Understanding the Reactivity of Trimethylsilyldiazoalkanes Participating in [3+2] Cycloaddition Reactions towards Diethylfumarate with a Molecular Electron Density Theory Perspective

Abstract

A Molecular Electron Density Theory (MEDT) study is presented here for [3+2] cycloaddition (32CA) reactions of three trimethylsilyldiazoalkanes with diethyl fumarate. The presence of silicon bonded to the carbon of these silyldiazoalkanes changes its structure and reactivity from a pseudomonoradical to that of a zwitterionic one. A one-step mechanism is predicted for these polar zw-type 32CA reactions with activation enthalpies in CCl₄ between 8.0 and 19.7 kcal·mol⁻¹ at the MPWB1K (PCM)/6-311G(d,p) level of theory. The negative reaction Gibbs energies between −3.1 and −13.2 kcal·mole⁻¹ in CCl₄ suggests exergonic character, making the reactions irreversible. Analysis of the sequential changes in the bonding pattern along the reaction paths characterizes these zw-type 32CA reactions. The increase in nucleophilic character of the trimethylsilyldiazoalkanes makes these 32CA reactions more polar. Consequently, the activation enthalpies are decreased and the TSs require less energy cost. Non-covalent interactions at the TSs account for the stereoselectivity found in these 32CA reactions involving the bulky trimethylsilyl group.

1. Introduction

Since the last decade, trimethylsilyldiazomethane [1] has been a popular synthetic reagent owing to its commercial availability. This mild, safe, and efficient alternative has been used for the esterification of naturally occurring carboxylic acids [1,2], preparation of silylenol ethers [3], synthesis of gem-silylboronate esters [4], and ring expansion reactions [5], while one of the most important applications of trimethylsilyldiazoalkanes is the generation of functionalized pyrazolines from [3+2] cycloaddition (32CA) reactions with alkene derivatives [6,7] (Scheme 1).

32CA reactions of trimethylsilyldiazoalkanes shelter the unique influence of both steric and electronic effects and have thus invited chemists to explore the mechanism and selectivities over the last four decades. In 1971, Brook and Jones [7] reported 32CA reactions of 1-phenyl-trimethylsilyldiazomethane with methyl vinyl ketone (Scheme 1).

In 1989, Hwu and Wang [8] reviewed the steric influence of trimethylsilyl group in organic synthesis, and subsequently in 1990, Padwa and Wannmaker [9] studied the steric control of trimethylsilyl group on the 32CA reactions of diazoalkanes with trimethylsilyl substituted alkynes.

Whitlock and Carreira [10] performed the enantioselective synthesis of ent-Stellettamide A with antifungal and cytotoxic activities from the 32CA reaction of trimethylsilyldiazomethane (Scheme 2).

In 2016, Mlostoń proposed a diradical reaction mechanism for the 32CA reactions of hetaryl thioketones with trimethylsilyl substituted diazomethane [11]. Further, in 2019, he reported the 32CA reactions of trimethylsilyldiazomethane with dicyanofumarate and with dicyanomaleate [12] (see Scheme 3). This reaction proceeds with the elimination of methyl cyanoformate molecule from the cycloadduct and, subsequently, the pyrazole ring system was obtained after aromatization.

Bassindale and Brook [13] performed the 32CA reactions of 1-trimethylsilyl-1-diazoethane (TSDE) 1, 1-phenyl-1-trimethylsilyldiazomethane (TSDP) 2 and ethyl-1-trimethylsilyl diazoacetate (TSDA) 3 with diethyl fumarate (DFM) 4 (Scheme 4) to examine the effect of organosilicon substituents on the product composition.

Experimentally, the relative rates of addition of the diazoalkanes TSDE 1, TSDP 2, and TSDA 3 to DFM 4 in carbon tetrachloride (CCl₄) at room temperature (Scheme 4) decreases in the order TSDE 1 (1.0) > TSDP 2 (2 × 10⁻²) > TSDA 3 (≈2.5 × 10⁻⁷) [13]. The relative reactivity of silyldiazoalkanes 1–3 with DFM 4 was interpreted by Bassindale and Brook [13] from their thermal stability, steric inhibition, and resonance effects, and considering the influence of these effects on the CNDO/2 calculated FMO energies. The low reactivity of TSDA 3 was explained as an outcome of the extraordinary ground state (GS) stability of the CNDO/2 calculated HOMO energy.

With the advent of advanced computations since the last two decades, and the proposal of the pioneering Density Functional Theory (DFT) by Kohn and Sham [14], the use of semi-empirical methods of calculations have been replaced by the DFT calculations and it has been possible to develop new theoretical outlook on organic reactions.

