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

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

Luis R. Domingo 1,* , Mar Ríos Gutiérrez 1,2,* and Jorge Castellanos Soriano 3

1 Department of Organic Chemistry, University of Valencia, Dr. Moliner 50, Burjassot, 46100 Valencia, Spain 2 Department of Chemistry and Chemical Biology, McMaster University, 1280 Main Street West, Hamilton, ON L8S 4L8, Canada 3 Department of Chemistry, Polytechnic University of Valencia, Camí de Vera, s/n, 46022 Valencia, Spain; [email protected] * Correspondence: [email protected] (L.R.D.); [email protected] (M.R.G.)

Received: 5 September 2020; Accepted: 10 November 2020; Published: 13 November 2020

Abstract: 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 2-methylpropene were selected. The electronic structure of the reagents has been characterized through the Electron Localisation Function (ELF) and the Conceptual DFT. The energy proﬁles of the two regioisomeric reaction paths and ELF topology 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 X1 end 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 single bonds has a lower energy demand at the least electronegative X1 atom than at the Z3 one.

Keywords: non-polar [3+2] cycloaddition reactions; regioselectivity; molecular electron density theory; electronegativity; molecular mechanism

1. Introduction Cycloaddition reactions are one of the most useful tools in organic synthesis as they permit to obtain cyclic organic compounds with a regio- and/or stereoselective fashion [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 implies the 1,3-addition of an ethylene derivative to a three-atom-component (TAC) (see Scheme1). Depending Organicson its2020 structure,, 1, TACs can be classiﬁed as bent TACs (B-TACs) or linear TACs (L-TACs). 2 of 18

SchemeScheme 1. 32CA 1. 32CA reaction reaction scheme scheme and and simplified simpliﬁed Lewis structure structure of of bent bent (B) (B) and and linear linear (L) TACs.(L) TACs.

Many of the TACs participating in 32CA reactions are non-symmetric with respect to the central Organics 2020, 1, 19–35; doi:10.3390/org1010003 www.mdpi.com/journal/organics atom. When ethylenes, such as 1-substituted or 1,1-disubstituted 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 single 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 properties, only one of them will have a synthetic interest; consequently, formation of a mixture of two regioisomers involves 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 predict the formation of reaction mixtures.

Scheme 2. Formation of regioisomeric cycloadducts in 32CA reactions involving non-symmetric reagents.

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-centre interaction between the most nucleophilic and electrophilic sites of the reagents [6]. While the analysis of the electrophilicity [9] ω and nucleophilicity [10] N indices allows characterizing the chemical properties of the reagents participating in polar processes, analysis of the Parr functions [11] allows characterizing the most electrophilic and nucleophilic centres of a molecule. However, unlike DA reactions, many 32CA reactions have low polar character, even non-polar, and consequently, the polar model to predict regioselectivity fails 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. Accordingly, 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 [12]. Recent advances made in the theoretical understanding of 32CA reactions based on MEDT have allowed establishing a very good correlation between the electronic structure of the simplest TACs and their reactivity towards ethylene [16]. Accordingly, depending on the electronic structure of the simplest TACs, pseudodiradical, pseudoradical, carbenoid and zwitterionic, 32CA reactions have been classified into pseudodiradical-type (pdr-type), pseudomonoradical-type (pmr-type), carbenoid-type (cb- type) and zwitterionic-type (zw-type) reactions [16], respectively, in such a manner that while pdr-type

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Organics 2020, 1 20 Scheme 1. 32CA reaction scheme and simplified Lewis structure of bent (B) and linear (L) TACs.

Many of the TACs TACs participating in 32CA reactions are non-symmetric with respect to the central atom. When When ethylenes, ethylenes, such such as as 1-substituted 1-substituted or or 1,1-disubstituted 1,1-disubstituted ethylenes, ethylenes, are are also also non-symmetric, non-symmetric, at least least a apair pair of ofregioisomeric regioisomeric cycloadducts cycloadducts can canbe formed be formed along along the reaction the reaction (see Scheme (see Scheme 2). Unlike2). Diels–AlderUnlike Diels–Alder (DA) reactions, (DA) reactions, which are which highly are highlyregioselective regioselective yielding yielding a single a cycloadduct single cycloadduct [5], 32CA [5], reactions32CA reactions are not are as notselective, as selective, yielding yielding a mixture a mixture of the of two the feasible two feasible regioisomers. regioisomers. As regioisomers As regioisomers are structuralare structural isomers isomers with with physical physical and and chemical chemical diff dierentﬀerent properties, properties, only only one one of ofthem them will will have have a synthetica synthetic interest; interest; consequently, consequently, fo formationrmation of of a amixture mixture of of two two regi regioisomersoisomers involves involves a a loss loss of of the synthetic yield. Thus, Thus, the the understand understandinging of of the the origin origin of of the the regioselectivity regioselectivity in in 32CA 32CA reactions reactions is is an importantimportant goal in order to predict the formation of reaction mixtures.mixtures.

Scheme 2.2. FormationFormation of of regioisomeric regioisomeric cycloadducts cycloadducts in 32CA in 32CA reactions reactions involving involving non-symmetric non-symmetric reagents. reagents. The regioselectivity of polar 32CA reactions was investigated in 2004 [6] by using the global and localThe reactivity regioselectivity indices defined of polar within 32CA the reactions Conceptual was DFTinvestigated (CDFT) [in7, 82004]. That [6] studyby using suggested the global that and for localasynchronous reactivity 32CA indices reactions defined associated within the to polarConceptu processes,al DFT the (CDFT) regioselectivity [7,8]. That is consistentlystudy suggested explained that forby theasynchronous most favourable 32CA two-centre reactions interactionassociated betweento polar theprocesses, most nucleophilic the regioselec andtivity electrophilic is consistently sites of explainedthe reagents by [6 ].the While most the favourable analysis of thetwo-centre electrophilicity interaction [9] ω andbetween nucleophilicity the most [10 nucleophilic] N indices allows and electrophiliccharacterizing sites the chemicalof the propertiesreagents [6]. of theWhile reagents the participatinganalysis of inthe polar electrophilicity processes, analysis [9] ωof and the nucleophilicityParr functions [ 11[10]] allows N indices characterizing allows thecharacterizing most electrophilic the ch andemical nucleophilic properties centres of ofthe a molecule.reagents participatingHowever, unlike in polar DA processes, reactions, analysis many 32CA of the reactions Parr functions have low [11] polar allows character, characterizing even non-polar, the most electrophilicand consequently, and nucleophilic the polar model centres to predict of a regioselectivitymolecule. However, fails in unlike this type DA of reactions, cycloaddition many reactions. 32CA reactionsIn 2016, have Domingo low polar proposed character, the Moleculareven non-pola Electronr, and Density consequently, Theory [12the] (MEDT)polar model for the to studypredict of regioselectivitythe reactivity in fails Organic in this Chemistry, type of cycloaddition in which changes reactions. in the electron density, and not MO interactions, as theInFrontier 2016, Domingo Molecular proposed Orbital the (FMO) Molecular theory Electr proposedon Density [13], are Theory responsible [12] (MEDT) for the for feasibility the study of ofan the organic reactivity reaction. in Accordingly,Organic Chemistry, in MEDT, in severalwhich quantum-chemicalchanges in the electron tools based density, on theand analysis not MO of interactions,the electron density,as the Frontier such as theMolecular analysis Orbital of the CDFT(FMO) reactivity theory proposed indices [7[13],,8], theare topologicalresponsible analysis for the feasibilityof the Electron of an Localisationorganic reaction. Function Accordingly, (ELF) [14 in] andMEDT, the several Quantum quantum-chemical Theory of Atoms tools in Molecules based on the(QTAIM) analysis [15 ],of are the used electron to rigorously density, studysuch as the th chemicale analysis reactivity of the CDFT in Organic reactivity Chemistry indices [12 ].[7,8], the topologicalRecent analysis advances of made the Electr in theon theoretical Localisation understanding Function (ELF) of 32CA [14] reactions and the basedQuantum on MEDT Theory have of Atomsallowed in establishing Molecules (QTAIM) a very good [15], correlation are used to between rigorously the electronicstudy the structurechemical ofreactivity the simplest in Organic TACs Chemistryand their reactivity[12]. towards ethylene [16]. Accordingly, depending on the electronic structure of the simplestRecent advances TACs, pseudodiradical made in the theoretical, pseudoradical unders, carbenoidtanding of and 32CA zwitterionic, reactions based 32CA on reactions MEDT have allowedbeen classified establishing into pseudodiradical- a very good correlationtype (pdr-type) between, pseudomonoradical- the electronic typestructure(pmr-type) of the, carbenoid-typesimplest TACs and(cb-type) their andreactivity zwitterionic-type towards ethylene(zw-type) [16].reactions Accordingly, [16], depending respectively, on inthe such electronic a manner structure that of while the simplestpdr-type 32CATACs, reactionspseudodiradical can be, pseudoradical carried out, verycarbenoid easily, andzw-type zwitterionic,32CA reactions 32CA reactions demand have adequate been classifiednucleophilic into/electrophilic pseudodiradical- activationstype (pdr-type) to take, place pseudomonoradical- (see Scheme3).type (pmr-type), carbenoid-type (cb- type) Theseand zwitterionic-type findings have provided (zw-type) a rationalisation reactions [16], of respectively, experimental in outcomes such a manner [17–21 that]. In while 2017, Zakipdr-type and co-workers reported the synthesis of a series of enantiomerically pure isoxazolines by 32CA reactions of substituted aryl nitrile oxides 2 with tomentosin 1, a sesquiterpene lactone extracted from Dittrichia viscosa (see Scheme4)[ 22]. The interest of this reaction was that, although tomentosin 1 presents up to sixteen different approach modes associated with two regio- and two diastereofacial reaction paths for each of the four C C and C O double bond systems, only one product was isolated under smooth − − conditions. Thus, when benzonitrile oxide (2, Ar=Ph) was used, the corresponding spiro-isoxazoline 3 was obtained in 72% yield [22]. Organics 2020, 1, 3 of 18

