molecules Article The Nitrilimine–Alkene Cycloaddition Regioselectivity Rationalized by Density Functional Theory Reactivity Indices Giorgio Molteni 1 and Alessandro Ponti 2,* 1 Dipartimento di Chimica, Università degli Studi di Milano, via C. Golgi 19, 20133 Milano, Italy; [email protected] 2 Istituto di Scienze e Tecnologie Molecolari, Consiglio Nazionale delle Ricerche, via C. Golgi 19, 20133 Milano, Italy * Correspondence: [email protected]; Tel.: +39-02-5031-4280 Academic Editor: Luis R. Domingo Received: 8 November 2016; Accepted: 19 January 2017; Published: 26 January 2017 Abstract: Conventional frontier molecular orbital theory is not able to satisfactorily explain the regioselectivity outcome of the nitrilimine–alkene cycloaddition. We considered that conceptual density functional theory (DFT) could be an effective theoretical framework to rationalize the regioselectivity of the title reaction. Several nitrilimine–alkene cycloadditions were analyzed, for which we could find regioselectivity data in the literature. We computed DFT reactivity indices at the B3LYP/6-311G(2d,p)//B3LYP/6-31G(d,p) and employed the grand potential stabilization criterion to calculate the preferred regioisomer. Experimental and calculated regioselectivity agree in the vast majority of cases. It was concluded that predominance of a single regioisomer can be obtained by maximizing (i) the chemical potential difference between nitrilimine and alkene and (ii) the local softness difference between the reactive atomic sites within each reactant. Such maximization can be achieved by carefully selecting the substituents on both reactants. Keywords: 1,3-dipolar cycloaddition; nitrilimine; alkene; regioselectivity; conceptual density functional theory; reactivity indices; softness 1. Introduction Nitrilimines are 1,3-dipolar species which belong to the class of nitrilium betaines [1]. Except for a few examples [2,3], these are labile intermediates [4] which can be generated in situ by the three ways depicted in Figure1, namely: (i) base-promoted dehydrohalogenation of hydrazonoyl halides or nitrohydrazones; (ii) thermolysis of 2,5-disubstituted tetrazoles; and (iii) oxidation of aldehyde hydrazones [5]. Cycloaddition of the reactive nitrilimine intermediate A towards an array of unsaturated species gives rise to a variety of five-membered heterocycles [5]. Focusing to the alkenes as the dipolarophilic counterpart, their cycloaddition with A represents a general method for the synthesis of 4,5-dihydropyrazoles [6]. It can be easily argued that the relative orientation of the reacting species implies a regioselectivity problem. As far as monosubstituted alkenes are concerned, the nitrilimine cycloaddition with both electron-rich and electron-poor dipolarophiles generally provides 5-substituted-4,5-dihydropyrazoles (in the following: 5-substituted pyrazolines) B as the unique regioisomer. This is the case of aryl-, alkyl-, alkoxy-, alkoxycarbonyl-, and amino-alkenes [5]. Molecules 2017, 22, 202; doi:10.3390/molecules22020202 www.mdpi.com/journal/molecules Molecules 2017, 22, 202 2 of 12 Molecules 2017, 22, 202 2 of 12 1 N 2 R N R NN R1 R1 N NH R2 N NH R2 Y base Ox H Y = Cl, Br, NO2 _ + R1 N N R2 A X1 X2 X1 R1 R1 X2 R1 X1 and N 1 N X1 N X2 N X N N R2 R2 R2 BCD Figure 1. 1. GeneralGeneral picture picture describing describing the form theation formation of nitrilimine of nitrilimineintermediate intermediate (A) and their regioselectivity (A) and their towardsregioselectivity mono- towards(B) and 1,2-disubstituted mono- (B) and 1,2-disubstituted (C,D) alkenes. (C,D) alkenes. The current current view view to toexplain explain the the nitrilimine–alkene nitrilimine–alkene cycloaddition cycloaddition regioselectivity regioselectivity is based is basedupon theupon perturbation the perturbation approach approach (frontier (frontier molecular molecular orbital orbital (FMO) (FMO) theory) theory) [7,8]. [7,8 ].Within Within this this frame, frame, cycloadditions to to electron-rich alkenes are LUMO-d LUMO-dipoleipole controlled giving rise to 5-substituted pyrazolines [7]. [7]. On On the other hand, in the case of electron-poor alkenes, a dominant HOMO-dipole control should be at work giving a prevalence of 4-substituted pyrazolines. Since such a prevision is inin contrast with experimental facts, an explanation accounting for for the formation of 5-substituted pyrazolines has has been been proposed proposed assuming assuming that steric that re stericquirements requirements should overcome should overcome electronic effects electronic [5]. effectsIn [the5]. case of 1,2-disubstituted alkenes as the dipolarophilic species, nitrilimine cycloaddition generallyIn the provides case of 1,2-disubstituteda mixture of the possible alkenes pyrazolines as