Computational study of regio- and stereoselectivity in aza-diene cycloadditions with ethyl vinyl ether and methyl acrylate as ethylene derivatives

Abstract

Within the context of Molecular Electronic Density Theory (MEDT), this study investigates the hetero-Diels–Alder (HDA) reaction among aza-diene 1 and ethyl vinyl ether 2a (reaction 1) and methyl acrylate 2b (reaction 2) applying Density Functional Theory (DFT) simulations at the M06-2X/6-311+G(d,p) level of approximation. The results of the local reactivity indices analysis based on the Parr functions confirmed the regiochemistry experimentally observed. Exploration of potential energy surfaces (PESs) indicated the formation of 2-ethoxy-4-phenyl-3,4-dihydro-2H-pyridine-6-carbonitrile α-regioisomer (reaction 1) and methyl 6-cyano-4-phenyl-3,4-dihydro-2H-pyridine-3-carboxylate β-regioisomer (reaction 2). Conceptual DFT reactivity indices show that 1-aza-butadiene is a strong electrophile, ethyl vinyl ether is a strong nucleophile, and methyl acrylate is a weak nucleophile. Electron localization function and quantum theory of atoms in molecules topological analyses of the electronic structures of the transition state structure reveal a high degree of similarity in their electron density distributions, highlighting the asynchronous nature of the reaction mechanism, a conclusion further supported by BET analysis, favoring a total agreement with experimental findings.

Within MEDT, this study explores two HDA reactions of aza-diene 1 with ethyl vinyl ether 2a and methyl acrylate 2b DFT at the M06-2X/6-311+G(d,p) level.

1. Introduction

The Diels–Alder (DA) reaction is one of the most fundamental cycloaddition processes in organic chemistry.^1–5 It enables the construction of six-membered rings with high regio- and stereocontrol under mild conditions and with 100% atom economy. Because of these features, it has become a cornerstone transformation in modern synthetic methodology, where a detailed understanding of its electronic mechanism is essential for rational reaction design.

This framework has been extended to hetero-Diels–Alder (HDA) reactions, in which at least one heteroatom is incorporated into one of the two unsaturated molecules.^6–8 Among these systems, 1-aza-dienes are of particular interest due to their ability to generate nitrogen-containing heterocycles such as tetrahydropyridines, which are widely present in biologically active molecules and natural products.^9–11 However, their reactivity is generally lower than that of classical dienes, mainly due to the intrinsic stability of the C N π-bond, which reduces the electrophilic character of the system and limits its cycloaddition reactivity.^12,13

To overcome this limitation, several activation strategies have been developed, particularly the introduction of electron-withdrawing substituents. In this context, Trione et al.¹⁰ demonstrated that 2-cyano-1-aza-dienes exhibit significantly enhanced reactivity in HDA reactions. The presence of a nitrile group at the C2 position plays a key role in activating the diene scaffold, thereby enabling efficient cycloadditions with a wide range of ethylene derivatives. This reactivity is further tuned by the nature of the substituent on the nitrogen atom, which modulates the electronic properties of the system. In particular, an ethoxycarbonyl substituent (R = CO₂Et) markedly increases the electrophilic character of the aza-diene 1 (Scheme 1), leading to highly efficient reactions carried out in solution under mild conditions. With ethyl vinyl ether 2a (Scheme 1), the reaction proceeds with high α-regioselectivity at room temperature (25 °C), affording the cycloadduct in 92% yield with excellent cis selectivity (14 : 1), consistent with a preferential endo approach. In contrast, with methyl acrylate 2b (Scheme 1), a comparable yield (91%) is obtained under slightly harsher conditions (81 °C), but the regioselectivity switches to the β-adduct while maintaining a strong cis preference (10 : 1). Overall, the nitrile and N-ethoxycarbonyl groups act cooperatively to enhance reactivity, whereas the electronic nature of the ethylene derivatives governs the final regio- and stereochemical outcome through frontier orbital interactions.

Scheme 1. Experimental HDA reactions involving the aza-diene 1 with ethyl vinyl ether 2a and methyl acrylate 2b.

From a mechanistic standpoint, Density Functional Theory (DFT) has proven to be a powerful tool for the investigation of cycloaddition reactions, as it allows the characterization of transition state structures (TSs) and activation barriers.^14–16

Beyond the classical orbital interaction model, Molecular Electron Density Theory (MEDT) provides a more fundamental description of chemical reactivity based on the analysis of electron density reorganization along the reaction coordinate.¹⁷ This approach is particularly suitable for polar cycloaddition processes such as HDA reactions, where electron density flow plays a decisive role in determining both reactivity and selectivity.^18,19 Depending on the electronic nature of the reaction partners, DA cycloadditions may proceed through different mechanistic pathways, including single-step synchronous or asynchronous processes, as well as stepwise pathways involving zwitterionic or radical intermediates.²⁰

Within this context, the present work aims to investigate the mechanism of the HDA reaction between a 2-cyano-1-aza-diene bearing an ethoxycarbonyl substituent 1 and ethyl vinyl ether 2a and methyl acrylate 2b using DFT and MEDT approaches.¹⁰ The study focuses on the origin of regioselectivity, the role of reaction polarity, and the electron density redistribution along the reaction pathway, in order to provide a comprehensive understanding of the factors governing reactivity and selectivity in this system.

