Ionic Diels–Alder reaction of 3-bromofuran toward the highly electron deficient cyclobuteniminium cation: a regio- and stereoselectivity, and molecular mechanism study using DFT

Abstract

A theoretical study at the MPWB1K/6-311G(d,p) level was performed on the energetic, regio- and stereoselectivity as well as the molecular mechanism of an ionic Diels–Alder (I-DA) reaction of aromatic diene D10, 3-bromofuran, toward highly electron-deficient dienophile Dph11, the cyclobuteniminium cation, in the presence of chloroform. The calculated relative Gibbs free energies indicate that the studied reaction takes place in a complete regio- and stereoselective manner in which the nucleophilic C1 carbon atom of diene D10 is attacked by the strongly electrophilic C6 carbon atom of Dph11 passing through an asynchronous exo transition state TS1x and affording the corresponding cycloadduct CA1x as the unique product in excellent agreement with the experimental outcomes. The relatively high activation Gibbs free energy and slight exergonic nature of this I-DA reaction are related to the aromatic character of D10, estimated using simple isodesmic reactions, which is lost during the cycloaddition. The reasonable regioselectivity presented by the investigated reaction can be explained using calculated electrophilic and nucleophilic Parr functions at the reactive sites of the reagents. On the other hand, a great destabilizing steric repulsion between bulky bromine substitution of D10 and the iminium moiety of Dph11 along the endo stereoselective approach is responsible for the predominance of the exo approach over the endo one. Moreover, an ELF topological analysis of the bonding changes along this I-DA reaction supports a non-concerted two-stage one-step molecular mechanism.

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1. Introduction

Diels–Alder (DA) reactions are among the most useful organic reactions in the toolbox of the synthetic organic chemist because of their ability to create regio- and/or stereoselectivity six-membered cyclic motifs with organic molecules.¹ In a DA reaction, discovered by Otto Diels and Kurt Alder in 1920s,² an s-cis diene is attacked with a dienophile to generate the corresponding cycloadduct. The diversity of the functional groups which can be substituted in both diene and dienophile skeletons makes the DA reaction one of the most valuable synthetic organic reactions.³

In the vast majority of textbooks, the reaction between butadiene 1 and ethylene 2 furnishing cyclohexene 3 is presented as the prototype of DA reaction though such reaction demands harsh experimental conditions to take place. In other words, after 17 hours at 150 °C and 900 atmospheres cyclohexene 3 is produced with a yield of 78% (see Scheme 1).²

Scheme 1

A given DA reaction can considerably be accelerated if adequate substitutes with the opposite electronic nature exist on both diene and dienophile frameworks. Such acceleration can be achieved by an increase of the electron-rich character of the diene (the nucleophilicity), together with the increase of the electron-deficient character of the dienophile (the electrophilicity), or vice versa. In this manner, the global electron density transfer (GEDT) at the corresponding transition state (TS) structure will be enhanced as a driving force which, in turn, leads to a significant decrease in the corresponding activation barrier.⁴

Based on the polar character of DA reaction between cyclopentadiene and twelve substituted ethylenes Domingo et al. have recently classified these reactions into three different types as non-polar, polar, and ionic DA reactions.⁵ While non-polar DA (N-DA) reactions are characterized with a GEDT and activation energy less than 0.15e and higher than 18 kcal mol⁻¹, respectively, the polar DA (P-DA) reactions are identified by 0.15e < GEDT < 0.40e and an activation energy ranging from 17 to 5 kcal mol⁻¹. Accordingly, ionic DA (I-DA) reactions which are an extreme case of the P-DA reactions in which one of the two reagents is an ionic species show a GEDT higher than 0.40e and negative activation energy. While the synthetic applicability of N-DA reactions is extremely limited due to harsh reaction conditions required for these type of DA reactions, the feasibility of a P-DA reaction increases with the polar character of the reaction.⁵ These behaviors can easily be anticipated by analyzing the electrophilicity ω index⁶ and the nucleophilicity N index,⁷ defined within the conceptual density functional theory (DFT),⁸ at the ground state of the reagents. Moreover, it has well been established that the mechanistic aspects of cycloaddition reactions can considerably be affected by the increase of electrophilicity difference (Δω) between reagents. In other words, a stepwise mechanism can be preferred over the one-step mechanism with a noticeable increase in the value of Δω.^9,10

Very recently, a set of DA reactions have experimentally been studied by Lumbroso et al.¹¹ In the first reaction, keteniminium salts 4 undergo a [2 + 2] cycloaddition with the acetylene 5 affording highly electron deficient cyclobuteniminium dienophiles 6 as reactive intermediates which, in the next step, participate in an I-DA reaction toward various electron rich dienes 7 resulting corresponding formal [2 + 4] cycloadducts 8 that, via the subsequent hydrolysis step, convert into cyclobutanone 9 as the highly functionalized building blocks in good yield (see Scheme 2).

