Unveiling the Origin of the Selectivity and the Molecular Mechanism in the [3+2] Cycloaddition Reaction of N-aryl-C-carbamoylnitrone with N-arylitaconimide

Abstract

The [3+2] cycloaddition reaction of N-aryl-C-carbamoylnitrone (nitrone 1) with N-arylitaconimide (ethylene 2) was computationally studied using the B3LYP/6-31G(d) level of theory. An analysis of the different energetic profiles and the transition states’ optimized structures clearly indicated that this 32CA occurred through a non-polar, asynchronous, one-step mechanism, favoring the formation of the ortho–endo cycloadduct, as observed experimentally. The analysis of the reactivity indices derived from the conceptual DFT explains well the low polarity of this 32CA reaction. Parr functions and a dual reactivity descriptors analysis correctly explained the regioselectivity ortho of this 32CA reaction. Solvent effects did not modify the obtained selectivity but it increased the activation energies and decreased the exothermic character of this 32CA reaction. A thermodynamic parameters analysis indicated that this 32CA wascharacterized by an ortho regioselectivity and endostereoselectivity and exothermic and exergonic characters.

1. Introduction

Heterocyclic compounds are important structures as they have a great importance in biological and pharmaceutical fields [1]. They are considered promising targets and central unit structures in the drug discovery process [2]. The most important pharmaceutical properties of heterocyclic compounds are antidepressant [3], antimicrobial [4], antibacterial [5] and anticancer [6]. The large spectrum of the applications of these compounds made scientists interested in the synthesis of this type of molecule with increased biological activities. Heterocycles are important scaffolds that are used extensively as replacement structures of functional groups in order to modulate the polarity of the drug and, therefore, increase its bioavailability [7].

Isoxazolidines are important heterocycles which contain five atoms, with N and O atoms in an adjacent position. Due to their different biological activities, the synthesis of these types of molecules has been the essential axis of many research groups. Additionally, they have been used as synthetic intermediates, namely for β-amino alcohol preparation. In addition, these compounds have been used for anticonvulsant, antibiotic and antitubercular activities [8,9]. One of the most important methods for the preparation of this kind of molecule is the [3+2] cycloaddition (32CA) reaction between nitrones and alkenes [10]. The 32CA reaction is an important and efficient synthetic method that is used extensively for the synthesis of tremendous five-membered nitrogen-, oxygen- and sulfur-containing heterocyclic compounds [11]. Many natural and synthetic biologically active molecules contain spiroheterocycles [12]. These compounds are endowed by many unique properties [13]. Thereby, these compounds have many applications in many fields [14,15] and thus they are largely used as constructive molecules in order to synthesize biologically active, relevant molecules [16,17].

The challenge today in organic synthesis is how to prepare pure compounds with a high yield using a simple and efficient method. The main goal of theoretical chemists in the prediction or the interpretation of certain chemical procedure results is understanding and improving the properties of these procedures and their products. Understanding the factors controlling the selectivity of organic reactions may help with controlling the peri-, chemo-, regio-, stereo-and diastereoselectivity of the preparation of pure, biologically actives molecules [18].

Nitrones are three atomic components (TACs) [19] which may react with various types of unsaturated skeletons to produce heterocyclic scaffolds [20]. The reactivity behaviors of these important TAC structures depends on the substituent and also on the reactive partner. Thus, it can react as an electrophile [21,22,23], especially when it possesses an electron-withdrawing group at the carbon atom of the nitrone system, as well as where the dipolarophilepossesses an electron-realizing group, which enhances its nucleophilicity. On the other hand, in major cases, the nitrone is classified as a nucleophile [24,25], in which it reacts with a large amount of electrophilic dipolarophiles.

An interesting case of a 32CA reaction involving N-aryl-C-carbamoylnitrone (nitrone 1) and N-arylitaconimide (ethylene 2) was described recently by Teterina et al. [26] In this 32CA reaction, a mixture of stereoisomeric [3+2] cycloadductswasformed, in which one cycloadduct was obtained with a major quantity (10/1) (Scheme 1).