2. Computational methods

All molecular structures were optimized using DFT at the M06-2X/6-311+G(d,p) level of theory,²¹ as implemented in Gaussian 16 (Revision B.01).²² This level of theory has been shown to be effective for studying this type of cycloaddition reactions, providing reliable descriptions of TSs and activation barriers.^23–25 This level of theory has been widely used for studying cycloaddition reactions and provides a reasonable description of TSs and activation barriers.^22–24 However, M06-2X has been reported to overestimate activation energies for bimolecular HDA reactions involving vinyl-alkyl ethers.²⁶ The nature of stationary points was confirmed by harmonic vibrational frequency calculations, where minima exhibited no imaginary frequencies and TSs showed a single imaginary frequency. Intrinsic Reaction Coordinate (IRC) calculations were performed to verify the connectivity between reactants, TSs, and products.¹⁴ Global electron density transfer (GEDT)²⁷ was evaluated from Natural Bond Orbital (NBO)²⁸ charges to quantify the extent of charge transfer between interacting fragments along the reaction pathway. Reactivity was analyzed using Conceptual DFT descriptors,^29–35 including chemical potential [µ = (ε_H + ε_L)/2],²⁹ global hardness (η = ε_L − ε_H),³¹ electrophilicity index (ω = µ²/2η),³² and the nucleophilicity index [N = ε_H (Nu) − ε_H (TCE)],³³ where ε_H and ε_L represent the energies of the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO), respectively. Non-covalent interactions (NCIs)³⁶ were characterized using the Reduced Density Gradient (RDG) approach implemented in NCIPLOT.³⁷ Topological analyses were performed using the Quantum Theory of Atoms in Molecules (QTAIM),³⁸ and Electron Localization Function (ELF) methods,³⁹ as implemented in Multiwfn⁴⁰ and TopMod.⁴¹ The evolution of bonding along the reaction coordinate was investigated using Bonding Evolution Theory (BET).^42–44

3. Result and discussion

3.1. ELF topological analysis at the ground state of the reagents

To gain insight into their electronic features, an ELF topological analysis was first performed on the reactants. Through this approach, the key electronic factors governing the behavior of reactants during the studied cycloaddition process can be clearly identified. The most significant ELF valence basin populations and the basin attractor positions of aza-diene 1, ethyl vinyl ether 2a and methyl acrylate 2b are given in Fig. 1.

Fig. 1. ELF basin isosurfaces (η = 0.75) and their populations (in e) of key basins of 1 and 2a–b.

The ELF topological analysis of 1 displays a single monosynaptic basin V(N4), integrating a population of 2.65e, associated with the lone pairs of the N4 nitrogen atom as well as three disynaptic basins V(C1,C2), V(C3,N4) and V(C2,C3) integrating a total population of 3.28e, 2.91e, and 2.26e, respectively, associated with the C1–C2 and C3–N4 double bonds and C2–C3 single bond. On the other hand, the ELF topological analysis of 2a and 2b show the presence of one disynaptic basin, V(C5,C6), integrating a total population of 3.59e, and 3.41e, respectively, associated with the C5–C6 double bond (Fig. 1).

The proposed Lewis-like structures, based on ELF valence basin populations and NPA charges, are represented in Scheme 2. The charge distribution in aza-diene 1 reveals a pronounced intramolecular polarization. In particular, the N4 nitrogen atom (−0.49e) and the C1 and C2 carbon atoms (−0.09e and −0.25e, respectively) exhibit significant negative character, whereas the C3 carbon center, a bear a noticeable positive charge (+0.22e).

Scheme 2. The suggested Lewis-type structures and the natural atomic charges in terms of the average number of electrons e, of the aza-diene 1, ethyl vinyl ether 2a and methyl acrylate 2b.

For ethyl vinyl ether 2a, the NPA analysis indicates an asymmetric charge distribution across the vinyl fragment. The C5 carbon atom is significantly electron-rich (−0.48e), while the C6 carbon atom is slightly positively charged (+0.16e), consistent with the strong electron-donating effect of the alkoxy substituent through resonance. This polarization enhances the electrophilic character of the α-carbon (C6), favoring its interaction with nucleophilic centers of the aza-diene 1.

In the case of methyl acrylate 2b, both C5 and C6 carbon atoms display negative charges (−0.29e and −0.31e, respectively), reflecting a more delocalized and less polarized π-system. This charge distribution is consistent with the electron-withdrawing nature of the ester group, which stabilizes the π-system but reduces the nucleophilic differentiation between the two carbon centers.

3.2. Analysis of the CDFT reactivity indices at the ground state of the reagents

Several studies on DA reactions have demonstrated that the analysis of reactivity indices derived from CDFT constitutes an effective approach for understanding the reactivity patterns governing cycloaddition reactions.⁴⁵ The CDFT indices, namely the electronic chemical potential µ, chemical hardness η, electrophilicity ω and nucleophilicity N indices of the reagents are given in Table 1.

Table 1. M06-2X/6-311+G(d,p) CDFT descriptors (eV) of the reactants.

