, in good agreement with the experimental observations. These energy values clearly indicate that the presence of the CO₂Me groups in the cyclopropane ring of BCPC 8 favours the ortho/endo pathway, decreasing the corresponding activation energy from 16.4 (TS-10-on) in the 32CA reaction between nitrone 7 and BCP 10 to 12.0 kcal mol⁻¹ in the 32CA reaction of nitrone 7 with BCPC 8. The high exothermic character of this 32CA reaction makes the cycloaddition irreversible.

Table 3 MPWB1K/6-31G(d) total (E, in a.u.) and relative^a (ΔE, in kcal mol⁻¹) energies, in gas phase and in toluene, of the stationary points involved in the 32CA reaction of nitrone 7 with BCPC 8

	Gas phase		Toluene
	E	ΔE	E	ΔE
a Relative to 7 and 8.
7	−439.94778		−439.95239
8	−842.37274		−842.37827
MC-8-on	−1282.33217	−7.31	−1282.33957	−5.6
TS-8-on	−1282.30146	12.0	−1282.30824	14.1
TS-8-ox	−1282.29169	18.1	−1282.29885	20.0
TS-8-mn	−1282.29716	14.7	−1282.30464	16.3
TS-8-mx	−1282.29604	15.4	−1282.30342	17.1
9-on	−1282.37986	−37.2	−1282.38582	−34.6
9-ox	−1282.38565	−40.9	−1282.39132	−38.1
9-mn	−1282.38122	−38.1	−1282.38830	−36.2
9-mx	−1282.38681	−41.6	−1282.39306	−39.6

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Single point energy calculations at the MPWB1K/6-31+G(d) level increases the activation energies by ca. 3 kcal mol⁻¹ and decreases the exothermicities between 4 and 5 kcal mol⁻¹ as a consequence of a higher stabilisation of reagents than TSs and cycloadducts (see Table S2 in ESI†). However, inclusion of diffuse functions does not modify the selectivities.

Just as in the 32CA reaction of nitrone 7 with BCP 10, the inclusion of solvent effects of toluene increases the gas phase activation energies by 2.1 (TS-8-on), 1.9 (TS-8-ox), 1.6 (TS-8-mn) and 1.7 (TS-8-mx) kcal mol⁻¹. Moreover, solvent effects slightly decrease the exothermic character of the reaction; the changes are 2.6 (9-on), 2.8 (9-ox), 1.9 (9-mn) and 2.0 (9-mx) kcal mol⁻¹. In spite of the increase of the activation energy and the decrease of the exothermic character, the solvent effect does not modify the selectivity found in gas phase.

The values of the enthalpies, entropies and Gibbs free energies and the relative ones associated with the four reactive channels belonging to the 32CA reaction between nitrone 7 and BCPC 8 are summarized in Table 4. The Gibbs free energy profile of the 32CA reaction between nitrone 7 and BCPC 8 is given in Fig. 3. Analysis of the activation enthalpy shows a preference for the ortho/endo pathway (ΔH = 14.8 kcal mol⁻¹), in agreement with the computed activation energy. Addition of the entropic contribution increases the activation Gibbs free energy corresponding to the ortho/endo pathway to 34.2 kcal mol⁻¹ favouring kinetically the formation of 9-on as the single cycloadduct, in good agreement with the experimental outcomes. Note that while formation of MC-8-on is exothermic by 4.0 kcal mol⁻¹, it is endergonic by 18.3 kcal mol⁻¹; consequently, in the Gibbs free energy surfaces these MCs are not a minimum between the reagents and the corresponding TSs.

Table 4 MPWB1K/6-31G(d) enthalpies (H, in a.u.), entropies (S, in cal mol⁻¹ K⁻¹) and Gibbs free energies (G, in a.u.), and the relative^a ones (ΔH in kcal mol⁻¹, ΔS in cal mol⁻¹ K⁻¹ and ΔG in kcal mol⁻¹, respectively), computed at 398.15 K and 1 atm in toluene, for the stationary points involved in the 32CA reaction between nitrone 7 and BCPC 8

System	H	ΔH	S	ΔS	G	ΔG
a Relative to 7 and 8.
7	−439.78289		102.7		−439.84557
8	−842.09831		160.1		−842.19609
MC-8-on	−1281.88765	−4.0	204.3	−58.4	−1282.01242	18.3
TS-8-on	−1281.85764	14.8	212.0	−50.8	−1281.98708	34.2
TS-8-ox	−1281.85004	19.6	204.2	−58.6	−1281.97471	42.0
TS-8-mn	−1281.85426	16.9	206.7	−56.1	−1281.98049	38.4
TS-8-mx	−1281.85317	17.6	212.3	−50.5	−1281.98282	36.9
9-on	−1281.93941	−36.5	199.7	−63.1	−1282.06134	−12.4
9-ox	−1281.93314	−32.6	201.8	−61.0	−1282.05638	−9.2
9-mn	−1281.93487	−33.7	199.4	−63.5	−1282.05662	−9.4
9-mx	−1281.93417	−33.2	199.9	−62.9	−1282.05624	−9.2

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Fig. 3 Gibbs free energy profile (ΔG, in kcal mol⁻¹) of the 32CA reaction between nitrone 7 and BCPC 8.