Our axis of research focuses on explaining the origin of the regio- and stereoselectivities, as well as the molecular mechanism nature, of organic reactions, namely cycloaddition reactions [27,28,29,30,31]. The main goal of this work is to understand the origin of regio- and stereoselectivities as well as the molecular mechanism of the32CA reaction performed by Teterina et al. [26] through a MEDT [32] study.

2. Computational Methods

In order to perform this MEDT study, we used the following programs and methods:

-

The Gaussian 09 [33] was used for the optimization of all the stationery points, namely, the reagents, transition states and cycloadducts.

-

The B3LYP/6-31G(d) was the used for the DFT method for all the calculations [34,35,36].

-

The frequency calculations were used to confirm that the optimized stationery points were TSs or minimums. The structure of the TSs were used to confirm that the mechanism was one step or stepwise by performing intrinsic reaction coordinate (IRC) calculations [37], in which the obtained curve indicates that the TS structure is connected to the two minimums, in the forward direction to the cycloadduct and in the reverse direction to the separated reagents.

-

The solvent effects of dichloromethane were investigated using the polarizable continuum model (PCM) [36,37,38] within the self-consistent reaction field (SCRF) [39,40,41] through single-point calculations on the optimized gas phase structures.

-

The values of thermochemistry properties such as Gibbs free energies, enthalpies and entropies were calculated using standard statistical thermodynamics at 298.15 K and 1 atm through the optimized gas phase structures [42].

-

The electrophilicity index (ω) [43], which is a measure of the molecule’s ability to accept electrons, is given by the relation ω = (μ²/2η).

-

The electronic chemical potential (μ) and the chemical hardness (η) were calculated directly from the energies of the frontier molecular orbitals ε_HOMO and ε_LUMO, respectively, by the following relations: μ = (ε_HOMO + ε_LUMO)/2 and η = ε_LUMO − ε_HOMO [44].

-

The nucleophilic index [45], (N), which is a measure of the molecular power of the donating electrons, is given by the relation N = ε_HOMO(Nu) − ε_HOMO(TCE), in which TCE is tetracyanoethylene, which is taken as the reference due to its low HOMO energy.

-

The Parr functions [46], namely, the electrophilic index ($P_K^{+}$) and nucleophilic one ($P_K^{-}$), which allowed us to characterize the most electrophilic and nucleophilic atoms in a molecule, were obtained by an analysis of the Mulliken atomic spin density of the radical anion and the radical cation, respectively, of the studied molecule.

-

The dual reactivity descriptors were used in order to determine, atthe same time, the nucleophilic and the electrophilic atomic region in the studied molecule. These descriptors were obtained from the difference between nucleophilic and electrophilic Fukui functions [47] as follow:

$$\Delta f\left(r\right)\approx f^{+}\left(r\right)-f^{-}\left(r\right)={\rho }_{N+1}\left(r\right)+{\rho }_{N-1}\left(r\right)-2{\rho }_N\left(r\right)$$

where ρ_{N+1 ®}®_(r) an®_N−1(r) are the electronic densities at point r for a system with (N + 1), (N) and (N − 1) electrons, respectively.

-

The Wiberg bond indices were used to analyze the synchronicity of the mechanism [48].

-

The global electron density transfer (GEDT) [49] was calculated with the natural atomic charges (q). These lasts were obtained by a natural population analysis (NPA) computation [50].

3. Results and Discussion

This part is divided into three sections: first, we begin our study by analyzing the global reactivity descriptors of the separated reactants and the local reactivity indices to determine the regioselectivity and the reactivity of the reagents associated with this 32CA reaction. In the second section, we perform an analysis on the geometries and polar character of this 32CA reaction. In the last section, an analysis of the energetic profiles of all the reactive paths through the gas phase, in solution and finally with consideration of all the experimental conditions, such as temperature (25 °C), solvent nature (dichloromethane) and pressure (1 atmosphere), is conducted.

3.1. Analysis of Reactivity

Several previous studies on cycloaddition reactions showed that CDFT reactivity descriptors are important tools to predict the reactivity of organic reagents in their ground state [51,52,53,54]. Thus, the conceptual DFT global reactivity indices [55] were calculated using the mentioned equations (see above) and are gathered in

Table 1. CDFT global reactivity indices of nitrone 1 and ethylene 2 (in eV).