32CA reactions can be carried out very easily, zw-type 32CA reactions demand adequate nucleophilic/electrophilic activations to take place (see Scheme 3).

Organics 2020, 1, 3 of 18

Organics32CA 2020reactions, 1 can be carried out very easily, zw-type 32CA reactions demand adequate21 nucleophilic/electrophilic activations to take place (see Scheme 3).

Scheme 3. Reactivity models associated to the four different TAC structures.

These findings have provided a rationalisation of experimental outcomes [17−21]. In 2017, Zaki and co-workers reported the synthesis of a series of enantiomerically pure isoxazolines by 32CA reactions of substituted aryl nitrile oxides 2 with tomentosin 1, a sesquiterpene lactone extracted from Dittrichia viscosa (see Scheme 4) [22]. The interest of this reaction was that, although tomentosin 1 presents up to sixteen different approach modes associated with two regio- and two diastereofacial reaction paths for each of the four C−C and C−O double bond systems, only one product was isolated under smooth conditions. Thus, when benzonitrile oxide (2, Ar = Ph) was used, the corresponding Scheme 4. SynthesisSynthesis of spiro-isoxazoline derivatives of tomentosin 1. spiro-isoxazoline 3 was obtained in 72% yield [22]. An MEDT study of this 32CA reaction accounted for the total chemo- and regioselectivity experimentally observed, emphasized the zw-type reactivity of the benzonitrile oxide 2, and revealed that thethe reactionreaction takes takes place place through through a non-concerteda non-concertedtwo-stage two-stage one-step one-stepmechanism mechanism [23] initialized[23] initialized with withthe formation the formation of the of C theC C single−C single bond bond involving involving the β -conjugatedthe β-conjugated carbon carbon of tomentosin of tomentosin1. 1. − In 2019, 2019, Ait Ait Itto Itto et et al. al. reported reported the the 32CA 32CA reactions reactions of (R)-carvone of (R)-carvone 4 with4 withdiaryl diaryl nitrilimines nitrilimines (NIs) (NIs)5a−d 5aand–d arylnitrileand arylnitrile oxides oxides (NOs) (NOs) 7a−7ad –ind dichloromethanein dichloromethane (DCM), (DCM), yielding yielding pyrazoles pyrazoles 6a6a−–dd and isoxazoles 8a−–d, respectively (see Scheme 55))[ [24].24]. These These 32CA 32CA reactions presented total regio- and chemoselectivity, obtainingScheme 4. a Synthesis mixture of spiro-isoxazoline a pair of diastereoisomersdiastereoisomers derivatives of resulting tomentosin from 1. the attack of these TACs by thethe twotwo facesfaces ofof thethe twotwo CC−C double bonds of (R)-carvone 4. Interestingly, Interestingly, both regio- and − chemoselectivityAnOrganics MEDT 2020, 1 ,study were oppositeof this 32CA for the reaction two TACs. accounted for the total chemo- and regioselectivity4 of 18 experimentally observed, emphasized the zw-type reactivity of the benzonitrile oxide 2, and revealed that the reaction takes place through a non-concerted two-stage one-step mechanism [23] initialized with the formation of the C−C single bond involving the β-conjugated carbon of tomentosin 1. In 2019, Ait Itto et al. reported the 32CA reactions of (R)-carvone 4 with diaryl nitrilimines (NIs) 5a−d and arylnitrile oxides (NOs) 7a−d in dichloromethane (DCM), yielding pyrazoles 6a−d and isoxazoles 8a−d, respectively (see Scheme 5) [24]. These 32CA reactions presented total regio- and chemoselectivity, obtaining a mixture of a pair of diastereoisomers resulting from the attack of these TACs by the two faces of the two C−C double bonds of (R)-carvone 4. Interestingly, both regio- and chemoselectivity were opposite for the two TACs.

SchemeScheme 5. 32CA 5. 32CA reactions reactions of of (R)-carvone (R)-carvone 4 with diaryl diaryl NIs NIs 5a5a–d– andd and aryl-NOs aryl-NOs 7a–d7a. –d.