Reactants	ε H	ε L	µ	η	ω	N
1	−8.1	−2.2	−5.2	5.9	2.3	2.8
2a	−7.7	1.8	−2.9	9.5	0.4	3.2
2b	−9.5	−0.3	−4.9	9.2	1.3	1.3

The electronic chemical potential of 1 (−5.2 eV) is lower than that of ethyl vinyl ether 2a (−2.9 eV) and methyl acrylate 2b (−4.9 eV), indicating that the GEDT in this DA reaction will take place from 2a and 2b to 1, consistent with a reverse electron density flux (REDF).⁴⁶ Aza-diene 1, with an electrophilicity index ω of 2.3 eV, is classified as a strong electrophile, while its nucleophilicity index N of 2.8 eV indicates a moderate nucleophilic character within the electrophilicity and nucleophilicity scales. Ethyl vinyl ether 2a, with ω = 0.4 eV and N = 3.2 eV, behaves as weak electrophile and a strong nucleophile. In contrast, methyl acrylate 2b, with ω = 1.3 eV and N = 1.3 eV, behaves as a, a moderate electrophile and a weak nucleophile as it was established in ref. 47.

Along a polar reaction involving the participation of nonsymmetric reagents, the most favorable reactive channel is that involving the initial two-center interaction between the most electrophilic center of the electrophile and the most nucleophilic center of the nucleophile.⁴⁸ Recently, Domingo proposed the electrophilic P_k⁺ and nucleophilic P_k⁻ Parr functions⁴⁹ as powerful tools in the study of the local reactivity in polar processes. Hence, in order to characterize the most nucleophilic and the most electrophilic centers of the species involved in these HDA reactions, and, thus, to explain the regioselectivities experimentally observed, the electrophilic P_k⁺ and nucleophilic P_k⁻ Parr functions of both reactants were analyzed (Fig. 2).

Fig. 2. 3D representations of the Mulliken atomic spin densities of the radical cations and anions of aza-diene 1, ethyl vinyl ether 2a methyl acrylate 2b, along with their electrophilic P_k⁺ and nucleophilic P_k⁻ Parr functions.

Analysis of the nucleophilic P_k⁻ Parr functions at the reactive sites of ethyl vinyl ether 2a and methyl acrylate 2b indicates that the C5 carbon atom, with a P_k⁻ value of 0.62 and 0.51, respectively, are the most nucleophilic center of these species (Table S2). On the other hand, analysis of the electrophilic P_k⁺ Parr functions at the reactive sites of 1 indicates that the C1 carbon and the N4 nitrogen atoms are the most electrophilic centers of this species, having a value of P_k⁺ = 0.30 and 0.26, respectively (Table S2). Therefore, the primary nucleophile–electrophile interaction is expected to occur between C5 of 2a/2b and C1 of 1, which corresponds to the main bonding interaction governing the cycloaddition process.¹⁰

3.3. Kinetic and thermodynamic analysis

Due to the nonsymmetric structure of the aza-diene 1, four different competitive reaction paths are feasible for each reaction: aza-diene 1 with ethyl vinyl ether 2a (reaction 1), and with methyl acrylate 2b (reaction 2) (Scheme 3).

Scheme 3. HDA reactions of aza-diene 1 with ethyl vinyl ether 2a and methyl acrylate 2b.

Each reaction can proceed through two possible regioisomeric paths, ortho/meta, and two stereoisomeric approach modes, endo/exo. All calculations were realized in the gas phase. The four TSs localized and characterized and the corresponding 3,4-dihydropyridine derivative cycloadducts are denoted: TS1-on, TS1-ox, TS1-mn, TS1-mx, CA1-on, CA1-ox, CA1-mn, and CA1-mx, for the 1 + 2a HDA reaction, and TS2-on, TS2-ox, TS2-mn, TS2-mx, CA2-on, CA2-ox, CA2-mn, and CA2-mx, for 1 + 2b HDA reaction (Scheme 3). The relative energies, Gibbs free energies and enthalpies, in chloroform, are gathered in Table 1. The relative energies in the gas phase are given in the SI (see Table S1).

Table 2 indicates that the two HDA reactions are thermodynamically favorable in vacuo, as evidenced by negative enthalpy and Gibbs free energy changes for all cycloadducts. The calculated free energy variations span from −27.21 to −33.36 kcal mol⁻¹ for 1 + 2a HDA reaction (Fig. 3), and from −30.58 to −35.67 kcal mol⁻¹ for 1 + 2b HAD (Fig. 4), confirming that cycloadduct formations are both exothermic (Fig. S1 and S2) and exergonic.

Table 2. M06-2X/6-311+G(d,p) thermodynamic and kinetic parameters (ΔE, ΔH, ΔG, in kcal mol⁻¹ and ΔS, in cal mol⁻¹ K⁻¹), of the studied HDA reactions.