Reactant	HOMO	LUMO	µ	η	ω	N
Nitrone 1	−5.74	−2.05	−3.89	3.68	2.06	3.39
Ethylene 2	−6.39	−1.80	−4.09	4.58	1.83	2.74

.

From Table 1, the values of the global reactivity µ of both nitrone 1 and ethylene 2 clearly indicate that nitrone 1 had the highest value, indicating the flux direction of the GEDT from nitrone 1 towards ethylene 2. Thus, nitrone 1 will react as a nucleophile, while ethylene 2 as an electrophile. Otherwise, by comparing the electrophilicity indices of both reagents, we can notice that nitrone 1 (ω = 2.06 eV) is more electrophilic than ethylene 2 (ω = 1.83 eV). This behavior is in contradiction with what was obtained using electronic chemical potential behavior. On the other hand, the nucleophilicity indices analysis indicated that nitrone 1 (N = 3.39 eV) is a more nucleophilic reagent than ethylene 2 (N = 2.74 eV), in agreement with the electronic chemical potential analysis and in contradiction with the electrophilicity indices analysis. In addition, we can notice that all the reactivity indices of both reactants are close, indicating that the 32CA reaction between them will occur with a low polar character. This fact may be due to the presence of electron-withdrawing groups in both reagents, namely, the amide function.

3.1.1. Analysis of Regioselectivity

Using Parr Functions

The local Parr function indices together with their atomic spin density (ASD), 3D maps of the radical anions ofnitrone 1 and ethylene 2 and the radical cations ofnitrone 1 and ethylene 2 are illustrated in Figure 1.

First, we began our analysis by the proposition that nitrone 1 is a nucleophile and ethylene 2 is an electrophile. Thus, an analysis of the electrophilic $P_K^{+}$ Parr function of ethylene 2 indicated that the carbon atom C5 (for atom numbering, see Scheme 1) is the most electrophilic center, with $P_{C5}^{+}$ = 0.49. For nitrone 1, the most electrophilic center is located on the O1 oxygen atom with $P_{O1}^{+}$ = 0.21. Consequently, the most nucleophilic center (O₁) of the nucleophile (nitrone 1) will interact with the most electrophilic center (C₅) of the electrophile (ethylene 2), leading to the formation of a meta regioisomer, in contradiction with the experimental data.

For the nucleophilic $P_K^{-}$ Parr function indices, we can notice that the highest index in ethylene 2 is located at carbon atom C5 ($P_{C5}^{-}$ = 0.044) while, for the electrophilic $P_K^{+}$ Parr function indices of nitrone 1, the highest value is located at carbon atom C3 ($P_{C3}^{-}$ = 0.245). Consequently, the favorable interaction between the nucleophilic center and the electrophilic center is that between (C₅) of ethylene 2 with C₃ of nitrone 1, generating the ortho regioisomer cycloadducts, in agreement with the experimental data. Therefore, nitrone 1 is the electrophilic reagent and ethylene 2 is the nucleophilic one.

Using Dual Descriptors

Figure 2 shows the dual reactivity descriptors tri-dimensional (3D) maps of nitrone 1 and ethylene 2. Note that the turquoise lobes indicate the nucleophilic regions, while the purple lobes indicate the electrophilic regions. Thus, for the nitrone 1 reagent, an analysis of the dual descriptors corresponding to the reactive region O1=N2=C3 of nitrone 1 shows that O1 and C3 has a nucleophilic character while C3 has an electrophilic character. On the other hand, for ethylene 2, the C4 and C5 reactive atoms have an electrophilic character in which the C4 carbon atom is slightly more electrophilic than the C5 one. These behaviors indicate that the most plausible interaction will occur between the O1 reactive center of nitrone 1 and the C4 atom of ethylene 2, allowing the formation of the ortho regioisomer cycloadducts, in great accordance with the experimental outcomes, energy profiles (see later) and Parr function analyses.

3.2. Geometries of TSs and Reaction Polarity Analysis

The optimized structures of the transition states associated with the 32CA reaction of nitrone 2 with ethylene 1 together with the lengths of the new bonds and their Wiberg bond indices are given in Figure 3.