An MEDTAn MEDT study study of theseof these 32CA 32CA reactions reactions allowedallowed explaining explaining the the different different behaviours behaviours of these of these TACsTACs [18]. [18]. The The topological topological analysis analysis of of the the ELF ELF ofof diaryl NI NI 5a5a andand aryl aryl NO NO 7a allowed7a allowed characterizing characterizing theirtheir electronic electronic structure structure as as carbenoid carbenoid and and zwitterioniczwitterionic TACs, TACs, respectively, respectively, thus thus presenting presenting different different cb- andcb- zw-typeand zw-typereactivities, reactivities, which which were were confirmed confirmed byby an ELF ELF topological topological analysis analysis of the of theC−C, C CC,−N C N and C−O single bond formation along the most favourable reaction path associated with these 32CA− − and C O single bond formation along the most favourable reaction path associated with these 32CA reactions.− This MEDT study supported the classification of 32CA reactions into pdr-, pmr-, cb- and zw- pdr- pmr- cb- reactions.type. This MEDT study supported the classification of 32CA reactions into , , and zw-type . Organic reactions can also be classified as non-polar and polar reactions, in such a way that organic reactions are favoured with the increase of the polar character of the reaction [25]. In 2014, Domingo proposed the analysis of the global electron density transfer (GEDT) [26,27] 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, organic reactions have been classified as forward electron density flux (FEDF) and reverse electron density flux (REDF) reactions, depending on the direction of the flux of the electron density at the TS [28]. Non-polar reactions are classified as null electron density flux (NEDF) reactions [29]. 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 “normal electron demand” [30] within Sustmann’s classification [31], it is classified as an NEDF reaction because of being non-polar; note that the GEDT at this DA reaction is negligible, 0.0 e [32]. Many TACs such as zwitterionic nitrones have nucleophilic character. Consequently, they react with strong electrophilic ethylenes, such as methyl acrylate or nitroethylene through a polar mechanism with high regioselectivity [33]. In these polar zw-type 32CA reactions, the analysis of the Parr functions 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 [34]. In addition, many ethylene derivatives such as 2-methylpropene 9 do not have an electrophilic character, and consequently, the corresponding 32CA reactions have non-polar character. Note that many of the most common TACs neither have an electrophilic character as a consequence of the high electron density accumulation at the three centres of the TAC and, therefore, the corresponding reactions with nucleophilic ethylene derivatives will also have a low polar character. Since non-polar 32CA reactions have not been studied as much as polar 32CA reactions, the 32CA cycloadditions of the nine simplest TACs 10 to 18 shown in Table 1 with 2-methylpropene 9 are herein studied within MEDT in order to understand the origin of the regioselectivity in non-polar 32CA reactions (see Scheme 6).

Organics 2020, 1 22

Organic reactions can also be classified as non-polar and polar reactions, in such a way that organic reactions are favoured with the increase of the polar character of the reaction [25]. In 2014, Domingo proposed the analysis of the global electron density transfer (GEDT) [26,27] 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, organic reactions have been classified as forward electron density flux (FEDF) and reverse electron density flux (REDF) reactions, depending on the direction of the flux of the electron density at the TS [28]. Non-polar reactions are classified as null electron density flux (NEDF) reactions [29]. 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 “normal electron demand” [30] within Sustmann’s classification [31], it is classified as an NEDF reaction because of being non-polar; note that the GEDT at this DA reaction is negligible, 0.0 e [32]. Many TACs such as zwitterionic nitrones have nucleophilic character. Consequently, they react with strong electrophilic ethylenes, such as methyl acrylate or nitroethylene through a polar mechanism with high regioselectivity [33]. In these polar zw-type 32CA reactions, the analysis of the Parr functions 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 [34]. In addition, many ethylene derivatives such as 2-methylpropene 9 do not have an electrophilic character, and consequently, the corresponding 32CA reactions have non-polar character. Note that many of the most common TACs neither have an electrophilic character as a consequence of the high electron density accumulation at the three centres of the TAC and, therefore, the corresponding reactions with nucleophilic ethylene derivatives will also have a low polar character. Since non-polar 32CA reactions have not been studied as much as polar 32CA reactions, the 32CA cycloadditions of the nine simplest TACs 10 to 18 shown in Table1 with 2-methylpropene 9 are herein studied within MEDT in order to understand the origin of the regioselectivity in non-polar 32CA reactions (see Scheme6). Organics 2020, 1, 5 of 18 Table 1. Atom composition, name and structural classification of the nine TACs 10–18 studied herein. Table 1. Atom composition, name and structural classification of the nine TACs 10–18 studied herein. X1 N2 Z3 Name Structure −X1−−N2−Z3 Name Structure 10 10H CH2CNH−NHCH−CH2 azomethineazomethine ylide ylide bent bent 2 − − 2 11 11 H CH2CN−NCH−CH nitrile nitrile ylide ylide linear linear 2 − − 12 H C NH NH azomethine imine bent 12 2 H−2C−NH− −NH azomethine imine bent 13 H C N N diazomethane linear 13 2 H−2C−−N−N diazomethane linear 14 HC N NH nitrile imine linear 14 HC− −−N−NH nitrile imine linear 15 H2C NH O nitrone bent 15 H−2C−NH− −O nitrone bent 16 HC N O nitrile oxide linear 16 HC− −−N−O nitrile oxide linear 17 NH N N azide linear − − 18 17 NNHN −ON−N azide nitrous oxide linear linear 18 −N−−N−O nitrous oxide linear

SchemeScheme 6. Selected 6. Selected 32CA 32CA reactions reactions of of three three bent,bent, 10,, 1212 andand 1515, and, and six six linear, linear, 11, 1113, 1413,, 1614, ,1716 and, 17 18and, 18, simplestsimplest TACs TACs with with 2-methylpropene 2-methylpropene9 .9.

2. Computational Methods All stationary points were optimised using the B3LYP functional [35,36], together with the 6- 311G(d,p) basis set [37]. This functional has been widely used in the study of 32CA reactions [38−41]. The optimisations were carried out using the Berny analytical gradient optimisation method [42,43]. The stationary points were characterized by frequency computations in order to verify that TSs have one and only one imaginary frequency. The intrinsic reaction coordinate (IRC) paths [44] 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 González– Schlegel integration method [45,46]. The electronic structures of the stationary points were characterized by Natural Population Analysis (NPA) [47,48] and by the topological analysis of the ELF [14]. CDFT reactivity indices [7,8] were computed at the B3LYP/6-31G(d) level as original reactivity scales were established at that method, using the equations given in reference 8. A non-published study of the electrophilicity and nucleophilicity indices of 25 single organic molecules computed using different DFT functionals and basis sets proved excellent linear correlations between them. 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 [49]. ELF studies were performed with the TopMod program [50], 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 [51], while the ELF localisation domains were represented with the Paraview software at an isovalue of 0.75 a.u. [52,53].

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2. Computational Methods All stationary points were optimised using the B3LYP functional [35,36], together with the 6-311G(d,p) basis set [37]. This functional has been widely used in the study of 32CA reactions [38–41]. The optimisations were carried out using the Berny analytical gradient optimisation method [42,43]. The stationary points were characterized by frequency computations in order to verify that TSs have one and only one imaginary frequency. The intrinsic reaction coordinate (IRC) paths [44] 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 González–Schlegel integration method [45,46]. The electronic structures of the stationary points were characterized by Natural Population Analysis (NPA) [47,48] and by the topological analysis of the ELF [14]. CDFT reactivity indices [7,8] were computed at the B3LYP/6-31G(d) level as original reactivity scales were established at that method, using the equations given in reference 8. A non-published study of the electrophilicity and nucleophilicity indices of 25 single organic molecules computed using diﬀerent DFT functionals and basis sets proved excellent linear correlations between them. The GEDT [18] was computed by the P 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 [49]. ELF studies were performed with the TopMod program [50], 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 [51], while the ELF localisation domains were represented with the Paraview software at an isovalue of 0.75 a.u. [52,53].

3. Results and Discussion The present MEDT study has been divided into four parts: (i) in Section 3.1, a study of the electronic structure of the TACs through 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 10–18 with 2-methylpropene 9 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 electron density with respect to reagents, and thus, to understand the origin of regioselectivity.

