Introduction

The isoxazolidine ring constitutes a pivotal structural motif found in a multitude of naturally occurring and biologically active compounds, serving as a fundamental scaffold that mimics various natural building blocks and playing a critical role in drug development [1]. Numerous derivatives of this N–O containing five-membered heterocycle have been characterized, exhibiting diverse pharmacological properties, including antiviral [2], antibacterial [3], and anticancer activity [4]. Among the synthetic approaches, the [3 + 2] cycloaddition (32CA) processes have emerged as the most popular and efficient method for the construction of such complex heterocyclic molecules [5]. Specifically, the 32CA reactions involving cyclic nitronate 1 and the double bonds of dimethyl maleate 2 enable the facile synthesis of two diastereomeric isoxazolidines, 3 and 4 (see Scheme 1) [6]. The six-membered cyclic nitronates can be synthesized in the form of individual diastereomers and enantiomers via non-catalyzed [7, 8] and Lewis acid catalyzed [9] hetero-Diels–Alder of nitroalkenes to olefins. Experimental investigations for the reaction of cyclic nitronate 1 dimethyl maleate 2 by Denmark et al. [6] have elucidated the orbital control of these processes, aligning with the principles of Frontier Molecular Orbital (FMO) theory. The experimental results show that an exo orientation is generally preferred. In a complete reversal of the precedent with acyclic nitronates, dimethyl maleate gave a single product resulting from exo approach to nitronates. Accordingly, the associated reaction mechanism is worth investigating in terms of quantum chemical calculations and has not been addressed till date in terms of the MEDT.

Scheme 1
scheme 1

32CA reactions of nitronate 1 to dimethyl maleate 2

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In the past two decades, the field of computational chemistry has witnessed substantial advancements, leading to the development of specialized software applications tailored for reaction studies [10]. These computational tools empower theoretical chemists to discern intricate mechanistic intricacies. In 2016, Domingo introduced the molecular electron density theory (MEDT) [11], which offers insights into how changes in electron density influence molecular reactivity. Over the past 7 years, the MEDT framework has been employed to analyze various facets of 32CA reactions, encompassing regio- [12], stereo- [12,13,14,15], and chemoselectivity [16, 17], reactivity [18,19,20], substituent effects [21, 22], and other critical aspects [23,24,25]. In this study, a comprehensive MEDT investigation of the 32CA reaction between nitronate 1 and dimethyl maleate 2 (Scheme 1) is presented. Additionally, we explore the role of diastereoselectivity in the interaction of cycloadducts 3 and 4 with the SARS-CoV-2 protein.

This paper is structured into five main sections: (1) An analysis of the electron localization function (ELF) [26] is conducted to elucidate the electronic structure at the ground state (GS) of reagents 1 and 2. (2) Conceptual density functional theory (CDFT) [27, 28] indices are employed to predict electronic flux and polar character in the reagents. (3) The potential energy surface (PES) is systematically examined along the feasible reaction pathways of the investigated 32CA reactions to identify stationary points. (4) ELF topological analysis [26] and QTAIM (Quantum Theory of atoms-in-molecules) [29] parameters are computed to investigate the electronic structure of the located transition states (TSs). (5) Finally, molecular docking studies are conducted to explore the interactions of cycloadducts 3 and 4 with the SARS-CoV-2 main protease.

The global electron density transfer (GEDT) [35] was calculated from the natural bond orbital (NBO) calculations [46, 47] at the TSs using the formula GEDT where q denotes the NBO-derived charges.