Scheme 2

The [2 + 2] cycloaddition of keteniminium salts which are the nitrogen analogues of ketenes, also known as heterocumulenes, was first introduced in 1974 by Ghosez et al.¹² in which these salts, as a more electrophilic alternative to ketenes, react with less nucleophilic alkenes.¹³ Due to the higher stability, reactivity, and regioselectivity, application of keteniminium salts in [2 + 2] cycloadditions toward unsaturated compounds has received more attention in comparison with the homologous ketenes.^11,14

Herein, a DFT study on the I-DA reaction between electron rich diene D10 and highly electron-deficient cationic dienophile Dph11, experimentally reported by Lumbroso et al.,¹¹ is studied at the MPWB1K/6-311G(d,p) level in order to characterize the energetic, regio- and stereoselectivity, as well as reaction mechanism of this process (see Scheme 3). An electron localization function (ELF)^15–18 topological analysis of the most relevant points along the intrinsic reaction coordinate (IRC)¹⁹ curve of the I-DA reaction between D10 and Dph11 is performed in order to characterize the bonding changes along the studied I-DA reaction, and thus to establish the molecular mechanism of this reaction.^20–22

Scheme 3 Reaction paths involved in I-DA reaction of aromatic diene D10 toward highly electron deficient dienophile Dph11.

2. Computational details

Recently, Truhlar's group²³ have shown the MPWB1K hybrid meta density functional theory method (HMDFT) gives good results for thermochemistry and thermochemical kinetics and excellent saddle point geometries. Consequently, in the present study, DFT computations were carried out using the MPWB1K exchange-correlation functional, together with the standard 6-311G(d,p) basis set.²⁴ Optimizations were performed using the Berny analytical gradient optimization method.²⁵ The stationary points were characterized by frequency calculations in order to verify that TSs have one and only one imaginary frequency. The IRC paths¹⁹ were traced in order to check the energy profiles connecting each TS to the two associated minima of the proposed mechanism using the second order González–Schlegel integration method.²⁶ Solvent effects of chloroform (ε = 4.71) in the optimizations were taken into account using the polarizable continuum model (PCM) as developed by Tomasi's group²⁷ in the framework of the self-consistent reaction field (SCRF).²⁸ Values of enthalpies, entropies, and Gibbs free energies in chloroform were calculated with standard statistical thermodynamics at 298 K and 1 atm.²⁴ The electronic structures of stationary points were analysed by a simple natural population analysis (NPA).²⁹ The ELF study was performed with the TopMod program³⁰ using the corresponding monodeterminantal wave functions of the selected structures along the IRC curve. All computations were carried out with the Gaussian 09 suite of programs.³¹

The global electrophilicity index ω (ref. 6) is given by the following expression, ω = μ²/2η based on the electronic chemical potential, μ, and the chemical hardness, η. Both quantities may be approached in terms of the one-electron energies of the frontier molecular orbital HOMO and LUMO, ε_H and ε_L, as μ ≈ (ε_H + ε_L)/2 and η ≈ (ε_L − ε_H), respectively.³² The global nucleophilicity index N,⁷ based on the HOMO energies obtained within the Kohn–Sham scheme,³³ is defined as N = ε_HOMO (Nu) − ε_HOMO (TCE) in which (Nu) denotes nucleophile. This relative nucleophilicity index refers to tetracyanoethylene (TCE). Nucleophilic P_k⁻ (ref. 34) and radical P^°_k (ref. 35) Parr functions were obtained through the analysis of the Mulliken atomic spin density (ASD) of the radical cation of diene D10 and of the neutral radical of dienophile Dph11, respectively. The local electrophilicity index, ω_k, and local nucleophilicity index, N_k, were calculated using ω_k = ωP^°_k and N_k = NP_k⁻ equations.^36,37

3. Results and discussion

The present study is divided into three parts: (i) first, the reaction paths involved in the I-DA of diene D10 with dienophile Dph11 yielding corresponding cycloadducts CAs (see Scheme 3) is studied; (ii) in the second part, an analysis of the global and local DFT reactivity indices of the reagents involved in this reaction is performed in order to explain reactivity and complete regioselectivity provided by the I-DA reaction between D10 and Dph11; and (iii) finally, an ELF topological analysis along I-DA reaction between diene D10 and dienophile Dph11 is carried out in order to characterize the molecular mechanism in this cycloaddition reaction.

