Introduction

Allenes present an intriguing group of reacting counterparts in [3 + 2] cycloaddition (32CA) reactions owing to the presence of two cumulative unsaturations [1]. Although the simplest allene shows limited reactivity in the 32CA reactions with C-phenyl-N-methyl nitrone 1, incorporation of electron-deficient substituents (such as cyano (2), carbomethoxy (3), phenylsulfonyl (4), methoxy (5), fluoro (6)) overcomes the unreactive nature, affording high yield of isoxazolidines under milder reaction conditions with site selectivity towards the generation of CA4-5 and CA5-6 addition (Scheme 1) [2,3,4,5,6,7]. Nitrone-allene 32CA reactions show well-established applications in the total synthesis of alkaloids and natural products [8], and also exhibit interesting selectivity and mechanistic implications. Recently, Lee et al. have reported the mechanism and selectivity of the intermolecular 32CA reactions of nitrones with activated allenes [9].

Scheme 1
scheme 1

Intermolecular 32CA reactions of nitrones and allenes

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An interesting alternative to explore the reactivity of unactivated allenes was designed by Lebel and Banucci in 1970 [10] from the intramolecular [3 + 2] cycloaddition (IM32CA) reactions of allenic nitrones, and was also reported by Padwa et al. [11] in 1993 to proceed smoothly affording reasonably good yields. The IM32CA reactions consist of both nitrone and the allenic function suitably placed in the same molecule and exhibit interesting site selectivity for the two allenic double bonds depending on the substrate. For instance, the IM32CA reaction of exocyclic nitrone 7 affords isoxazolidine 8 by addition along the terminal C5-C6 double bond, while the allenic nitrone 9 involves addition along the internal C4-C5 double bond and affords the bridged bicyclic isoxazolidine 10 (Scheme 2).

Scheme 2
scheme 2

IM32CA reactions of allenic nitrones 7 and 8

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The IM32CA reaction of the allenic nitrone 11 generated from 5,6-heptadien-2-one and N-methylhydroxylamine hydrochloride in ethanol afforded unsaturated bicyclic isoxazolidine 14 with complete site selectivity for addition along the C5-C6 terminal double bond [10] (Scheme 3). The cyclization of the homologue nitrone 12 under similar reaction conditions afforded the bicyclic adducts 15 by addition along the terminal C5-C6 double bond, and 16 by addition along the terminal C4-C5 double bond, while the latter undergoes acid-catalyzed ethanol addition to the exocyclic double bond to afford the ethers 17 and 18 (Scheme 3). The homologue nitrone 13 (n = 4) proceeded with exclusive site selectivity for addition along the internal C4-C5 double bond of the allenic function, leading to the bicyclic adduct 19 (Scheme 3). These experimental findings imply that the separation of the nitrone and the allenic functions plays the decisive role in the mode of cyclization. Although the generation of preferred adducts have been advocated qualitatively by considering the strain factor in some cases to eliminate the possibility of the competing site selectivity, yet the correlation of molecular reactivity with the electron density changes along the two feasible cumulative unsaturations are worth investigating to outline the plausible mechanism and accordingly analyze the observed selectivity of these IM32CA reactions.

Scheme 3
scheme 3

IM32CA reactions of allenic nitrones 11, 12 and 13

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The molecular electron density theory [12] (MEDT) proposed by Domingo in 2016 studies the role of electron density changes in the molecular reactivity and has emerged as an appealing alternative to the FMO theory for analysis of organic reactions. Several aspects of [3 + 2] cycloaddition (32CA) reactions [13, 14] have been successfully studied within the MEDT framework, namely the strain promotion [15, 16], reactivity [17, 18], catalysis [19, 20], substituent effects [21, 22], regio- [23, 24], stereo [25, 26] and chemoselectivity [27, 28]. Very recently, we have reported the MEDT studies for the IM32CA reactions of nitrones [29] at the MPWB1K/6-311G(d,p) level of theory, recommended as a precise computational model for the analysis of 32CA reactions.

This MEDT report is presented in five sections: (1) first, the topological analysis of the electron localization function [30, 31] (ELF) at the ground state (GS) of the reagents is performed to correlate the electronic structure and the molecular reactivity; (2) second, the electronic behaviour at the GS of the reagents is analyzed on the basis of the global reactivity indices defined with the conceptual density functional theory [32, 33] (CDFT); (3) then, the potential energy surface (PES) along the feasible reactions paths is studied to locate the stationary points and analyze the energy profile with the evaluation of global electron density transfer [34] (GEDT) at the TSs to assess the polar character; (4) the mechanistic implications are studied in terms of the bonding evolution theory [35] (BET) to analyze the changes in electron density along the preferred reaction paths; (5) finally, the electronic structure at the TSs is analyzed from the ELF study, while the interatomic interactions are characterized from the AIM [36, 37] (atoms-in-molecules) parameters and subsequent NCI-Plot [38] visualization.