	ΔE	ΔG	ΔH	ΔS	−TΔS	Populations
1 + 2a
TS1-on	0.25	18.55	1.16 (6.25%)	−58.33	17.39 (93.75%)	99.99
TS1-ox	7.31	24.73	8.02 (32.43%)	−56.03	16.70 (67.57%)	0.01
TS1-mn	9.92	27.54	10.72 (38.92%)	−56.43	16.82 (61.08%)	—
TS1-mx	10.99	29.15	11.71 (40.17%)	−58.49	17.44 (59.83%)	—
CA1-on	−48.53	−27.21	−44.80	−59.02	17.60	—
CA1-ox	−54.84	−33.36	−50.86	−58.69	17.50	—
CA1-mn	−52.50	−30.36	−48.61	−61.23	18.26	—
CA1-mx	−48.79	−27.43	−44.83	−58.37	17.40	—
1 + 2b
TS2-on	5.55	18.30	9.91 (54.15%)	−43.44	8.39 (45.85%)	17.35
TS2-ox	9.75	20.86	14.07 (67.45%)	−42.83	6.79 (32.55%)	0.29
TS2-mn	4.29	17.28	8.70 (50.35%)	−44.52	8.58 (49.65%)	79.59
TS2-mx	7.20	19.39	11.56 (59.62%)	−42.99	7.84 (40.38%)	2.77
CA2-on	−46.87	−31.95	−39.72	−45.19	7.77	—
CA2-ox	−47.46	32.69	−40.25	−40.68	7.56	—
CA2-mn	−45.97	−30.58	−38.73	−45.73	8.15	—
CA2-mx	−50.67	−35.67	−43.28	−43.63	7.61	—

Fig. 3. M06-2X/6-311+G(d,p) Gibbs free energy profile for the 1 + 2a HDA reaction.

Fig. 4. M06-2X/6-311+G(d,p) Gibbs free energy profile for the 1 + 2b HDA reaction.

The activation Gibbs free energy analysis reveals a clear differentiation among the regio- and stereochemical pathways of the studied HDA reactions. For the 1 + 2a reaction, the ortho–endo approach, TS1-on, exhibits the lowest activation Gibbs free energy, with a ΔG° value of 18.55 kcal mol⁻¹, indicating that it is the kinetically preferred pathway. In comparison, the corresponding ortho–exo approach, TS1-ox, has a higher activation barrier of 24.73 kcal mol⁻¹, resulting in a difference of 6.18 kcal mol⁻¹. According to the 5 kcal mol⁻¹ criterion, TS1-ox can therefore be considered kinetically forbidden relative to TS1-on. The meta pathways, TS1-mn and TS1-mx, exhibit even higher activation barriers of 27.54 and 29.15 kcal mol⁻¹, respectively, corresponding to differences of 8.99 and 10.60 kcal mol⁻¹ relative to TS1-on.

These results clearly support the strong kinetic preference for the ortho–endo pathway in the 1 + 2a reaction. For the 1 + 2b reaction, the lowest activation Gibbs free energy is obtained for the meta–endo approach, TS2-mn, with a ΔG° value of 17.28 kcal mol⁻¹. The other pathways, TS2-on, TS2-mx, and TS2-ox, exhibit activation barriers of 18.30, 19.39, and 20.86 kcal mol⁻¹, respectively. Their energy differences relative to TS2-mn are only 1.02, 2.11, and 3.58 kcal mol⁻¹¹, respectively. Thus, none of these pathways exceeds the 5 kcal mol⁻¹ threshold, indicating that they cannot be considered kinetically forbidden according to this criterion. Nevertheless, the lowest barrier of TS2-mn is consistent with the preferential formation of the meta–endo product.

Consequently, the calculation of L. Boltzmann⁵⁰ populations shows that the ortho–endo pathway is more favored kinetically (Table 2). This strong kinetic bias dictates the initial regioselectivity of this reaction. For the 1 + 2b HDA reaction, the reversed regioselectivity favorized the meta pathway, in which TS2-mn becomes kinetically more dominant. However, the stereoisomeric endo approach remains the preferred one for both reactions. The observed reversal of regioselectivity, which confirm the experimental finding, may be due to the ethylene possessing an electron-donating group in the first reaction (R = OEt), and an electron-withdrawing group in the second one (R = CO₂Me). To quantify the enthalpic and entropic contributions to the regio- and stereoselectivity of the studied HDA reactions, we partitioned ΔG° into two terms, ΔH° and −TΔS° (see Table 2). According to the obtained results, we concluded that: (i) the entropic contribution is higher in the 1 + 2a reaction, whereas the enthalpic contribution becomes more important in the 1 + 2b reaction; (ii) the favored pathways, ortho–endo (1 + 2a) and meta–endo (1 + 2b), show different enthalpic and entropic contributions compared with the other pathways; and (iii) the preferred endo stereoisomeric approach corresponds to TS1-on (1 + 2a) and TS2-mn (1 + 2b).

The TSs geometries of the 1 + 2a and 1 + 2b studied HDA cycloadditions are depicted in Fig. 5 and 6 together with the length of new forming C1–C5(C6) and C5(C6)–N4 bonds (see Scheme 3 for the nomenclature). To assess the asynchronicity of the studied HDA reactions, an analysis was conducted on all stationary points. Key parameters, such as the interatomic distance between reaction centers (r), the distance progress index (l) and the asymmetry index Δl,⁵¹ as well as the dipole moments are presented in Table 3.