3.1. Study of the reaction paths involved in I-DA reaction between D10 and Dph11

Due to the asymmetry of both reagents, four competitive channels are feasible for the I-DA reaction between 3-bromofuran D10 and cyclobuteniminium Dph11. As shown in Scheme 3, they are related to the two stereoisomeric approach modes of the iminium moiety of Dph11 relative to the bromine substituent of D10, named endo and exo, and the two regioisomeric approach modes of the C1 carbon atom of D10 toward the C6, via channel #1, or C7, via channel #2, carbon atoms of Dph11. An analysis of the stationary points involved in the two stereoisomeric paths indicates that this I-DA reaction takes place through a one-step mechanism. Consequently, four TSs, TS1x, TS1n, TS2x, and TS2n and four corresponding formal [4 + 2] cycloadducts, CA1x, CA1n, CA2x, and CA2n were located and characterized on the potential energy surface (PES) of this reaction. It is worth noting that “x” and “n” abbreviations denote exo and endo, respectively. Relative enthalpies, ΔH, entropies, ΔS, and Gibbs free energies, ΔG, for the species involved in the I-DA reaction between D10 and Dph11 in the presence of chloroform are displayed in Table 1.

Table 1 MPWB1K/6-311G(d,p) relative^a enthalpies, ΔH, entropies, ΔS, and Gibbs free energies, ΔG, calculated at 298 K for the spices involved in I-DA reaction between D10 and Dph11 in the presence of chloroform

Species	ΔH (kcal mol^−1)	ΔS (cal mol^−1 K^−1)	ΔG (kcal mol^−1)
a Relative to D10 + Dph11.
TS1x	10.9	−49.0	25.5
TS1n	19.6	−48.4	34.0
CA1x	−17.4	−54.0	−1.3
CA1n	−7.5	−57.9	9.7
TS2x	13.6	−49.6	28.4
TS2n	18.3	−47.1	32.4
CA2x	−17.4	−53.2	−1.5
CA2n	−9.6	−58.0	7.7

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As can be seen, while activation enthalpies are 10.9 and 19.6 kcal mol⁻¹ for TS1x and TS1n, respectively, these values are 13.6 and 18.3 kcal mol⁻¹ for TS2x and TS2n, respectively. On the other hand, reaction enthalpies imply that formation of the corresponding formal [4 + 2] CAs is exothermic; −17.4 (CA1x), −7.5 (CA1n), −17.4 (CA2x), and −9.6 (CA2n) kcal mol⁻¹. Due to the bimolecular nature of DA reaction, both activation and reaction entropies are negative acting as an unfavourable factor in the formation of TSs and corresponding CAs. In the case under investigation, activation and reaction entropies vary from −49.6 to −47.1 cal mol⁻¹ K⁻¹ and −58.0 to −53.2 cal mol⁻¹ K⁻¹, respectively (see Table 1). When unfavourable entropy term, TΔS, is summed to the enthalpy changes, a significant increase is produced in both activation and reaction Gibbs free energies. While the relative Gibbs free energies for the species involved in the I-DA between D10 and Dph11 are given in the last column of Table 1, corresponding profile is depicted in Fig. 1.

Fig. 1 MPWB1K/6-311G(d,p) relative Gibbs free energy diagram in the presence of chloroform for I-DA reaction of D10 toward Dph11 (see Scheme 3 for details).

Calculated relative Gibbs free energies together with the corresponding diagram displayed in Fig. 1 clearly indicate that the I-DA reaction under study presents a complete C1–C6 regio- and exo stereoselective fashion in excellent agreement with the experimental outcomes.¹¹ In other words, the I-DA reaction between D10 and Dph11 takes place via the electrophilic attack of C6 carbon atom of Dph11 on the C1 carbon atom of D10 passing through TS1x yielding CA1x as the unique thermodynamically and kinetically reachable cycloadduct. The relative Gibbs free energies also imply that while exo cycloadducts are slightly exergonic, the endo ones are endergonic. The quite exo stereoselectivity along C1–C6 regioisomeric pathway is related to a great destabilizing steric repulsion between bulky bromine substitution of D10 and iminium moiety of Dph11 along the endo approach.

As mentioned in the introduction, the polar character of DA reactions is a favourable factor determining the feasibility of the reaction. However, this favourable factor may be influenced by other electronic factors such as the aromatic character of the reagents involved in the cycloaddition. For instance, the unfavourable activation energies found in the P-DA reactions of five-membered aromatic heterocyclic compounds furan 14 and N-methyl pyrrole 15 with bicyclic enone 16, shown in Scheme 4, have been associated with the loss of the aromatic character of these five-membered aromatic heterocyclic compounds along the reaction. This behavior was supported by studying the aromatic character of these compounds through a series of isodesmic reactions.³⁸

Scheme 4 The P-DA reaction of five-membered aromatic heterocyclic compounds 14 and 15 with bicyclic enone 16.

