Unveiling the synthesis of spirocyclic, tricyclic, and bicyclic triazolooxazines from intramolecular [3 + 2] azide-alkyne cycloadditions with a molecular electron density theory perspective

The intramolecular [3+2] cycloaddition (32CA) reactions of azido alkynes leading to spirocyclic, tricyclic, and bicyclic triazolooxazines has been studied within the molecular electron density theory (MEDT) at the MPWB1K/6-311G(d,p) level. The electron localization function (ELF) characterizes the azido alkynes as zwitterionic species. Analysis of the conceptual DFT indices allows classifying the azide moiety as the electrophilic counterpart and the alkyne as the nucleophilic one. These 32CA reactions are under kinetic control with the activation free energies of 23.4–26.7 kcal mol−1. Along the reaction path, the pseudoradical centre is created initially at C4, consistent with the Parr function analysis; however, the sequence of bond formation is controlled by the energetically feasible formation of the six-membered oxazine ring. The intermolecular interactions at the transition states were characterized from the quantum theory of atoms in molecules (QTAIM) study and the non-covalent interaction (NCI) gradient isosurfaces.

With no doubt, the metal catalyzed intermolecular version of the azide-alkyne 32CA reaction has widespread utility in the synthesis of high value-added organic products. However, the relatively unexplored intramolecular version is also worthwhile for the construction of unique heterocyclic structural scaffolds as reported by Li et al. [11] in 2009. In 2010, Majumdar et al. [12] synthesized 1,2,3-triazole fused dibenzo [1,5] diazocine derivatives from intramolecular azide-alkyne 32CAs. Very recently, in 2021, Mazur et al. [13] have reported the catalyst free intramolecular azide-alkyne 32CA reaction leading to 1,2,3-triazolobenzodiazepinones. The intramolecular 32CA reactions require strategic positioning of the azide and the alkyne functionalities in the same reagent to allow the appropriate structural framework for the cycloaddition. The O-alkylation of azido alcohol 5 with a propargylic halides 6, 7 generates the so called "azido alkyne" reagent 8 which undergoes thermally induced intramolecular 32CA reaction to give the triazolooxazine 9 in quantitative yields (Scheme 2). Such reactions do not require metal induced catalysis and generally proceed with exclusive regioselectivity.
In 2018, Cobb et al. [14] extended the scope of intramolecular azide alkyne 32CA reactions to synthesize the azido alkynes 10-12 and their intramolecular cyclization to spirocyclic triazolooxazines 13-15 with potent antiviral activity against MHV (Murine Hepatitis Virus) (Scheme 3). Li et al. [11] installed the alkyne functionality in the cyclo azido alcohols to generate the azido alkyne 16 leading to the tricyclic tricyclooxazines 17 in quantitative yields (Scheme 3). They also reported Since the last five decades, analysis of organic reactions was based on the frontier molecular orbital (FMO) theory until in 2016 Domingo [15] proposed the molecular electron density theory (MEDT) as a promising alternative to study numerous organic reactions by identifying the role of electron density changes in the molecular reactivity. MEDT [15][16][17] has been applied successfully to study varied aspects of cycloaddition reactions since last 5 years such as strain promotion [18,19], substituent effects [20,21], chemoselectivity [22,23], stereoselectivity and regioselectivity [24,25], and catalysis [26].
Herein, we present the MEDT study for the intramolecular azide-alkyne 32CA reactions reported by Cobb et al. [14] for the synthesis of antiviral spirocyclic triazolooxazines. The intramolecular 32CA reactions reported by Li et al. [11] for the synthesis of bicyclic and tricyclic triazolooxazines have also been studied herein within the MEDT perspective to obtain a complete comprehension of the reactivity and mechanism of intramolecular azide-alkyne 32CA reactions.
This MEDT study has been presented in six sections: (1) The conceptual density functional theory [30,31] (CDFT) analysis at the ground state (GS) structures was performed to characterize the chemical behaviour and the electronic flux between the azide and alkyne moieties of the azido alkynes 10, 11, 12, 16, and 18. (2) The electron localization function [32,33] (ELF) of these azido alkynes was analysed to correlate the electronic structure and the molecular reactivity. (3) The potential energy surfaces (PES) of the intramolecular 32CA reactions were followed to study the energy profile. (4) The topological analysis of the ELF at the transition states (TSs) and along the reaction path was  performed to structure the plausible mechanism. (5) Finally, the interactions at the TSs were characterized by analyzing the quantum theory of atoms-in molecules (QTAIM) parameters [34,35] and the non-covalent interaction (NCI) gradient isosurfaces [36].