Fig. 5. Geometries of the TSs involved in the 1 + 2a DA cycloaddition. The distances between the C1–C5(C6) and C5(C6)–N4 interacting centers are reported in Ångströms (Å), with Δd representing the difference between these values [dC1–C5(C6)–dC5(C6)–N4]. Unique imaginary frequencies are indicated in green (cm⁻¹). GEDT values of the 2a moiety, expressed as the average number of electrons e, are shown in blue.

Fig. 6. Geometries of the TSs involved in the 1 + 2b DA cycloaddition. The distances between the C1–C5(C6) and C5(C6)–N4 interacting centers are reported in Ångströms (Å), with Δd representing the difference between these values [dC1–C5(C6)–dC5(C6)–N4]. Unique imaginary frequencies are indicated in green (cm⁻¹). GEDT values of the 2b moiety, expressed as the average number of electrons e, are shown in blue.

Table 3. M06-2X/6-311+G(d,p) key parameters of the critical structure parameters of the of the studied HDA reactions.

	r C–C (Å)	l C–C	r N–C (Å)	l N–C	Δl
1 + 2a
TS1-on	2.095	0.661	2.441	0.271	0.390
CA1-on	1.565		1.412
TS1-ox	2.087	0.639	2.308	0.430	0.209
CA1-ox	1.534		1.470
TS1-mn	2.384	0.458	2.006	0.625	0.167
CA1-mn	1.546		1.459
TS1-mx	2.234	0.534	2.096	0.437	0.097
CA1-mx	1.524		1.458
1 + 2b
TS2-on	2.100	0.634	2.193	0.503	0.131
CA2-on	1.538		1.465
TS2-ox	2.100	0.633	2.191	0.500	0.133
CA2-ox	1.536		1.461
TS2-mn	2.334	0.481	2.035	0.619	0.138
CA2-mn	1.537		1.474
TS2-mx	2.328	0.483	2.075	0.576	0.093
CA2-mx	1.535		1.457

For the 1 + 2a cycloaddition, the ortho TSs, TS1-on and TS1-ox, exhibit C1–C5 distance progress indexes of 0.661 and 0.639, respectively, compared with 0.271 and 0.430 for the corresponding N4–C6 bonds, indicating that C1–C5 bond formation is more advanced in both cases. Along the meta pathway, TS1-mn and TS1-mx show C1–C6 indexes of 0.458 and 0.534, respectively, while the corresponding N4–C5 values are 0.625 and 0.437. Thus, N4–C5 formation is more advanced in TS1-mn, whereas the opposite trend is observed for TS1-mx. For the 1 + 2b cycloaddition, the ortho TSs, TS2-on and TS2-ox, display C1–C5 indexes of 0.634 and 0.633, respectively, and N4–C6 indexes of 0.503 and 0.500, indicating a consistently more advanced formation of the C1–C5 bond. For the meta pathway, the C1–C6 indexes are 0.481 and 0.483 for TS2-mn and TS2-mx, respectively, whereas the corresponding N4–C5 indexes are 0.625 and 0.437. Consequently, N4–C5 formation is more advanced than C1–C6 formation in both meta TSs, although the difference is substantially more pronounced for TS2-mn.

To further elucidate the electronic nature of the investigated HDA reactions, the GEDT²⁷ values at the different TSs were analyzed (Fig. 5 and 6). According to Domingo's classification, cycloaddition reactions characterized by GEDT values close to 0.0e are considered non-polar, whereas those exhibiting GEDT values higher than 0.2e correspond to polar processes.²⁷ For the 1 + 2a HDA reaction, the computed GEDT values are 0.33e, 0.46e, 0.30e, and 0.30e for TS1-on, TS1-ox, TS1-mn, and TS1-mx, respectively. These relatively high values clearly indicate the strongly polar character of this cycloaddition. Among these TSs, TS1-ox exhibits the largest GEDT value, revealing a more pronounced electron density transfer and, consequently, a higher polar character along this reaction pathway. In the case of the 1 + 2b HDA reaction, the GEDT values decrease to 0.11e, 0.18e, 0.07e, and 0.06e for TS2-on, TS2-ox, TS2-mn, and TS2-mx, respectively. These results suggest that the polar character strongly depends on the reaction pathway. Indeed, TS2-ox exhibits the largest GEDT value (0.18e), indicating the most pronounced polar character, whereas TS2-mn and TS2-mx display weakly polar or nearly non-polar characteristics. The lower GEDT values obtained for several TSs of the 1 + 2b reaction indicates a less efficient electron density transfer compared with the 1 + 2a system. Moreover, the positive sign of all GEDT values demonstrates that the electron density flux occurs from ethylene derivatives 2a/2b toward compound 1, confirming that these HDA reactions proceed through a REDF mechanism.²⁷

3.4. Topological examination of the ELF at the TSs

The topological analysis afforded valuable insight into the electronic structures of the most favorable TSs involved in the investigated HDA reactions. Fig. 7 and 8 present the distributions of the basin attractors together with the ELF localization domains corresponding to the TSs of the 1 + 2a and 1 + 2b HDA cycloadditions, respectively.

Fig. 7. ELFs domains (isosurface, η = 0.75) at the TS of the 1 + 2a HDA reactions. The electron populations had been given in brackets.

