A Molecular Electron Density Theory Study of the [3+2] Cycloaddition Reaction of an Azomethine Ylide with an Electrophilic Ethylene Linked to Triazole and Ferrocene Units

The [3+2] cycloaddition (32CA) reaction of an azomethine ylide (AY) with an electrophilic ethylene linked to triazole and ferrocene units has been studied within the Molecular Electron Density Theory (MEDT) at the ωB97X-D/6-311G(d,p) level. The topology of the electron localization function (ELF) of this AY allows classifying it as a pseudo(mono)radical species characterized by the presence of two monosynaptic basins, integrating a total of 0.76 e, at the C1 carbon. While the ferrocene ethylene has a strong electrophilic character, the AY is a supernucleophile, suggesting that the corresponding 32CA reaction has a high polar character and a low activation energy. The most favorable ortho/endo reaction path presents an activation enthalpy of 8.7 kcal·mol−1, with the 32CA reaction being exergonic by −42.1 kcal·mol−1. This reaction presents a total endo stereoselectivity and a total ortho regioselectivity. Analysis of the global electron density transfer (GEDT) at the most favorable TS-on (0.23 e) accounts for the high polar character of this 32CA reaction, classified as forward electron density flux (FEDF). The formation of two intermolecular hydrogen bonds between the two interacting frameworks at the most favorable TS-on accounts for the unexpected ortho regioselectivity experimentally observed.


Introduction
The construction of enantiomerically pure compounds has experienced a significant progress during recent decades by asymmetric reactions using organocatalysis, chiral susbtrates/auxiliaries, and reagents able to control the stereochemistry of desired enantioselective molecules. To synthesize pharmacologically active chiral molecules for specific receptors or proteins, the establishment of structure−function relationships and mechanistic studies are indispensable. The [3+2] cycloaddition (32CA) reactions, which have proved to be highly selective, efficient, environment-friendly and atom-economical, are among the most efficient asymmetric reactions to construct pharmacologically active chiral molecules in a regio-and/or stereoselective fashion [1][2][3][4].
Organic chemists have been extensively made great efforts to understand the electronic structure of three-atom-components (TACs) generated in situ as intermediates in 32CA reactions. Based on the recently proposed Molecular Electron Density Theory (MEDT) [5], four different types of TACs, namely zwitterionic (zw), carbenoid (cb), pseudo(mono)radical (pmr), and pseudodiradical (pdr) TACs, and their reactivity towards ethylene have been characterized [6]. Notably, pseudo(mono)radical and pseudodiradical TACs are very reactive due to their instability. These electronic structures and the corresponding reactivities can be modified by substitution.
TACs are very reactive due to their instability. These electronic structures and the corresponding reactivities can be modified by substitution.
Pyrrolidines are five-membered heterocyclic compounds used as pharmacologically relevant scaffolds in drug design [7][8][9], which can be easily constructed by 32CA reaction of AYs with olefins (see Scheme 1). On the other hand, the introduction of a spiro-ring in heterocyclic compounds is a widely used strategy in drug design to provide additional conformational restriction. Thus, the 32CA reaction of exocyclic AY 4 generated from isatin, i.e., a dicarbonyl compound, yields spirooxindoles 6, which possesses significant pharmacological properties [10][11][12][13][14]. MEDT studies of the 32CA reactions of the simplest AY 7, CH2-NH-CH2 [15], and carbonyl ylide 8, CH2-O-CH2 [16], have shown that the presence of a pseudoradical center at each one of the two methylene carbons of these TACs causes the corresponding pdr-type 32CA reactions with non-activated ethylenes to have an unappreciable activation energy, lower than 1.0 kcal·mol −1 . However, the presence of an electron-releasing phenyl group and electron-withdrawing (EW) carboxyl -CO2R or nitrile -CN groups at the two methylenes of the simplest AY 7, just as AY 1, stabilizes its pseudodiradical electronic structure, modifying the experimental reactivity of these substituted AYs to that of pseudo(mono)diradical [17], carbenoid [18], or even zwitterionic TACs [19].
Recently, Barakat and co-workers experimentally studied the synthesis of spirooxindoles 11 and 12 via 32CA reactions of AYs 9, generated from substituted isatins and secondary amines, with disubstituted olefins, in excellent regio-and stereoselectivity (see Scheme 2) [20][21][22]. The plausible reaction mechanism was suggested to take place via an endo stereoisomeric path in which the substitution of the olefin derivatives 10 plays a crucial role in the regioselective formation of the products 11 or 12. Scheme 2. 32CA reactions of AYs 9 derived from indol-2,3-diones.