In order to assert the role of the aromatic character of 3-bromofuran D10 in the high activation Gibbs free energies found in its I-DA reaction toward Dph11, the isodesmic reactions,³⁹ shown in Scheme 5, were studied.

Scheme 5 Isodesmic reactions considered for the evaluation of resonance stabilization energy (RSE) of diene D10 (top) and furan (bottom) as reference. Isodesmic energies, ΔE, were calculated at the MPWB1K/6-311G(d,p) level.

The relative energies of the isodesmic reactions given in Scheme 5 indicate that the presence of the bromine atom in 3-boromofuran D10 causes a noticeable decrease in the aromatic stabilization of furan. While the aromatic character of 3-boromofuran D10 is significantly reduced in comparison with furan, D10 still exhibits a relatively considerable extent of aromatic character and its destruction along cycloaddition toward Dph11 can be responsible for the large activation Gibbs free energies found in the studied I-DA reaction. This factor also makes the formation of CAs slightly exergonic or even endergonic (see Table 1).

Optimized geometries of TSs involved in the I-DA reaction under study including some selected bond distances and corresponding unique imaginary frequencies are given in Fig. 2. As shown, the lengths of the C1–C6 and C4–C7 forming bonds are 1.956 and 2.822 Å at TS1x and 1.914 and 2.677 Å at TS1n. Similarly, the lengths of the C1–C7 and C4–C6 forming bonds are 2.671 and 1.936 Å at TS2x and 2.611 and 1.895 Å at TS2n. The extent of the asynchronicity can be measured from the difference between the distances, d₁ and d₂, of the two new single bonds which are being formed at the TSs, i.e., Δd = d₁ − d₂.⁴⁰ The values of Δd for TS1x, TS1n, TS2x, and TS2n are 0.857, 0.763, 0.735, and 0.716 Å, respectively. The values of Δd evidence that while a relatively large degree of asynchronicity is found for the TSs involved in the I-DA reaction under investigation, except for the most favourable TS1x, there is no significant difference between degrees of asynchronicity associated with these TSs. On the other hand, analysis of the atomic motion at the unique imaginary frequency of TS1x obviously shows that this motion is mainly associated with the C1 and C6 atoms along C1–C6 regioisomeric bond-forming path (channel #1 in Scheme 3), the movement of the C4 and C7 atoms being negligible.

Fig. 2 MPWB1K/6-311G(d,p) optimized geometries of TSs involved in the I-DA reaction between D10 and Dph11 in the presence of chloroform including some selected bond distances, in Å, and corresponding unique imaginary frequencies, in cm⁻¹.

In spite of a relatively high asynchronicity found in TS1x, analysis of the corresponding IRC profile evidently rules out the existence of any stable intermediate associated with the two-center C1–C6 attack along the predominant C1–C6 regioisomeric pathway (channel #1 in Scheme 3) indicating that I-DA reaction between D10 and Dph11 in the most favourable TS1x takes place via a two-stage one-step mechanism,⁴¹ i.e., while the C1–C6 bond formation takes place along the electrophilic attack of the C6 carbon atom of Dph11 on the C1 carbon atom of D10 in the first stage of the reaction, the C4–C7 bond formation is carried out in the second stage once the first C1–C6 bond is practically formed. This claim will be confirmed with the aid of ELF topological analysis of the most relevant points along the IRC curve of the most favourable TS1x (see later).

3.2. DFT analysis based on the global and local reactivity indexes

Global reactivity indices defined within the conceptual DFT⁸ are powerful tool to explain the reactivity and regioselectivity in the cycloaddition reactions. The global indexes, namely, electronic chemical potential (μ), chemical hardness (η), global electrophilicity (ω), and global nucleophilicity (N) for D10 and Dph11 are presented in Table 2. The electronic chemical potential of D10, −3.28 eV, is higher than that of Dph11, −9.30 eV, indicating that D10 and Dph11 will act as nucleophile and electrophile, respectively, along a strongly polar DA reaction. In consequence, along the I-DA reaction of D10 toward Dph11 the GEDT will take place from the former toward the latter. An NPA analysis clearly shows that a GEDT value of 0.43e takes place from D10 fragment toward Dph11 one at the most favourable TS1x in clear agreement with the ionic nature of this cycloaddition.⁵ It is worth to note that while a very low activation energy is expected for the studied DA reaction due to its ionic nature, the loss of aromatic character of D10 along the reaction with Dph10 accounts for the relatively high activation Gibbs free energy of 25.5 kcal mol⁻¹ found at the most favourable TS1x.