3.1. ELF Topological Analysis of Reagents 9 to 18 ELF, ﬁrst constructed by Becke and Edgecombe [14] and further developed by Silvi and Savin [54], permits the establishment of a straightforward quantitative connection between the electron density distribution and the chemical structure. A useful correlation between the electronic structure and the reactivity of the simplest TACs participating in 32CA reactions towards ethylene has been established [16]. Thus, the topological analysis of the ELF of the nine TACs 10–18 and 2-methylpropene 9 was performed in order to predict their reactivity in 32CA reactions [16]. The populations of the most signiﬁcant valence basins are listed in Table2, while the ELF basin attractor positions are shown in Figure1. A picture of the ELF localisation domains of four representative TACs characterizing the four types of TACs, i.e., pseudodiradical, pseudo(mono)radical, carbenoid and zwitterionic, is shown in Figure2. The ELF-based Lewis-like structures together with the natural atomic charges of the nine TACs are also shown in Figure1. At azomethine ylide 10, two pairs of monosynaptic basins, V(C1) and V’(C1), and V(C3) and V’(C3), integrating a total of 0.86 e each pair, are observed at the C1 and C3 carbon ends. These ELF V(Ci) monosynaptic basins are related with the presence of two pseudoradical centers [55] at azomethine ylide 10, thus being considered as a pseudodiradical TAC. Note that pseudoradical centers in a tetrahedric Organics 2020, 1 24 carbon are characterized by the presence of one V(C1) monosynaptic basin, while those in a trigonal planar carbon are usually characterized by the presence of two V(C1) and V’(C1) monosynaptic basins.

Table 2. Populations of the most signiﬁcant ELF valence basins, in average number of electrons, e, of the nine TACs 10–18 and 2-methylpropene 9.

Basins 10 11 12 13 14 15 16 17 18 19 Organics 2020V(X1), 1, 0.43 0.29 0.35 0.49 1.64 3.44 4.06 7 of 18 V’(X1) 0.43 0.24 0.35 0.49 presents V(X1,N2)two monosynaptic 2.59 basins 2.98, V(C1) 2.96 and 3.04 V’(C1), 2.21 with 3.72a total low 5.50 population 2.41 4.18of 0.53 e, at the C1 carbon (seeV’(X1,N2) Table 2), being associated with a pseudoradical 2.27 center. NeitherV(N2,Z3) pseudoradical 2.59 nor 2.04 carbenoid 1.89 centres 3.65 appear 2.27 in 1.47 TACs 1.97 15−18, 1.66but there 1.91 are disynaptic V’(N2,Z3) 1.98 2.48 basins, V(X1,N2), V’(X1,N2), V(N2,Z3) and V’(N2,Z3), whose populations are associated to multiple V(Z3) 0.43 1.90 3.50 1.92 3.29 3.00 5.57 3.81 5.50 bonds, thusV’(Z3) being considered 0.43 as zwitterionic 1.92 TACs [16]. The 2.84 V(Z3) monosynaptic basins present at these TACs,V(C4,C5) which are associated to C, N or O non-bonding electron density regions, correspond1.76 with the lone V’(C4,C5)pairs of the Lewis-like structures (see Figure 1). 1.76

Figure 1. ELFELF basin basin attractor attractor positions, positions, ELF-based ELF-based Lewis-like Lewis-like structures structures and and TAC TAC classifications, classiﬁcations, together with with calculated calculated natural natural atomic atomic charges, charges, in in average average number number of of electrons electrons e, e, of of TACs TACs 1010−–1818.. Negative charges are coloured in red, positive charges inin blue,blue, andand negligiblenegligible chargescharges inin green.green.

On the other side, the population of the V(X1,N2) and V(N2,Z3) disynaptic basins associated to the L-TACs indicates that, except nitrile imine 14, nitrile oxide 16 and nitrous oxide 18, which have a propargylic structure, X1≡N2−Z3, the other TACs have a rather allenic structure, X1=N2=Z3. Finally, 2-methylpropene 9 shows the presence of a pair of disynaptic basins, V(C4,C5) and V(C4,C5), with a total population of 3.52 e, respectively, being associated to an underpopulated C4−C5 double bond.

Organics 2020, 1 25 Organics 2020, 1, 8 of 18

FigureFigure 2. 2. B3LYP/6-311G(d,p)B3LYP/6-311G(d,p) ELF ELF localisation localisation domains domains represented represented at an atisosurface an isosurface value of value ELF of= 0.75,ELF =together0.75, together with the with populations, the populations, given in given average in average number number of electrons, of electrons, e, of the e, valence of the valencebasins characterizingbasins characterizing the type the of type TAC of TACfor forazomethine azomethine ylide ylide 10,10 pseudodiradical, pseudodiradical, ,diazomethane diazomethane 1313, , pseudo(mono)radicalpseudo(mono)radical, ,nitrile nitrile imine imine 1414, ,carbenoid, carbenoid, and and nitrone nitrone 1515, ,zwitterionic. zwitterionic. V(X1,N2) V(X1,N2) and and V(N2,Z3) V(N2,Z3) disynapticdisynaptic basins basins are are represented represented in in green, green, V(C,H) V(C,H) and and V(N2,H) V(N2,H) protonated protonated ba basinssins are are represented represented in in turquoise,turquoise, V(C), V(C), V(N) V(N) and and V(O) V(O) monosynaptic monosynaptic basins basins are are represented represented in in red, red, and and C(C), C(C), C(N) C(N) and and C(O) C(O) corecore basins basins are are represented represented in in pink. pink.

ELFAt azomethine topological imineanalysis12 andof the diazoalkane nine TACs13 10,− two18 shows pairs of that monosynaptic while some basins,zwitterionic V(C1) TACs and V’(C1), such asintegrating nitrone a6 total correspond of 0.60 e andwith 0.98 Huisgen’s e, respectively, 1,2-dipolar are observed structure at the [56], trigonal pseudodiradical planar C1 carbon. and pseudo(mono)radicalFor these TACs, these TACs, V(C1) such monosynaptic as azomethine basins ylide are related10 and withdiazomethane the presence 13 of, correspond one pseudoradical with Firestone’scenter at the radical C1 carbon structures of these [57]. TACs, However, thus being it is interesting considered to as remarkpseudoradical that whileTACs. pseudodiradical and pseudo(mono)radicalAt nitrile ylide TACs11 and are nitrile species imine with14 ,a one stable single closed-shell V(Ci) monosynaptic electronic structure basin, integrating [55], actual 1.90 radical e (11 ) speciesand 1.64 have e (14 open-shell), is observed electronic at the structures. C3 and C1 carbon, respectively, being associated to one carbenoid center,NPA both analysis being of thus the considerednatural atomic as carbenoid charges at TACs. the nine Note TACs that 10 nitrile−18 shows ylide that,11 also except presents for nitrile two oxidemonosynaptic 16, azide basins,17 and V(C1)nitrous and oxide V’(C1), 18, all with TACs a totalhas a low rather population negatively of charged 0.53 e,at framework the C1 carbon (see Figure(see Table 2), 2thus), being ruling associated out the withcommonly a pseudoradical acceptedcenter. charge distribution of a 1,2-zwitterionic Lewis structureNeither [16].pseudoradical These atomicnor charge carbenoid distributions centres appearresult from in TACs the more15–18 electronegative, but there are disynaptic character basins,of the C,V(X1,N2), N and O V’(X1,N2),atoms than V(N2,Z3) the H atoms and bound V’(N2,Z3), to them. whose Consequently, populations the are atomic associated charge to multipledistribution bonds, on thethus TACs being does considered not come as from zwitterionic resonant electronic TACs [16]. st Theructures, V(Z3) but monosynaptic from the anisotropic basins present distribution at these of theTACs, electron which density are associated generated to by C, the N or different O non-bonding nuclei belonging electron densityto the TAC regions, [16]. correspond with the lone pairs of the Lewis-like structures (see Figure1). 3.2. AnalysisOn the of other the Global side, theand population Local CDFT of Re theactivity V(X1,N2) Indices and at the V(N2,Z3) GS of the disynaptic Reagents basins associated to the L-TACs indicates that, except nitrile imine 14, nitrile oxide 16 and nitrous oxide 18, which have a The analysis of the reactivity indices based on CDFT has become a useful tool for the study of propargylic structure, X1 N2 Z3, the other TACs have a rather allenic structure, X1=N2=Z3. reactivity in polar reactions≡ [8].− Therefore, in order to establish the polar or non-polar character of Finally, 2-methylpropene 9 shows the presence of a pair of disynaptic basins, V(C4,C5) and these 32CA reactions, an analysis of CDFT reactivity indices was performed. The CDFT indices were V(C4,C5), with a total population of 3.52 e, respectively, being associated to an underpopulated C4 C5 calculated at the B3LYP/6-31G(d) computational level since it was used to define the electrophilicity− double bond. and nucleophilicity scales [8]. The B3LYP/6-31G(d) global indices, namely, the electronic chemical ELF topological analysis of the nine TACs 10–18 shows that while some zwitterionic TACs such as potencial, µ, chemical hardness, η, electrophilicity, ω, and nucleophilicity, N, at the GS of TACs 10 to nitrone 6 correspond with Huisgen’s 1,2-dipolar structure [56], pseudodiradical and pseudo(mono)radical 18 and 2-methylpropene 9, are given in Table 3. TACs, such as azomethine ylide 10 and diazomethane 13, correspond with Firestone’s radical structures [57]. However, it is interesting to remark that while pseudodiradical and pseudo(mono)radical TACs are species with a stable closed-shell electronic structure [55], actual radical species have open-shell electronic structures. NPA analysis of the natural atomic charges at the nine TACs 10–18 shows that, except for nitrile oxide 16, azide 17 and nitrous oxide 18, all TACs has a rather negatively charged framework (see Figure2), thus ruling out the commonly accepted charge distribution of a 1,2-zwitterionic Lewis