Thus, the 32CA reaction of AY 13 with phenyl vinyl sulphone 14 yields the spirooxindole 15 with total meta regio-and endo stereoselectivity (see Scheme 3) [23]. A MEDT study of the 32CA reaction of model AY 16 with phenyl vinyl sulphone 14 [24] showed that this 32CA reaction takes place via a two-stage one-step [25] mechanism involving a highly asynchronous transition-state structure (TS), with a high endo stereoselectivity and high meta regioselectivity. The reaction presents a very low activation enthalpy, 5.7 Scheme 2. 32CA reactions of AYs 9 derived from indol-2, 3-diones. Thus, the 32CA reaction of AY 13 with phenyl vinyl sulphone 14 yields the spirooxindole 15 with total meta regio-and endo stereoselectivity (see Scheme 3) [23]. A MEDT study of the 32CA reaction of model AY 16 with phenyl vinyl sulphone 14 [24] showed that this 32CA reaction takes place via a two-stage one-step [25] mechanism involving a highly asynchronous transition-state structure (TS), with a high endo stereoselectivity and high meta regioselectivity. The reaction presents a very low activation enthalpy, 5.7 kcal·mol −1 , as a consequence of the strong polar character of the reaction; the global electron density transfer (GEDT) [26] at the most favorable meta/endo TS was 0.31 e. This behavior is a consequence of the supernucleophilic character of AY 16 and the strong electrophilic character of vinyl sulphone 14. The meta regioselectivity was explained by the more favorable Herein, the 32CA reaction of AY 21 with ferrocene ethylene 22 yielding spirooxindole 23, as a computational model of the 32CA reaction studied by Barakat et al., is theoretically studied within the MEDT in order to understand the behavior of the 32CA reactions involving ferrocene ethylene derivatives (see Scheme 4) and the origin of the unexpected ortho regioselectivity. The ferrocene scaffold is an interesting organometallic architecture with a diversity of applications in medicine, photochemistry, as well as a building block for many organic synthetic transformations [28][29][30][31]. Many synthesized or naturally occurring organic compounds incorporating the ferrocene unit possess pharmacological activity which is sold in the market or in more advanced preclinical stages. Introducing the ferrocene synthon into the spirooxindoles scaffold is challenging for experimental chemists.
Very recently, Barakat et al. have experimentally reported the 32CA reaction of AY 18 with ethylene derivative 19, in the synthesis of spirooxindoles 20, with high ortho regioand endo stereoselectivity (see Scheme 4) [45]. Interestingly, this 32CA shows an opposite regioselectivity to that shown in the reaction with vinyl sulphone 14 (see Scheme 3).
Molecules 2022, 27, x FOR PEER REVIEW 3 of 16 kcal·mol −1 , as a consequence of the strong polar character of the reaction; the global electron density transfer (GEDT) [26] at the most favorable meta/endo TS was 0.31 e. This behavior is a consequence of the supernucleophilic character of AY 16 and the strong electrophilic character of vinyl sulphone 14. The meta regioselectivity was explained by the more favorable two-center interaction between the most nucleophilic center of AY 16, the C1 carbon, and the more electrophilic center of phenyl vinyl sulphone 14, the C4 carbon, anticipated by the analysis of the Parr functions [27].
The ferrocene scaffold is an interesting organometallic architecture with a diversity of applications in medicine, photochemistry, as well as a building block for many organic synthetic transformations [28][29][30][31]. Many synthesized or naturally occurring organic compounds incorporating the ferrocene unit possess pharmacological activity which is sold in the market or in more advanced preclinical stages. Introducing the ferrocene synthon into the spirooxindoles scaffold is challenging for experimental chemists.
Very recently, Barakat et al. have experimentally reported the 32CA reaction of AY 18 with ethylene derivative 19, in the synthesis of spirooxindoles 20, with high ortho regioand endo stereoselectivity (see Scheme 4) [45]. Interestingly, this 32CA shows an opposite regioselectivity to that shown in the reaction with vinyl sulphone 14 (see Scheme 3). Herein, the 32CA reaction of AY 21 with ferrocene ethylene 22 yielding spirooxindole 23, as a computational model of the 32CA reaction studied by Barakat et al., is theoretically studied within the MEDT in order to understand the behavior of the 32CA reactions involving ferrocene ethylene derivatives (see Scheme 4) and the origin of the unexpected ortho regioselectivity.

Results and Discussion
The present MEDT study has been divided in four sections: (i) first, an ELF topological analysis at the ground state of AY 21 and ferrocene ethylene derivative 22 is performed; (ii) in the second part, the conceptual DFT (CDFT) reactivity indices at the ground state of the reagents are analyzed; (iii) in the third part, the competitive reaction paths associated with the 32CA reaction of AY 21 with ferrocene ethylene 22 are studied; and (iv) the origin of the ortho regioselectivity is finally analyzed.

ELF Topological Analysis at the Ground State of AY 21 and Ferrocene Ethylene Derivative 22
The topological analysis of the electron localization function (ELF) [46] at the ground state allows a quantitative and qualitative description of the electronic structure of organic molecules [47]. Given the structure−reactivity relationship found in TACs [6], an ELF topological analysis of AY 21 was first performed in order to characterize its electronic structure and gain some insight about its reactivity. The most significant ELF basin attractor positions and valence basin populations of AY 21 and ferrocene ethylene 22 are given in Figure 1.

Results and Discussion
The present MEDT study has been divided in four sections: (i) first, an ELF topological analysis at the ground state of AY 21 and ferrocene ethylene derivative 22 is performed; (ii) in the second part, the conceptual DFT (CDFT) reactivity indices at the ground state of the reagents are analyzed; (iii) in the third part, the competitive reaction paths associated with the 32CA reaction of AY 21 with ferrocene ethylene 22 are studied; and (iv) the origin of the ortho regioselectivity is finally analyzed.