Computational methods

Optimization of the reagents, TSs and the products was done using Berny analytical gradient optimization method [39] at the MPWB1K/6-311G(d,p) level of theory. The stationary points were characterized as minima by the absence of imaginary frequency, while the TSs by one imaginary frequency along each reaction path. Solvent effects in ethanol were considered by full optimization at the same computational level using polarized continuum model within the self-consistent reaction field (SCRF) framework [40,41,42]. The relative enthalpies, entropies and free energies were calculated at 298 K and 1 atm in ethanol. The intrinsic reaction coordinate [43] (IRC) calculations using the second-order Gonzales-Schlegel integration method [44, 45] were performed to verify the reaction path connecting the reactants and the products. The GEDT at the TSs was determined by GEDT (f) = \(\sum\limits_{q \in f} q\), where q is the NBO-derived charge [46, 47] at the considered reacting framework. The reactivity indices defined within the CDFT, namely the electronic chemical potential μ [48], global hardness η [49], global electrophilicity ω [50, 51] and nucleophilicity N [52], were calculated according to reference [32].

All calculations were performed using Gaussian 03 suite of programs [53]. The electron localization function [30, 31] (ELF) ((high-quality grid with a spacing of 0.06 Bohr) and AIM [36, 37] parameters were calculated using the Multiwfn software [54]. The ELF localization domains were visualized using the UCSF Chimera software [55] at an isovalue 0.86 and Visual Molecular Dynamics (VMD 1.9.3.) was used to visualize the NCI isosurfaces [56].

Results and discussion

ELF topological analysis at the ground state (GS) of the reactants

The ELF [30, 31] allows characterizing the electronic structures at the GS of the reagents and accordingly establishing the correlation with molecular reactivity. The three atom components (TACs) participating in 32CA reactions can be classified as pseudodiradical, pseudo(mono)radical, carbenoid and zwitter-ionic, respectively, within the MEDT framework [12,13,14]. The pseudodiradical TACs [57] are associated with the presence of two pseudoradical centres (monosynaptic basin integrating less than 1 e), and show highest reactivity, while the pseudo(mono)radical [58] and carbenoid TACs [59] show relatively lower reactivity and are associated respectively with the presence of a pseudoradical and a carbenoid (monosynaptic basin integrating approximately 2 e) centre. The zwitter-ionic TACs [23] show the least reactivity in 32CA reactions and do not show the presence of pseudoradical and carbenoid centres. The most significant ELF valence basin populations, attraction positions and the ELF localization domains at the GS of the allenic nitrones 11, 12 and 13 are represented in Fig. 1. The ELF of 11, 12 and 13 show the presence of monosynaptic V(O1) and V′(O1) basins integrating 5.96–5.97 e associated with the non-bonding electron density at O1 oxygen. The N2-C3 and N2-O1 bonding regions integrate at 3.92–3.94 e and 1.43–1.44 e respectively associated with the N2-C3 double bond and N2-O1 single bond. The allenic moiety shows the presence of disynaptic V(C4,C5) and V′(C4,C5) basins integrating 3.68–3.75 e associated with the underpopulated C4-C5 double bond and the disynaptic V(C5,C6) and V′(C5,C6) basins integrating 3.70–3.77 e associated with the underpopulated C5-C6 double bond. Thus, the absence of pseudoradical and carbenoid centre in the allenic nitrones 11, 12 and 13 allows their classification as the zwitter-ionic TACs associated with high energy barrier.

Fig. 1
figure 1

MPWB1K/6-311G(d,p) calculated total electron density (isovalue = 0.1) and ELF localization domains (isovalue = 0.81) of gas phase allenic nitrones 11, 12 and 13 along with the most significant ELF basin populations. Protonated basins are shown in blue, monosynaptic basins in red, disynaptic basins in green and the core basins in black colour. ELF attractor positions are shown in pink colour

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After establishing the electronic structure of the TACs, the proposed Lewis-like structures on the basis of ELF study is represented in Fig. 2 along with the NBO-derived charges. O1 of the nitrone moiety is negatively charged by −0.60 e, while C3 is positively charged by + 0.25 e, with the negligible charge 0.08 e at N2. In the allenic part, the terminal C6 carbon is negatively charged by −0.47 e, while C4 shows the negative charge of −0.28 e and −0.29 e owing to the alkyl chain substitution.