Computational methods

The optimization of reagents, transition states (TSs), and cycloadducts entailed the utilization of the Berny analytical gradient optimization approach [30]. Employed for this purpose was the M06-2X [31] functional in tandem with D3 dispersion correction [32] and the 6-311G(d,p) basis set [33]. The M06-2X functional has been endorsed as a suitable computational approach for investigating 32CA reactions in various recent works [16, 34,35,36]. Transition states were ascertained through the observation of a single imaginary frequency, while minima were confirmed by the absence of any imaginary frequencies. The global electron density transfer (GEDT) [37] was calculated from the natural bonding orbitals (NBO) [38] at the TSs using the formula GEDT \(f=\sum q\), where q denotes the NBO-derived charges. The calculation of CDFT indices [28, 39] relied on the B3LYP/6-31G(d) method to delineate the reagents in accordance with conventional reactivity scales [40]. The verification of the minimum energy reaction pathway between reagents, transition states (TSs), and cycloadducts was accomplished via intrinsic reaction coordinate (IRC) computations [41, 42]. The investigation of solvent effects in benzene was carried out employing the polarizable continuum model (PCM) within the self-consistent reaction field (SCRF) framework [43, 44].

The electronic chemical potential (μ) [27], chemical hardness (η) [45], electrophilicity index (ω) [40], and nucleophilicity index (N) [46] were determined using Eqs. (1) to (4) based on the HOMO (EHOMO) and LUMO (ELUMO) energies:

$$\mu \approx \frac{{E}_{\text{HOMO}}+{E}_{\text{LUMO}}}{2}$$
(1)
$$\upeta \approx {E}_{\text{LUMO}}-{E}_{\text{HOMO}}$$
(2)
$$\omega \approx \frac{{\mu }^{2}}{2\upeta }$$
(3)
$$N={E}_{\text{HOMO}}-{E}_{\text{HOMO }(\text{tetracyanoethylene})}$$
(4)

TopMod program [47] and Multiwfn [48] were used to conduct the topological analysis of the ELF and QTAIM [26, 29, 49]. The bonding evolution theory (BET) [50] study of the bonding changes along the experimentally favorable reaction path involving nitronate 1 and dimethyl maleate 2 was also performed. Visualization of the ELF localization domains was performed using Paraview software [51]. All calculations were executed with Gaussian 16 [52].

The compounds 3 and 4, once optimized, were utilized to conduct molecular docking through AutoDock Vina 1.2.0 [53]. The three-dimensional structures of the molecular target were obtained from the Protein Data Bank (PDB) (www.rcsb.org), specifically the SARS-CoV-2 (2019-nCoV) main protease (PDB: 6LU7). Receptor preparation involved the removal of heteroatoms (water and ions), addition of polar hydrogen, and charge assignment. Active sites were defined by grid boxes of suitable dimensions surrounding the bound co-crystal ligands. The docking study was executed with Autodock Vina 1.2.0 [53], and visualization was facilitated by Discovery Studio software [54].

Results and discussion

Analysis of the ELF topology of the reactants nitronate 1 and dimethyl maleate 2

The ELF, initially formulated by Becke and Edgecombe [26] and further developed by Silvi and Savin [49], provides a precise mathematical model for characterizing the electronic structure within a chemical system. The ELF model identifies core, bonding, and non-bonding localization attractors in distinct electronic regions. To classify the three atom components (TACs) involved in 32CA reactions, Domingo’s topological analysis of the ELF is instrumental, categorizing them as pseudodiradical, pseudo(mono)radical, carbenoid, and zwitterionic TACs [11, 55]. Figure 1 illustrates the ELF localization regions and crucial valence basin populations for the optimized reagents nitronate 1 and dimethyl maleate 2 at the M06-2X-D3/6-311G(d,p) level of theory.

Fig. 1
figure 1

M06-2X-D3/6-311G(d,p) basin attractor of nitronate 1 and dimethyl maleate 2 and the ELF localization domains. Protonated basins are shown in blue, monosynaptic basins in red, disynaptic basins in green, and attractor positions in purple (Isovalue = 0.80). Also shown are the suggested Lewis-type structures and the natural atomic charges in terms of the average number of electrons e. Negative charges are shown in red and positive charges in blue

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In the ELF analysis of nitronate 1, two monosynaptic basins V(O1) and V′(O1) with a combined population of 5.83e are associated with the non-bonding electron density on the oxygen atom O1. Additionally, two V(C3,N2) disynaptic basins with a total population of 4.20e are linked to the C3-N2 double bond, and a V(N2,O1) disynaptic basin integrating 1.65e is linked to the N2-O1 single bond. Nitronate 1 falls into the category of a zwitterionic TAC, lacking a pseudoradical or carbenoid center. The ELF of dimethyl maleate 2 shows disynaptic basins V(C4,C5) and V′(C4,C5) with a total population of 5.32e related to the C4-C5 double bond. Figure 1 shows the Lewis-like structures of the reactants nitronate 1 and dimethyl maleate 2, as well as the charges from the NBO.