ELF Topological Analysis at the Ground State of AY 21 and Ferrocene Ethylene Derivative 22
The topological analysis of the electron localization function (ELF) [46] at the ground state allows a quantitative and qualitative description of the electronic structure of organic molecules [47]. Given the structure−reactivity relationship found in TACs [6], an ELF topological analysis of AY 21 was first performed in order to characterize its electronic structure and gain some insight about its reactivity. The most significant ELF basin attractor positions and valence basin populations of AY 21 and ferrocene ethylene 22 are given in Figure 1. The ELF of AY 21 shows the presence of two monosynaptic basins, V(C1) and V'(C1), integrating a total of 0.77 e, one V(C1,N2) disynaptic basin integrating 2.29 e and one V(N2,C3) disynaptic basin integrating 3.43 e, characterizing the C1-N2-C3 AY core. While the V(C1,N2) disynaptic basin is associated with a C1-N2 single bond, the V(N2,C3) disynaptic basin is associated with a somewhat underpopulated N2-C3 double bond. The presence of the two monosynaptic basins at the C1 carbon integrating less than 1.0 e, which are associated with a pseudoradical C1 center [15], allows the classification of AY 21 as a pseudo(mono)radical TAC participating in pmr-type 32CA reactions [6]. The ELF of AY 21 shows the presence of two monosynaptic basins, V(C1) and V'(C1), integrating a total of 0.77 e, one V(C1,N2) disynaptic basin integrating 2.29 e and one V(N2,C3) disynaptic basin integrating 3.43 e, characterizing the C1-N2-C3 AY core. While the V(C1,N2) disynaptic basin is associated with a C1-N2 single bond, the V(N2,C3) disynaptic basin is associated with a somewhat underpopulated N2-C3 double bond. The presence of the two monosynaptic basins at the C1 carbon integrating less than 1.0 e, which are associated with a pseudoradical C1 center [15], allows the classification of AY 21 as a pseudo(mono)radical TAC participating in pmr-type 32CA reactions [6].
On the other hand, the ELF of ferrocene ethylene derivative 22 shows the presence of two disynaptic basins, V(C4,C5) and V'(C4,C5) integrating a total of 3.32 e, a V(C5,C6) disynaptic basin integrating 2.29 e, one V(C6,O7) disynaptic basin integrating 2.25 e, and two monosynaptic basins, V(O7) and V'(O7) integrating a total of 5.35 e. While the two V(C4,C5) and V'(C4,C5) disynaptic basins are associated with an underpopulated C4-C5 double bond, the V(C6,O7) disynaptic basin is associated with a carbonyl C6-O7 single bond, resulting from a strong polarization of the C6-O7 bonding region towards the electronegative O7 oxygen, which shows a non-bonding region with a high electron density.
Natural Population Analysis (NPA) [48,49] of the charge distribution shows that the two reactive carbons of AY 21 are negligibly charged by less than ± 0.08 e while the N2 nitrogen is negatively charged by −0.26 e. Interestingly, the natural charges of ethylene derivative 22 indicate that the C4 and C5 carbons are negatively charged by −0.32 and −0.09 e, respectively while the carbonyl C6 carbon is strongly positively charged by 0.53 e as a consequence of the strong polarization of the carbonyl C6-O7 bonding region towards the electronegative O7 oxygen, which has a negative charge of −0.60 e.

CDFT Analysis at the Ground State of the Reagents
The reactivity indices defined within CDFT [50,51] have shown to be powerful tools to understand the reactivity in polar reactions [52]. The global reactivity indices, namely, the electronic chemical potential µ, chemical hardness η, electrophilicity ω, and nucleophilicity N indices, of AY 21 and ferrocene ethylene 22 are gathered in Table 1. The electronic chemical potential [53] of AY 21 with µ = −2.79 eV is higher than that of ferrocene ethylene 22 with µ = −3.53 eV, indicating that along a polar 32CA reaction the GEDT [26] will take place from AY 21 to ferrocene ethylene 22, the corresponding polar 32CA reaction being classified as of forward electron density flux (FEDF) [54].
AY 21 presents an electrophilicity ω index [55] of 1.17 eV, being classified as a moderate electrophile within the electrophilicity scale [51], and a nucleophilicity N index [56] of 4.67 eV, being classified as a strong nucleophile within the nucleophilicity scale [51]. The strong nucleophilic character of AY 21, higher than 4.0 eV, allows its classification as a supernucleophile [57]. On the other hand, ferrocene ethylene 22 presents an electrophilicity ω index of 1.72 eV, being classified as a strong electrophile, and a nucleophilicity N index of 3.78 eV, being also classified as a strong nucleophile. The supernucleophilic character of AY 21, together with the strong electrophilic character of ferrocene ethylene 22, indicates that the corresponding 32CA reaction will have a high polar character, being classified as FEDF [54].