After the proposal of Molecular Electro Density theory [15] (MEDT) by Domingo in 2016, it has been possible to correlate the GS electronic structure of three-atom-components (TACs) and their molecular reactivity [16], which allowed proposing a standard classification [15,16] for the simplest TACs into zwitterionic, carbenoid, pseudoradical, and pseudodiradical. Interestingly, the reactivity of these TACs in 32CA reactions has put forward a useful classification of the 32CA reactions into zwitterionic type (zw-type), carbenoid type (cb-type), pseudo(mono)radical type (pmr-type), and pseudodiradical type (pdr-type), reactions, with progressive decrease in the activation energies along the series. The zw-type reactions are associated with high energy barrier, which is demanding to overcome through sufficient nucleophilic-electrophilic activations [17,18], while the pdr-type 32CA reactions show low activation energies and can be performed very easily. This classification has allowed characterizing the simplest diazoalkane as a pseudoradical TAC participating in pmr-type 32CA reactions (see Figure 1) [19].

Herein, an MEDT study for 32CA reactions of silyldiazoalkanes 1–3 with DFM 4 (Scheme 4), experimentally reported by Bassindale and Brook, [13] is carried out in order to understand how the presence of silicon on these silyldiazoalkanes changes the structure and reactivity of these TACs, and thus, explain the experimental outcomes.

We have presented this study into six sections: (1) In Section 3.1, the Electron Localization Function (ELF) topological study [20] at the GS structures of trimethylsilyldiazalkanes 1–3 is performed to obtain their respective classification as a TAC [16] and consequently to assess their molecular reactivity in 32CA reactions. (2) In Section 3.2, the Conceptual Density Functional Theory [21,22] (CDFT) indices at the GS of 1–4 are analyzed to comprehend the polar character.(3) In Section 3.3, the potential energy surface (PES) along the competitive reaction paths is studied and the energy profiles are analyzed along with the Global Electron Density Theory [23] (GEDT) calculations at the TSs to confirm the polar character of the reactions. (4) In Section 3.4, a Bonding Evolution Theory [24] (BET) analysis along the 32CA reaction of TSDE 1 and TSDA 3 with DFM 4 is carried out in order to perform a comparative study explaining the relative reactivity of these TACs. (5) In Section 3.5, the ELF of the TSs is studied. Finally, (6) in Section 3.6, the Bader’s Quantum Theory of Atoms-in Molecules [25,26] (QTAIM) parameters have been calculated at the reacting sites of the TSs. The Non-Covalent Interactions (NCI) at the TSs is realized through visualization by means of Independent Gradient Model [27] (IGM) analysis based on promolecular density.

2. Computational Methods

The stationary points are optimized at the MPWB1K [28]/6-311G(d,p) [29] level using the Berny analytical gradient optimization method [30]. The use of MPWB1K functional with the 6-311G(d,p) basis set for the analysis of 32CA reactions follows from the single point energy calculations at the CCSD(T)/cc-pVTZ level reported by Domingo in 2018 [17].

Frequency calculations were performed for the optimized geometries to confirm that the transition state structures (TSs) have only one imaginary frequency and that a local minimum has no imaginary frequencies (all positive frequencies). The connection of the corresponding reactants and products via the TSs along the minimum energy reaction pathway was verified through IRC [31] computations using the Gonzales–Schlegel integration method [32,33].

The 32CA reactions were studied using the polarizable continuum model [34,35] (PCM) in the experimental solvent CCl₄. The solvent was modeled using the self-consistent reaction field [36,37,38] (SCRF) method. The enthalpies, Gibbs free energies, and entropies were calculated in gas phase and toluene with the standard statistical thermodynamics at 298.15 K and 1 atm.

The natural population analysis [39,40] (NPA) was performed at the TSs to obtain the natural atomic charges (q) of the atoms and the summation of these charges at each framework, i.e., the GEDT (f) [23], was computed to determine the direction of the electron density flux at the TSs.

$$\mathrm{GEDT}\left(f\right)={\displaystyle \sum _{q\in f}q}$$

Equations reviewed in reference [22] have been used to calculate the CDFT indices [21,22]. All calculations were done using the Gaussian 16 package [41].

Topological analysis of the ELF [20], QTAIM [25,26], and the IGM [27] study was performed using Multiwfn software [42]. IGM isosurfaces were visualized by the VMD [43] program. The Paraview software [44,45] at an isovalue of 0.75 a.u was used to represent the ELF localization domains.

