Understanding the Origin of the Regioselectivity in Non-polar [3+2] Cycloaddition Reactions through the Molecular Electron Density Theory

The regioselectivity in non-polar [3+2] cycloaddition (32CA) reactions has been studied within the Molecular Electron Density Theory (MEDT) at the B3LYP/6-311G(d,p) level. To this end, the 32CA reactions of nine simplest three-atom-components (TACs) with 2methylpropane were selected. The electronic structure of the reagents has been characterised through the Electron Localisation Function (ELF) and the Conceptual DFT. The energy profiles of the two regioisomeric reaction paths and ELF of the transition state structures are studied to understand the origin of the regioselectivity in these 32CA reactions. This MEDT study permits to conclude that the least electronegative ends X1 atom of these TACs controls the asynchronicity in the C−X (X = C,N,O) single bond formation, and consequently, the regioselectivity. This behaviour is a consequence of the fact that the creation of the non-bonding electron density required for the formation of the new C−X single bonds has a lesser energetic cost at the least electronegative X1 atom than that at the Z3 one. Keyword: non-polar [3+2] cycloaddition reactions; regioselectivity; molecular electron density theory; electronegativity. Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 6 September 2020 doi:10.20944/preprints202009.0147.v1 © 2020 by the author(s). Distributed under a Creative Commons CC BY license.


Introduction
Cycloaddition reactions are one of the most useful tools to obtain cyclic compounds, due to their feasibility to create regio-and/or stereoselectively cyclic organic molecules [1,2].
[3+2] cycloaddition (32CA) reactions are an important class of cycloaddition allowing the formation of five-membered heterocycles of great pharmaceutical and industrial interest [3,4]. This kind of cycloaddition implicates the 1,3-addition of an ethylene derivative to a three-atom-component (TAC) (see Scheme 1). Depending on its structure, TACs can be classified as bent TACs (B-TACs) or linear TACs (L-TACs). Scheme 1. 32CA reaction scheme and simplified Lewis structure of bent (B) and linear (L) TACs.
Many of the TACs participating in 32CA reactions are non-symmetric with respect to the central atom. When ethylenes, such as 1-substituted or 1,1-disubtituted ethylenes, are also non-symmetric, at least a pair of regioisomeric cycloadducts can be formed along the reaction (see Scheme 2). Unlike Diels-Alder (DA) reactions, which are highly regioselective yielding a unique cycloadduct [5], 32CA reactions are not as selective, yielding a mixture of the two feasible regioisomers. As regioisomers are structural isomers with physical and chemical different proprieties, only one of them will have a synthetic interest; consequently, formation of a mixture of two regioisomers involved a loss of the synthetic yield. Thus, the understanding of the origin of the regioselectivity in 32CA reactions is an important goal in order to predicts the formation of reaction mixtures.
The regioselectivity of polar 32CA reactions was investigated in 2004 [6] by using the global and local reactivity indices defined within the Conceptual DFT (CDFT) [7,8].
That study suggested that for asynchronous 32CA reactions associated to polar processes, the regioselectivity is consistently explained by the most favourable two-center interactions between the highest nucleophilic and electrophilic sites of the reagents [6].
While the analysis of the electrophilicity [9]  and nucleophilicity [10] N indices allows characterise the chemical proprieties of the reagents participation in polar processes, analysis of the Parr function [11] allows to characterise the most electrophilic and nucleophilic centers of a molecule. However, unlike DA reactions, many 32CA reactions have low even non-polar character, and consequently, the polar model to predict regioselectivity fail in this type of cycloaddition reactions.
In 2016 Domingo proposed the Molecular Electron Density Theory [12] (MEDT) for the study of the reactivity in Organic Chemistry, in which changes in the electron density, and not MO interactions, as the Frontier Molecular Orbital (FMO) theory proposed [13], are responsible for the feasibility of an organic reaction. In MEDT, several quantum-chemical tools based on the analysis of the electron density, such as the analysis of the CDFT reactivity indices [7,8], the topological analysis of the Electron Localisation Function (ELF) [14] and the Quantum Theory of Atoms in Molecules (QTAIM) [15] are used to rigorously study the chemical reactivity in Organic Chemistry [11]. Scheme 3. Reactivity models associated to four different TAC structures.