In a polar 32CA reaction involving non-symmetric species, the most favorable reaction path is that involving the two-center interaction between the most electrophilic and the most nucleophilic centers of the two reagents [58]. Many studies have shown that the electrophilic P k + and nucleophilic P k − Parr functions [27], resulting from the excess of spin electron density gathered via the GEDT, are among the most accurate tools for the analysis of the local reactivity in polar and ionic processes [52]. Hence, according to the characteristics of the reagents, the nucleophilic P k − Parr functions of AY 21 and the electrophilic P k + Parr functions of ferrocene ethylene 22 were analyzed (see Figure 2).  The two C1 and C3 carbons of AY 21 are nucleophilically activated by Pk − = 0.38 and 0.32, respectively, with the C1 carbon being the most nucleophilic center of the TAC. Note that the N2 nitrogen is nucleophilically deactivated (Pk − = −0.12). On the other hand, the βconjugated C4 position of ferrocene ethylene 22 is the most electrophilically activated of this species (Pk + = 0.25).
Based on the analysis of the Parr functions, the meta regioisomer is expected to be the preferred one as a consequence of the slightly higher nucleophilic activation of the C1 carbon of AY 21 than that of the C3 one.

Analysis of the Competitive Reaction Paths Associated with the 32CA Reaction of AY 21 with Ferrocene Ethylene 22
In order to determine the mechanism of this 32CA reaction, the competitive reaction paths associated with the 32CA reaction of AY 21 with ferrocene ethylene 22 were analyzed. Due to the non-symmetry of both reagents, two pairs of endo and exo stereoisomeric reaction paths and two pairs of ortho and meta regioisomeric ones are possible (see Scheme 5). The analysis of the stationary points found along with these reaction paths indicates that this 32CA reaction takes place through a one-step mechanism. The ωB97X-D/6-311G(d,p) relative electronic energies, in gas phase and in methanol, are given in Table 2. Total electronic energies are given in Table S1 in Supplementary Materials.
An exhaustive analysis of the potential energy surface associated with this 32CA reaction allowed finding a series of molecular complexes (MCs), which are in equilibrium, in an early stage of the reaction. The most favorable MC-on, which opens the ortho/endo reaction path, is found to be 25.6 kcal·mol −1 more stable than the separated reagents (see Scheme 5). The two C1 and C3 carbons of AY 21 are nucleophilically activated by P k − = 0.38 and 0.32, respectively, with the C1 carbon being the most nucleophilic center of the TAC. Note that the N2 nitrogen is nucleophilically deactivated (P k − = −0.12). On the other hand, the β-conjugated C4 position of ferrocene ethylene 22 is the most electrophilically activated of this species (P k + = 0.25). Based on the analysis of the Parr functions, the meta regioisomer is expected to be the preferred one as a consequence of the slightly higher nucleophilic activation of the C1 carbon of AY 21 than that of the C3 one. In order to determine the mechanism of this 32CA reaction, the competitive reaction paths associated with the 32CA reaction of AY 21 with ferrocene ethylene 22 were analyzed. Due to the non-symmetry of both reagents, two pairs of endo and exo stereoisomeric reaction paths and two pairs of ortho and meta regioisomeric ones are possible (see Scheme 5). The analysis of the stationary points found along with these reaction paths indicates that this 32CA reaction takes place through a one-step mechanism. The ωB97X-D/6-311G(d,p) relative electronic energies, in gas phase and in methanol, are given in Table 2. Total electronic energies are given in Table S1 in Supplementary Materials.
An exhaustive analysis of the potential energy surface associated with this 32CA reaction allowed finding a series of molecular complexes (MCs), which are in equilibrium, in an early stage of the reaction. The most favorable MC-on, which opens the ortho/endo reaction path, is found to be 25.6 kcal·mol −1 more stable than the separated reagents (see Scheme 5). Some appealing conclusions can be obtained from the analysis of the relative energies of the stationary points involved in this 32CA reaction: (i) the most favorable TS-on is found to be 17.1 kcal·mol −1 below the separate reagents; (ii) however, when the formation of MC-on is considered, the activation energy of this 32CA reaction becomes positive at 8.5 kcal·mol −1 ; (iii) this 32CA reaction is strongly exothermic by −49.9 kcal·mol −1 . Consequently, the formation of the experimental spirooxindole 23 takes place by kinetic control. Note that the reaction is strongly exergonic by −22.4 kcal·mol −1 (see later); (iv) this 32CA reaction is completely ortho regioselective, as TS-mn is found to be 5.3 kcal·mol −1 above TS-on; and (v) this 32CA reaction is completely endo stereoselective, as TS-ox is found to be 8.3 kcal·mol −1 above TS-on.
Inclusion of solvent effects of methanol stabilizes all species by between 15.3 and 19.7 kcal·mol −1 ; the reagents are the most stabilized [59]. As a consequence, the relative energies of the TSs increase by between 2.5 and 5.9 kcal·mol −1 . In methanol, the activation energy increases by 0.9 kcal·mol −1 , and the 32CA reaction remains completely regio-and stereoselective, as TS-mn and TS-ox are found to be 4.0 and 5.0 kcal·mol −1 , respectively, above TSon. The 32CA reaction remains strongly exothermic by −45.2 kcal·mol −1 .  Some appealing conclusions can be obtained from the analysis of the relative energies of the stationary points involved in this 32CA reaction: (i) the most favorable TS-on is found to be 17.1 kcal·mol −1 below the separate reagents; (ii) however, when the formation of MC-on is considered, the activation energy of this 32CA reaction becomes positive at 8.5 kcal·mol −1 ; (iii) this 32CA reaction is strongly exothermic by −49.9 kcal·mol −1 . Consequently, the formation of the experimental spirooxindole 23 takes place by kinetic control. Note that the reaction is strongly exergonic by −22.4 kcal·mol −1 (see later); (iv) this 32CA reaction is completely ortho regioselective, as TS-mn is found to be 5.3 kcal·mol −1 Molecules 2022, 27, 6532 8 of 16 above TS-on; and (v) this 32CA reaction is completely endo stereoselective, as TS-ox is found to be 8.3 kcal·mol −1 above TS-on.