Computational methods
The Berny analytical gradient optimization method [37] was used to optimize the azido alkynes, TSs, and triazolooxazines using the MPWB1K [38] functional with the 6-311G(d,p) basis set [39]. The use of MPWB1K functional has been recommended in several recent studies [16][17][18][19][20][21][22][23][24] as a precise computational level to study 32CA reactions. The located TSs were verified by the presence of one imaginary frequency, while the minima were verified by the absence of imaginary frequency. The CDFT indices [30,31] were calculated at the B3LYP/6-31G(d) level to characterize the reagents within the standard reactivity scales [31]. The minimum energy reaction pathway between the azido alkynes, TSs, and triazolooxazines were verified from the intrinsic reaction coordinate (IRC) calculations [40][41][42].
The topological analysis of the ELF [32,33] and QTAIM [34,35] was carried out using Multiwfn software [51] using high-quality grid. The ELF localization domains were visualized using UCSF-Chimera software [52], and NCI gradient isosurfaces were visualized using VMD software [53]. All calculations were performed using Gaussian 16 suite of programs [54].

Analysis of the CDFT indices
The conceptual DFT [30,31,43] (CDFT) indices have been applied in the reactivity analysis of several Diels Alder and 32CA reactions [30] to predict the electronic character of the reacting counterparts and consequently the direction of electronic flux. Accordingly, the global CDFT indices, namely  the electronic chemical potential (μ) [30,43], chemical hardness [30,44] (η), global electrophilicity [30,45] (ω), and the nucleophilicity [30,46] (N) at the ground state (GS) of the reagents are given in Table 1. The standard CDFT reactivity scales are defined at B3LYP/6-31G(d) computational level [45,46] and has therefore been used to characterize the reagents within the respective standard scales.
The electrophilicity ω index of the azido alkyne 10 is 1.51 eV being classified as a strong electrophile within the electrophilicity scale [45], while its nucleophilicity N index is 2.12 eV being classified as a moderate nucleophile within the nucleophilicity scale [46]. On the other hand, the azido alkynes 11 (ω = 1.45 eV) and 12 (ω = 1.49 eV) are classified as moderate electrophiles and moderate nucleophiles (2.00 < N < 3.00 eV). Note that the electrophilicity ω index of the azido alkyne 10 is higher than that of 11 and 12 and the nucleophilicity N index of azido alkyne 10 is lower than that of 11 and 12 owing to the terminal alkynyl substitution.
The electrophilicity ω index of the azido alkynes 16 and 18 are 1.14 eV and 1.06 eV respectively, being classified as the moderate electrophiles, and the nucleophilicity indexes are 2.56 eV and 2.64 eV, being classified as the moderate nucleophiles. The electronic chemical potential μ of 16 and 18 are −3.65 eV and −3.54 eV, suggesting higher tendency to share electronic charge compared to the azido alkynes 10, 11, and 12.  When the non-symmetric electrophilic-nucleophilic pair approaches each other, the most feasible two-centre interaction takes place between the most nucleophilic centre of the nucleophile and the most electrophilic centre of the electrophile. Domingo et al. [47] proposed the electrophilic P k + Parr functions and the nucleophilic P k − Parr functions derived from the Mulliken atomic spin densities (MASDs) to predict the local reactivity at the reacting counterparts. Accordingly, the MASDs of the radical anion and the radical cation of the azido alkyne 10 along with the nucleophilic P k − Parr functions at the alkyne moiety and the electrophilic P k + Parr functions at the azide are represented in Fig. 1. Note that C4 (P k − = 0.052) of the alkyne moiety is the more nucleophilic centre than C5 (P k − = 0.026), while N3 (P k + = 0.071) is the more electrophilic centre than N1 (P k + = −0.007), thus predicting a feasible two-centre interaction between N3 and C4 along the intramolecular 32CA reaction. Note that C4 and C5 of the alkyne moiety are not electrophilic and the radical anion does not show any MASD isosurface at the alkyne moiety (Fig. 1).