From Figure 3, we can notice that the lengths of the new bonds O−C and C−C are 1.96 and 2.28 Å for the TSmn and 1.90 and 2.32 Å for the TSmx. In addition, in TSox, the lengths of the O−C and C−C new bonds are 2.41 and 2.06 Å and in TSon the length of these bonds are 2.45 and 2.01 Å. Note that the C−C single bond formation occurs in a distance between 2.0–1.9 Å while the C−O one is between 1.8 and 1.7Å [19]. Thus, these values indicate an asynchronous mechanism for the ortho paths, in which the C−C new bond formation is more advanced than that of the C−O one. For the non-favored pathways, these geometrical parameters account for a synchronous mechanism.

An analysis using the Wiberg bond indices [48] was performed to confirm the nature of this mechanism through the NBO method [50].

The values of the BO associated with the C–O and C–C new bonds are 0.43 and 0.33 for TSmn, 0.46 and 0.31 for TSmx, 0.19 and 0.46 for TSon and 0.21 and 0.43 for TSox. We can notice at the ortho pathways that the C–C bond formation is more advanced than that of the C–C one.In contrast, for the meta paths, the mechanism is slightly synchronous.

The analysis of the GEDT values allows us to determine the polar character of this 32CA reaction. Indeed, several previous studies [56,57,58] established that the polar reactions are more feasible and precede faster with low activation energies [59]. Thus, for the studied 32CA reaction of nitrone 1 with ethylene 2, the computed GEDT values were calculated at the ethylene 2 fragment, in which the negative values are an indicator for the way the flux of the GEDT comes from nitrone 1 towards ethylene 2.

The values of the GEDT are 0.01e for TSmn and TSmx, 0.02e for TSon and 0.03e for TSmx. The very low values of the GEDT point out the non-polar character of this 32CA reaction, justifying well the similitude of the electronic properties as obtained previously in the CDFT reactivity indices analysis [60].

3.3. Energy Profiles Analysis

3.3.1. Gas Phase Electronic Energy Analysis

In general, in the cycloaddition reactions, when the structure of the reagents is asymmetric, we can have four reactive competitive pathways. Thus, the present 32CA reaction is the case, therefore, that we used to study two regioisomeric channels, the ortho and meta, and two stereoisomeric approaches, the endo and exo. Thereby, the four transition states are TSmn, TSmx, TSon and TSox and are associated with the corresponding cycloadducts CAmn, CAmx, CAon and CAox, respectively (See Scheme 2). The computed total and relative energies in the gas phase and in the dichloromethane solution of the stationery points involved in the present 32CA reaction are given in

Table 2. Values of total and relative energy in gas phase and in dichloromethane solution of stationery points of the32CA reaction between nitrone 1 and ethylene 2.

System	E (a.u)	ΔE (kcal/mol)	E (a.u)	ΔE (kcal/mol)
	Gas Phase		Dichloromethane
Alkene	−629.81087		−629.823074
Nitrone	−879.26189		−879.27378
TSmn	−1509.06612	4.17	−1509.08303	8.68
TSmx	−1509.06713	3.54	−1509.08269	8.89
TSon	−1509.07438	−1.02	−1509.08977	4.45
TSox	−1509.05882	8.75	−1509.07558	13.36
CAmn	−1509.11571	−26.95	−1509.13108	−21.47
CAmx	−1509.11574	−26.97	−1509.13074	−21.26
CAon	−1509.12384	−32.05	−1509.13821	−25.95
CAox	−1509.11167	−24.41	−1509.12653	−18.62

.

From Table 2 and by an analysis of the gas phase energies, we clearly see that the ortho–endo approach has the lowest activation energy (E_a = −1.02 kcal/mol) and has a negative sign, which accounts for the corresponding cycloadduct being the kinetically favored cycloadduct, in which its formation is spontaneous (E_a < 0). Additionally, we can see that all the reactive paths are irreversible since the relative energies of the corresponding cycloadducts are negative (ΔE_Cas < 0). Therefore, all the cycloadducts are stable compounds, indicating that the studied 32CA reaction is under a kinetic control, mainly leading to the formation of the cycloadduct CAon, in accordance with the experimental observations.