Inclusion of solvent effects of methanol stabilizes all species by between 15.3 and 19.7 kcal·mol −1 ; the reagents are the most stabilized [59]. As a consequence, the relative energies of the TSs increase by between 2.5 and 5.9 kcal·mol −1 . In methanol, the activation energy increases by 0.9 kcal·mol −1 , and the 32CA reaction remains completely regio-and stereoselective, as TS-mn and TS-ox are found to be 4.0 and 5.0 kcal·mol −1 , respectively, above TS-on. The 32CA reaction remains strongly exothermic by −45.2 kcal·mol −1 .
The ωB97X-D/6-311G(d,p) thermodynamic data of the 32CA reaction of AY 21 with ferrocene ethylene 22 were further analyzed. The relative enthalpies, entropies, and Gibbs free energies are given in Table 3, while the thermodynamic data are given in Table S2 in Supplementary Materials. A representation of the enthalpy and Gibbs free energy profiles associated with the four competitive reaction paths is given in Figure 3. The inclusion of the thermal corrections to the electronic energies in methanol increases the relative enthalpies only by between 0.8 and 3.4 kcal·mol −1 . Indeed, they have a markedly low incidence in the relative enthalpies of the TSs, which only increase by between 0.8 and 1.1 kcal·mol −1 with respect to the electronic energies in methanol. Considering the activation enthalpies, TS-ox and TS-mx are found to be more than 3.7 kcal·mol −1 higher in enthalpy than TS-on. The inclusion of entropies to enthalpies increases the relative Gibbs free energies by between 16.1 and 20.3 kcal·mol −1 as a consequence of the unfavorable activation entropies associated with these bimolecular processes, which are found in the range −47.6 and −60.  The geometries of MC-on and the four TSs are given in Figures 4 and 5, respectively. At MC-on, the two interacting frameworks, which are separated by a distance of ca. 3.11 Å , present a parallel rearrangement (see Figure 4). At the more favorable ortho TSs, the distances between the two pairs of C3-C4 and C1-C5 interacting carbons are 2.112 and 2.704 Å , respectively, at TS-on and 2.126 and 2.562 Å , respectively, at TS-ox, while at the meta TSs, the distances between the two pairs of C1-C4 and C3-C5 interacting carbons are: 2.081 and 2.633 Å , respectively, at TS-mn and 2.320 and 2.268 Å , respectively, at TSmx (see Figure 5). These distances indicate that while the most favorable TS-on shows a high geometrical asynchronicity with ∆l = 0.59 Å , the most unfavorable TS-mx shows a very low geometrical asynchronicity with ∆l = 0.05 Å . The most favorable highly asynchronous TS-on is associated with a two-center interaction between the C3 carbon of AY 21, the second most nucleophilic center of this TAC, and the β-conjugated C4 carbon of ferrocene ethylene 22, the most electrophilic center of this ethylene derivative.
A detailed analysis of the geometry of the most favorable TS-on shows that one of the hydrogens of the ferrocene framework of ethylene 22 is located at 2.439 Å of the carbonyl oxygen atom of AY 21, and one hydrogen of the dihydropyrrole ring of AY 21 is located at 2.418 Å of the carbonyl oxygen atom of ferrocene ethylene 22 (see Figure 5). These distances suggest the presence of two hydrogen bonds (HBs) between the hydrogen and oxygen centers. Interestingly, these HBs which are already present at the most stable MC-on, with H-O distances of 2.341 and 2.377 Å , respectively (see Figure 4), may account for the ortho and endo selectivity found in this 32CA reaction. The formation of these HBs, with the first one exhibited by a slight twist of the cyclopentadienyl ring with respect to the C4-C5 double bond, could be responsible for the lower entropy associated with TSon, i.e., 230.2 cal·mol −1 ·K −1 , than that of TS-mn, i.e., 239.7 cal·mol −1 ·K −1 (see Table S2 in Supplementary Material) and, consequently, for the loss of ortho regioselectivty when relative Gibbs free energies are considered (see Table 3).
On the other hand, the analysis of the geometry of the regioisomeric TS-mn suggests the presence of only one HB between the carbonyl O7 oxygen of ferrocene ethylene 22 and one of the dihydropyrrole hydrogen of AY 21, with a H-O distance of 2.337 Å (see Figure   Figure 3. ωB97X-D/6-311G(d,p) enthalpy ∆H in kcal mol -1 (blue) and Gibbs free energy ∆G in kcal mol -1 (red) profiles, at 65 • C in methanol, for the 32CA reaction of AY 21 with ferrocene ethylene 22.