3. Results and Discussion

3.1. ELF Topological Analysis of Trimethylsilyldiazoalkanes TSDE 1, TSDP 2, and TSDA 3, and Diethyl Fumarate DFM 4

The ELF concept was constructed by Becke and Edgecombe [20] and chemical bonds were subsequently classified by the topological analysis of the ELF by Silvi and Savin [46]. Within the MEDT framework [16], the GS electronic structure of the TACs and their reactivity profile are correlated. Consequently, ELF of trimethylsilyldiazoalkanes 1–3 have been studied to analyze their reactivity in 32CA reactions.

Table 1. The Electron Localization Function (ELF) valence basin populations (in average number of electrons, e) at the GS structures of the reagents 1–4, calculated using MPWB1K functional with the 6-311G(d,p) basis set.

	1	2	3	4
V(N1)	3.82	3.74	3.63
V(N1,N2)	1.79	1.81	1.89
V’(N1,N2)	1.90	1.91	1.97
V(C3,N2)	3.07	3.06	2.93
V(C3,C6)	1.87	2.17	2.36
V(C3,Si)	3.19	3.07	3.11
V(C4,C5)				1.67
V’(C4,C5)				1.65

lists the significant valence basin populations. The ELF localization domains, the proposed ELF-based Lewis-like structures, and the natural atomic charges of TSDE 1, TSDP 2, TSDA 3, and DFM 4 are given in Figure 2, while a representation of ELF localization domains of TSDE 1 is shown in Figure 3.

The electronic structure at the N1-N2-C3 moiety of silyldiazoalkanes TSDE 1, TSDP 2, and TSDA 3 is presented from the total integrating basin populations at the attractor positions. The V(N1) monosynaptic basin is associated with the N1 nitrogen lone pair, integrating 3.82 e (1), 3.74 e (2), and 3.63 e (3). It is interesting to note from Figure 2 that the ELF of TSDE 1 shows two attractors associated with the monosynaptic basin V(N1), while a single attractor corresponding to the V(N1) monosynaptic basin is shown for TSDP 2 and TSDA 3, suggesting the influence of substituent effects on the electronic framework of the trimethylsilyldiazoalkanes.

The C3-N2 and N1-N2 double bonds are underpopulated, respectively, being associated with the V(C3,N2) disynaptic basin, integrating 3.07 e (1), 3.06 e (2), and 2.93 e (3) and V(N1,N2) and V’(N1,N2) disynaptic basins integrating 3.69 e (1), 3.72 e (2), and 3.86 e (3).

ELF topology of these silyldiazoalkanes shows also the presence of one V(C3,C6) disynaptic basin, integrating 1.87 e (1), 2.17 e (2), and 2.36 e (3), associated with the underpopulated C3-C6 single bond, and one V(C3,Si) disynaptic basin, integrating 3.19 e (1), 3.07 e (2) and 3.11 e (3), associated with the overpopulated C3-Si single bond. The high populations of the V(C3,Si) disynaptic basins result from the delocalisation of the electron density of the pseudoradical V(C3) monosynaptic basin present in the simplest diazomethane 11 (see Figure 1) into the neighbouring silicon center. This behaviour accounts for the change of the pseudo(mono)radical structure of the simplest diazomethane 11 to the zwitterionic one of silyldiazoalkanes 1–3.

The C4-C5 double bond in DFM 4 is underpopulated, being associated with the V(C4,C5) and V’(C4,C5) disynaptic basins with the total integrating population 3.32 e.

The natural atomic charges at N1, N2 and C3 are given in Figure 2. N1 and N2 nitrogens show negligible charges, while the C3 carbon is negatively charged with values −0.46 e (1), −0.44 e (2) and −0.55 e (3). Thus, the computed charges rule out the conventional zwitterionic Lewis electronic structure of the diazoalkanes. Note that the zwitterionic classification [16] used herein for the TACs 1–3 does not consider charges, instead the specific bonding pattern is taken into account.

3.2. Analysis of the CDFT Indices of the Reactants

The reactivity of TACs and ethylenes participating in 32CA reactions [16] can be successfully comprehended from the analysis of CDFT indices [21,22]. The B3LYP/6-31G(d) computational level is employed for CDFT analysis to assess the reactivities in accordance to the standard electrophilicity [47] and nucleophilicity scales (see

Table 2. Conceptual Density Functional Theory (CDFT) indices of TSDE 1, TSDP 2, TSDA 3, and DFM 4 calculated at the B3LYP/6-31G(d) level. The electronic chemical potential and chemical hardness are denoted by μ and η while the electrophilicity and nucleophilicity indices are denoted by ω and N, respectively. All values are represented in eV.