On the order hand, organic reactions can also be classified as non-polar and polar reactions, in that way that organic reactions are favoured with the increase of the polar character of the reaction [17]. In 2014, Domingo proposed the analysis of the global electron density transfer (GEDT) [18,19] at the transition state structures (TSs) as a measure of the polar character of a reaction. Reactions with GEDT values below 0.05 e correspond to non-polar processes, while values above 0.20 e correspond to polar processes. Very recently, the organic reactions have been classified as the forward electron density flux (FEDF) and reverse electron density flux (REDF), depending on the direction of the flux of the electron density at the TS [20]. Non-polar reactions are classified as the null electron density flux (NEDF). This classification is unequivocal as the GEDT is a measure of the actual electron density transfer at the TSs. Thus, while the DA reaction between butadiene and ethylene was classified as the "normal electron demand" [21] within the Sustmann `s classification [22], it is classified as reaction of NEDF to be non-polar; note that the GEDT at this DA reaction is negligible, 0.0 e [23].
Many TACs as zwitterionic nitrones have nucleophilic character. Consequently, they react with electrophilic ethylenes such as methyl acrylate or nitroethylene through a polar mechanism with high regioselectivity [24]. In these polar zw-type 32CA reactions the analysis of the Parr function allows explaining the observed regioselectivity.
However, TACs as nitrile oxides, which participate in zw-type 32CA reactions with low polar character, show low reactivity and low regioselectivity [25]. In addition, many ethylenes derivatives such as 2-methylpropane or styrene have not electrophilic character, and consequently, the corresponding 32CA reactions will have non-polar character. Note that many of the TACs have not electrophilic character as a consequence of the high electron density accumulation at the three centres of the TAC.
Since non-polar 32CA reactions have not been studied as much as polar 32CA reactions, the 32CA cycloadditions of the nine simplest TACs 1 to 9 shown in Table 1 with 2-methylpropane 10 are herein studied within MEDT in order to understand the origin of the regioselectivity in non-polar 32CA reactions (see Scheme 4).

Computational Methods
All stationary points were optimised using the B3LYP functional [26,27], together with the 6-311G(d,p) basis set [28]. The optimisations were carried out using the Berny analytical gradient optimisation method [29,30]. The stationary points were characterised by frequency computations in order to verify that TSs have one and only one imaginary frequency. The intrinsic reaction coordinate (IRC) paths [31] were traced in gas phase in order to check and obtain the energy profiles connecting each TS to the two associated minima of the proposed mechanism, i.e. reactants and products, using the second order Gonzá lez-Schlegel integration method [32,33].
The electronic structures of the stationary points were characterised by NPA [34,35], and by the topological analysis of the ELF [14]. CDFT reactivity indices [7,8] were computed at the B3LYP/6-31G(d) level using the equations given in reference 8. The GEDT [18] was computed by the sum of the atomic charges (q) of the atoms belonging to each framework at the TSs; GEDT = qf.
All computations were carried out with the Gaussian 16 suite of programs [36]. ELF studies were performed with the TopMod program [37], using the corresponding B3LYP/6-311G(d,p) monodeterminantal wavefunctions and considering the standard cubical grid of step size of 0.1 Bohr. The molecular geometries and ELF basin attractor positions were visualised using the GaussView program [38], while the ELF localisation domains were represented by means of the Paraview software at an isovalue of 0.75 a.u. [39,40].

Results and Discussions
The present MEDT study has been divided into four parts: i) in section 3.1, a study of the electronic structure of TACs through an ELF topological and NPA analyses is performed; ii) in section 3.2, an analysis of the CDFT reactivity indices at the ground state (GS) of the reagents is carried out; iii) in section 3.3, a study of the reactivity and regioselectivity in the 32CA reactions of the nine TACs 1 -9 with 2-methylpropene 10 is made; and finally iv) in section 3.4, an ELF topological analysis of the more favourable regioisomeric TSs is carried out in order to understand the changes in electronic density with respect to reagents, and thus, understand the origin of regioselectivity.