It is interesting to highlight that while the activation enthalpies suggest that this 32CA reaction is completely ortho regioselective, in full agreement with the experimental outcomes [45], the activation Gibbs free energies markedly decrease the ortho regioselectivity as TS-mn is only 0.5 kcal·mol −1 above TS-on. This behavior is a consequence of the more unfavorable activation entropy associated with the ortho TSs (see later).
The geometries of MC-on and the four TSs are given in Figures 4 and 5, respectively. At MC-on, the two interacting frameworks, which are separated by a distance of ca. 3.11 Å, present a parallel rearrangement (see Figure 4). At the more favorable ortho TSs, the distances between the two pairs of C3-C4 and C1-C5 interacting carbons are 2.112 and 2.704 Å, respectively, at TS-on and 2.126 and 2.562 Å, respectively, at TS-ox, while at the meta TSs, the distances between the two pairs of C1-C4 and C3-C5 interacting carbons are: 2.081 and 2.633 Å, respectively, at TS-mn and 2.320 and 2.268 Å, respectively, at TS-mx (see Figure 5). These distances indicate that while the most favorable TS-on shows a high geometrical asynchronicity with ∆l = 0.59 Å, the most unfavorable TS-mx shows a very low geometrical asynchronicity with ∆l = 0.05 Å. The most favorable highly asynchronous TS-on is associated with a two-center interaction between the C3 carbon of AY 21, the second most nucleophilic center of this TAC, and the β-conjugated C4 carbon of ferrocene ethylene 22, the most electrophilic center of this ethylene derivative.     Finally, the analysis of the GEDT [26] at TS-on permits the assessment of the polar character of this 32CA reaction. GEDT values lower than 0.05 e correspond to non-polar processes, while GEDT values higher than 0.20 e correspond to high polar processes. The GEDT value at the two stereoisomeric ortho TSs is 0.23 e. This high value is a consequence of the supernucleophilic character of AY 21 and the strong electrophilic character of ferrocene ethylene 22. The flux of the electron density, which goes from AY 21 to ferrocene ethylene 22, allows classifying this 32CA reaction as FEDF, in clear agreement with the analysis of the CDFT indices. The high polar character of this 32CA reaction accounts for the fact that, considering the relative enthalpies, TS-on is located below the separated reagents (see Table 3) [60]. Figure 6 shows the ELF [46] basin attractor positions of MC-on and TS-on. The ELF of MC-on presents similar features to those of the separate reagents, i.e., AY 21 and ferrocene ethylene 22 (see Figure 1). The AY framework of MC-on shows the presence of one V(C1) monosynaptic basin, integrating 0.33 e, already present at pseudo(mono)radical AY 1, while the C4-C5 double bond of the ferrocene ethylene moiety is characterized by the A detailed analysis of the geometry of the most favorable TS-on shows that one of the hydrogens of the ferrocene framework of ethylene 22 is located at 2.439 Å of the carbonyl oxygen atom of AY 21, and one hydrogen of the dihydropyrrole ring of AY 21 is located at 2.418 Å of the carbonyl oxygen atom of ferrocene ethylene 22 (see Figure 5). These distances suggest the presence of two hydrogen bonds (HBs) between the hydrogen and oxygen centers. Interestingly, these HBs which are already present at the most stable MC-on, with H-O distances of 2.341 and 2.377 Å, respectively (see Figure 4), may account for the ortho and endo selectivity found in this 32CA reaction. The formation of these HBs, with the first one exhibited by a slight twist of the cyclopentadienyl ring with respect to the C4-C5 double bond, could be responsible for the lower entropy associated with TS-on, i.e., 230.2 cal·mol −1 ·K −1 , than that of TS-mn, i.e., 239.7 cal·mol −1 ·K −1 (see Table S2 in Supplementary Material) and, consequently, for the loss of ortho regioselectivty when relative Gibbs free energies are considered (see Table 3).
On the other hand, the analysis of the geometry of the regioisomeric TS-mn suggests the presence of only one HB between the carbonyl O7 oxygen of ferrocene ethylene 22 and one of the dihydropyrrole hydrogen of AY 21, with a H-O distance of 2.337 Å (see Figure 5). Thus, the presence of an additional HB at the most favorable TS-on accounts for the change of regioselectivity in this 32CA reaction.