Table 2 MPWB1K/6-311G(d,p) global electronic chemical potential, μ, global hardness, η, global electrophilicity, ω, and global nucleophilicity, N, in eV, for reactants involved in the studied I-DA reaction

Reactants	μ	η	ω	N
D10	−3.28	8.42	1.27	2.89
Dph11	−9.30	7.64	11.32	−2.72

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Table 3 Valence basin populations N calculated from the ELF of some selected points, P1–P15, along the IRC curve associated with the most favourable TS1x of I-DA reaction between D10 and Dph11. Point P7 is TS1x. d(C1–C6) and d(C4–C7) are given in Å. The values of GEDT, obtained using NPA analysis, are given in e

	P1	P2	P3	P4	P5	P6	P7	P8	P9	P10	P11	P12	P13	P14	P15
d(C1,C6)	2.933	2.719	2.44	2.1	2.063	2.000	1.988	1.649	1.614	1.604	1.583	1.577	1.572	1.567	1.561
d(C4,C7)	3.326	3.142	2.997	2.912	2.906	2.895	2.893	2.815	2.682	2.537	2.269	2.209	2.147	2.085	2.022
GEDT	0.05	0.12	0.20	0.31	0.34	0.38	0.43	0.61	0.60	0.57	0.47	0.44	0.41	0.38	0.35
V(C1,C2)	3.48	3.44	3.36	2.89	2.81	2.71	2.69	2.31	2.27	2.25	2.20	2.19	2.18	2.17	2.16
V(C2,C3)	2.51	2.53	2.58	2.69	2.71	2.74	2.75	2.97	3.03	3.08	1.68	1.67	1.67	1.68	1.68
V′(C2,C3)											1.56	1.61	1.65	1.68	1.70
V(C3,C4)	3.37	3.34	3.28	3.14	3.12	3.07	3.06	2.77	2.73	2.69	2.65	2.64	2.40	2.35	2.29
V(C6,C7)	3.10	3.07	3.02	2.88	2.75	2.65	2.62	2.17	2.14	2.12	2.06	2.04	2.02	2.00	1.98
V(O5)	4.05	4.05	4.04	4.07	4.07	4.09	4.09	4.17	4.21	4.28	4.42	2.76	2.68	2.60	2.56
V′(O5)												1.74	1.86	1.98	2.07
V(C1)				0.41	0.49
V(C4)													0.24
V(C6)					0.11
V(C7)										0.45	0.66	0.72	0.78
V(C1,C6)						0.79	0.83	1.60	1.65	1.69	1.76	1.77	1.79	1.81	1.83
V(C4,C7)														1.14	1.25

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The global electrophilicity index for D10, 1.27 eV, and Dph11, 11.32 eV, allows these compounds to be classified as moderate and very strong electrophiles, respectively, within the electrophilicity scale.⁴² On the other hand, the global nucleophilicity index for D10, 2.89 eV, and Dph11, −2.72 eV, permits them to be categorized as moderate and very weak nucleophiles, respectively.⁴³ Analysis of these global indices indicates that along an I-DA reaction, D10 will act as moderate nucleophile while Dph11 will act as very strong electrophile. When an electrophile–nucleophile pair is approached, the most favourable reactive channel is that associated with the initial two-center interaction between the most electrophilic center of electrophile and the most nucleophilic center of nucleophile. Recently, Domingo has proposed the nucleophilic P_k⁻ (ref. 34) and radical P^°_k (ref. 35) Parr functions derived from the excess of spin electron density reached via the GEDT process from the nucleophile to the electrophile which are widely used as a powerful tool in the study of the local reactivity in polar processes.^10,44,45 Herein, in order to explain regioselectivity observed experimentally in the I-DA reaction under study, Parr functions including corresponding local reactivity indexes for reactive sites directly involved in the I-DA reaction between D10 and Dph11 are analysed. As D10 and Dph11, respectively, act as nucleophile and electrophile; the nucleophilic P_k⁻ Parr function for C1 and C4 atoms of D10 as well as corresponding local nucleophilicity indices, and radical P^°_k Parr function for C6 and C7 atoms of Dph11 together with corresponding local electrophilicity indices are calculated and depicted in Scheme 6.