	μ	η	ω	N
1	−3.12	4.60	1.06	3.70
2	−3.22	4.11	1.27	3.84
3	−3.89	4.84	1.56	2.80
4	−4.84	5.39	2.18	1.58

) [48].

The electronic chemical potentials [49] μ of these silyldiazoalkanes, μ = −3.12 eV (1), −3.22 eV (2), and −3.89 eV (3), are higher than that of DFM 4, μ = −4.84 eV, suggesting that along a polar 32CA reaction, the electron density will flux from these silyldiazoalkanes to DFM 4.

The silyldiazoalkanes TSDE 1 and TSDP 2 are classified as moderate electrophiles [47,50] with ω = 1.06 (1) and 1.27 eV (2) and TSDE 3 as a strong electrophile with ω = 1.56 eV. On the standard nucleophilicity scale [48], TSDE 1 and TSDP 2 show values higher than 3.00 eV (N= 3.70 (1) and 3.84 (2) eV) and are classified as strong nucleophiles [51], while TSDA 3, N= 2.80 eV is classified as a moderate nucleophile. Thus, increase in electrophilicity is observed due to the presence of carbethoxy substituent in TSDA 3, relative to the presence of methyl and phenyl substituents in TSDE 1 and TSDP 2.

DFM 4 is classified as a strong electrophile with electrophilicity index ω = 2.18 eV and as a weak nucleophile with nucleophilicity index N = 1.58 eV.

Consequently, along these 32CA reaction, DFM 4 will behave as a strong electrophile while silyldiazoalkanes 1–3 will behave as nucleophiles, in clear agreement with the electronic chemical potentials of these species.

3.3. Analysis of the Energy Profile of the Stationary Points along the Feasible Reaction Paths for 32CA Reactions of TSDE 1, TSDP 2, and TSDA 3, with DFM 4

Due to the molecular symmetry of DFM 4, the regiochemical preference is not feasible for these 32CA reactions. On the other hand, due to the non-symmetry of these silyldiazoalkanes, two stereoisomeric reaction paths are feasible depending on the approach mode of the bulky trimethylsilyl group with respect to the carboxylate group present at the C4 carbon of DFM 4. Along the two feasible stereoisomeric reaction paths, the reactants, TSDE 1, TSDP 2, TSDA 3, and DFM 4, TSs, TS1, TS2, TS3, TS4, TS5, and TS6, and the corresponding pyrazolines, 5–10, were located and characterized for the 32CA reactions (Scheme 5). At TS1, TS3, and TS5, the bulky trimethylsilyl group is located over the C4 carboxylate group, while at TS2, TS4, and TS6 it is far. The relative energies, enthalpies, entropies, and free energies of the TSs and the cycloadducts are listed in

Table 3. MPWB1K/6-311G(d,p) relative energies ∆E in kcal·mol⁻¹, enthalpies, ∆H in kcal·mol⁻¹, entropies, ∆S in cal·mol⁻¹·K⁻¹, and Gibbs free energies, ∆G in kcal·mol⁻¹, computed at 298.15 K and 1 atm in gas phase and in CCl₄, of the TSs and products of 32CA reactions of TSDE 1, TSDP 2, and TSDA 3, with DFM 4. The Global Electron Density Theory (GEDT) is given in e.

		Gas Phase				CCl4
	∆E	∆H	∆S	∆G	GEDT	∆E	∆H	∆S	∆G	GEDT
TS1	9.4	10.4	−58.6	27.9	0.27	9.7	10.3	−55.5	26.8	0.28
5	−32.4	−29.4	−61.3	−11.2		−32.5	−29.4	−61.8	−11.0
TS2	7.6	8.1	−56.1	24.9	0.26	7.6	8.0	−55.7	24.6	0.27
6	−32.3	−29.5	−54.7	−13.3		−32.4	−29.7	−55.1	−13.2
TS3	14.0	14.4	−52.1	29.9	0.23	14.5	14.7	−52.5	30.4	0.24
7	−28.0	−25.9	−59.2	−8.2		−27.4	−25.4	−58.6	−8.0
TS4	11.3	10.8	−53.4	26.7	0.21	11.6	11.8	−53.6	27.8	0.22
8	−25.8	−24.6	−62.8	−5.9		−25.7	−24.5	−63.1	−5.7
TS5	18.6	19.0	−51.8	34.4	0.19	19.3	19.7	−50.8	34.9	0.20
9	−20.3	−17.7	−49.6	−2.9		−20.5	−17.9	−49.9	−3.1
TS6	15.6	15.2	−54.5	31.4	0.19	16.4	16.5	−51.0	31.7	0.20
10	−21.4	−19.6	−54.0	−3.5		−21.6	−19.8	−55.1	−3.3

.