Fig. 8. ELFs domains (isosurface, η = 0.75) at the TS of the 1 + 2b HDA reactions. The electron populations had been given in brackets.

For both the 1 + 2a and 1 + 2b HDA processes, all the examined TSs exhibit very similar ELF patterns, differing only slightly in basin populations. The ELF analysis reveals the presence of four disynaptic basins, namely V(C1,C2) (2.11–3.03e), V(C3,N4) (2.09–2.87e), V(C5,C6) (2.62–3.14e), and V(C2,C3) (2.25–2.99e), associated with the C1–C2, C3–N4, and C5–C6 double bonds, as well as the C2–C3 single bond, respectively. In addition, a monosynaptic basin V(N4), related to the nonbonding electron density localized on the N4 nitrogen atom, is observed with populations ranging from 2.37 to 2.91e. More specifically, TS1-on and TS1-ox show the presence of a V(C5) monosynaptic basin, integrating of 0.33 and 0.41e, respectively, associated with the formation of one pseudoradical center at the C5 carbon (see Fig. 7). The occurrence of a monosynaptic basin V(C5) with a population of 0.16e is also detected in TS2-on of the 1 + 2b HDA reaction (Fig. 8).

3.5. QTAIM analysis of the TSs

As shown in Table 4, two new bond critical points (BCPs) are observed in the transition-state (TS) structures: for the ortho pathway, they are located between the C1 and C5 atoms and between the C6 and N4 atoms, whereas for the meta pathway, they appear between the C1 and C6 atoms and between the C5 and N4 atoms.

Table 4. Topological parameter values of the electron density [ρ(r), a.u] and of its Laplacian [∇²ρ(r), a.u] at the C⋯N and C⋯C bond critical points of the TSs associated with the 1 + 2a and 1 + 2b HDA reactions.

Structures	CP1 (C–N)		CP2 (C–C)
TSs	ρ	∇ 2 ρ(r)	ρ	∇ 2 ρ(r)
1 + 2a
TS1-on	0.03260	0.07678	0.06777	0.03531
TS1-ox	0.04176	0.08323	0.06913	0.03437
TS1-mn	0.07895	0.08318	0.04186	0.04723
TS1-mx	0.06526	0.08935	0.05219	0.04742
1 + 2b
TS2-on	0.05445	0.08699	0.06551	0.03885
TS2-mx	0.05490	0.08523	0.06574	0.04036
TS2-mn	0.07193	0.08940	0.04343	0.05074
TS2-mx	0.06613	0.09253	0.04374	0.04976

For both the 1 + 2a and 1 + 2b HDA reactions, all the TSs are characterized by electron density values, ρ(r), lower than 0.1 a.u. at the two BCPs, together with small positive values of ∇²ρ(r). These findings indicate the presence of non-covalent interactions within the interacting regions, suggesting that the formation of the new C–N and C–C covalent bonds has not yet begun at the TSs. This interpretation is consistent with the ELF analysis (Fig. 7 and 8) as well as with the geometrical parameters of the TS structures (Fig. 5 and 6). For the ortho pathways of both the 1 + 2a and 1 + 2b HDA reactions, the endo and exo TSs exhibit higher ρ(r) values at the C1–C5 BCP (≈0.07 a.u) than at the C6–N4 BCP (0.03–0.05 a.u), indicating that the C1–C5 bond formation is more advanced than the C6–N4 bond. For the meta pathways of both the 1 + 2a and 1 + 2b HDA reactions, the endo and exo TSs display larger electron density values at the C6–N4 BCP (0.06–0.08 a.u) than at the C1–C5 BCP(0.04–0.05 a.u), indicating that the formation of the C6–N4 bond is more advanced than that of the C1–C5 bond. These findings further highlight the asynchronous nature of the cycloaddition process.

3.6. NCIs analysis of the TSs

The NCI³⁶ is a very applied method to study the weak interactions. In order to study the selectivity of the HDA reactions, the NCI method is used. The NCI analysis was highlighted by performing a single-point calculation on each optimized TS geometry. Then, the corresponding plots of the electron density [ρ(r)] versus the reduced density gradient were obtained by using multiwfn, plotted using the VMD program,⁵² and visualized by IfranView program.⁵³ The scatter maps and the corresponding RDG isosurfaces of the NCI of the HDA reactions of aza-diene 1 with ethyl vinyl ether 2a (reaction 1), and methyl acrylate 2b (reaction 2) for all optimized TSs in the gas phase are given in Fig. 9 and 10, respectively. In the graphs, the X-axis represent the sign(λ₂)ρ function, while the Y-axis represent the RDG one. For the 1 + 2a HDA reaction, the plot of the NCI attractive region (left region) at TS1-on shows a denser region compared to those of TS1-ox, TS1-mn, and TS1-mx. The repulsive (right region) and weak interactive regions (center region) show more spikes for all TSs, indicating more repulsive NCIs like steric interactions associated with the benzene ring aza-diene 1 and ethyl group of vinyl ether 2a, and between the cianide and carbonyle groups of 1. Therefore, both the darker green surface between the oxygen atom of ester group of 1 and hydrogen linked to C5 carbon atom of 2a and oxygen atom of ethoxy group of 1 at TS1-on and TS1-ox (see Fig. 9) show the presence of a weak hydrogen bonds, which leads to the stronger stabilization of TS1-on and TS1-ox compared to TS1-mn and TS1-mx and subsequently to the observed ortho regioselectivity. For the 1 + 2b HDA reaction, the plot of the NCI attractive region shows a denser attractive region at TS2-on and TS2-ox, but more spikes in repulsive region compared to TS2-mn and TS2-mx. The weak interactive regions show a lot of spikes for all TSs, indicating more repulsive NCIs like steric interactions associated with the benzene ring aza-diene 1 and ester group of vinyl 2b, and between the cianide and carbonyle groups of 1 (see Fig. 10).