Fig. 2
figure 2

Proposed Lewis-like structures together with the natural atomic charges in average number of electrons, e, of the allenic nitrones 11, 12 and 13. Negative, negligible and positive charges are shown in red, green and blue colours, respectively

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Analysis of the CDFT indices

The reactivity indices defined with the CDFT [32, 33] have been employed in numerous studies [12,13,14,15,16,17,18,19,20,21,22] to analyze the electronic behaviour at the GS of the reagents. The electronic chemical potential µ [48], chemical hardness η [49], global electrophilicity ω [50, 51] and global nucleophilicity N [52] at the GS of the allenic nitrones 11, 12 and 13 are calculated at the B3LYP/6-31G(d) level of theory (Table 1) to characterize the reagents within the standard electrophilicity and nucleophilicity scales defined at the same computational level [51]. The electronic chemical potentials µ of the allenic nitrones are between −2.75 eV and −2.83 eV, showing minimal increase from 11 to 13 with the increase in the alkyl chain length separation between the nitrone and the allene moieties. The nitrones are classified as marginal electrophiles (ω < 0.80 eV) within the electrophilicity scale and strong nucleophiles (N > 3.00 eV) within the standard nucleophilicity scale.

Table 1 B3LYP/6-31G(d) calculated electronic chemical potential µ, chemical hardness η, global electrophilicity ω and global nucleophilicity N, in eV at the ground state of the allenic nitrones 11, 12 and 13
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Exploring the potential energy surface along the IM32CA reactions of the allenic nitrones 11–13

Herein, the two feasible reaction channels associated with the IM32CA reactions of allenic nitrones 11–13 involving the addition of the nitrone moiety to the terminal C5-C6 double bond and to the internal C4-C5 double bond have been studied (Scheme 4).

Scheme 4
scheme 4

Studied reaction paths for the IM32CA reactions of allenic nitrones

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Search for the stationary points along these reaction paths allowed locating the reagents, only one TS and the bicyclic adduct in each case, suggesting one-step mechanism. The TSs and adducts associated with the addition along the C5-C6 and C4-C5 double bonds are respectively prefixed as TS1 and TS2, followed by 2, 3 and 4 respectively indicating the number of CH2 groups separating the nitrone and the allenic function. Thus, TS1-2, TS1-3 and TS1-4 are the TSs associated with the addition of the nitrone moiety of the reagents 11, 12 and 13 along the C5-C6 double bond respectively leading to the bicyclic adducts 14, 15 and 20, while TS2-2, TS2-3 and TS2-4 are associated with the addition of nitrone moiety of the reagents 11, 12 and 13 along the C4-C5 double bond respectively leading to the bicyclic adducts 21, 16 and 19. The relative energies, enthalpies, entropies and free energies in ethanol of the TSs and adducts are given in Table 2. The total thermodynamic data are gathered in the Supplementary Information. The studied IM32CA reactions are exergonic, with reaction free energies between −17.3 and −35.1 kcal mol−1, suggesting kinetic control and show activation free energies between 22.2 and 34.9 kcal mol−1, consistent with the zw- type character. Some appealing conclusions can be derived from the relative free energies. (1) For the IM32CA reaction of nitrone 11, the activation free energy of TS1-2 associated with addition along the C5-C6 bond is lowered by 5.9 kcal mol−1 relative to that of TS2-2 associated with the addition along the C4-C5 bond. This is in complete agreement with the experimental results [10] showing exclusive formation of the unsaturated bicyclic isoxazolidine 14. (2) The activation free energy of TS1-2 is lowered than that of TS1-3 and TS1-4 by 4.3 and 12.7 kcal mol−1 suggesting that the addition of the nitrone moiety to the terminal C5-C6 double bond of the allenic function is relatively more feasible when the nitrone and the allene groups are separated by two methylene units. (3) For the IM32CA reaction of nitrone 13, the activation free energy of TS2-4 associated with addition along the C4-C5 bond is lowered by 7.7 kcal mol−1 relative to that of TS1-4 associated with the addition along the C5-C6 bond. This is in complete agreement with the experimental results showing exclusive formation of the bicyclic isoxazolidine 19 [10]. (3) These unimolecular IM32CA reactions show negative relative entropies of the TSs between −9.2 and −20.4 kcal mol−1 and that of the adducts are between −12.7 and −25.6 kcal mol−1. Note that the relative entropies of 19 and 20 differ by 0.1 kcal mol−1, that of 15 and 16 differ by 2.2 kcal mol−1 and that of 14 and 21 differ by 2.8 kcal mol−1 suggesting the influence of ring size on the entropy differences of the two possible adducts. Inclusion of thermodynamic correction decreases the activation enthalpies by 0.6–1.3 kcal mol−1 relative to the activation energies, while the reaction enthalpies are increased by 0.4–1.9 kcal mol−1 relative to the reaction energies.