The geometries of the TSs associated with the 32CA reaction of nitrone 7 with BCPC 8 are given in Fig. 4. The lengths of the C–C and O–C forming bonds at the TSs are 2.236 and 2.122 Å at TS-8-on, 2.215 and 2.144 Å at TS-8-ox, 2.426 and 1.917 Å at TS-8-mn, 2.270 and 1.967 Å at TS-8-mx.

Fig. 4 MPWB1K/6-31G(d) optimised structures of the TSs of the 32CA reaction of nitrone 7 with BCPC 8. Lengths are given in Angstroms. The MPWB1K/6-31+G(d) distances are shown in parenthesis.

An analysis of the geometry of MC-8-on (see Fig. 5) indicates that the carbonyl oxygen atom of one of the two carboxylate groups present in the cyclopropane moiety of BCPC 8 is located at a distance of 2.37 Å from the nitrone C3–H hydrogen atom, which is shortened to 2.19 Å at TS-8-on. This geometric arrangement accounts for the large stabilization of MC-8-on through the formation of a non-classical hydrogen-bond (HB) in an earlier stage of the reaction. An analysis of the geometry of the MPWB1K/6-31+G(d) optimised TS-8-on indicates that the inclusion of diffuse functions does not modify the non-classical CH⋯O HB (see Fig. 4).

Fig. 5 Optimised structure of MC-8-on. Lengths are given in Angstroms.

Bond order (BO) values have been used to analyse the extent in the bond formation at the TSs. Thus, MPWB1K/6-31G(d) Wiberg bond indices³¹ were computed using the NBO method. The BO values for the C–C and O–C forming bonds at the TS associated with this 32CA reaction are 0.29 and 0.29 at TS-8-on, 0.32 and 0.28 at TS-8-ox, 0.24 and 0.38 at TS-8-mn and 0.30 and 0.37 at TS-8-mx. These values suggest that the bond formation process at the meta TSs is slightly more asynchronous than at the ortho TSs, in which the formation of the O–C bond is slightly more advanced than that of the C–C one. Note that at the most favorable TS-8-on, analysis of the C–C and O–C BO values indicates a synchronous bond formation process.

The values of the GEDT, which takes place from nitrone 7 to BCPC 8, are 0.08 e (TS-8-on), 0.09 e (TS-8-ox), 0.12 e (TS-8-mn) and 0.08 e (TS-8-mx). These very low values indicate that this zw-type 32CA reaction has a non-polar character, in agreement with the obtained high activation energies.⁹

3.3 ELF topological analysis along the formation of the C–C and O–C single bonds associated with the most favourable ortho/endo reactive channel of the 32CA reaction of nitrone 7 with BCPC 8

Several theoretical studies have shown that the ELF topological analysis of the changes of electron-density along a reaction path can be used as a valuable tool to understand the bonding changes along the reaction path, and consequently to establish the molecular mechanisms.³² After an analysis of the electron-density, the ELF provides basins, which are the domains in which the probability of finding an electron pair is maximal.³³ The basins are classified as core basins and valence basins. The latter are characterised by the synaptic order, i.e., the number of atomic valence shells in which they participate. Thus, there are monosynaptic, disynaptic, trisynaptic basins and so on.³⁴ Monosynaptic basins, labelled V(A), correspond to lone pairs or non-bonding regions, while disynaptic basins, labelled V(A, B), connect the core of two nuclei A and B and, thus, correspond to a bonding region between A and B. This description recovers the Lewis bonding model, providing a very suggestive graphical representation of the molecular system.

Very recently, Ríos-Gutiérrez et al. performed a Bonding Evolution Theory (BET) study of the mechanism of 32CA reactions of nitrones with electron-deficient (ED) ethylenes.³⁵ Interestingly, this BET study showed that while the formation of the C–C single bond begins at ca. 2.0 Å, the formation of the O–C bond begins at the very short distance of 1.6 Å. This study emphasized that the asynchronicity based on the topological analysis of the bonding changes along the reaction is contrary to that obtained by the analysis of the geometrical parameters or the BO values, which predict a more synchronous process.