Finally, the analysis of the GEDT [26] at TS-on permits the assessment of the polar character of this 32CA reaction. GEDT values lower than 0.05 e correspond to non-polar processes, while GEDT values higher than 0.20 e correspond to high polar processes. The GEDT value at the two stereoisomeric ortho TSs is 0.23 e. This high value is a consequence of the supernucleophilic character of AY 21 and the strong electrophilic character of ferrocene ethylene 22. The flux of the electron density, which goes from AY 21 to ferrocene ethylene 22, allows classifying this 32CA reaction as FEDF, in clear agreement with the analysis of the CDFT indices. The high polar character of this 32CA reaction accounts for the fact that, considering the relative enthalpies, TS-on is located below the separated reagents (see Table 3) [60]. Figure 6 shows the ELF [46] basin attractor positions of MC-on and TS-on. The ELF of MC-on presents similar features to those of the separate reagents, i.e., AY 21 and ferrocene ethylene 22 (see Figure 1). The AY framework of MC-on shows the presence of one V(C1) monosynaptic basin, integrating 0.33 e, already present at pseudo(mono)radical AY 1, while the C4-C5 double bond of the ferrocene ethylene moiety is characterized by the presence of two disynaptic basins, V(C4,C5) and V'(C4,C5), integrating a total of 3.27 e (see Figures 1  and 6). presence of two disynaptic basins, V(C4,C5) and V'(C4,C5), integrating a total of 3.27 e (see Figures 1 and 6). The most relevant feature of TS-on is the creation of a new V(C3) monosynaptic basin integrating 0.49 e, while the V(C1) monosynaptic basins present at MC-on is slightly depopulated to 0.29 e. This new monosynaptic basin, which is created at the second most nucleophilic center of AY 21 (see Parr functions in Figure 2), is demanded for the subsequent creation of the first new C3-C4 single bond [26]. On the other hand, the two disynaptic basins associated with the C4-C5 partial double bond present at ferrocene ethylene 22 and MC-on merge into one single V(C4-C5) disynaptic basin at TS-on after losing 0.71 e from ethylene 22. This ELF analysis of TS-on, which accounts for the non-concerted nature of this one-step 32CA reaction, supports the previous analysis based on the geometrical parameters.

Origin of the Ortho/Endo Regioselectivity
As has been aforementioned, the geometries of the more favorable MC-on and TSon suggest the presence of two HBs between the carbonyl oxygen atoms and the ring hydrogen atoms, which might be responsible for the unexpected ortho regioselectivity (see Figures 4 and 5r). Thus, in order to confirm their presence, a topological analysis of the electron density associated with the intermolecular non-covalent interactions (NCI) taking place at both stationary points was performed by means of the Independent Gradient Model [61,62] (IGM). The corresponding isosurfaces are represented in Figure 7. The most relevant feature of TS-on is the creation of a new V(C3) monosynaptic basin integrating 0.49 e, while the V(C1) monosynaptic basins present at MC-on is slightly depopulated to 0.29 e. This new monosynaptic basin, which is created at the second most nucleophilic center of AY 21 (see Parr functions in Figure 2), is demanded for the subsequent creation of the first new C3-C4 single bond [26]. On the other hand, the two disynaptic basins associated with the C4-C5 partial double bond present at ferrocene ethylene 22 and MC-on merge into one single V(C4-C5) disynaptic basin at TS-on after losing 0.71 e from ethylene 22. This ELF analysis of TS-on, which accounts for the non-concerted nature of this one-step 32CA reaction, supports the previous analysis based on the geometrical parameters.

Origin of the Ortho/Endo Regioselectivity
As has been aforementioned, the geometries of the more favorable MC-on and TS-on suggest the presence of two HBs between the carbonyl oxygen atoms and the ring hydrogen atoms, which might be responsible for the unexpected ortho regioselectivity (see Figures 4 and 5). Thus, in order to confirm their presence, a topological analysis of the electron density associated with the intermolecular non-covalent interactions (NCI) taking place at both stationary points was performed by means of the Independent Gradient Model [61,62] (IGM). The corresponding isosurfaces are represented in Figure 7. IGM-δginter at MC-on shows a green surface between the main interacting regions of both AY and ethylene frameworks and two additional green surfaces involving the two carbonyl oxygen atoms and one of the cyclopentadienyl or dihydropyrrole hydrogen atoms. While the more extended surface is related to the non-covalent interactions in the bond formation region, which turns to a blue-to-red color at TS-on as a consequence of the higher proximity between the two frameworks and the more advanced C3-C4 bond formation, the two surfaces in the O-H regions are related to weak HBs with δginter signatures and instrinsic bond strength index (IBSI) [63] values of ca. 0.03 a.u. These surfaces become smaller, and the respective HBs weaker, at TS-on due to a slight elongation of the corresponding O-H distances by 0.065 and 0.013 Å . Although their contributions to the intermolecular interactions [64] are lower than 4%, with the O(Et)-H(AY) interaction contributing 0.6% more than the O(AY)-H(Et) interaction, their presence seems to outweigh the more favorable electrophilic/nucleophilic electronic interactions involving the most nucleophilic C1 pseudoradical center along the meta/endo path [24], thus leading to the ortho/endo selectivity.
Finally, the IGM-δginter at the regioisomeric TS-mn shows the presence of only one HB between the carbonyl O7 oxygen of ferrocene ethylene 22 and one of the dihydropyrrole hydrogens of AY 21 (see Figure S1 in Supplementary Material). Consequently, the additional HB present at the most favorable TS-on can explain the fact that this TS is 5.4 kcal·mol −1 more stable than TS-mn, and, consequently, the origin of the unexpected ortho regioselectivity of this 32CA reaction [45].

Materials and Methods
The ωB97X-D [65] functional, together with the standard 6-311G(d,p) basis set [66], which includes d-type polarization for second-row elements and p-type polarization functions for hydrogen atoms, were used in this MEDT study. The TSs were characterized by the presence of only one imaginary frequency. The Berny method was used in optimizations [67,68]. The IRC [69] calculations were performed to establish the unique connection between the TSs and the corresponding minima [70,71] phase structures at the same computational level using the polarizable continuum model (PCM) [72,73] in the framework of the self-consistent reaction field (SCRF) [74][75][76]. Values of ωB97X-D/6-311G(d,p) enthalpies, entropies, and Gibbs free energies in methanol were calculated with standard statistical thermodynamics at 337.8 K and 1 atm [66], by PCM frequency calculations at the solvent optimized structures.