Table 2 MPWB1K/6-311G(d,p) relative energies in gas phase and the relative energies, enthalpies, entropy and free energies in ethanol at 298.15 K, in kcal·mol−1, of TSs and cycloadducts for the IM32CA reactions of allenic nitrones 11, 12 and 13
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The MPWB1K/6-311G(d,p) optimized geometries of the TSs in ethanol are shown in Fig. 3, with the bond distances between the four interacting atomic centres, GEDT and the imaginary frequencies in gas phase and ethanol are given in Table 3. The distances between the C–C interacting centres are greater than 2.0 Å, and that between the C-O interacting centres are greater than 1.9 Å suggesting that the formation of new C–C and C-O covalent bond formation has not been started at the TSs, considering the formation of C–C bonds at 1.9–2.0 Å and the C-O bonds at 1.7–1.8 Å [13]. This is in complete agreement with the ELF and AIM studies (“ELF and AIM topological analyses of the electron density at the TSs associated with the IM32CA reactions” section). Note that TS2-2, TS2-3 and TS2-4 associated with the addition along the C4-C5 double bond are more asynchronous and relatively more advanced compared to TS1-2, TS1-3 and TS1-4 associated with the addition along the C5-C6 double bond.

Fig. 3
figure 3

MPWB1K/6-311G(d,p) optimized geometries of the TSs in ethanol

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Table 3 MPWB1K/6-311G(d,p) calculated forming bond distances (Å), imaginary frequencies (cm−1) at optimized TSs and GEDT in average number of electrons associated with the IM32CA reactions of allenic nitrones 11, 12 and 13
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The GEDT [34] allows evaluating the flux of electron density at the TSs and hence the polar character. GEDT values above 0.2 e are associated with polar reactions, while those below 0.1 e are the non-polar ones. Accordingly, the calculated GEDT values at the TSs are given in Table 4. In both gas phase and ethanol, the GEDT values are between 0.01 and 0.06 e, indicating non-polar character allowing the classification of these zw- type 32CA reactions as the null electron density transfer (NEDF) [60] type. The predicted non-polar character is consistent with the calculated high activation parameters associated mainly with the rupture of the C–C double bond revealed from the ELF topological analysis along the reaction paths (“Revealing the molecular mechanism and flux of electron density along the reaction paths associated with the IM32CA reactions of the allenic nitrones 11 and 13” section).

Table 4 ELF valence basin populations at the MPWB1K/6-311G(d,p) optimized gas phase TSs associated with the IM32CA reactions of the allenic nitrones 11, 12 and 13
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Revealing the molecular mechanism and flux of electron density along the reaction paths associated with the IM32CA reactions of the allenic nitrones 11 and 13

The bonding evolution theory (BET) [35] is a quantum chemical methodology to establish the molecular mechanism of a chemical reaction by studying the nature of electronic rearrangement along a reaction path. The bonding changes are analyzed topologically and energetically within the MEDT perspective, allowing a complete understanding of the bonding changes and the origin of the energy profile. Herein, the molecular mechanism of the preferred reaction paths for the IM32CA reaction of the allenic nitrones 11 and 13, leading to the adducts 14 and 19, is studied. The complete BET studies are given in the Supplementary material. In this section, we explain the appealing conclusions arising from these BET studies in a chemical fashion.