Analysis of the ELF topology of the reagents
The topological analysis of the ELF allows understanding the electronic structure and characterizes the bonding and nonbonding regions in a molecule. The ELF valence basin populations at the GS of the reagents are given in Table 2, while the ELF localization domains are represented in Fig. 2 [15,16,24]. The presence of a monosynaptic basin  On the other hand, the TACs with one pseudoradical centre are the pseudo(mono)radical ones and show comparable reactivity as the carbenoid TACs, the latter being associated with the presence of a carbenoid centre. The zwitter-ionic TACs show the least reactivity (high activation energy barrier) and do not show the presence of pseudoradical or carbenoid centres [24].
The absence of any pseudoradical or carbenoid centre in the azide moiety of the azido alkynes 10, 11, 12, 16, and 18 classifies its zwitter-ionic TAC character associated with the high activation energy (see "Study of the PES of the intramolecular 32CA reactions") demanding appropriate electrophilic-nucleophilic interactions. The proposed Lewislike structures on the basis of ELF valence basin populations and the natural atomic charges are given in Scheme 4. Note that C4 of the azido alkynes 10, 16

Study of the PES of the intramolecular 32CA reactions
The search for the stationary points along the potential energy surface (PES) of the intramolecular reactions allowed locating the azido alkynes 10, 11, 12, 16, and 18; the TSs TS1-TS5, and the triazolooxazines 13, 14, 15, 17, and 19 (Scheme 5). These 32CA reactions follow one-step mechanism.  The total and relative energies of the reagents, TSs, and the products are given in Table 3, and the thermodynamic parameters, namely the enthalpies, entropies and free energies in toluene at 110 °C are given in Table 4. The studied energy profile allows arriving at some appealing conclusions. (1) The 32CA reactions show negative reaction free energies between −67.8 and −71.6 kcal mol −1 in toluene, suggesting highly exergonic reactions under kinetic control and hence irreversible. (2) The activation energy of TS1 is lowered than that of TS2 and TS3 by 2.7 kcal mol −1 and 2.1 kcal mol −1 in gas phase and by 2.4 and 2.3 kcal mol −1 in toluene. The activation enthalpy of TS1 is lowered than that of TS2 and TS3 by 2.3 kcal mol −1 and 2.4 kcal mol −1 . Note that the activation enthalpies of TS4 and TS5 are increased   (Table 1).
(3) The thermodynamic corrections in toluene decrease the activation energies by 1-1.3 kcal mol −1 relative to the activation enthalpies, and the reaction energies by 1.8-2.7 kcal mol −1 relative to the reaction enthalpies. Note that these reactions show high activation enthalpies and Gibbs free energies (greater than 20 kcal mol −1 ) characteristic of the zwitter-ionic character of the azide moiety ("Analysis of the ELF topology of the reagents"). (4) These unimolecular reactions show negative entropies of activation between −6.6 and −10.4 kcal mol −1 and negative entropies of reaction between −10.9 and −15.3 kcal mol −1 . The unfavourable entropies result in the increase of the activation free energies by 1.9-3.1 kcal mol −1 relative to the activation enthalpies and the reaction free energies by 3.2-5.9 kcal mol −1 .
Consequently, the activation free energies of these 32CA reactions are between 23.4 and 26.7 kcal mol −1 .
The MPWB1K/6-311G(d,p) optimized gas phase geometries of the TSs associated with the 32CA reactions are displayed in Fig. 3. The lengths of the N1-C5 and N3-C4 forming bonds are 2.124 and 2.148 Å at TS1, 2.103 and 2.189 Å at TS2, 2.133 and 2.161 Å at TS3, 2.088 and 2.182 Å at TS4, and 2.096 and 2.177 Å at TS5. (1) Considering that the C-N bond formation takes place at 1.8-1.9 Å, it can be predicted that the formation of new N1-C5 and N3-C4 single bonds has not been started at the TSs, in conformity with the ELF study at the TSs (see "Topological analysis of the ELF at the TSs and along the reaction path associated with the intramolecular reaction"). (2) The difference in the forming bond distances ∆d are 0.024, 0.086, 0.028, 0.094, and 0.081 respectively at TS1, TS2, TS3, TS4, and TS5, suggesting minimal asynchronicity. Note that the N1-C5 forming bond distance is shorter than the N3-C4 one, in agreement with the earlier N1-C5 bond formation along the reaction pathway predicted from the bonding evolution theory study (see "Topologcal analysis of the AIM at the TSs involved in the 32CA reactions") (3) Inclusion of solvent effects in toluene causes unappreciable changes in the forming bond distances at the TSs.