In terms of charges, O1 in nitronate 1 carries a negative charge of 0.402e, while N2 has a positive charge of 0.176e, and C3 has a positive charge of 0.060e. In contrast, dimethyl maleate 2 exhibits negative charges of 0.118 and 0.117 on C4 and C5 carbon atoms, respectively.

Analysis of the CDFT indices

The study of CDFT reactivity indices [27, 28] provides an initial insight into the direction of electronic flow between reactants. CDFT indices were calculated for nitronate 1 and dimethyl maleate 2 at the B3LYP/6-31G(d) level of theory, in line with established reactivity scales [28, 40, 46]. These indices are the electronic chemical potential µ, the chemical hardness η, the electrophilicity ω, and the nucleophilicity N, all expressed in eV. The electronic chemical potential μ of nitronate 1 is found to be − 3.71 eV and exceeds that of dimethyl maleate 2, which is − 4.94 eV (see Table 1). This discrepancy indicates an electronic flux from nitronate 1 to dimethyl maleate 2 during the 32CA reaction. Nitronate 1, with an electrophilicity index (ω) of 1.26 eV, is considered a moderate electrophile, while dimethyl maleate 2, with ω of 2.12 eV, is a strong electrophile. Nitronate 1 is classified as a strong nucleophile (N = 3.04 eV), and dimethyl maleate 2 (N = 1.66 eV) is classified as moderate nucleophiles according to the standard nucleophilicity scale [46].

Table 1 The chemical hardness η, chemical potential µ, global electrophilicity ω, and global nucleophilicity N, in eV, of the ground-state electronic of nitronate 1 and dimethyl maleate 2 calculated at the B3LYP/6-31G(d) level of theory
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Analysis of the potential energy surface

The 32CA reaction between nitronate 1 and dimethyl maleate 2 proceeds through two stereoisomeric pathways, exo and endo. Stationary points were identified along these pathways, revealing transition states TS1 and TS2 leading to the formation of cycloadducts 3 and 4. This suggests a one-step mechanism for the 32CA reaction, as shown in Scheme 2.

Scheme 2
scheme 2

The stereoisomeric paths for the 32CA reactions of nitronate 1 and dimethyl maleate 2

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Taking account that the M06-2X functional was not able to reproduce the experimental selectivity, this 32CA reaction was further studied at the MPWB1K/6‐311G(d,p) computation level. The relative electronic energies, enthalpies, free energies, and entropies of TSs in benzene and their respective products are presented in Table 2. The investigation of the energy profile can yield interesting results. The 32CA reaction exhibits exergonic behavior in benzene, with negative reaction free energies, indicating kinetic control and irreversibility. The above statement is in full agreement with the experimental results, which demonstrate the formation of cycloadducts 3 and 4 [6]. The activation enthalpy of TS1 is 2.2 kcal.mol−1, while TS2 exhibits an activation enthalpy of 4.4 kcal.mol−1 (endo path) using M06-2X functional (see Fig. 2). However, these values slightly increased to 3.9 kcal.mol−1 for TS1 and 5.9 kcal.mol−1 for TS2 when MPWB1K functional was used. The value of relative Gibbs free energies was also increased by 6 and 8.8 kcal.mol−1 for TS1 and TS2, respectively, using MPWB1K functional. Domingo and co-workers [56] have classified the polar reactions into forward and reverse electron density flux (FEDF and REDF) reactions based on the analysis of the GEDT at the TSs. In FEDF cycloaddition reactions, the electron density always fluxes from the TAC or diene towards the ethylene. Non-polar 32CA reactions showing a GEDT lesser than 0.05e are classified as null electron density flux (NEDF). As the analysis of the electron density flux is performed at the actual TSs, this classification is unambiguous. Table 2 also presents the GEDT observed in the TSs, which were used to determine their respective orientations. The analysis of transition states indicates a forward electron density flux (FEDF) [57], signifying a polar reaction. The identified transition states exhibit a GEDT with values of 0.128e and 0.133e.