Fig. 9. NCI isosurfaces (isovalue = 0.4) associated with the density overlap at all TSs involved in the 1 + 2a HDA reaction, for −0.02 < sign(λ₂) ρ_had < 0.02 a.u.

Fig. 10. NCI isosurfaces (isovalue = 0.4) associated with the density overlap at all TSs involved in the 1 + 2b HDA reaction, for −0.02 < sign(λ₂) ρ < 0.02 a.u.

3.7. Bonding evolution theory (BET) analysis

To better understand the mechanism of the HDA reaction between 1 and 2a–b, BET analysis was performed for most favorable pathways. For each BET analysis, the reported basins are those with an evolving electron population of along the IRC.

3.7.1. BET analysis of the most favorable pathway TS1-on associated with the 1 + 2a HDA reaction

In the SSD-I domain [d(C1–C5) = 3.084 Å, d(C6–N4) = 3.004 Å], five distinct electron density basins associated with the reactants can be identified. These include: (i) a monosynaptic basin, V(N4), corresponding to the lone-pair electron density localized on the N4 nitrogen atom, with an electron population close to 2.67e; (ii) three disynaptic basins assigned to the π-bonds, namely V(C1,C2), V(C3,N4), and V(C5,C6), exhibiting electron populations of 3.26e, 2.91e and 3.55e, respectively; and (iii) the disynaptic basin V(C2,C3), associated with the C2–C3 σ-bond, whose population is 2.33e (Fig. 11).

Fig. 11. Electron populations had evolution for selected basins along the IRC for the TS1-on path of the 1 + 2a HDA reaction.

The transition from SSD-I to SSD-II [d(C1–C5) = 2.095 Å, d(C6–N4) = 2.441 Å] is characterized by the emergence of two new pseudoradical centers located at C1 and C5 within the 1 and 2a fragments, exhibiting electron populations of 0.21e and 0.34e, respectively (Fig. 12). These centers originate from the concurrent reduction in the populations of the disynaptic basins V(C1,C2) and V(C5,C6) (Fig. 12).

Fig. 12. ELF basin isosurfaces for selected points that are representative of each of the SSDs found along the IRC corresponding to the TS1-on pathway of the 1 + 2a HDA reaction and its reaction coordinate.

Subsequently, both basins merge in domain III [d(C1–C5) = 1.976 Å, d(C6–N4) = 2.387 Å] to generate a new disynaptic basin, V(C1,C5) (0.85e), associated with the formation of the C1–C5 single bond through a cusp-C type catastrophe (Scheme 4). Furthermore, during SSD-IV [d(C1–C5) = 1.630 Å, d(C6–N4) = 2.126 Å], an additional V(C6) monosynaptic basin emerges at the 2a fragment, with an electron population of 0.10e, characterizing the C6 carbon as a pseudoradical center. The formation of this pseudoradical center results from the progressive depopulation of the C5–C6 bonding region, which decreases by about 0.58e. Finally, the last SSD-V domain [d(C1–C5) = 1.574 Å, d(C6–N4) = 1.856 Å] reveals the final electron redistribution with the creation of the C6–N4 bond via the appearance through a cusp catastrophe of the V(C6,N4) basin (1.26e) (Scheme 4). It occurs via the disappearance of the former V(C6) basin and the population loss of the V(N4) basin.

Scheme 4. Lewis structures along the IRC corresponding to the TS1-on pathway of the 1 + 2a HDA reaction.