Herein, in order to understand the formation of the C–C and O–C single bonds along the most favourable ortho/endo reactive channel associated with the 32CA reaction of nitrone 7 with BCPC 8, and thus to establish the molecular mechanism of this 32CA reaction, an ELF topological analysis of the MPWB1K/6-31G(d) wavefunctions of the most relevant points involved in the formation of the C–C and O–C single bonds along the IRC associated with TS-8-on has been performed. The population of the most significant valence basins of the corresponding points is displayed in Table 5, while the attractor positions of the valence basins of the aforementioned points are presented in Fig. 6.

Table 5 Valence basin populations N calculated from the ELF at some selected points of the most favourable ortho/endo reactive channel associated with the 32CA reaction of nitrone 7 with BCPC 8. Lengths are given in Angstroms. The GEDT obtained by NBO analysis is given in e

	MC-8-on	TS-8-on	P1	P2	P3	P4	9-on
d(C3–C4)	3.588	2.236	2.020	1.947	1.747	1.727	1.534
d(O1–C5)	3.257	2.122	1.971	1.915	1.731	1.709	1.420
GEDT	0.00	0.08	0.01	−0.02	−0.14	−0.15	−0.23
V(O1, N2)	1.41	1.27	1.21	1.17	1.01	1.00	0.98
V(N2, C3)	3.85	2.85	2.24	2.13	2.00	1.98	1.85
V(N2)		1.23	1.69	1.84	2.13	2.17	2.37
V(C4, C5)	1.81	2.84	2.45	2.35	2.19	2.16	2.02
V′(C4, C5)	1.87
V(O1)	2.89	3.00	2.96	2.99	3.42	2.74	2.51
V′(O1)	3.14	3.02	2.90	2.90	2.80	2.78	2.60
V(C5)			0.18	0.22
V(O1, C5)						0.73	1.31
V(C3)			0.45
V(C4)		0.80	1.03
V(C3, C4)				1.58	1.78	1.79	1.93

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Fig. 6 ELF attractor positions of the most relevant points associated with the formation of the C3–C4 and O1–C5 single bonds along the most favourable ortho/endo regioisomeric channel associated with the 32CA reaction of nitrone 7 with BCPC 8. The electron-populations, in e, are given in brackets.

The ELF picture of MC-8-on, d(C3–C4) = 3.588 Å and d(O1–C5) = 3.257 Å (see Scheme 4 for atom numbering), which is a minimum in the PES connecting TS-8-on with the separated reagents, nitrone 7 and BCPC 8, recovers the topological characteristics of the separated reagents. The ELF analysis of MC-8-on shows two monosynaptic basins, V(O1) and V′(O1), with a population of 2.89 e and 3.14 e, as well as two disynaptic basins, V(O1, N2) and V(N2, C3), with a population of 1.41 e and 3.85 e, associated with the oxygen O1 lone pairs and the O1–N2 single and N2=C3 double bond regions of the nitrone framework, respectively. The low electron-density found for the V(O1, N2) disynaptic basin together with the high population of the V(O1) and V′(O1) monosynaptic basins point out a significant polarisation of the O1–N2 single bond towards the oxygen O1 atom. In addition, the ELF topology of MC-8-on also shows two disynaptic basins, V(C4, C5) and V′(C4, C5), integrating 1.81 e and 1.87 e, which belong to the C4=C5 double bond region of the ethylene framework. At MC-8-on, there is no GEDT.

At the most favourable ortho/endo TS involved in the 32CA between nitrone 7 and BCPC 8, TS-8-on, d(C3–C4) = 2.236 Å and d(O1–C5) = 2.122 Å, the O1–N2 and N2–C3 bonding regions remain characterised by two V(O1, N2) and V(N2, C3) disynaptic basins whose populations has experienced a depopulation to 1.27 e and 2.85 e, while the C4=C5 double bond of BCPC 8 has strongly been depopulated, being now characterised by the presence of one V(C4, C5) disynaptic basin integrating 2.84 e. The most relevant feature of this TS is the presence of one V(C4) monosynaptic basin, integrating 0.80 e, and one V(N2) monosynaptic basin, with a population of 1.23 e, which is related to the nitrogen N2 lone pair present in isoxazolidine 9-on. Note that the C4 carbon of BCPC 8 is the most electrophilic center of this molecule (see later). While the electron population of the V(C4) monosynaptic basin at this TS comes from the strong depopulation of the C4=C5 double bond region of BCPC 8, the creation of the V(N2) monosynaptic basin proceeds mainly from the depopulation of the N2=C3 double bond region of nitrone 7 and, in a lesser extent, from the lost electron-density of the V(O1, N2) disynaptic basin. At this TS, the GEDT presents a very low value, 0.08 e, emphasising the non-polar character of this zw-type 32CA reaction.