These 32CA reactions show activation enthalpies between 8.1 (TS2) and 19.0 (TS5) kcal·mol⁻¹ in gas phase, and between 8.0 (TS2) and 19.7 (TS5) kcal·mol⁻¹ in CCl₄ at 298 K (see Table 3). The exergonic character is evident from the reaction Gibbs free energies between −13.3 (6) and −2.9 (9) kcal·mol⁻¹ in gas phase, and between −13.2 (6) and −3.1 (9) kcal·mol⁻¹ in CCl₄ (see Table 3).

The studied energy profile allows arriving at some important conclusions: (i) Consideration of solvent effects in CCl₄ shows minimal changes in the activation and reaction enthalpies within 1 kcal·mol⁻¹, this difference being slightly higher to 1.3 kcal·mol⁻¹ for TS6; (ii) the activation enthalpy of 32CA reaction of TSDE 1 with DFM 4 is lower than that of the 32CA reactions of TSDP 2 and TSDA 3 with DFM 4 by 3.8 (2.7 kcal·mol⁻¹ in gas phase) and 8.5 (7.1 kcal·mol⁻¹ in gas phase) in CCl₄, respectively, at 298 K. This agrees well with the experiments, in which the 32CA reaction of TSDP 2 with DFM 4 is 2 × 10⁻² times slower than that of TSDE 1 with DFM 4, while the 32CA reaction of TSDA 3 with DFM 4 is 2.5 × 10⁻⁷ times slower than that of TSDE 1 with DFM 4 (see Scheme 4); [12]. (iii) For each 32CA reaction, the approach of the bulky trimethylsilyl group in TSDE 1, TSDP 2, and TSDA 3 avoids steric interaction with the COOEt substituent of DFM 4 in the favored TS, evident from the lowering of the activation enthalpy of TS2 by 2.3 kcal·mol⁻¹ (2.3 kcal·mol⁻¹ in gas phase) relative to TS1, that of TS3 lowered by 2.9 kcal·mol⁻¹ (3.6 kcal·mol⁻¹ in gas phase) relative to TS4, and that of TS6 lowered by 3.2 kcal·mol⁻¹ (3.8 kcal·mol⁻¹ in gas phase) relative to TS5; (iv) the negative Gibbs free energies of these 32CA reactions suggests exergonic character, which makes them irreversible; and finally, (v) The activation Gibbs free energies are increased by between 15.4 and 17.5 kcal·mol⁻¹ in gas phase and between 15.2 and 16.6 kcal·mol⁻¹ in CCl₄ relative to the activation enthalpies, owing to the entropy consideration of these bimolecular reactions. The exergonic character of these 32CA reactions are decreased between 14.8 and 18.7 kcal·mol⁻¹ in gas phase and between 14.8 and 18.8 kcal·mol⁻¹ in CCl₄.

The gas phase optimized geometries of the TSs are given in Figure 4. These TSs geometries show minimal changes on inclusion of solvent effects in CCl₄. The distances between C3 and C4, and between N1 and C5 in the TSs, are higher than 2.0 Å. The formation of C-C and C-N bonds start at 2.0–1.9 and 1.9–1.8 Å, respectively [16]. Consequently, these 32CA reactions involve early TSs in which the C-C and C-N bond formation has not yet been started.

Finally, the GEDT [23] at the TSs are calculated and analyzed to predict the polar character of these 32CA reactions. The computed GEDT at gas phase optimized TSs are 0.27 e at TS1, 0.26 e at TS2, 0.23 e at TS3, 0.21 e at TS4, 0.19 e at TS5, and 0.19 e at TS6 (see Table 3), suggesting polar processes characterized by GEDT values above 0.20 e. In CCl₄, the GEDT values at the TSs do not show any substantial change (see Table 3). The predicted polar character of these zw-type 32CA reactions agrees with the CDFT analysis at the GS of the reagents (Table 2).

Note that the polarity decreases progressively when the methyl substituent of TSDE 1 is replaced by phenyl in TSDP 2 and with carbethoxy group in TSDA 3, attributed to the decrease in the nucleophilicity from TSDE 1 to TSDA 3 (Table 2), resulting in less reaction polarity with highly electrophilic DFM 4.

3.4. BET Study of the 32CA Reaction of TSDE 1 and TSDA 3 with DFM 4

The sequential changes in the bonding pattern along the 32CA reactions of DFM 4 with TSDE 1 and with TSDA 3 have been characterized and compared by BET [24] study; the details are given in Section 1 and Section 2 in Supplementary Materials.