(1) The molecular mechanism associated with the IM32CA reactions of the allenic nitrones 11 and 13 are represented in Schemes 5 and 6 respectively. The IM32CA reaction of 11 can be topologically characterized by eight differentiated phases while that of 13 by seven topological phases. (2) For the IM32CA reaction of 11, the starting structure of the phases is denoted as S0-I, S1-I, S2-I, S3-I, S4-I, S5-I, S6-I and S7-I, and for that of 13 is represented as S0-II, S1-II, S2-II, TS2-4, S3-II, S4-II and S5-II. (3) For the IM32CA reaction of 11, S1-I is associated with the creation of non-bonding electron density at N2 nitrogen with energy cost (EC) of 15.4 kcal·mol−1, S2-I is associated with the rupture of C5-C6 double bond with energy cost (EC) of 16.2 kcal·mol−1, S3-I is associated with the formation of pseudoradical centre at C3 with energy cost (EC) of 16.6 kcal·mol−1 and TS1-2 with the EC of 16.9 kcal·mol−1 belongs to Phase-III. Therefore, the activation energy associated with this IM32CA reaction is related to the formation of non-bonding electron density at N2 nitrogen, rupture of C5-C6 double bond and the creation of pseudoradical centre at C3 carbon. The subsequent phases are related to the creation of pseudoradical centre at C5 (S4-I), formation of C3-C5 single bond (S5-I), creation of pseudoradical centre at C6 (S6-I) and finally the formation of O1-C6 single bond (S7-I). The ELF localization domains of these structures are given in Fig. 4. The formation of second O1-C6 bond begins when the first C3-C5 bond formation has been completed by 94%, suggesting two-stage one-step mechanism.

Scheme 5
scheme 5

Simplified representation of the molecular mechanism of the reaction path associated with the IM32CA reaction of allenic nitrone 11 leading to adduct 14 arising from the topological analysis of the ELF

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Scheme 6
scheme 6

Simplified representation of the molecular mechanism of the reaction path associated with the IM32CA reaction of allenic nitrone 13 leading to adduct 19 arising from the topological analysis of the ELF

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Fig. 4
figure 4

MPWB1K/6-311G(d,p) ELF localization domains of S4-I, S5-I, S6-I and S7-I associated with the formation of C3-C5 and O1-C6 bonds in the IM32CA reaction of allenic nitrone 11 (protonated basins are shown in blue, monosynaptic basins in red, disynaptic basins in green and the core basins in black colour (isovalue = 0.85). The ELF attractors are shown in pink colour

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(4) For the IM32CA reaction of 13, S1-II is associated with the creation of non-bonding electron density at N2 nitrogen and rupture of the C4-C5 double bond with energy cost (EC) of 17.2 kcal·mol−1, TS2-4 is associated with the formation of pseudoradical centre at C4 with energy cost (EC) of 17.8 kcal·mol−1. Therefore, the activation energy associated with this IM32CA reaction is related to the formation of non-bonding electron density at N2 nitrogen, rupture of C4-C5 double bond and the creation of pseudoradical centre at C4 carbon. The subsequent phases are related to the creation of pseudoradical centre at C3 (S2-II), creation of pseudoradical centre at C5 (S3-II), formation of C3-C4 single bond (S4-II) and finally the formation of O1-C5 single bond (S5-II). The ELF localization domains of these structures are given in Fig. 5. The formation of second O1-C5 bond begins when the first C3-C4 bond formation has been completed by 77%, suggesting asynchronous one-step mechanism for this IM32CA reaction. (5) The minimal GEDT along the reaction path to reach the TSs establishes non-polar character of these IM32CA reactions consistent with the high activation energies.

Fig. 5
figure 5

MPWB1K/6-311G(d,p) ELF localization domains of S2-II, S3-II, S4-II and S5-II associated with the formation of C3-C4 and O1-C5 bonds in the IM32CA reaction of allenic nitrone 13 (protonated basins are shown in blue, monosynaptic basins in red, disynaptic basins in green and the core basins in black colour (isovalue = 0.85). The ELF attractors are shown in pink colour

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ELF and AIM topological analyses of the electron density at the TSs associated with the IM32CA reactions