Scheme 6 MPWB1K/6-311G(d,p) calculated nucleophilic Parr function for C1 and C4 atoms of D10 as well as corresponding local nucleophilicity indices, and radical Parr function for C6 and C7 atoms of Dph11 together with corresponding local electrophilicity indices.

It is worthy to note that a cationic species such as Dph11 receives an amount of electron density from the neutral nucleophile, D10, that in the extreme case to receiving an amount equivalent to one electron, the cationic species turns into a neutral radical species. Thus, in order to analyze local reactivity in Dph11, the radical Parr functions should be used.⁴⁶

As presented in Scheme 6, the local electrophilicity index, ω_k, for C6 and C7 carbon atoms of Dph11 is 7.24 and −2.03 eV, respectively. On the other hand, the local nucleophilicity index, N_k, for C1 and C4 carbon atoms of D10 is 1.47 and 1.01 eV, respectively. It should be noted that negative value of ω_k obtained for C7 carbon atom of Dph11 is a direct consequence of the negative radical Parr function, −0.18, found for this center indicating local deactivation of this center.³⁸ The most electrophilic activation found on C6 carbon atom of Dph11 and the most nucleophilic activation found on C1 carbon atom of D10, in one hand, and deactivation found on the C7 carbon atom of Dph11, in the other hand, is responsible for the two-center C1–C6 interaction found at the most favourable TS1x leading to the predominant C1–C6 regioisomeric pathway (channel #1 in Scheme 3) along corresponding I-DA reaction. In other words, the regioselectivity predicted according to the calculated local reactivity indexes is in excellent agreement with the unique regioisomeric CA1x observed experimentally.¹¹

3.3. ELF topological analysis of the I-DA reaction between D10 and Dph11

A great deal of work has emphasized that the ELF topological analysis of the bonding changes along a reaction path is a powerful tool to establish the molecular mechanism of a reaction.^47–49 After an analysis of the electron density, ELF provides basins which are the domains in which the probability of finding an electron pair is maximal. The basins are classified as core and valence basins. The latter are characterized by the synaptic order, i.e., the number of atomic valence shells in which they participate.⁵⁰ Thus, there are monosynaptic, disynaptic, trisynaptic basins and so on. Monosynaptic basins, labelled as V(A), correspond to lone pairs or non-bonding regions, while disynaptic basins, labelled as 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. The ELF topological analysis of significant organic reactions involving the formation of new C–C single bonds has shown that it begins in the short C–C distance range of 1.9–2.0 Å by merging two monosynaptic basins, V(Cx) and V(Cy), into a new disynaptic basin V(Cx,Cy) associated with the formation of the new Cx–Cy single bond.⁵¹ The Cx and Cy carbons characterized by the presence of the monosynaptic basins, V(Cx) and V(Cy), are called pseudoradical centers.⁵²

In order to understand the molecular mechanism of the I-DA reaction between D10 and Dph11, an ELF topological analysis of the MPWB1K/6-311G(d,p) wave functions of some relevant points along the IRC profile associated with the most favourable TS1x was performed. ELF topological analysis of the IRC associated with the reaction between D10 and Dph11 via the most favourable TS1x allows for the characterization of 15 relevant points, P1–P15, between reagents and the formal [4 + 2] CA1x. All electronic density changes are sequential, allowing us to portray a detailed insight of the mechanism of the investigated I-DA reaction. The N populations of the most significant ELF valence basins at specific points along the IRC together with the atomic numbering are displayed in Table 3. The attractor positions for the most relevant points associated with the formation of CA1x are shown in Fig. 3.

Fig. 3 ELF attractor positions for the most relevant points associated with the formation of C1–C6 and C4–C7 single bonds along the I-DA reaction between D10 and Dph11.