At P1, d(C3–C4) = 2.020 Å and d(O1–C5) = 1.971 Å, two relevant topological changes associated with the formation of the C3–C4 and O1–C5 single bonds are observed: a new V(C3) monosynaptic basin integrating 0.45 e is created together with a new V(C5) monosynaptic basin integrating 0.18 e. The population of these monosynaptic basins comes from the depopulation of the V(N2, C3) and V(C4, C5) disynaptic basins to 2.24 e and 2.45 e, respectively. Together with the creation of the new V(C5) monosynaptic basin, the total population of the V(O1) and V′(O1) monosynaptic basins has decreased to 5.86 e. At the same time, the populations of the V(C4) monosynaptic basin and the V(N2) monosynaptic basin present at TS-8-on have increased to 1.03 e and 1.69 e. Note that the two V(C3) and V(C4) monosynaptic basins are demanded for the formation of the first C3–C4 single bond. At this point, GEDT is again almost negligible, 0.01 e.

At P2, d(C3–C4) = 1.947 Å and d(O1–C5) = 1.915 Å, the first most relevant topological change along the IRC is observed. The V(C3) and V(C4) monosynaptic basins present at P1 are merged into the new V(C3, C4) disynaptic basin, which presents an electron-population of 1.58 e (see Fig. 6). This topological change indicates that the formation of the C3–C4 single bond has already started at a length of 1.95 Å through the C-to-C coupling of the two C3 and C4 pseudoradical centers present at P1.³⁰ Meanwhile, the population of the V(C5) monosynaptic basin slightly increases to 0.22 e simultaneously with the decrease of the population of the V(C4, C5) disynaptic basin by 0.10 e, and the population of the V(O1, N2) and V(N2, C3) disynaptic basins continue decreasing, contributing to the increase of the electron-density gathered at the nitrogen N2 atom to 1.84 e, which can be almost considered a lone pair. The total population of the V(O1) and V′(O1) monosynaptic basins remains practically unchanged. At P2, there is a slight change in the flux direction of the GEDT, −0.02 e.

At P3, d(C3–C4) = 1.447 Å and d(O1–C5) = 1.731 Å, the most notable topological change is the disappearance of the V(C5) monosynaptic basin present at the previous P2. Interestingly, this disappearance is accompanied by a significant increase of the total population of the V(O1) and V′(O1) monosynaptic basins by 0.33 e to reach a higher population than that found at P1. The electron-population lost by the V(O1, N2) and V(N2, C3) disynaptic basins since reaching 1.01 e and 2.00 e is completely collected at the nitrogen N2 atom, the population of the V(N2) monosynaptic basin being increased by 0.29 e. This fact suggests that there is a relation between the V(C5) monosynaptic basin present at P1 and P2 and the oxygen O1 lone pairs. It can also be observed that the N2–C3 bonding region has already acquired single bond character. In addition, the V(C3, C4) disynaptic basin appeared at the previous P2 has increased its population to 1.78 e as the consequence of the depopulation of the V(C4, C5) disynaptic basin to 2.19 e, which indicates that the C4–C5 bond can be already considered as a single bond too. The GEDT that now fluxes from the ethylene framework towards the nitrone one moderately increases until reaching the value of 0.14 e.

At P4, d(C3–C4) = 1.727 Å and d(O1–C5) = 1.709 Å, the second most relevant change along the reaction path is observed. A new V(O1, C5) disynaptic basin appears with a population of 0.73 e (see Fig. 6) at the same time that the V(O1) and V′(O1) monosynaptic basins are strongly depopulated by 0.70 e to reach 5.52 e. This topological change indicates that the formation of the second O1–C5 single bond has already begun at a length of 1.71 Å through the donation of some electron-density of the oxygen O1 lone pairs of the nitrone framework to the C5 carbon of the ethylene moiety. The electron-population of the other basins scarcely varies. The GEDT remains almost unchanged.