The GEDT [26] values were computed by using the equation GEDT(f) = Σqf, where q are the natural charges [48,49] of the atoms belonging to one of the two frameworks (f) at the TS geometries. Global and local CDFT indices [50,51] were calculated by using the IGM-δg inter at MC-on shows a green surface between the main interacting regions of both AY and ethylene frameworks and two additional green surfaces involving the two carbonyl oxygen atoms and one of the cyclopentadienyl or dihydropyrrole hydrogen atoms. While the more extended surface is related to the non-covalent interactions in the bond formation region, which turns to a blue-to-red color at TS-on as a consequence of the higher proximity between the two frameworks and the more advanced C3-C4 bond formation, the two surfaces in the O-H regions are related to weak HBs with δg inter signatures and instrinsic bond strength index (IBSI) [63] values of ca. 0.03 a.u. These surfaces become smaller, and the respective HBs weaker, at TS-on due to a slight elongation of the corresponding O-H distances by 0.065 and 0.013 Å. Although their contributions to the intermolecular interactions [64] are lower than 4%, with the O(Et)-H(AY) interaction contributing 0.6% more than the O(AY)-H(Et) interaction, their presence seems to outweigh the more favorable electrophilic/nucleophilic electronic interactions involving the most nucleophilic C1 pseudoradical center along the meta/endo path [24], thus leading to the ortho/endo selectivity.
Finally, the IGM-δg inter at the regioisomeric TS-mn shows the presence of only one HB between the carbonyl O7 oxygen of ferrocene ethylene 22 and one of the dihydropyrrole hydrogens of AY 21 (see Figure S1 in Supplementary Material). Consequently, the additional HB present at the most favorable TS-on can explain the fact that this TS is 5.4 kcal·mol −1 more stable than TS-mn, and, consequently, the origin of the unexpected ortho regioselectivity of this 32CA reaction [45].

Materials and Methods
The ωB97X-D [65] functional, together with the standard 6-311G(d,p) basis set [66], which includes d-type polarization for second-row elements and p-type polarization functions for hydrogen atoms, were used in this MEDT study. The TSs were characterized by the presence of only one imaginary frequency. The Berny method was used in optimizations [67,68]. The IRC [69] calculations were performed to establish the unique connection between the TSs and the corresponding minima [70,71] phase structures at the same computational level using the polarizable continuum model (PCM) [72,73] in the framework of the self-consistent reaction field (SCRF) [74][75][76]. Values of ωB97X-D/6-311G(d,p) enthalpies, entropies, and Gibbs free energies in methanol were calculated with standard statistical thermodynamics at 337.8 K and 1 atm [66], by PCM frequency calculations at the solvent optimized structures.
The GEDT [26] values were computed by using the equation GEDT(f) = Σq f , where q are the natural charges [48,49] of the atoms belonging to one of the two frameworks (f) at the TS geometries. Global and local CDFT indices [50,51] were calculated by using the equations given in reference [51], using the B3LYP/6-31G(d) method, because the original nucleophilicity and electrophilicity scales were established at that level [51].
The Gaussian 16 suite of programs was used to perform the calculations [77]. ELF [46] analyses of the ωB97X-D/6-311G(d,p) monodeterminantal wavefunctions were performed by using the TopMod [78] package with a cubical grid of step size of 0.1 Bohr. Molecular geometries and ELF basin attractors were visualized by using the GaussView program [79]. IGM analysis was carried out with the IGMPlot software [62].

Conclusions
The 32CA reaction of AY 21, derived from isatin and L-proline, with ferrocene ethylene 22, yielding spirooxindole 23, has been studied within MEDT at the ωB97X-D/6-311G(d,p) computational level. Analysis of the ELF topology of AY 21 indicated that this TAC has a pseudo(mono)radical structure characterized by the presence of two monosynaptic basins, integrating a total of 0.77 e, at the C1 carbon. The analysis of the CDFT reactivity indices indicated that ferrocene ethylene 22 has a strong electrophilic characteristic, while AY 21 is a supernucleophile, suggesting that the corresponding 32CA reaction has a high polar character. The most favorable reaction path via the ortho/endo TS-on presents an activation enthalpy of 8.7 kcal·mol −1 , with the 32CA reaction being strongly exothermic by −42.1 kcal·mol −1 . Analysis of the activation enthalpies indicated that this reaction presents a complete endo stereoselectivity and a complete ortho regioselectivity, in agreement with the experimental outcomes. Analysis of the GEDT at the most favorable TS-on, 0.23 e, accounts for the high polar character of this 32CA reaction, classified as FEDF. The presence of two HBs between the two carbonyl oxygens and the two ring hydrogens at the most favorable TS-on, which are already present at MC-on, appear to be responsible for the unexpected ortho regio-and endo stereoselectivity found in this 32CA reaction involving the pseudo(mono)radical AY 21.