Starting from P1, d(C1–C6) = 2.933 Å and d(C4–C7) = 3.326 Å, the most relevant basins are those corresponding to the interacting systems on both D10 and Dph11, i.e., the C1–C2, C3–C4, and C6–C7 double bonds. In this way, while the C1–C2 and C3–C4 bonding region of D10 are represented by a unique V(C1,C2) and V(C3,C4) disynaptic basins with a population of 3.48e and 3.37e, respectively, the C6–C7 double bond of Dph11 is characterized by the presence of unique disynaptic basin, V(C6,C7), with a population of 3.10e. As presented in Table 3, there are no significant changes in the ELF valence basin shapes at points P2 and P3 except some minor changes in their populations. Going toward TS1x, at P4, d(C1–C6) = 2.100 Å and d(C4–C7) = 2.912 Å, a new V(C1) monosynaptic basin emerges over the C1 carbon of D10, integrating 0.41e. As can be seen, the electronic density of this basin mainly comes from the V(C1,C2) disynaptic basin, which is depopulated to 2.89e. At P5, d(C1–C6) = 2.063 Å and d(C4–C7) = 2.906 Å, while the V(C1) monosynaptic basin increases its population to 0.49e, a new V(C6) monosynaptic basin appears over the C6 carbon of Dph11 with the population of 0.11e. Therefore, at this point the two pseudoradical centers required for the C1–C6 single bond formation are present. At P6, d(C1–C6) = 2.000 Å and d(C4–C7) = 2.895 Å, one of the most relevant bonding changes along this I-DA reaction takes place. The two V(C1) and V(C6) monosynaptic basins present at P5 merge into new V(C1,C6) disynaptic basin, with an initial integration of 0.79e. Consequently, at P6 the formation of the first C1–C6 single bond begins. It is worth to mention that the V(C1,C2) disynaptic basin has lost 0.77e from P1 to P6, being the driving force of the C1–C6 single bond formation. At P7, d(C1–C6) = 1.988 Å and d(C4–C7) = 2.893 Å, which corresponds to the TS of reaction, except the increase of V(C1,C6) disynaptic basin population to 0.83e, there are not any significant changes in the ELF valence basin shapes in comparison with P6.

At P8, d(C1–C6) = 1.649 Å and d(C4–C7) = 2.815 Å, while the V(C1,C6) disynaptic basin population increases to 1.60e implying that the previously formed C1–C6 single bond becomes stronger, another important change occurs. At this point, a relatively major depopulation can clearly be observed in V(C6,C7) disynaptic basin in comparison with the slight depopulation along P1 to P7; that is, in going from P7 to P8, the V(C6,C7) disynaptic basin population suddenly decreases from 2.62 to 2.17e. This depopulation indicates that a noticeable change in the electron density of C6–C7 double bond is taking place. The direct consequence of such depopulation is to gather electron density on the C7 carbon atom of Dph11 leading to the formation of V(C7) monosynaptic basin at the next points. While point P9 is not associated with the significant changes in the ELF valence basin shapes, at P10, d(C1–C6) = 1.604 Å and d(C4–C7) = 2.573 Å, a V(C7) monosynaptic basin appears over the C7 carbon of Dph11, integrating 0.45e. As can be seen, the electronic density of this basin comes mainly from the V(C6,C7) disynaptic basin, which is depopulated to 2.12e. At P11, d(C1–C6) = 1.583 Å and d(C4–C7) = 2.269 Å, the V(C2,C3) disynaptic basin which has consecutively increased its population along P1 to P10 splits up into two disynaptic basins, V(C2,C3) and V′(C2,C3), with an integration of 1.68 and 1.56e, respectively. Therefore, at P11 the C2–C3 double bond present in CA1x has already been created. A slight increase in the V(C7) monosynaptic and V(C1–C6) disynaptic basins population is also observed at P11. While at P12 a very similar pattern to those found at P11 is observed, the unique difference is that the V(O5) disynaptic basin which has consecutively increased its population along P1 to P11 splits up into two disynaptic basins, V(O5) and V′(O5), with an integration of 2.76 and 1.74e, respectively. At P13, d(C1–C6) = 1.572 Å and d(C4–C7) = 2.147 Å, a V(C4) monosynaptic basin appears over the C4 carbon of D10, integrating 0.24e. As can be seen, the electronic density of this basin comes mainly from the V(C3,C4) disynaptic basin, which is depopulated to 2.40e. Therefore, at this point the two pseudoradical centers required for the C4–C7 single bond formation are present. At P14, d(C1–C6) = 1.567 Å and d(C4–C7) = 2.085 Å, the second most relevant bonding changes along this I-DA reaction takes place. The two V(C4) and V(C7) monosynaptic basins present at P13 merge into the new V(C4,C7) disynaptic basin, with an initial integration of 1.14e. Consequently, at P14, the formation of the second C4–C7 single bond begins. It is worth noting that at this point the V(C1,C6) disynaptic basin population is 1.81e. If this value is compared with that obtained in CA1x, 1.93e, one can easily be concluded that when the formation of second C4–C7 single bond starts, the formation of C1–C6 single bond, started at P6, is almost completed by more than of 93% in clear agreement with the two-stage one-step mechanism. Finally, from P15 to final cycloadduct CA1x, only basin population changes take place. As displayed in Table 3, the GEDT consecutively increases supporting the formation of the first C1–C6 single bond. The maximum GEDT of 0.61e is reached at P8 and after that, there is a decrease of GEDT as a consequence of a retrodonation process associated with the formation of the second C4–C7 single bond. The IRC profile associated with the most favourable TS1x including the position of points P1–P15, considered in the ELF topological study, is depicted in Fig. 4. As shown, while stage I includes points P1 to P10, stage II includes points P10 through P15.