Organics 2020, 1 26 structure [16]. These atomic charge distributions result from the more electronegative character of the C, N and O atoms than the H atoms bound to them. Consequently, the atomic charge distribution on the TACs does not come from resonant electronic structures, but from the anisotropic distribution of the electron density generated by the diﬀerent nuclei belonging to the 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 non-polar 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, ω, and nucleophilicity, N, at the GS of TACs 10 to 18 and 2-methylpropene 9, are given in Table3.

Table 3. B3LYP/6-31G(d) global CDFT indices, namely, the electronic chemical potential µ, the chemical hardness η, and the electrophilicity ω and nucleophilicity N indices, in eV, at the GS of TACs 10 to 18 and 2-methylpropene 9.

Reagent µ η ω N 10 1.82 4.47 0.37 5.07 − 11 2.90 5.45 0.77 3.50 − 12 2.70 5.02 0.72 3.92 − 13 3.64 4.73 1.40 3.11 − 14 3.55 5.87 1.07 2.64 − 15 3.43 5.55 1.06 2.92 − 16 3.40 7.97 0.73 1.75 − 17 4.24 6.54 1.37 1.62 − 18 4.92 8.79 1.37 0.19 − − 9 2.83 7.37 0.55 2.60 −

The electronic chemical potential [7] µ of the nine TACs ranges from 1.81 (10) to 4.92 (18) eV, − − while that of 2-methylpropene 9 is 2.83 eV. Except for TACs 10–12, TACs 13–18 have lower chemical − potential than 2-methylpropene 9, suggesting that the electron density will flux from 2-methylpropene 9 towards those TACs. On the other hand, in general, the hardness [58] η of these TACs increases along this series of TACs. Thus, while azomethyne ylide 10 has a η = 4.47 eV, azide 18 has a η = 8.79 eV. Thus, azomethyne ylide 10 is the softest TAC, while azide 18 is the hardest TAC. The electrophilicity ω index [9] of these TACs ranges from 0.37 (10) to 1.37 (18) eV.Thus, while TACs 10, 11, 12 and 16 are classified as marginal electrophiles, TACs 13, 14, 15, 17 and 18 are classified as moderate electrophiles within the electrophilicity scale [8]. On the other hand, while the nucleophilicity N index [10] for TACs 10, 11, 12 and 13 is higher than 3.0 eV, being classified as strong nucleophiles, TACs 11, 14, and 15 are classified as moderate nucleophiles, and TACs 16 to 18, having a nucleophilicity N index lower than 2.0 eV,are classified as marginal nucleophiles within the nucleophilicity scale [8]. The high nucleophilicity N index of azomethyne ylide 10 permits its classification as a supernucleophile [59]. The electrophilicity ω and nucleophilicity N indices of 2-methylpropene 9 are 0.55 and 2.60 eV, respectively, being classified as a marginal electrophile and a moderate nucleophile. Thus, while 2-methylpropene 9 will never participate as electrophile in polar reactions, it could participate as nucleophile only towards strong electrophilic species, which is not the case. 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 Organics 2020, 1 27 centre of the electrophile and the most nucleophilic centre of the nucleophile [6]. In this context, Organics 2020, 1, + 10 of 18 the electrophilic Pk and nucleophilic Pk− Parr functions [11] derived from the excess of spin electron density reached via the GEDT [26] process from the nucleophile toward the electrophile have shown to analysis of the nucleophilic 𝑃 Parr functions will permit to predict the regioselectivity in a FEDF be32CA one reaction. of the most accurate and insightful tools for the study of the local reactivity in polar and ionic + processes.Interestingly, Although in the 32CA 32CA reactions reaction of under FEDF, study zwitterionic will have nitrone a low polar16 shows character, a reverse the electrophilicregioselectivityPk andthan nucleophilic pseudoradicalP k−diazomethaneParr functions 13 of and three carbenoid selected TACs, nitrile a iminepseudoradical 14. Thus,, diazomethane while diazomethane13, a carbenoid, 13 and nitrile imineimine14 14, andpresent a zwitterionic, the most nucleophilic nitrone 15, as center well asat 2-methylpropenethe pseudoradical 9and, were carbenoid analysed C1 in carbons, order to characterizenitrone 15 presents what would the most be the nucleophilic corresponding center regioselectivity at the O3 oxygen. in polar 32CA reactions (see Figure3).

Figure 3.3. 3D representations of the MullikenMulliken atomic spin densitiesdensities of thethe radicalradical cationcation andand radicalradical anion ofof diazomethanediazomethane 13,, nitrilenitrile imineimine 1414,, nitronenitrone 1515,, andand 2-methylpropene2-methylpropene 9,9, togethertogether withwith thethe − + + nucleophilic P𝑃𝑘 (left side) and electrophilicP 𝑃𝑘 (right side) Parr functions. nucleophilic k− (left side) and electrophilic k (right side) Parr functions.

3.3. StudyElectrophilic of the Reactivity and nucleophilic and Regioselectivity substituted in ethylenesthe 32CA Reactions have the mostof TACs electrophilic 10−18 with and 2- nucleophilic Methylpropene 9 + centers at the non-substituted CH2 methylene carbon of the ethylene [33]; see the electrophilic Pk and nucleophilic P Parr functions of 2-methylpropene 9 in Figure3. Analysis of the electrophilic P+ Except for azomethinek− ylide 10, the rest of the reagents do not present molecular symmetry; thus,k and nucleophilic P Parr functions of the three selected TACs shows that along polar 32CA reactions, eight of the selectedk− 32CA reactions can occur through two competitive regioisomeric reaction paths; a change in regioselectivity will be expected depending on whether the reaction is classiﬁed as FEDF the first ones, denoted as r1, are related to the formation of the X1−C4 single bond, while the second or REDF [28]. As many of the TACs are more nucleophilic than electrophilic, see Table3, analysis of ones, denoted as r2, are associated to the formation of the Z3−C4 bond (see Scheme 7). Searching for the nucleophilic P Parr functions will permit to predict the regioselectivity in a FEDF 32CA reaction. the stationary pointsk− along each of the two regioisomeric reaction paths revealed only one TS and its Interestingly, in 32CA reactions of FEDF, zwitterionic nitrone 16 shows a reverse regioselectivity corresponding cycloadduct; thus, these 32CA reactions are meant to occur through a one-step than pseudoradical diazomethane 13 and carbenoid nitrile imine 14. Thus, while diazomethane 13 and mechanism. Relative energies of the stationary points involved in the nine 32CA reactions are given in Table 4.