Finally, at isoxazolidine 9-on, d(C3–C4) = 1.534 Å and d(O1–C5) = 1.420 Å, it is noteworthy that the O1–C5 and O1–N2 single bonds are very polarised toward the oxygen atom, the population of the V(O1, C5) and V(O1, N2) disynaptic basins and that of the V(O1) and V′(O1) monosynaptic basins integrating 1.31 e and 0.98 e, and 2.51 e and 2.60 e, respectively. The nitrogen N2 lone pair and the V(C3, C4) disynaptic basin have increased their populations to 2.37 e and 1.85 e, while the C4–C5 single bond presents an electron-population of 2.02 e. At isoxazolidine 9-on, the GEDT has reached a large negative value, −0.23 e, as a consequence of the strong polarisation of the O1–C5 single bond.

Some appealing conclusions can be drawn from the ELF topological analysis of the most relevant points involved in the formation of the C3–C4 and O1–C5 single bonds along the IRC associated with the most favourable ortho/endo reactive channel of the 32CA reaction between nitrone 7 and BCPC 8: (i) the formation of the C3–C4 single bond begins at a distance of 1.95 Å following Domingo's recently proposed pattern:³⁰ (a) depopulation of the double bond regions; (b) formation of two non-bonding V(C) and V(C′) monosynaptic basins; and (c) formation of a new V(C, C′) disynaptic basin through the merger of the electron-density of the aforementioned monosynaptic basins; (ii) formation of the O1–C5 single bond begins with the creation of a new V(O1, C5) disynaptic basin at the very short distance of 1.71 Å. The electron-density of this new V(O1, C5) disynaptic basin mainly proceeds from the electron-density of one V(O1) monosynaptic basin associated with the lone pairs of the nitrone O1 oxygen atom. This pattern for the formation of the O1–C5 single bond is similar to that recently found for the formation of the O–C single bond along the zw-type 32CA reaction of nitrone 7 with ED acrolein 12, in which the electron-density of the new O–C single bond comes from the nitrone oxygen lone pair;³⁵ (iii) the formation of the C3–C4 single bond begins by a two-center interaction involving the most electrophilic center of BCPC 8, the C4 carbon; (iv) while the analysis of the bond lengths of the two C3–C4 and O1–C5 forming bonds along the IRC suggests a synchronous bond formation process, the ELF topological analysis of the bond formation along the reaction path suggests a non-concerted two-stage one-step mechanism,³⁶ in which the formation of the second O1–O5 single bond begins once the first C3–C4 is practically formed. Similarly, the BO values of the C3–C4 and O1–C5 forming bonds at TS-8-on, 0.29 and 0.29, respectively, suggest a synchronous bond formation process. Consequently, while the BO values in the range from 1.0 to 3.0 can be used as a measure of the bonding electron-density between two neighbouring atoms, BO values in the range from 0.0 to 1.0 cannot provide any information about the bonding evolution along the reaction coordinate;³⁵ and finally, (v) the most favourable ortho regioisomeric channel of the non-polar 32CA reaction of nitrone 7 with BCPC 8 shows a great similarity along the formation of the C–C and O–C single bonds with that observed in the unfavourable ortho regioisomeric channel of the zw-type 32CA reaction of nitrone 7 with acrolein 12.³⁵ This fact indicates a similar mechanism for the formation of the C–C and O–C single bonds along the ortho regioisomeric channels of 32CA reactions of nitrones with ED ethylenes, supporting the general model for the bonding changes along the two regioisomeric channels associated with these important reactions.³⁵

3.4 NCI analysis of TS-8-on

An analysis of the geometry of TS-8-on shows that the carbonyl oxygen atom of one of the two carboxylate groups of BCPC 8 is positioned towards the nitrone C3–H hydrogen atom, with an O–H distance of 2.19 Å. This short distance suggests the formation of a non-classical HB, present also in MC-8-on, which could justify the stabilisation of MC-8-on and TS-8-on. In order to explain the stabilisation of these species by the formation of a HB between the carbonyl oxygen atom and the nitrone hydrogen atom, an NCI analysis,²² was performed. Fig. 7 represents the reduced density gradient for MC-8-on and TS-8-on, while Fig. 8 displays low-gradient isosurfaces, subject to the constraint of low density, for these species.

Fig. 7 Plots of the RDG versus the electron-density multiplied by the sign of the second Hessian eigenvalue for (a) MC-8-on and (b) TS-8-on. Both quantities are given in a.u.

Fig. 8 NCI gradient isosurfaces of (a) MC-8-on and (b) TS-8-on. Blue indicates strong attractive interactions while red indicates strong non-bonded overlap.