3.7.2. BET analysis of the most favorable pathway TS2-mn associated with the 1 + 2b HDA reaction

Fig. 13 displays the evolution of the electron population of the main basins involved in the formation of CA2-mn while the representing ELF isosurfaces are given in Fig. 14. As shown in both figures, five SSDs are required to characterize the topological changes associated with the formation of the two new single bonds, C1–C6 and C5–N4 (atom numbering is given in Scheme 3), along the reaction coordinate. In the initial domain, SSD-I [d(C1–C6) = 3.137 Å, d(C5–N4) = 3.106 Å], four significant basins are distinguished: V(C1,C2) (3.26e), V(C2,C3) (2.32e), V(C3,N4) (2.93e), and V(C5,C6) (3.34e), which correspond to the C1–C2, C2–C3, C3–N4 and C5–C6 bonds in 1 and 2a, respectively, as well as to the lone electron pair of the N4 nitrogen atom in 1 [V(N4), 2.68e]. At the end of this domain, several basins such as V(C1,C2), V(C3,N4), and V(C5,C6) present a slight decrease in their electronic populations by 0.36, 0.38, and 0.31e, respectively, which highlights depopulations from double to single bonds. On the other hand, the population of the V(C2,C3) basin increases to 2.80e, pointing out the beginning of the transformation of the C2–C3 single bond into a double one. During the transition from SSD-I to SSD-II [d(C1–C6) = 2.293 Å, d(C5–N4) = 1.988 Å], a new V(C5) monosynaptic basin appears at the C5 carbon atom with a total population of 0.03e, characterizing the C5 carbon as a pseudoradical center (Scheme 5). This population arises primarily from the decrease in the V(C5,C6) basin, which loses nearly the same amount of electron density. The population of the V(N4) center continues to increase in the subsequent domain (Fig. 14). In addition, an electronic distribution takes place at the SSD-III [d(C1–C6) = 2.253 Å, d(C5–N4) = 1.940 Å] and the SSD-IV [d(C1–C6) = 3.240 Å, d(C5–N4) = 3.327 Å] domains with the creation of two new monosynaptic V(C6) and V(C1) basins, respectively (Fig. 14). These monosynaptic basins characterize the C6 and C1 carbons as two pseudoradical centers which are demanded for the subsequent C1–C6 single bond formation. They collect their populations of 0.27e and 0.22e from the V(C5,C6) and V(C1,C2) basins, respectively. At the onset of the fifth domain, SSD-V [d(C1–C6) = 2.126 Å, d(C5–N4) = 1.800 Å], the monosynaptic basins V(C5) and V(N4) merge to form the disynaptic basin V(C5,N4), marking the emergence of the C5–N4 bond. During SSD-V, its electron population increases progressively from 1.03 to 1.63e. Concurrently, another topological rearrangement occurs through the coalescence of the V(C1) and V(C6) monosynaptic basins, giving rise to the disynaptic V(C1,C6) basin, whose population evolves from 0.81 to 1.76e along this domain (Scheme 5). The appearance of these two disynaptic basins provides clear evidence for the formation of the C1–C6 and C5–N4 single bonds through cusp catastrophes.

Fig. 13. Electron populations had evolution for selected basins along the IRC for the TS2-mn path of the 1 + 2b HDA reaction.

Fig. 14. ELF basin isosurfaces for selected points that are representative of each of the SSDs found along the IRC corresponding to the TS2-mn pathway of the 1 + 2b HDA reaction and its reaction coordinate.

Scheme 5. Lewis structures along the IRC corresponding to the TS2-mn pathway of the 1 + 2b HDA reaction.

4. Conclusion

The HDA reactions between aza-diene 1 and ethyl vinyl ether 2a (1 + 2a), as well as methyl acrylate 2b (1 + 2b), were investigated within the framework of MEDT at the M06-2X/6-311+G(d,p) level of theory. This study aims to provide a detailed understanding of the reaction mechanisms and to elucidate the factors governing the experimentally observed selectivities. Global and local DFT-based reactivity indices indicate that 1 behaves as a strong electrophile with moderate nucleophilic character, whereas ethyl vinyl ether 2a acts as a weak electrophile and a strong nucleophile. In contrast, methyl acrylate 2b is characterized as a moderate electrophile and a weak nucleophile. In addition, analysis of the Parr functions successfully accounts for the observed regioselectivity, rationalizing the ortho preference in the 1 + 2a reaction and the meta selectivity in the 1 + 2b process.

The highly polar nature of these HDA reactions, supported by the significant GEDT values at the TSs, accounts for the very low activation energies associated with the most favorable TS1-on and TS2-mn. The polar 1 + 2a HDA reaction displays endo stereoselectivity and complete ortho regioselectivity, while the polar 1 + 2b HDA reaction exhibits endo stereoselectivity and complete meta regioselectivity, in good agreement with experimental observations.

For the 1 + 2a HDA reaction, geometrical parameter analysis of the two ortho TSs reveals a highly asynchronous mechanism. In contrast, TS1-mn exhibits a slightly more synchronous character, whereas TS1-mx follows a clearly asynchronous process. For the 1 + 2b reaction, both TSs along the ortho pathway indicate a synchronous mechanism, while the meta pathway proceeds through an asynchronous mechanism. These mechanistic features are also supported by BET analysis. Furthermore, ELF and QTAIM topological analyses of the electronic structure of all TSs in both 1 + 2a and 1 + 2b reactions demonstrate a high degree of similarity in electron density distribution.

Author contributions

Mohamed Chellegui and Lakhdar Benhamed, writing, investigation, validation, methodology. Mohamed H. Mohamed contribute to the interpretation and discussion of the results, critically revised the manuscript, and provided substantial assistance with the English language editing and improvement of the scientific presentation. Ali Ben Ahmed, editing, reviewing, and supervision. All authors have read and approved the final version of the manuscript.

Conflicts of interest

There are no conflicts to declare.

Data availability

The data supporting this article have been included as part of the supplementary information (SI). Supplementary information: thermodynamic data, reactants properties and Cartesian coordinates of all the stationary points. See DOI: https://doi.org/10.1039/d6ra07752h.