ELF Topological Analysis of reagents 1 to 10
A useful correlation between the electronic structure and the reactivity of simplest TACs participating in 32CA reactions has been established [16]. ELF, first constructed by Becke and Edgecombe [14] and further illustrated by Silvi and Savin [41], permits stabilising a straightforward quantitative connection between the electron density distribution and the chemical structure. Consequently, the topological analysis of the ELF of the nine TACs 1 -9 was performed to predict its reactivity in 32CA reactions [16]. In addition, the ELF of 2-methylpropene 10 was also analysed. The populations of the most significant valence basins are listed in in Table 2, while the ELF basin attractor positions are given in Figure   1. A picture of the ELF localisation domains of four representative TACs characterising the four types of TACs, pseudodiradical, pseudo(mono)radical, carbenoid, zwitterionic, is shown in Figure 2. The ELF-based Lewis-like structures together with the natural atomic charges of the nine TACs are shown in Figure 1.  At nitrile ylide 2 and nitrile imine 5, one single V(Ci) monosynaptic basins, integrating 1.90 e (2) and 1.64 e (5), are observed at the C3 and C1 carbon, respectively, being associated to one carbenoid center, thus being considered 2 and 5 as carbenoid TACs. Note that nitrile ylide 2 also present two monosynaptic basins, V(C1) and V'(C1), a total low population of 0.53 e, at the C1 carbon. (see Table 2) The V(Z3) monosynaptic basins present at these zwitterionic TACs, which are associated to N or O non-bonding electron density regions, correspond with the lone pair of the Lewis structures (see Figure   1).  ELF topological analysis of the nine TACs 1 -9 shows that while zwitterionic TACs such as nitrone 6 correspond with the Huisgen's 1,2-dipole structure [43], pseudodiradical and pseudo(mono)radical TACs, such as azomethine ylide 1 and diazomethane 4, correspond with the Firestone's radical structures [44]. However, it is interesting to remark that while pseudodiradical and pseudo(mono)radical TACs are species with a stable closed-shell electronic structure, actual radical species have openshell electronic structures [42].
NPA analysis of the natural atomic charges at the nine TACs 1 -9 shows that, except for azide 8 and nitrous oxide 9, all TACs has the atoms negatively charges (see Figure 2), thus ruling out the commonly accepted charge distribution of a 1,2-zwitterionic Lewis structure [16]. These atomic change distributions result of the more electronegative character of the C, N and O atoms than that of the H one. Consequently, the anisotropy atomic charge distribution on TACs cannot come from resonant electronic structures, but the anisotropic distribution of the electron density generated by the different atoms belonging to a TAC. [16] 3.2. Analysis of the global and local CDFT reactivity indices, at the GS of the reagents.
The analysis of the reactivity indices based on CDFT has become a useful tool for the study of reactivity in polar reactions [8]. Therefore, in order to establish the polar or nonpolar character of these 32CA reactions, an analysis of CDFT reactivity indices was performed. The CDFT indices were calculated at the B3LYP/6-31G(d) computational level since it was used to define the electrophilicity and nucleophilicity scales [8]. The B3LYP/6-31G(d) global indices, namely, the electronic chemical potencial, µ, chemical hardness, η, electrophilicity, , and nucleophilicity, N, at the GS of TACs 1 to 9 and 2methylpropane 10, are given in Table 3. The electronic chemical potential [7] µ of the nine TACs ranges from −1.81 (1) to The electrophilicity ω index [9] of these TACs ranges from 0.37 eV (1)  As the polar character of organic reactions is mainly controlled by electrophilic species, the low electrophilic character of these species suggests that the corresponding 32CA reactions will have low polar character.