The BET study of the 32CA reactions of DFM 4 with TSDE 1 allows arriving at some important conclusions: (i) Identification of the catastrophes along this reaction path divides the 32CA reaction into nine different phases. (ii) From S1-I to S4-I, the C3-N2 bonding region of TSDE 1 is depopulated to create the N2 lone pair and pseudoradical centre at C3, while at S5-I, the C4-C5 bonding region of DFM 4 is depopulated to create pseudoradical centre at C4. From S1-I to S5-I, the energy cost (EC) is 7.6 kcal·mol⁻¹, equal to the activation energy of TS2. (iii) Phase VII begins at S7-I, identified by the formation of the disynaptic V(C3,C4) basin (see Figure 5) integrating 1.26 e. At this IRC point, the formation of first C3-C4 single bond at the C-C distance of 1.96 Å begins by the coupling of C3 and C4 pseudoradicals. The V(C5) monosynaptic basins created in Phase VI, which is demanded for the subsequent N1-C5 single bond formation, has reached a populations of 0.33 e. (iv) Phase IX begins at S9-I, identified by the formation of disynaptic V(N1,C5) basin (see Figure 5) integrating 1.32 e. At this IRC point, the formation of second N1-C5 single bond at the N-C distance of 1.77 Å begins by the coupling of the pseudoradical centre at C5 carbon and the non-bonding electron density at N1 nitrogen.

BET study of the 32CA reactions of DFM 4 with TSDA 3 allowed arriving at some important conclusions: (i) Identification of the catastrophes along this reaction path divides the 32CA reaction into nine different phases. (ii) From S1-II to S4-II, the C3-N2 bonding region of TSDA 3 is depopulated to create the N2 lone pair and pseudoradical centre at C3, while at S5-II, the C4-C5 bonding region of DFM 4 is depopulated to create pseudoradical centre at C4. From S1-II to S5-II, the EC is 15.5 kcal·mol⁻¹, equal to the 99% of the activation energy of TS6. (iii) Phase VII begins at S7-II, identified by creation of the disynaptic V(C3,C4) basin integrating 1.10 e. At this IRC point, the formation of first C3-C4 single bond at the C-C distance of 2.00 Å begins by the coupling of C3 and C4 pseudoradicals. (iv) Phase IX begins at S9-II, identified by the formation of disynaptic V(N1,C5) basin integrating 1.30 e. At this IRC point, the formation of second N1-C5 single bond at the N-C distance of 1.74 Å begins by the coupling of the pseudoradical centre at C5 carbon and the non-bonding electron density at N1 nitrogen.

The comparative BET study of the 32CA reactions of DFM 4 with TSDA 1 and with TSDA 3 allows arriving at some important conclusions: (i) These two 32CA reactions show considerable similitude in the sequential changes of the bonding pattern along the reaction path. The EC demanded to reach the IRC point S5-I, which corresponds to 100% of the activation energy of the 32CA reaction of DFM 4 with TSDA 1, is 7.9 kcal·mol⁻¹ lower than that required to reach the IRC point S5-II, which corresponds to 99.9% of the activation energy of the 32CA reaction of DFM 4 with TSDA 3. Note that primarily, the C3-N2 and C4-C5 bonding regions are depopulated along the reaction path to reach the activation energies. The difference in activation energy of the two reactions suggests that the observed acceleration in the 32CA reaction of TSDE 1 is the outcome of the feasible depopulation of the C4-C5 bonding region in DFM 4 relative to that in the 32CA reaction of TSDA 3.

The GEDT at S5-I is 0.26 e and at S5-II is 0.19 e, suggesting the role of increased GEDT to lower the EC; as a result, the olefinic double bond in DFM 4 is easily depopulated in these polar 32CA reactions [52]. It is also interesting to note that the merging of two V(C4,C5) disynaptic basins into one V(C4,C5) for the 32CA reaction of TSDE 1 with DFM 4 at S2-I requires EC of 2.4 kcal·mol⁻¹, while the similar change in bonding pattern for the 32CA reaction of TSDA 3 with DFM 4 at S2-II is 9.4 kcal·mol⁻¹; (ii) the present MEDT study suggests that the C4-C5 double bond of DFM 4 is easily depopulated to create the two pseudoradicals due to increased GEDT along the polar 32CA reaction of TSDE 1 with DFM 4 compared to that of the 32CA reaction of TSDA 3 with DFM 4 [52].

3.5. ELF Topological Analysis at the TSs

The ELF valence populations at the TSs are given in

Table 4. The ELF valence basin populations (in average number of electrons, e) of the TSs, calculated using MPWB1K functional with the 6-311G(d,p) basis set.