3.3.2. Solvent Effects

To shed light onto the solvation effects, we performed an analysis on the energy profiles, taking into account the nature of the solvent (dichloromethane) in our calculations. From Table 2 and by a comparison between the relative energy values in the gas phase and in the solution phase of the stationary points, namely, the transition states and cycloadducts, the remarkable change is an increase in the activation energies by values between 4 and 5 kcal mol⁻¹. In addition, there are decreases in the relative energies of the cycloadducts, which account for a decrease in the exothermic character of this 32CA reaction. The increase in the activation energies and the decrease in the exothermic character are mainly due to the better solvation of nitrone 1 and ethylene 2 than the corresponding TSs and CAs [61]. Therefore, the solvent does not make any changes on the selectivity observed in the gas phase study of this 32CA reaction.

3.3.3. Thermochemistry Analysis

Because this 32CA reaction occurred in the liquid phase and demanded certain experimental conditions, to study the effects of the experimental conditions of this 32CA reaction, we performed supplementary calculations on enthalpy, entropy and free energy, which were calculated by taking into account the temperature, pressure and nature of the solvent. The values of the total and relative thermochemistry parameters are given in

Table 3. Values of total and relative thermodynamic properties for the stationery points associated with the 32CA reaction of nitrone 1 with ethylene 2.

System	H	∆H	S	∆S	G	∆G
Alkene	−629.636002		102.186		−629.68453
Nitrone	−878.976215		144.081		−879.044638
TSon	−1508.600621	7.28	209.023	106.837	−1508.699885	18.38
Tsox	−1508.560719	32.31	204.023	101.837	−1508.657608	44.90
TSmn	−1508.568092	27.69	203.132	100.946	−1508.664558	40.54
TSmx	−1508.555116	35.83	199.318	97.132	−1508.649771	49.82
Caon	−1508.645213	−20.70	209.115	106.929	−1508.744521	−9.63
Caox	−1508.644865	−20.49	209.978	107.792	−1508.744583	−9.67
Camn	−1508.652843	−25.49	211.35	109.164	−1508.753212	−15.09
Camx	−1508.64097	−18.04	210.757	108.571	−1508.741057	−7.46

.

From the values of the thermochemistry parameters, we can notice that the ortho–exo reactive pathway is always the more favored one. In addition, the exothermic character of this 32CA is not modified, since all the cycloadducts have negative values of relative enthalpy. On the other hand, the high values of the activation free energies that are increased by 11.10, 12.59, 12.85 and 13.99 when compared to the activation enthalpies for Tson, Tsox, TSmn and TSmx, respectively, are due to the consideration of the entropic contribution in the calculations. The negative sign of the relative free energies of the cycloadducts indicates that this 32CA reaction has an exergonic character. Consequently, the inclusion of the temperature, pressure and solvent nature in the calculations indicate that this 32CA is ortho regioselective under kinetic control and has exothermic and exergonic characters.

4. Conclusions

In this research work, we were able to carry out a computational study of regio- and stereoselectivities as well as on the molecular mechanism associated with the 32CA reaction of nitrone 1 with ethylene 2 within a B3LYP/6-31G(d) level of theory.

• The CDFT global reactivity indices explain the low polar character of this 32CA reaction, which is related to the close electronic parameters of the reagents.
• An analysis on reactivity and selectivity using the local indices obtained from the Parr functions explain well the experimentally ortho regioselectivity and indicates that nitrone 1 is an electrophile while ethylene 2 is a nucleophile.
• The analysis of regioselectivity using dual reactivity indices allows us to explain well the observed ortho regioselectivity.
• The analysis of the molecular mechanism of this 32CA reaction using the GEDT and Wiberg indices indicated that it is a non-polar, one-step, asynchronous mechanism for the favored ortho pathways and synchronous for the meta ones.
• The energy profile gas phase analysis showed that the studied 32CA reaction was characterized by an ortho regioselectivity and an endo stereoselectivity, in accordance with the experimental observation.
• The analysis of the solvent effects indicated that dichloromethane did not have any influence on the selectivity but it increased the activation energies and decreased the relative energies of the cycloadducts associated with this 32CA reaction.
• A thermodynamic parameters analysis showed that this 32CA was ortho regioselective and endo stereoselective, was under kinetic control and had exothermic and exergonic characters.