Organics 2020, 1 28 nitrile imine 14 present the most nucleophilic center at the pseudoradical and carbenoid C1 carbons, nitrone 15 presents the most nucleophilic center at the O3 oxygen.

3.3. Study of the Reactivity and Regioselectivity in the 32CA Reactions of TACs 10–18 with 2-Methylpropene 9 Except for azomethine ylide 10, the rest of the reagents do not present molecular symmetry; thus, eight of the selected 32CA reactions can occur through two competitive regioisomeric reaction paths; the ﬁrst ones, denoted as r1, are related to the formation of the X1 C4 single bond, while the − second ones, denoted as r2, are associated to the formation of the Z3 C4 bond (see Scheme7). − Searching for the stationary points along each of the two regioisomeric reaction paths revealed only one TS and its corresponding cycloadduct; thus, these 32CA reactions are meant to occur through a one-step mechanism. Relative energies of the stationary points involved in the nine 32CA reactions are given in Table4. Organics 2020, 1, 11 of 18

Scheme 7. RegioisomericRegioisomeric reaction reaction paths paths associated associated to tothe the 32CA 32CA reactions reactions of ofTACs TACs 10−1018– 18withwith 2- 2-methylpropenemethylpropene 9.9 .

Table 4. Relative electronic energies, ∆E, in kcal mol 1, of the TSs and cycloadducts involved in the The activation energies associated to the nine· 32CA− reactions range from 8.8 (10) to 27.7 (18) 32CA reactions of TACs 10 to 18 with 2-methylpropene 9. kcal·mol−1, the reactions being exothermic by between 2.9 (18) and 59.5 (11) kcal·mol−1. Some appealing conclusionsTAC can be type drawn from TS-r1-n the rela TS-r2-ntive energies CA-r1-n given in CA-r1-n Table 4: (i) the most favourable 32CA reaction10 correspondspdr to that8.8 involving pseudodiradical54.6 azomethyne ylide 10, ΔEact = − 8.8 kcal·mol−1, while11 the most unfavourablecb 14.0 one corresponds 15.0 to that59.5 involving59.4 zwitterionic nitrous − − oxide 18, ΔEact = 27.712 kcal·mol−pmr1; (ii) except12.8 for diazomethane 15.3 13, the39.7 general trend36.7 of reactivity pdr- − − 13 pmr 20.4 23.1 23.1 27.0 type > pmd-type ≥ cb-type > zw-type is observed [16]; (iii) except for− the 32CA reaction− involving azide 14 cb 11.8 14.4 54.0 51.3 17, which is slightly r2 regioselective [33], seven of these 32CA reactions− are −r1 regioselective. Note 15 zw 14.4 19.8 27.1 22.0 − − that in the case of nitrone16 6, thezw r1 regioselectivity15.0 is opposite 19.9 to that38.3 observed in32.7 polar zw-type 32CA − − reactions involving 17electrophiliczw ethylenes23.7 [32]; (iv) the 23.1 regioselectivity,17.3 measured16.7 as ΔΔEact, ranges − − from 1.0 kcal·mol−1 18for the 32CAzw reaction27.7 involving nitrile 30.5 ylide 112.9 to 5.3 kcal·mol1.3 −1 for the 32CA − − reaction involving nitrone 15; excluding TACs 10, 11 and 17, the other four 32CA reactions can be consideredThe activation highly r1 energies regioselective associated with ΔΔ to theEact > nine 2.5 kcal·mol 32CA reactions−1; (v) considering range from the 8.8 strong (10) toexothermic 27.7 (18) −1 kcalcharactermol 1,of the the reactions 32CA beingreactions exothermic of TACs by between10−16, Δ 2.9Ereac (18 >) and22.3 59.5kcal·mol (11) kcal, thesemol 1.reactions Some appealing can be · − · − conclusionsconsidered canirreversible, be drawn and from consequently, the relative energies formation given of inthe Table r14 :regioisomeric (i) the most favourable cycloadducts 32CA is kinetically controlled; and (vi) in general, except for diazomethane 13, all r1 regioisomeric1 reaction corresponds to that involving pseudodiradical azomethyne ylide 10, ∆Eact = 8.8 kcal mol , · − whilecycloadducts the most are unfavourable thermodynamically one corresponds more stable to than that the involving r2 ones. zwitterionic Consequently, nitrous except oxide for the18, reactions involving TACs1 13 and 17, the r1 regioisomeric cycloadducts can also be considered the ∆Eact = 27.7 kcal mol ; (ii) except for diazomethane 13, the general trend of reactivity pdr-type > · − pmd-typethermodynamiccb-type control> zw-type product.is observed [16]; (iii) except for the 32CA reaction involving azide 17, ≥ whichConsidering is slightly r 2that regioselective in the series [33 of], TACs seven 11 of− these18 the 32CA X1 end reactions atom is are lessr1 electronegative regioselective. Notethan thatthe Z3 in theone, case i.e., ofthe nitrone electronegativity6, the r1 regioselectivity increases in isthe opposite order C to < thatN < observedO, and the in trigonal polar zw-type planar32CA arrangement reactions is less electronegative than the linear one, it is possible to conclude that the r1 regioselectivity involving electrophilic ethylenes [32]; (iv) the regioselectivity, measured as ∆∆Eact, ranges from observed in 1these 32CA reactions is kinetically controlled by the interactions1 between the least 1.0 kcal mol− for the 32CA reaction involving nitrile ylide 11 to 5.3 kcal mol− for the 32CA reaction electronegative· X1 end atom of these TACs and the methylene C4 carbon· of 2-methylpropene 9.

Table 4. Relative electronic energies, ∆E, in kcal.mol−1, of the TSs and cycloadducts involved in the 32CA reactions of TACs 10 to 18 with 2-methylpropene 9.

TAC type TS-r1-n TS-r2-n CA-r1-n CA-r1-n 10 pdr 8.8 −54.6 11 cb 14.0 15.0 −59.5 −59.4 12 pmr 12.8 15.3 −39.7 −36.7 13 pmr 20.4 23.1 −23.1 −27.0 14 cb 11.8 14.4 −54.0 −51.3 15 zw 14.4 19.8 −27.1 −22.0 16 zw 15.0 19.9 −38.3 −32.7 17 zw 23.7 23.1 −17.3 −16.7 18 zw 27.7 30.5 −2.9 −1.3