	TS1	TS2	TS3	TS4	TS5	TS6
V(N1)	3.57	3.60	3.57	3.59	3.52	3.52
V(N1,N2)	1.53	1.44	1.44	1.31	1.55	1.55
V’(N1,N2)	1.63	1.67	1.69	1.72	1.56	1.55
V(N2)	1.76	1.82	1.82	1.94	1.85	1.88
V(C3,N2)	2.07	2.07	2.05	2.05	2.05	2.03
V(C3,C6)	1.91	1.92	2.13	2.19	2.41	2.30
V(C3,Si)	2.27	2.28	2.25	2.28	2.31	2.29
V(C4,C5)	2.94	2.96	2.95	2.93	2.91	2.91
V(C3)	0.67	0.63	0.62	0.55	0.62	0.62
V(C4)	0.23	0.18	0.19	0.20	0.23	0.20

while the basin attractor positions at the more favorable stereoisomeric TSs are shown in Figure 6. A great similitude is observed in the geometrical aspects of the TSs (see Figure 4).

At the six TSs, the formation of the two pseudoradicals C3 and C4 carbons are observed, which are not present in either TSDE 1, TSDP 2, and TSDA 3 nor DFM 4. The two monosynaptic basins V(C3) and V(C4) associated with these pseudoradicals show the total integrating populations between 0.55 and 0.67 e and between 0.18 and 0.23 e, respectively. The C3-N2 and C4-C5 bonding regions at the TSs show depopulation relative to that in the reagents, which is demanded to create the pseudoradicals at C3 and C4 carbons. Note that the disynaptic V(C3,N2) basin integrating 3.07 e in TSDE 1 is depopulated to 2.07 e in TS1 and TS2, integrating 3.06 e in TSDP 2 is depopulated to 2.05 e in TS3 and TS4, and integrating 2.93 e in TSDP 3 is depopulated to 2.05 e in TS5 and to 2.03 in TS6. The C4-C5 bonding region in DFM 4 integrating 3.32 e is depopulated between 2.91 and 2.96 e at the TSs.

At the TSs, the formation of disynaptic V(C3,C4) and V(N1, C5) is not observed, suggesting that the formation of new single bonds occurs at the later phases along the reaction path and not at the TSs. This is in agreement with the optimized TS geometries showing the C-C and N-C forming bond lengths above 2.0 Å (Figure 4) and is also in conformity with the topological analysis of the AIM discussed in Section 3.6.

3.6. QTAIM and IGM Topological Analysis at TSs

The topological analysis of the AIM proposed by Bader and coworkers [25,26] was carried out to predict the nature of interatomic interactions at the TSs. The calculated QTAIM parameters, the electron density ρ, Laplacian of electron density ${\nabla }^2\rho (r_c)$, and energy density $E_{\rho (r_c)}$ in au, at the bond critical points (3,−1) at the TSs, are given in

Table 5. Quantum Theory of Atoms-in Molecules (QTAIM) parameters, the electron density ρ, Laplacian of electron density ${\nabla }^2\rho (r_c)$, and energy density $E_{\rho (r_c)}$ in au, at the bond critical points (3,−1) at the TSs associated with the formation of new C-C and N-C bonds.

	CP1 (C3-C4)			CP2 (N1-C5)
	ρ	${\nabla }^2{}_{\mathit{\rho }({\mathit{r}}_{\mathit{c}})}$	${\mathit{E}}_{\mathit{\rho }({\mathit{r}}_{\mathit{c}})}$	ρ	${\nabla }^2{}_{\mathit{\rho }({\mathit{r}}_{\mathit{c}})}$	${\mathit{E}}_{\mathit{\rho }({\mathit{r}}_{\mathit{c}})}$
TS1	0.072	0.031	−0.020	0.051	0.091	−0.005
TS2	0.066	0.036	−0.017	0.058	0.091	−0.008
TS3	0.069	0.036	−0.018	0.056	0.092	−0.007
TS4	0.063	0.037	−0.016	0.070	0.091	−0.014
TS5	0.073	0.030	−0.021	0.062	0.092	−0.010
TS6	0.073	0.031	−0.020	0.064	0.091	−0.011

.

The positive Laplacian of electron density, ${\nabla }^2\rho (r_c)$ at CP1 and CP2 suggest that the covalent interactions are absent at the interatomic reacting centers of the TSs, also evidenced from the low electron density ρ accumulation at the C3-N2 and N1-C5 bonding regions. Thus, the formation of new covalent bonds has not yet started at the TSs, an observation in complete agreement with the optimized TS geometries (Figure 4) and ELF topological study at the TSs (Table 4).