Along a polar reaction involving the participation of non-symmetric reagents, the most favourable reactive channel is that involving the initial two-centre interaction between the most electrophilic centre of the electrophile and the most nucleophilic centre of the nucleophile [6]. In this context, the electrophilic and nucleophilic Parr functions [11] derived from the excess of spin electron density reached via the GEDT [18] process from the nucleophile toward the electrophile have shown to be the most accurate and insightful tools for the study of the local reactivity in polar and ionic processes. Hence, in order to characterise the regioselectivity in polar 32CA reactions, the electrophilic and nucleophilic Parr functions of three selected TACs, a pseudoradical, diazomethane 4, a carbenoid, nitrile imine 5, and a zwitterionic, nitrone 6 and 2methylpropane 10, were analysed (see Figure 3).
Nucleophilic and electrophilic substituted ethylenes have the most nucleophilic and electrophilic centers at the non-substituted CH2 carbon of the ethylene [24]; see the electrophilic and nucleophilic Parr functions of 2-methylpropane 10 in Figure 3. TACs shows that along polar 32CA reactions, a change in regioselectivity will be expected depending on if the reaction is classified of FEDF or REDF [20]. As many of the TACs are strong nucleophiles, see Table 3, analysis of the electrophilic Parr functions will permit to predict the regioselectivity in a FEDF 32CA reaction.
Interestingly, zwitterionic nitrone 6 shows a reverse regioselectivity than pseudoradical diazomethane 4 and carbenoid nitrile imine 5. Thus, while diazomethane 4 and nitrile imine 5 present the most nucleophilic center at the pseudoradical and carbenoid C1 carbons, nitrone 6 presents the most nucleophilic centre at the O3 oxygen.  thus these 32CA reactions are meant to occur through one-step mechanism. Relative energies of the stationary points involved in the nine 32CA reactions are given in Table   4.
Considering that in the series of TACs 2 -9 the ends X1 atom is lesser electronegative than the Z3 one, i.e. the electronegativity increases in the order C < N < O, and trigonal planar (sp 2 ) < linear (sp), it is possible to conclude that the r1 regioselectivity observed in these 32CA reactions is kinetically controlled by the interactions between the least electronegative ends X1 atom of these TACs and the methylene C4 carbon of 2-methylpropane 10. The optimized geometries of the most favourable r1 regioisomeric TSs are shown in Figure 4, while the distances between C−C, C−N and C−O interacting centers at the two regioisomeric TSs are given in Table 6. Some appealing conclusions can be drawn from these geometrical parameters: i) the distance between the interacting centres at the finally iv) except for TS-r1-2, the distance involving the ends X1 atom of these TACs is shorter that that involving Z3 one. These behaviours point out that the interaction between the least electronegative X1 atom of these TACs with the methylene C4 carbon of 10 is lesser unfavourable and more advanced that that involving the more electronegative Z3 atom.  In order to evaluate the polar nature of these 32CA reactions, the GEDT [18]  classified as the FEDF, that of nitrous oxide 9 is classified as the REDF [20]. Note the change of the sing of the GEDT at TS-r1-1, 0.14 e, and at TS-r1-9, −0.19 e; thus, while azomethine ylide 1 acts as electron-donor, nitrous oxide 9 acts as electron-acceptor. This is a consequence of the strong nucleophilic character of 1 and the strong electrophilic character of 9 (see Table 3); and finally, iii) the non-polar 32CA reactions of nitrile imine 5 and nitrone 6 can be classified as the NEDT.

ELF topological analysis of the most favourable r1 regioisomeric TSs.
Finally, the electronic structure of the more favourable r1 regioisomeric TSs was analysed through a topological analysis of the ELF. The ELF basin populations of the nine TSs are given in Table 7, while a picture of the ELF basin attractor positions of the TSs is shown in Figure 5.