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

Organics 2020, 1 29 involving nitrone 15; excluding TACs 10, 11 and 17, the other four 32CA reactions can be considered 1 highly r1 regioselective with ∆∆Eact > 2.5 kcal mol− ; (v) considering the strong exothermic character · 1 of the 32CA reactions of TACs 10–16, ∆Ereac > 22.3 kcal mol , these reactions can be considered · − irreversible, and consequently, formation of the r1 regioisomeric cycloadducts is kinetically controlled; and (vi) in general, except for diazomethane 13, all r1 regioisomeric cycloadducts are thermodynamically more stable than the r2 ones. Consequently, except for the reactions involving TACs 13 and 17, the r1 regioisomeric cycloadducts can also be considered the thermodynamic control product. Considering that in the series of TACs 11–18 the X1 end atom is less electronegative than the Z3 one, i.e., the electronegativity increases in the order C < N < O, and the trigonal planar arrangement is less electronegative than the linear one, it is possible to conclude that the r1 regioselectivity observed in these 32CA reactions is kinetically controlled by the interactions between the least electronegative X1 end atom of these TACs and the methylene C4 carbon of 2-methylpropene 9. OrganicsThe 2020 optimized, 1, geometries of the most favourable r1 regioisomeric TSs are shown in Figure12 of4 18, while the distances between C C, C N and C O interacting centers at the two regioisomeric TSs are − − − givengiven inin TableTable5 .5. Some Some appealing appealing conclusions conclusions can can be drawnbe drawn from from these these geometrical geometrical parameters: parameters: (i) the (i) distancethe distance between between the the interacting interacting centres centres at theat ther1 r1 regioisomeric regioisomeric TSs TSs ranges ranges from from 2.442 2.442 Å Å (C (C−C)C) atat − TS-r1-10TS-r1-10 toto 1.9951.995 ÅÅ (C(C−N) at TS-r1-18;; (ii) (ii) the the C4 C4−X1X1 (X (X = C, N, O) distances decrease with the increase − − ofof thethe activationactivation energy;energy; i.e.,i.e., thethe moremore unfavourableunfavourable thethe TS,TS, thethe moremore advancedadvanced itit is;is; (iii)(iii) consideringconsidering thatthat thethe formationformation ofof thethe CC−C, CC−N and C−OO single single bonds begins in the short ranges of 2.00–1.90,2.00−1.90, − − − 1.90–1.801.90−1.80 andand 1.80–1.701.80−1.70 ÅÅ [[16],16], respectively,respectively, thesethese distancesdistances indicateindicate thatthat thethe formationformation ofof thethe C4C4−X1 − (C,(C, N,N, O)O) newnew singlesingle bondsbonds hashas notnot startedstarted yetyet atat anyany TSTS (see(see SectionSection 3.43.4);); and,and, ﬁnallyfinally (iv)(iv) exceptexcept forfor TS-r1-11TS-r1-11,, thethe distancedistance involvinginvolving thethe X1X1 endend atomatom ofof thesethese TACsTACs isis shortershorter thatthat thatthat involvinginvolving thethe Z3Z3 one.one. TheseThese behavioursbehaviours point point out out that that the the interaction interaction between between the leastthe least electronegative electronegative X1 atom X1 atom of these of TACsthese andTACs the and methylene the methylene C4 carbon C4 ofcarbon9 is less of unfavourable9 is less unfavourable and more and advanced more advanced that that involving that that theinvolving more electronegative the more electronegative Z3 atom. Z3 atom.

FigureFigure 4.4. GeometriesGeometries of thethe mostmost favourablefavourable rr11 regioisomericregioisomeric TSsTSs involvedinvolved in thethe 32CA32CA reactionsreactions ofof TACsTACs10 10to to18 18with with 2-methylpropene2-methylpropene9 9..

Table 5. Cx-Xy (X = C, N, O) distances, in angstroms Å, at the r1 and r2 regioisomeric TSs involved in the 32CA reactions of TACs 10 to 18 with 2-methylpropene 9.

TAC TS-r1-n TS-r2-n C4-X1 C5-X3 C4-X3 C5-X1 10 2.442 2.445 11 2.423 2.415 2.471 2.374 12 2.266 2.319 2.308 2.239 13 2.234 2.324 2.280 2.228 14 2.222 2.534 2.392 2.276 15 2.174 2.213 2.140 2.160 16 2.192 2.483 2.352 2.182 17 2.131 2.140 2.054 2.189 18 1.995 2.176 2.083 2.028

Organics 2020, 1 30

Table 5. Cx-Xy (X=C, N, O) distances, in angstroms Å, at the r1 and r2 regioisomeric TSs involved in the 32CA reactions of TACs 10 to 18 with 2-methylpropene 9.

In order to evaluate the polar nature of these 32CA reactions, the GEDT [18] at the TSs was analysed. Reactions with GEDT values below 0.05 e correspond to non-polar processes, while values above 0.20 e correspond to polar processes. The GEDT values measured at the TAC framework of the more favourable r1 regioisomeric TSs are 0.14 e at TS-r1-10, 0.09 e at TS-r1-11, 0.07 e at TS-r1-12, − 0.07 e at TS-r1-13, 0.03 e at TS-r1-14, 0.01 e at TS-r1-15, 0.05 e at TS-r1-16, 0.08 e TS-r1-17 and − − − − 0.19 e at TS-r1-18. Some appealing conclusions can be drawn from these GEDT values: (i) while the − 32CA reactions of azomethine ylide 10 and nitrous oxide 18 have polar character, those of TACs 11–17 have a low-polar or non-polar character; (ii) while the 32CA reaction of azomethine ylide 10 is classified as FEDF, that of nitrous oxide 18 is classified as REDF [28]. Note the change of the sign of the GEDT at TS-r1-10, 0.14 e, and at TS-r1-18, 0.19 e; thus, while azomethine ylide 10 acts as electron-donor, − nitrous oxide 18 acts as electron-acceptor. This is a consequence of the supernucleophilic character [59] of 10 and the moderate electrophilic character of 18 (see Table3); and finally, (iii) the non-polar 32CA reactions of nitrile imine 14 and nitrone 15 can be classified as NEDF [29].

3.4. 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 valence basin populations of the nine TSs are given in Table6, while a picture of the ELF basin attractor positions of the TSs is shown in Figure5. 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 ranging from 0.73 e (TS-r1-10) to 2.33 e (TS-r1-18). In general, the population of this V(N2) monosynaptic basin increases with the advanced character of the TS. Thus, its population, which mainly comes from the depopulation of the X1 N2 bonding region − of the TACs, reaches the maximum value at the ﬁnal cycloadducts. This V(N2) monosynaptic basin, which is not present at the TACs (see Table2), is associated to the N2 non-bonding electron density present at the ﬁnal cycloadduct. All C1 and C3 end carbons present one or two V(C) monosynaptic basins, integrating between 0.51 e (TS-r1-10) and 1.47 e (TS-r1-18). 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 15 and nitrile oxide 16 by depopulation of the C N2 bonding region. This behaviour, together − with the creation of the V(N2) monosynaptic basin, accounts for the higher activation energies of the TSs associated to zw-type 32CA reactions [16]. Note that these V(Ci) monosynaptic basins are demanded for the subsequent C C single bond formation [26]. − Except for the unfavourable TS-r1-18, the N and O centres show the presence of V(N) or V(O) monosynaptic basins, associated to N or O non-bonding electron density, which are already present at the corresponding TACs. Note that the formation of the subsequent N C or O C single bonds results − − Organics 2020, 1 31 from the participation of part of the non-bonding electron density of the N or O atoms and that of the pseudoradical carbon of the ethylene derivative. Finally, ELF of the ethylene framework shows the presence of one V(C4,C5) disynaptic basin, integrating between 3.06 e (TS-r1-18) and 3.41 e ((TS-r1-10). Note that the population of the V(C4,C5) disynapticOrganics basin 2020 at, 2-methylpropene1, 9 is 3.52 e. Along the reaction path, ongoing from14 theof 18 separated reagents to TSs, the C C bonding region of 2-methylpropene 9 is depopulated in order to generate, − after passing theAs the TSs, activation the V(C4) energies and associated V(C5) monosynaptic to these non-polar basins 32CA reactions required are for mainly the formationassociated to of the new the depopulation of the N2−X1 and C4−C5 bonds, which is required for the formation of the non- X C single bonds. As a consequence of this continue depopulation, the two V(C4,C5) and V’(C4,C5) − bonding electron density demanded for the single bond formation, i.e., the pseudoradical centres at disynapticcarbon basins atoms present [26], atthe 2-methylpropene different activation 9energihavees mergedfound in intotheseone 32CA single reactions V(C4,C5) depend disynapticon the basin at the ninepresence TSs. of the V(X1) (X = C, N, O) monosynaptic basins at the corresponding TACs, thus justifying the order of reactivity pseudodiradical > pseudoradical ≥ carbenoid > zwitterionic. Table 6. ELF valence basin populations of the TSs associated to the r1 regioisomeric reaction path of the 32CA reactionsTable 6. ELF of valence TACs basin10 to populations18 with 2-methylpropene of the TSs associated 9to, inthe averager1 regioisomeric number reaction of electrons, path of e. the 32CA reactions of TACs 10 to 18 with 2-methylpropene 9, in average number of electrons, e.