Finally, the ELF topological analysis at the TSs involved in the 32CA reactions was performed. The relevant valence basin populations are given in Table 4 and the ELF localization domains are shown in Fig. 6. TS1-2, TS1-3 and TS1-4 associated with the addition along the C5-C6 bond of the allenic nitrones 11, 12 and 13 present similar ELF topology, and that of TS2-2, TS2-3 and TS2-4 associated with the addition along the C4-C5 bond show similitude in the electronic structure. All six TSs show the presence of V(N2) monosynaptic basin integrating 1.19–1.32 e associated with the accumulation of non-bonding electron density at N2 nitrogen, which is not found in the allenic nitrones 11–13. The ELF of TS1-2, TS1-3 and TS1-4 shows the formation of V(C3) monosynaptic basin integrating 0.36–0.39 e associated with the presence of pseudoradical centre at C3, which is not found in TS2-2, TS2-3 and TS2-4. Note that to create the pseudoradical centre at C3 carbon and non-bonding electron density at N2 nitrogen, the N2-C3 bonding region at TS1-2, TS1-3 and TS1-4 experiences depopulation between 1.27 e and 1.41 e relative to the separated reagents, while this depopulation is between 0.98 e and 1.01 e at TS2-2, TS2-3 and TS2-4, since the non-bonding electron density at N2 nitrogen is only formed in these three TSs. The N2-O1 bonding region is also depopulated between 0.12 e and 0.15 e at TS1-2, TS1-3 and TS1-4 and between 0.15 e and 0.20 e at TS2-2, TS2-3 and TS2-4 to contribute for the accumulation of non-bonding electron density at the N2 nitrogen. Interestingly, TS1-4 shows the presence of V(C5) monosynaptic basin integrating 0.59 e deriving electron density from the C4-C5 bonding region, while no such change in electronic structure is observed in TS1-2 and TS1-3. On the other hand, TS2-2, TS2-3 and TS2-4 show the presence of V(C4) monosynaptic basin integrating 0.45 e, 0.37 e and 0.38 e respectively associated with the formation of pseudoradical centre at C4 carbon, the electron density of which comes from the depopulation of the C4-C5 bonding region along the reaction path. Note that the addition along the C5-C6 and C4-C5 bonds of the allenic nitrones show varied pattern of changes in electron density and accordingly follow different molecular mechanism. Finally, the absence of disynaptic basins associated with the formation of new covalent bonds reveal early nature of these TSs in each case in which the new covalent bonds have not been started.

Fig. 6
figure 6

MPWB1K/6-311G(d,p) ELF localization domains of the TSs associated with the IM32CA reactions of nitrones 11, 12 and 13 (protonated basins are shown in blue, monosynaptic basins in red, disynaptic basins in green and the core basins in black colour (isovalue = 0.85)

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The topological analysis of the AIM was performed to characterize the interatomic interactions at the TSs. The AIM parameters, namely the total electron density ρ and the Laplacian of electron density \(\nabla^{2} \rho (r_{c} )\), at the bond critical points BCP1 and BCP2 associated respectively with the forming C–C and C-O bonds are given in Table 5. The total electron density ρ less than 0.1 au and the positive Laplacian of electron density indicate non-covalent interactions in each case, consistent with the ELF topological analysis and the forming bond distances greater than 2.0 Å. The NCI isosurfaces at TS1-2, TS1-3 and TS1-4 represented in Fig. 7 show green isosurfaces at the interatomic regions, indicative of weak non-covalent interactions.

Table 5 Total electron density, ρ (a.u.), Laplacian of electron density \(\nabla^{2} \rho (r_{c} )\) (a.u.) of BCP1 and BCP2 at the TSs associated with the IM32CA reactions in gas phase and in ethanol
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Fig. 7
figure 7

NCI isosurfaces (isovalue = 0.5), in the range –0.04 < sign(λ2)ρ < 0.04 a.u., of TS1-2, TS1-3 and TS1-4

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Conclusion

The zw- type intramolecular 32CA reactions of allenic nitrones 11, 12 and 13 experimentally reported by Lebel and Banucci [10] have been studied within MEDT at the MPWB1K/6-311G(d,p) computational level. The topological analysis of the ELF of the nitrones 11, 12 and 13 allows establishing their zwitter-ionic structure. Analysis of the global reactivity indices defined within CDFT classifies the nitrones as strong nucleophiles and marginal electrophiles. These IM32CA reactions follow non-concerted one-step mechanism with asynchronous TSs. In the allenic nitrone 11, the nitrone and allenic frameworks are separated by two methylene groups and the addition is energetically preferred along the C5-C6 double bond, while for the allenic nitrone 13, in which the nitrone and allenic frameworks are separated by four methylene groups, the addition takes place exclusively along the C4-C5 double bond of the allene. This study allows understanding the cyclization selectivity in intramolecular 32CA reactions of allenic nitrones. The molecular mechanism revealed from the bonding evolution theory predicts varied changes in the electron density along the reaction paths associated with the IM32CA reactions of the nitrones 11 and 13. However, in each case, the early TSs are located in which the formation of new C–C and C-O covalent bonds have not been started.