the dipolarophilic C and D [5,6]. species, Here nitrilimine again, the cycloaddition FMO theory providesgenerally a provides qualitative a mixture rationale of thebased possible on the pyrazolines assumptionC andthatD the[5 ,6atomic]. Here coefficients again, the FMOof the theory C=C doubleprovides bond a qualitative must have rationale similar based values on [7]. the assumption that the atomic coefficients of the C=C double bondIn must light have of the similar above values statements, [7]. it may appear that the FMO treatment of the nitrilimine–alkene cycloadditionIn light of regioselectivity the above statements, looks somewhat it may appear puzz thatling the since FMO ad treatment hoc assumptions of the nitrilimine–alkene are required to rationalizecycloaddition the regioselectivityexperimental results. looks Thus, somewhat a theoreti puzzlingcal frame since able ad hocto predict assumptions the regioselectivity are required of to therationalize nitrilimine–alkene the experimental cycloaddition results. should Thus,a be theoretical needed since, frame to able the to best predict of our the knowledge, regioselectivity no improvementof the nitrilimine–alkene over the FMO cycloaddition treatment of this should subject be has needed been since,reported to yet. the A best direct of ourapproach knowledge, to the problemno improvement would encompass over the FMO locating treatment the regioisome of this subjectric transition has been states reported (TSs) yet. and A directcomparing approach the differenceto the problem in electronic would encompassor Gibbs energy locating with the the regioisomeric experimental transitionregioselection. states These (TSs) energies and comparing should bethe computed difference at in the electronic highest or affordable Gibbs energy level with of theo thery experimental and basis set, regioselection. possibly including These energiessolvent effects. should Suchbe computed a direct approach at the highest would affordable provide levelaccurate of theory results, and which basis however set, possibly would including be based solvent on the effects.global molecularSuch a direct energies. approach For would the synthetic provide accuratechemist, results,the results which would however be woulddifficult be to based transfer on the to globalother reactionsmolecular and energies. would not For provide the synthetic further chemist,or novel insi theght results in the would structure/regioselectivity be difficult to transfer relationship. to other reactionsWe therefore and would considered not provide using further the tools or novel provided insight by in conceptual the structure/regioselectivity density functional theory relationship. (DFT) [9,10],We a theoretical therefore framework considered which using made the tools it possible provided to rigorously by conceptual define densitymany chemical functional quantities theory (e.g.,(DFT) electronegativity)[9,10], a theoretical and framework to compute which them made from it possiblethe molecular to rigorously energy defineand electron many chemicaldensity. Conceptual DFT provides many reactivity indices summarizing the changes occurring when a quantities (e.g., electronegativity) and to compute them from the molecular energy and electron molecule accepts or donates electrons during a reaction. Often, both global (molecular) and local density. Conceptual DFT provides many reactivity indices summarizing the changes occurring when reactivity indices can be defined and calculated. For instance, the local softness can be defined as the a molecule accepts or donates electrons during a reaction. Often, both global (molecular) and local derivative of the electron density with respect to the electron chemical potential at fixed molecular reactivity indices can be defined and calculated. For instance, the local softness can be defined as geometry [11]. Local indices (usually condensed to atomic indices) form a practical toolkit to study the derivative of the electron density with respect to the electron chemical potential at fixed molecular the reactivity at different sites within a molecule and provide results expressed in a language appealing to the synthetic chemist. Molecules 2017, 22, 202 3 of 12 geometry [11]. Local indices (usually condensed to atomic indices) form a practical toolkit to study Moleculesthe reactivity 2017, 22 at, 202 different sites within a molecule and provide results expressed in a language appealing3 of 12 to the synthetic chemist. Regioselectivity is is clearly amenable to investig investigationation based on local (atomic) reactivity indices and literature offers many examples of regioselectivityregioselectivity of 1,3-dipolar cycloadditions (1,3-DCs) that were successfully explained explained using using DFT-based