BasinsBasins TS-r1-10 TS-r1-10 TS-r1-11 TS-r1-11 TS-r1-12TS-r1-12 TS-r1-13 TS-r1-13 TS-r1-14 TS-r1-14 TS-r1-15 TS-r1-15 TS-r1-16 TS-r1-16 TS-r1-17 TS-r1-17TS-r1-18 TS-r1-18 V(X1)V(X1) 0.630.63 0.510.51 0.590.59 0.91 0.44 0.44 1.47 1.471.33 1.333.38 3.383.84 3.84 V(X1,N2)V(X1,N2) 2.32 2.32 2.242.24 2.312.31 1.92 2.39 2.39 2.93 2.931.55 1.552.71 2.712.72 2.72 V’(X1,N2)V’(X1,N2) 1.55 1.55 V(N2)V(N2) 0.730.73 1.541.54 1.121.12 1.97 1.32 1.32 2.09 2.092.04 2.042.26 2.262.33 2.33 V(N2,Z3)V(N2,Z3) 2.30 2.30 1.671.67 1.711.71 1.55 1.24 1.24 1.88 1.881.49 1.492.71 2.711.44 1.44 V’(N2,Z3) 1.67 1.43 V’(N2,Z3) 1.67 1.43 V(Z3) 0.73 1.63 3.35 3.75 2.86 3.32 2.82 3.87 5.22 V(Z3) 0.73 1.63 3.35 3.75 2.86 3.32 2.82 3.87 5.22 V´(Z3) 2.99 2.82 0.40 V(C4,C5)V´(Z3) 3.41 3.30 3.35 3.31 2.99 3.25 3.232.82 3.20 3.140.40 3.06 V(C4,C5) 3.41 3.30 3.35 3.31 3.25 3.23 3.20 3.14 3.06

Figure 5. ELFFigure basin 5. ELF attractor basin attractor positions positions of the of the TSs TSs associated associated to the the r1r 1regioisomeric regioisomeric reaction reaction path of path of the 32CA reactionsthe 32CA of reactions TACs 10 ofto TACs18 with10 to 18 2-methylpropene with 2-methylpropene9. 9. Finally, the V(C1) monosynaptic basins present at the TSs, which are associated with a From the ELF topological analysis of the nine TSs, one relevant conclusion can be drawn. pseudoradical or carbenoid center required for the subsequent C1−C4 single bond formation, appear, Even despiteor are the already diﬀerent present behaviour at the TAC, ofat the least C, Nelectronegative and O end end centres, carbonthe atom nine of these TSs TACs. present As a similar electronicthese structure V(C1) monosynaptic [16]; all end basi carbonsns are created of the by TACs the depopu havelation one of V(C1) the neighboring monosynaptic C1−N2 bonding basin associated to a pseudoradical or carbene centre, while the nitrogen and oxygen end centres have V(N) or V(O) monosynaptic basins associated to N or O non-bonding electron density. Only changes in the population of these V(X) monosynaptic basins with the advanced character of the TSs are found. On the other Organics 2020, 1 32 hand, the C4 C5 double bond region of the ethylene framework shows a depopulation, which also − increases with the advanced character of the TS. However, neither V(C4) nor V(C5) monosynaptic basin is observed in the ethylene framework at the nine TSs. As the activation energies associated to these non-polar 32CA reactions are mainly associated to the depopulation of the N2 X1 and C4 C5 bonds, which is required for the formation of the − − non-bonding electron density demanded for the single bond formation, i.e., the pseudoradical centres at carbon atoms [26], the diﬀerent 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. ≥ Finally, the V(C1) monosynaptic basins present at the TSs, which are associated with a pseudoradical or carbenoid center required for the subsequent C1 C4 single bond formation, appear, or are already − present at the TAC, at the least electronegative end carbon atom of these TACs. As these V(C1) monosynaptic basins are created by the depopulation of the neighboring C1 N2 bonding region in − zwitterionic TACs, they demand a higher energy cost. On the other hand, in TACs in which the formation of the X1 C4 single bond involves the participation of a nitrogen or oxygen atom, formation − of these X1 C4 single bonds demands the donation of part of the non-bonding electron density of − these heteroatoms. Consequently, 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 end centre − involving the least electronegative X1 atom. This interpretation accounts for the regioselectivity found in these non-polar 32CA reactions.

4. Conclusions The 32CA reactions of nine simplest TACs 10–18 with 2-methylpropene 9 have been studied within MEDT at the MPWB1K/6-311G(d,p) computational level in order to understand the origin of the regioselectivity in non-polar 32CA reactions. Topological analysis of the nine simplest TACs 10–18 allows their classification into one of the four types of TACs: pseudodiradical, pseudo(mono)radical, carbenoid and zwitterionic ones. On the other hand, the NPA shows that many of the atoms of these TACs are negatively charged, thus ruling out the commonly accepted charge distribution of a 1,2-zwitterionic Lewis structure. CDFT classifies TACs 1, 2, 3 and 7 as marginal electrophiles, and TACs 13, 14, 15, 17 and 18 as moderate electrophiles. On the order hand, TACs 10, 12 and 13 are classified as strong nucleophiles, TACs 11, 14 and 15 as moderate nucleophiles, and TACs 16 to 18 as marginal nucleophiles. Consequently, only TACs 10, 12 and 13 will participate as strong nucleophiles in polar 32CA reactions of FEDF. The activation energies associated to the nine 32CA reactions range from 8.8 (10) to 27.7 (18) kcal mol 1, the reactions being exothermic by between 2.9 (18) and 59.5 (11) 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 17, which is slightly 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-r1-10 to 1.995 (C N) at TS-r1-18. − − The C X (X=C, N, O) distances decrease with the increase of the activation energy, i.e., the more − unfavourable the TS, the more advanced it is. Except for TS-r1-11, the distance involving the X1 end atom of these TACs is shorter that that involving the Z3 one. 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 9 are less unfavourable and more advanced than those 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 10 and 18 have polar character, those of TACs 11–17 have a low-polar or non-polar character. Organics 2020, 1 33

A comparative analysis of the topology of the ELF of the more favourable r1 regioisomeric TSs shows that they present a similar electronic structure. As the X1 C4 bond formation requires X1 − non-bonding electron density, the diﬀerent activation energies observed in these 32CA reactions mainly depend on the presence of V(X1) monosynaptic basins at the TACs and the energy cost associated to the depopulation of the N2 X1 and C4 C5 bonds, 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 of these TACs, which is required for the subsequent X1 C4 single bond formation, is responsible for the regioselectivity of − these low polar 32CA reactions.

Author Contributions: L.R.D. headed the subject, wrote the manuscript and performed calculations; M.R.G. headed the subject, performed calculations and wrote the manuscript; and J.C.S. performed calculations and wrote the manuscript. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by the Ministry of Science and Innovation (MICINN) of the Spanish Government, project PID2019-110776GB-I00 (AEI/FEDER, UE), and European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie, grant agreement No. 846181. Conﬂicts of Interest: There are no conﬂict to declare.

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