Fig. 4 The IRC profile associated with the most favourable TS1x including the position of points P1–P15 considered in the ELF topological study of I-DA reaction between D10 and Dph11. See the text for details.

Among investigated points, P10 presents a specific position sharing stage I into stage II. In other words, stage I starts from P1 passing through P4 and P5 where the monosynaptic basins emerge over C1 and C6 carbon atoms, reaching P6 where the C1–C6 single bond starts to form as the result of electrophilic attack of C6 on C1. Formation of the first C1–C6 single bond, during stage I, develops through P7, P8 and P9 reaching P10 where a large amount of C1–C6 single bond formation is completed. Stage II starts at P10 where the monosynaptic basin appears over C7 as a consequence of gathering a part of C6–C7 double bond electron density on C7. Stage II develops through P11, P12, and P13 reaching P14 where the much delayed C4–C7 single bond starts to form via the merging monosynaptic basins emerged over C7 in P10 and C4 in P13. Formation of the final cycloadduct CA1x can be considered as the end point of stage II which is also associated with the end point of cycloaddition. It is worth noting that as stage II proceeds, completion of C1–C6 single bond is uninterruptedly taking place.

In consequence, the ELF topological analysis clearly shows that the breaking of the C–C double bonds in D10 and Dph11 fragments and the formation of the C–C single and double bonds in the corresponding cycloadduct are non-concerted due to the changes in electron density required for the formation of the pseudoradical centers.⁵³ Such behaviour is opposite to the “concerted and close curve bonding changes” mechanism proposed by Woodward and Hoffmann in which a cyclic movement for electrons is considered along the cycloaddition reaction.⁵⁴

4. Conclusion

The energetic, regio- and stereoselectivity as well as the molecular mechanism of ionic Diels–Alder (I-DA) reaction of aromatic five-membered 3-boromofuran, diene D10, toward highly electron deficient cyclobuteniminium, dienophile Dph11, was theoretically studied using DFT methods at the MPWB1K/6-311G(d,p) level in the presence of chloroform.

The calculated relative Gibbs free energies indicate that exo transition state TS1x, leading to the unique cycloadduct CA1x observed experimentally, is the most favourable TS among the four feasible TSs located on the potential energy surface (PES) of the investigated cycloaddition.

The complete exo selective fashion provided by this I-DA reaction can be related to a great steric repulsion caused by the interaction between bulky bromine substitution of D10 and iminium moiety of Dph11 along the endo approach lacking the predominance of endo stereoisomer over the exo one.

Despite of ionic nature of the studied DA reaction, its relatively high activation Gibbs free energy and slight exergonic nature can be attributed to the aromatic character of D10, estimated using simple isodesmic reactions, which is lost during the reaction.

An analysis of the DFT reactivity indices in reagents indicates that the moderate nucleophilic character of D10 and very strong electrophilic character of Dph11 are responsible for the highly polar character of this I-DA reaction. Analysis of the nucleophilic P_k⁻ Parr functions in D10 and the radical P^°_k Parr functions in Dph11 offers an explanation of the complete regioselectivity found in this I-DA reaction. While the C1 carbon atom of D10 is the most nucleophilic center of diene, the C6 carbon atom of Dph11 is the most electrophilic center of dienophile. Consequently, the most favourable nucleophilic/electrophilic two center interactions along this I-DA reaction will take place between the C1 carbon atom of D10 and the C6 carbon atom of Dph11, in complete agreement with the fact that CA1x is formed as the unique product of this reaction.

Finally, ELF topological analysis of the bonding changes along the most favourable TS1x of I-DA reaction between D10 and Dph11 enables the characterization of at least 15 distinguishable points along corresponding IRC curve. The C1–C6 and C4–C7 single bonds are formed by coupling of two pseudoradical centers at points P6, d(C1–C6) = 2.000 Å and d(C4–C7) = 2.895 Å, and P14, d(C1–C6) = 1.567 Å and d(C4–C7) = 2.085 Å, with an initial population of 0.79 and 1.14e, respectively. This topological analysis supports the two-stage one-step mechanism easily characterized by a geometrical analysis of the changes in C–C lengths along cycloaddition. Interestingly, the exo TS1x associated with the studied reaction is found at the point characterized by point P7 along the IRC curve; i.e., at TS1x the C1–C6 single bond formation has already started, while the distance between the C4 and C7 carbon atoms is very high, 2.893 Å emphasizing the non-concerted nature of this I-DA reaction.

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