The IGM [27] analysis is employed as a useful tool to identify and characterize weak NCI. The IGM gradient isosurface adopted for the present study is 0.02 a.u represented for TS1, TS2, TS5, and TS6 in Figure 7. A very large isosurface extended across the region of interaction between C3-C4 and N1-C5 interacting fragments, indicating the existence of NCI, at the TSs. At TS1 and TS5, a large continuous isosurface for steric interaction between the trimethylsilyl group of TSDE 1, and TSDA 3 fragments and the carbethoxy group of the DFM 4 fragment is visualized, which is decreased considerably in TS2 and TS6, suggesting the decisive role of the steric influence of the bulky trimethylsilyl group on the stereoselectivity of the 32CA reactions.

TS2 and TS6 show similitude in the isosurfaces for NCI. Therefore, difference in the activation parameters of TS2 and TS6 is not the outcome of steric effects or other non-covalent interactions at the TSs. Instead, the lower activation energy of TS2 is due to increase in GEDT along the 32CA reaction causing reduction of the EC for depopulation of the C-C double bond in DFM 4, attributed to the increased polarity induced by the strong nucleophilicity of 1 and strong electrophilicity of 4, as compared to the moderate nucleophilicity of 3 (Table 2).

4. Conclusions

32CA reactions of three silyldiazomethane, TSDE 1, TSDP 2, and TSDA 3, with DFM 4 are investigated within the MEDT framework to understand the role of the trimethylsilyl group present in these TACs participating in 32CA reactions.

Topological analysis of the ELF of TSDE 1, TSDP 2, and TSDA 3 shows the delocalization of the pseudoradical electron density present at the carbon of the simplest diazomethane 11 into the neighboring silicon, changing its structure and reactivity to that of a zwitterionic TAC, thus enabling the participation of these silyldiazoalkanes in zw-type 32CA reactions.

The calculated CDFT indices at the GS structures of the reagents show strong nucleophilicity of TSDE 1 and TSDP 2 while TSDA 3 is a moderate nucleophile and DFM 4 is classified as a strong electrophile. Consequently, polar character of these 32CA reactions is comprehended, which is finally confirmed from the calculated GEDT values above 0.20 e at the TSs.

These 32CA reactions follow one-step mechanism. The activation enthalpy of the 32CA reaction of TSDE 1 with DFM 4 is lowered by 3.8 and 8.5 kcal·mol⁻¹ in CCl₄ relative to that of the 32CA reaction of TSDE 2 and TSDE 3 with DFM 4, respectively, which agrees well with the experimental outcome. These 32CA reactions show negative reaction Gibbs free energies and consequently the exergonic character makes them irreversible. At the preferred stereoisomeric TSs, the trimethylsilyl group of the silyldiazoalkanes is oriented to avoid steric interactions, rendering these 32CA reactions stereoselective.

BET studies for these 32CA reactions indicate that the C3-N2 and C4-C5 bonding regions are depopulated at the initial five phases for the creation of pseudoradicals at C3 and C4 carbons and N2 nitrogen lone pair at the TS geometry and finally the generation of new C3-C4 and N1-C5 single bonds takes place at the later phases. 32CA reactions of TSDE 1 show lower EC and higher GEDT values at the IRC points relative to that for the 32CA reactions of TSDE 3. Thus, the higher GEDT along the 32CA reaction of TSDE 1, one of the most nucleophilic species of this series, with DFM 4 favors easy rupture of the C-C double bonds, resulting in an acceleration of this reaction compared to the 32CA reactions of TSDP 2 and TSDA 3 with DFM 4, in clear agreement with the zw-type 32CA reactions. ELF study and topological analysis of the AIM at the TSs indicate that the new C3-C4 and N1-C5 bond formation is not started at the TSs in agreement with the geometrical analysis of the TSs. The steric influence of the trimethylsilyl group on the stereoselectivity is visualized from the IGM analysis.

Finally, it can be concluded that the presence of silicon bonded to the carbon of these silyldiazoalkenes, which enables the delocalization of the electron density of the pseudoradical center present in diazomethane 11, changes the structure and reactivity from that of a pseudomonoradical of diazoalkenes to that of a zwitterionic TAC. Thus, polarity plays a decisive role in the feasibility of these 32CA reactions. The increase in GEDT for the 32CA reaction of TSDE 1 with DFM 4 leads to less EC for the rupture of the C4-C5 double bond of DFM 4, required for the formation of the pseudoradical centers needed to form the new C-C and N-C sigma bonds in pyrazolines.