NCIs have a unique signature and their presence can be revealed solely by means of the electron-density analysis. They are highly non-local and manifest in real space as low-gradient isosurfaces with low densities. The sign of the Laplacian of the density, ∇²ρ, is a widely used tool to distinguish between different types of strong interactions.³⁷ To analyse bonding in more detail, the Laplacian is often decomposed into a sum of contributions. These components are the three eigenvalues λ_i of the electron-density Hessian matrix, such that ∇²ρ = λ₁ + λ₂ + λ₃. Analysis of these components has been widely applied to chemical bonding. The sign of λ₂ can be used to distinguish bonded (λ₂ < 0) from non-bonded (λ₂ > 0) interactions. Analysis of the sign of λ₂ thus helps to differentiate between different types of NCIs, whereas the density itself provides information about their strength. Therefore, in a representation of the reduced density gradient (RDG) versus electron-density, low-density low-gradient spikes lying at negative values indicate stabilising interactions; low-density low-gradient spikes at positive values indicate the lack of bonding, while if they are near zero they are indicative of weak attractive or repulsive interactions.²² The locations of these peaks are sensitive to the atom types involved, the interaction strengths and the level of theory used to obtain the density.

On the other hand, the gradient isosurfaces provide a useful visualization of NCIs as broad regions of real space, rather than simple pairwise contacts between atoms, and are coloured according to the corresponding values of sign(λ₂)ρ. Surfaces with very low density values (ρ < |0.005| a.u.) generally represent weaker dispersion interactions, while surfaces with slightly higher density values (|0.005| < ρ < |0.05| a.u.) represent stronger NCIs, including both attractive HBs and steric clashes. Thus, large negative values of sign(λ₂)ρ are indicative of attractive interactions (such as dipole–dipole or hydrogen bonding) and are coloured in blue, while if sign(λ₂)ρ is large and positive, the interactions are non-bonding and are coloured in red; values near zero indicate very weak van der Waals interactions, and are coloured in green.

The presence of a turquoise surface between the oxygen and hydrogen atoms in TS-8-on in Fig. 8b reveals the existence of an HB between them, which is evidenced by the low-density low-gradient turquoise spike at −0.022 a.u. in Fig. 7b. The green spikes at ca. −0.014 a.u. are indicative of weak van der Waals interactions, while the blue spike appearing at the large negative value of −0.056 a.u. is associated with the strong attractive interactions preceding the bond formation. This is evident from the degree of blue shading for the different interactions in Fig. 8b. Note that the blue spike associated with the strong attractive bond formation interactions that take place at TS-8-on is obviously not present in the graphic related to MC-8-on (see Fig. 7b and a, respectively), while that associated with the HB is already present, indicating that this non-classical HB is formed at the beginning of the reaction. Interestingly, the proximity of the spikes associated with the HB and the van der Waals interactions emphasizes the weakness of the former, in agreement with the colour surface itself, but it is significant enough to change the predicted regioselectivity (see later).

Finally, NCIs analysis of the MPWB1K/6-31+G(d) optimised TS-8-on indicates that the inclusion of diffuse functions does not modify the non-classical CH⋯O HB found at the MPWB1K/6-31G(d) level (see Fig. S1 and S2 in ESI†).

3.5 DFT-based reactivity indices analysis

The nature of the mechanism of these 32CA reactions has been analysed using the global indices, as defined in the context of DFT,³⁸ which are useful tools to understand the reactivity of molecules in their ground state as shown in recent studies devoted to Diels–Alder and 32CA reactions.^39,40 Table 6 collects the static global properties: electronic chemical potential, μ, chemical hardness, η, and global electrophilicity, ω, and nucleophilicity, N, of nitrone 7, BCPC 8 and BCP 10.

Table 6 MPWB1K/6-31G(d) electronic chemical potential (μ), chemical hardness (η), global electrophilicity (ω) and global nucleophilicity (N), in eV, of nitrone 7 and BCPC 8 and BCP 10

	μ	η	ω	N
BCPC 8	−3.62	6.73	0.97	3.24
Nitrone 7	−3.41	6.09	0.96	3.77
BCP 10	−3.29	6.84	0.79	3.52

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The electronic chemical potential of nitrone 7, μ = −3.42 eV, is similar to that of BCPC 8, μ = −3.29 eV and BCP 10, μ = −3.62 eV. Thereby, a very low GEDT will be expected along the reactions, suggesting a non-polar mechanism for these 32CA reactions.