Analysis of the basin populations of the nine TSs shows that they present great similitudes. All TSs show a V(N2) monosynaptic basin, with a population ranking from 0.73 e (TS-r1-1) to 2.33 e (TS-r1-9). In general, the population of these V(N2) monosynaptic basins increase with the advanced character of the TS. Thus, the population of this monosynaptic basin, which comes mainly of the depopulation of the X1−N2 bonding region of the TACs, reaches the maximum value at the final cycloadducts. These V(N2) monosynaptic basins, which are not present at the TACs (see Table 2), are associated to the N2 non-bonding electron density presents at the final cycloadduct.
All ends C1 and C3 carbons present one or two V(C) monosynaptic basins, integrating between 0.51 e (TS-r1-1) to 1.47 e (TS-r1-6). Interestingly, while these V(C) monosynaptic basins are already present at the pseudoradical and carbenoid TACs, they must be created at the zwitterionic TACs such as nitrone 6 and nitrile oxide 7 by depopulation of the C1−N2 bonding region. This behaviour, together with the creation of the V(N2) monosynaptic basin, account for the high activation energies of the TSs associated to the zw-type 32CA reactions [16]. Note that these V(Ci) monosynaptic basins are demanded for the subsequent C−C single bond formation [18]. As the activation energies associated to these non-polar 32CA reactions are mainly associated to the depopulation of the N2−X1 and C4−C5 bonding regions, which is required for the formation of the non-bonding electron density regions, i.e. the pseudoradical centers in carbon atoms [23,24], at the interacting centers, the dissimilar activation energies found in these 32CA reactions depend on the presence of the V(X1) (X = C,N,O) monosynaptic basins at the corresponding TACs, thus justifying the order of reactivity pseudodiradical > pseudoradical > carbenoid > zwitterionic.  it is reasonable to understand that the changes in electron density required for the formation of the new X1−C4 single bonds will take place more easily at the ends center involving the least electronegative X1 atom. These behaviors account for the regioselectivity found in these non-polar 32CA reactions.

Conclusions
The The activation energies associated to the nine 32CA reactions range from 8.8 (1) to 27.7 (9) kcal· mol -1 , the reactions being exothermic between 2.9 (9) and 59.5 (2) kcal· mol -1 . The general trend of reactivity, pdr-type > pmd-type > cb-type > zw-type, is observed in this series of 32CA reactions. Except for the 32CA reaction involving azide 8, which is low r2 regioselective, all these 32CA reactions are r1 regioselective.
Analysis of the geometries of the more favourable r1 regioisomeric TSs indicates that the distance between the interacting centres ranges from 2.442 (C−C) Å at TS-r1-1 to 1.995 (C−N) at TS-r1-9. The C−X (X = C,N,O) distances decrease with the increase of the activation energy; i.e. the more unfavourable the TS, more advanced is. Except for TS-r1-2, the distance involving the ends X1 atom of these TACs is shorter that that involving ends Z3 atom. These behaviours point out that in these non-polar 32CA reactions, the interactions between the least electronegative X1 atom of these TACs and the methylene C4 carbon of 10 are lesser unfavourable and more advanced that that involving the most electronegative Z3 atom.
The computed GEDT values at the more favourable r1 regioisomeric TSs indicate that while the 32CA reactions of TACs 1 and 9 have polar character, those of TACs 2 -8 have a low polar or non-polar character.
A comparative analysis of the ELF of the more favourable r1 regioisomeric TSs shows that they a present a similar electronic structure. As the activation energies associated to non-polar cycloaddition reactions are mainly associated to the depopulation of the N2−X1 and C4−C5 bonding regions demanded for the formation of the new V(X) monosynaptic basins, the different activation energies observed in these 32CA reaction depend on the presence of V(C) monosynaptic basins at the TACs, thus justifying the order of reactivity pseudodiradical > pseudoradical > carbenoid > zwitterionic.
From this MEDT study it is possible to conclude that the lesser energetic cost demanded for the creation of the non-bonding electron density at the least electronegative X1 atom, which is required for the subsequent X1−C4 single bond formation, is responsible for the regioselectivity of these low polar 32CA reactions.