Topological analysis of the ELF at the TSs and along the reaction path associated with the intramolecular reaction
The most significant ELF valence basin populations at the TSs are given in Table 5, while the ELF localization domains of TS1, TS4, and TS5 are shown in Fig. 4. The ELF at the Table 7 Total electron density, ρ (a.u.), and Laplacian of electron density ∇ 2 (r c ) (a.u.) of CP1 and CP2 at the TSs associated with the intramolecular 32CA reactions in gas phase  and N3-C4 bonds has not been started at the TSs, in agreement with the forming bond distances (Fig. 3).
In order to study the bonding changes along the intramolecular reaction and to establish the molecular mechanism, the topological analysis of the ELF along the 32CA reaction of the azido alkyne 10 has been carried out. The molecular mechanism represented by the Lewis-like structures derived from the ELF topology is shown in Scheme 6. The most significant valence basin populations of the selected IRC structures defining the ELF topological phases are given in Table 6, while the basin attractor positions of the relevant ELF structures associated with the formation of N1-C5 and N3-C4 bonds are shown in Fig. 5.
The conjunction of ELF study [32,33] and Thom's catastrophe theory [55], namely the bonding evolution theory (BET) study proposed by Krokidis et al. [56], allows structuring the molecular mechanism. This 32CA reaction takes place along 8 ELF topological phases. Phase I begins at the azido alkyne S0, which corresponds with the starting point of the IRC. Phase II is characterized by the creation of a new V(N2) monosynaptic basin with an initial population of 0.52 e associated with the formation of non-bonding electron density at S1. Note that the V(N1,N2) disynaptic basin is depopulated from 2.55 e at S0 to 2.37 e at S1, while the two V(N2,N3) and V′(N2,N3) disynaptic basins integrating the total population of 4.12 e at S0 are merged into one V(N2,N3) disynaptic basin integrating 3.83 e at S1. The energy cost (EC) associated with these bonding changes is 10.5 kcal mol −1 . Phase III begins at structure S2 (d(N3-C4) = 2.10 Å, d(N1-C5) = 2.08 Å) and is characterized by the creation of a new V(C4) monosynaptic basin, with an initial population of 0.26 e (see Fig. 5), which derives electron density from the C4-C5 bonding region, which experiences depopulation from 5.35 e at S1 to 4.90 e at S2. Phase IV begins at structure S3 (d(N3-C4) = 2.01 Å, d(N1-C5) = 2.00 Å) and is characterized by the creation of a new V(C5) monosynaptic basin, with an initial population of 0.11 e (see Fig. 5). Note that the C4-C5 bonding region is depopulated from 4.90 e at S2 to 4.59 e at S3. Phase V begins at structure S4 (d(N3-C4) = 1.95 Å, d(N1-C5) = 1.95 Å). In this phase, the non-bonding electron density at N1 nitrogen is split into two monosynaptic basins V(N1) (2.29 e) and V′(N1) (1.11 e), and subsequently in Phase VI, starting at S5 (d(N3-C4) = 1.90 Å, d(N1-C5) = 1.91 Å), the formation of first N1-C5 single bond takes place by the coupling of the pseudoradical centre at C5 and part of the non-bonding electron density of the N1 nitrogen. Phase VII begins at structure S6 (d(N3-C4) = 1.89 Å, d(N1-C5) = 1.90 Å). In this phase, the non-bonding electron density at N3 nitrogen is split into two monosynaptic basins V(N3) (3.78 e) and V′(N3) (0.40 e), and subsequently in Phase VII, starting at S7 (d(N3-C4) = 1.74 Å, d(N1-C5) = 1.76 Å), the formation of second N3-C4 single bond takes place by the coupling of the pseudoradical centre at C4 and part of the non-bonding electron density of the N3 nitrogen. From S7 to the product 13, the molecular geometry is relaxed by 66.8 kcal mol -1 .
This BET study allows arriving at some noteworthy conclusions: (1) the activation energy of 21.3 kcal mol −1 associated with the intramolecular 32CA reaction can be mainly related with the continuous depopulation of the N1-N2, N2-N3, and the C4-C5 bonding regions, demanded for the creation of the non-bonding electron density at the N2 nitrogen and the pseudoradical centre at the C4 carbon. (2) The pseudoradical centre at C4 carbon is created in Phase III earlier to that at C5 carbon created in Phase IV along the reaction path, which is consistent with the most nucleophilic centre at C4 carbon of the alkyne moiety as anticipated by the Parr function analysis (Fig. 1). However, the N1-C5 bond is formed earlier along the reaction path due to the energetically feasible formation of the six-membered spirocyclic ring resulting from the earlier N1-C5 bond formation, compared to the formation of the nine-membered spirocyclic ring resulting from the earlier N3-C4 bond formation. (3) The formation of second N3-C4 bond takes place when the first N1-C5 bond formation is completed by 59%, suggesting asynchronicity in the bond formation process, although not to a considerable extent, consistent with the minimal difference in the N1-C5 and N3-C4 forming bond distances (Fig. 3).