The electrophilicity and nucleophilicity indices of nitrone 7, ω = 0.96 and N = 3.77 eV, allow its classification as a moderate electrophile and a strong nucleophile based on the electrophilicity³⁹ and nucleophilicity⁴¹ scales. On the other hand, the electrophilicity and nucleophilicity indices of BCP 10 are ω = 0.79 and N = 3.52 eV, being classified on the borderline of marginal electrophiles and as a strong nucleophile. Therefore, it is expected that nitrone 7 and BCP 10 participate only as good nucleophiles in polar reactions. Consequently, this reaction will present a high activation energy and proceeds via a non-polar mechanism, as indicated by the previous GEDT analysis. The electrophilicity index of BCPC 8 is ω = 0.97 eV, being classified on the borderline of moderate electrophiles. In spite of the electrophilic activation of BCPC 8 with respect to BCP 10, the former is not electrophilic enough to participate in polar reactions. The higher electrophilic character of BCPC 8 than that of nitrone 7 together with the stronger nucleophilic character of the latter indicates that in this 32CA reaction the low flux of electron-density will go from nitrone 7 to BCPC 8, while in the 32CA reaction of nitrone 7 with BCP 10 there is an inversion in the direction of the GEDT, fluxing from BCP 10 to nitrone 7.

In polar cycloaddition reactions the most favourable reactive channel is that involving the initial two-center interaction between the most electrophilic and nucleophilic centers of both reagents. Recently, Domingo et al.²⁸ proposed the electrophilic P_k⁺ and nucleophilic P_k⁻ Parr functions derived from the changes of spin electron-density reached via the GEDT process from the nucleophile to the electrophile as powerful tools in the study of the local reactivity in polar processes. Accordingly, the electrophilic P_k⁺ Parr functions for nitrone 7 and BCPC 8, and the nucleophilic P_k⁻ Parr functions for nitrone 7 and BCP 10 are analysed in order to predict the most favourable electrophile/nucleophile two-center interaction in these 32CA reactions and, therefore, to explain the regioselectivity experimentally observed (Scheme 5).

Scheme 5 Electrophilic Parr functions for nitrone 7 and BCPC 8, in red, and nucleophilic Parr functions for nitrone 7 and BCP 10, in blue.

For the reaction between nitrone 7 and BCP 10, analysis of the nucleophilic P_k⁻ Parr functions of BCP 10 indicates that the C4 carbon atom is the most nucleophilic center of the molecule, P_k⁻ = 0.37. On the other hand, analysis of the electrophilic P_k⁺ Parr functions of nitrone 7 indicates that the O1 oxygen is the most electrophilic center of the nitrone framework, P_k⁺ = 0.17. Consequently, the most favourable nucleophilic/electrophilic two-center interaction along an asynchronous single bond formation will take place between the C4 carbon of BCP 10 and the O1 atom of nitrone 7, leading to the formation of the meta regioisomers, in clear agreement with the TSs analysis.

Similarly, for the reaction between nitrone 7 and BCPC 8, analysis of the electrophilic P_k⁺ Parr functions at BCPC 8 indicates that the C4 carbon atom is the most electrophilic center, P_k⁺ = 0.29. On the other hand, analysis of the nucleophilic P_k⁻ Parr functions of nitrone 7 reveals that the O1 oxygen is the most nucleophilic center P_k⁻ = 0.60. Thereby, the most favourable interaction will occur between the O1 oxygen of nitrone 7 and the C4 carbon of BCPC 8 leading to the formation of the meta regioisomers, in disagreement with the energies analysis and experimental data.

3.6 What is the origin of the ortho/endo selectivity?

A comparative analysis of the activation energies associated with the 32CA reactions of nitrone 7 with BCP 10 and BCPC 8 reveals that the main energy change caused by the inclusion of the carboxylate groups in the cyclopropane moiety is the stabilisation of TS-8-on by 4.4 kcal mol⁻¹ with respect to TS-10-on, while the other three TSs remain practically unchanged. Consequently, the presence of the carboxylate groups appears to have a significant effect only along the ortho/endo reactive channel.

Both, geometrical analysis and NCI topological analysis of the electron-density of TS-8-on evidence the presence of a non-classical HB interaction between the carbonyl oxygen atom of one of the two carboxylate groups of BCPC 8 and the nitrone C3–H hydrogen atom. Due to the low regioselectivity found in the non-polar 32CA reaction between nitrone 7 and BCP 10, ΔΔH^≠ = 0.6 kcal mol⁻¹, formation of this HB in TS-8-on, which can be estimated to be ca. 7 kcal mol⁻¹, overcomes this low energy and changes the regioselectivity predicted by the Parr functions. Interestingly, the proximity of the spikes associated with the HB and the van der Waals interactions emphasizes the weakness of the former, in agreement with the colour surface itself (see above), but it is significant enough to change the regioselectivity. Note that the exo stereoselective channels associated with the 32CA reaction between nitrone 7 and BCPC 8 remain meta regioselective, since TS-8-mx is 2.7 kcal mol⁻¹ below TS-8-ox.