Topological analysis of the AIM at the TSs involved in the 32CA reactions
The covalent and non-covalent interactions between the atomic pairs connected by a bond path can be characterized from the electron density accumulation and the Laplacian of electron density ∇ 2 (r c ) at the bond critical points (BCPs) proposed by Bader and Coworkers [34,35]. The BCPs, CP1 and CP2, are associated with the forming N3-C4 and N1-C5 bonds at the TSs. The total electron density, ρ (a.u.), and the Laplacian of electron density ∇ 2 (r c ) (a.u.) at CP1 and CP2 are given in Table 7. The total electron density accumulation at CP2 is higher than that at CP1, consistent with the earlier N1-C5 bond formation along the reaction path (see "Topological analysis of the ELF at the TSs and along the reaction path associated with the intramolecular reaction"). The positive Laplacian of electron density ∇ 2 (r c ) at the BCPs indicate non-covalent interaction (NCI) at the TSs, which is in conformity with the absence of V(N1,C5) and V(N3,C4) disynaptic basins predicted from the ELF study (see "Topological analysis of the ELF at the TSs and along the reaction path associated with the intramolecular reaction").
The decomposition of the Laplacian of electron density ∇ 2 (r c ) into three Eigen values λ 1 , λ 2 , and λ 3 of the electron density Hessian matrix allows identifying the NCIs by the sign of λ 2 . The NCI gradient isosurfaces at TS1, TS4, and TS5 are shown in Fig. 6. The forming N3-C4 and N1-C5 bonding regions show the same pattern at the isosurfaces with both blue and red surfaces in each case respectively characterizing the strong attractive NCIs and strong repulsive NCIs.

Conclusion
The intramolecular 32CA reactions of azido alkynes resulting in spirocyclic, tricyclic, and bicyclic triazolooxazines have been studied within the molecular electron density theory perspective at MPWB1K/6-311G(d,p) level of theory. Analysis of the CDFT indices predicts the nucleophilic character of the alkyne moiety, while the azide counterpart is predicted as the electrophilic one. The Parr function analysis predicts the terminal alkyne carbon C4 as the most nucleophilic centre, while the terminal nitrogen N3 is predicted as the most electrophilic centre. The bonding evolution theory study predicts earlier formation of the pseudoradical centre at C4 consistent with the Parr function analysis, but the N1-C5 bond formation takes place earlier along the reaction path, suggesting energetic feasibility for the formation of six-membered spirocyclic ring which outweighs the two centre interaction between the most electrophilic and most nucleophilic centres. These kinetically controlled 32CA reactions follow one-step mechanism with high activation enthalpies in toluene from 20.3 to 23.0 kcal mol −1 , while the activation free energies range from 23.4 to 26.7 kcal mol −1 due to the inclusion of unfavourable entropies of activation. The located early TSs do not show the formation of new N1-C5 and N3-C4 bonds, as evident from the geometrical parameters and the topological analysis of the ELF and the AIM. The activation energy is mainly associated with the formation of non-bonding electron density at N2 nitrogen and the pseudoradical centre at C4. The NCI gradient isosurfaces show strong attractive and strong repulsive noncovalent interactions at the interatomic bonding regions.