4. Conclusions

The role of the CO₂Me groups in the reactivity, selectivity and mechanism in the 32CA reactions of C-phenyl-N-methylnitrone 7 with BCPC 8 has been investigated using DFT methods at the MPWB1K/6-31G(d) level. To this end, a comparative study of the molecular mechanism and the regio- and stereoselectivities for the 32CA reactions of C-phenyl-N-methylnitrone 7 with BCPC 8 and BCP 10 has been performed. Four reactive channels associated with the ortho/meta regio- and endo/exo stereoselective approach modes have been explored and characterised for each reaction. The following conclusions can be drawn from our results:

(i) The 32CA reaction between nitrone 7 and BCP 10 takes place through a one-step mechanism. This 32CA reaction presents low selectivity. The low GEDT found at the corresponding TSs indicates the non-polar character of this zw-type 32CA reaction, explaining the high activation energy found in this 32CA reaction. 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 reagents than TSs and CAs.

(ii) The 32CA reaction of nitrone 7 with BCPC 8 proceeds via a one-step mechanism with a non-polar character leading to the formation of the ortho/endo cycloadduct as the kinetic product experimentally observed. Inclusion of solvent effects does not cause any remarkable change in the selectivity obtained in gas phase.

(iii) ELF topological analysis of the most relevant points involved in the formation of the C3–C4 and O1–C5 single bonds along the IRC associated with the most favourable ortho/endo reactive channel of the 32CA reaction between nitrone 7 and BCPC 8 indicates that while formation of the C3–C4 single bond begins at a distance of 1.95 by a C-to-C coupling of two pseudodiradical centers generated at the C3 and C4 atoms, formation of the O1–C5 single bond begins at the very short distance of 1.71 Å by the electron-density provided by the lone pairs of the nitrone O1 oxygen atom. This model for the formation of the C–C and O–C single bonds is similar to that recently described for the 32CA reactions between nitrones and ED ethylenes.³⁵

(iv) While the analysis of the bond lengths of the two C3–C4 and O1–C5 forming bonds along the IRC associated with the most favourable ortho/endo reactive channel of the 32CA reaction between nitrone 7 and BCPC 8 suggests a synchronous bond formation process, the ELF topological analysis of the bond formation along the reaction path suggests a non-concerted two-stage one-step mechanism³⁶ in which the formation of the second O1–O5 single bond begins once the first C3–C4 is practically formed. Consequently, it is relevant to emphasize that the analyses of the asynchronicity based on the bond lengths or BO values are not adequate when the formation of C–C and O–C single bonds is involved, a very usual feature in 32CA reactions.

(v) Analysis of the global DFT reactivity indices explains the electronic behaviour of these 32CA reactions. The non-polar character of these zw-type 32CA reactions and the high activation energies are the consequence of the poor electrophilic character of the reagents in spite of their strong nucleophilic character.

(vi) Analysis of the Parr functions predicts a meta regioselectivity for the 32CA reaction of nitrone 7 with BCPC 8, which is different than that experimentally observed.

(vii) NCI topological analysis of the electron-density of the most favourable TS-8-on suggests the formation of a non-classical HB between the carbonyl oxygen atom of one of the two carboxylate groups of BCPC 8 and the nitrone C3–H hydrogen atom. Formation of this non-classical HB, which provokes a stabilisation of ca. 7 kcal mol⁻¹, can overcome the low meta regioselectivity found in the 32CA reaction of nitrone 7 with BCP 10, explaining the ortho/endo selectivity experimentally found.

Acknowledgements

This work has been supported by the Ministerio de Economía y Competitividad of the Spanish Government; project CTQ2013-45646-P. M. R.-G. 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: B3LYP/6-31G(d) gas phase total and relative energies of the stationary points involved in the 32CA reaction of C-phenyl-N-methylnitrone 7 with BCP 10. MPWB1K/6-31+G(d)//MPWB1K/6-31G(d) gas phase total and relative energies of the stationary points involved in the 32CA reaction between C-phenyl-N-methylnitrone 7 with BCPC 8. Overlaid plots of the RDG versus the electron-density multiplied by the sign of the second Hessian eigenvalue for the MPWB1K/6-31G(d) and MPWB1K/6-31+G(d) optimised geometry of TS-8-on, as well as the corresponding NCI gradient isosurfaces and finally, MPWB1K/6-31G(d) gas phase computed total electronic energies and cartesian coordinates of all the stationary points involved in the studied 32CA reactions. The imaginary frequencies of the TSs are also included. See DOI: 10.1039/c5ra20268j

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