Table 2 M06-2X-D3/6-311G(d,p) and MPWB1K/6-311G(d,p) relative energies (∆E), enthalpies (∆H) and Gibbs free energies (∆G) in kcal.mol−1, relative entropies (∆S) in cal.mol−1.K−1, and calculated in benzene of the stationary points involved in the 32CA reaction with GEDT in average number of electrons
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Fig. 2
figure 2

Relative enthalpies, in kcal.mol−1, for the studied reaction of nitronate 1 and dimethyl maleate 2 in benzene at M06-2X-D3/6–311G(d,p) and MPWB1K/6-311G(d,p) (in parentheses) level of theory

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Figure 3 displays the optimized geometry of TS1 and TS2 in the gas phase. Examination of the geometry indicates that the distance between C3 and C4 is shorter than that between O1 and C5, with values of 2.11 and 2.13 Å, respectively, in TS1. However, an opposite trend was found in TS2 with a value of 2.28 Å for the C–C and 2.13 Å for the C-O bond. This finding indicates that TS2 exhibits a somewhat higher degree of asynchrony compared to TS1. The Wiberg bond index [58] between reacted atoms was computed from natural bond orbital analysis and listed in Table 1S. Analysis of the Wiberg bond index reveals that the studied reactive channels are not completely synchronous, because the degree of advancement of the two new bonds between two fragments is not equal in the corresponding transition states.

Fig. 3
figure 3

M06-2X-D3/6–311G(d,p) and MPWB1K/6-311G(d,p) (in parentheses) optimized geometry of TSs and cycloadducts in benzene (bond lengths in Å)

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Topological analysis of the ELF at the TSs

The topological characterization of the optimized transition states (TSs) associated with the 32CA reaction between nitronate 1 and dimethyl maleate 2 unveiled their electronic structures. The ELF localization domains and basin attractor locations for the transition states (TSs) involved in the 32CA reaction are depicted in Fig. 4. Analysis of the electron localization function (ELF) of TS1 revealed the presence of monosynaptic basins V(O1) and V′(O1), which together include a population of 5.71e. Similarly, ELF analysis of TS2 indicated the existence of monosynaptic basins V(O1) and V′(O1), with a combined population of 5.74 electrons, associated with the density of nonbonding electrons on the O1 oxygen atom. The ELF of TS1 and TS2 contains V(N2,C3) monosynaptic basins comprising a total population of 2.46e and 2.86e, respectively. These basins are associated with the C3-N2 bonding region. Furthermore, the monosynaptic basin V(N2) integrates 1.62e and 1.68e for TS1 and TS2, respectively. This basin is associated with the density of nonbonding electrons in the nitrogen N2. It is worth noting that there was a decrease in the electron population within the bonding region between C3 and N2. Specifically, the electron population decreased from 4.20e in the case of nitronate 1 to 2.46e in TS1 and 2.86e in TS2. This observation indicates that the double bond between C3 and N2 was cleaved in the transition states, resulting in the generation of nonbonding electron density on the nitrogen atom of N2. The population within disynaptic basin V(O1,N2) shows a decline, decreasing from 1.65e in nitronate 1 to 1.45e in TS1 and further to 1.38e in TS2. The predominant source of electron density in the monosynaptic basin of V(N2) can be attributed to the bonding region between N2 and C3. In TS1, two monosynaptic basins V(C3) and V(C4) with electron densities of 0.46e and 0.36e, respectively, indicate the establishment of pseudoradical centers at C3 and C4. These monosynaptic basins were not observed in TS2.

Fig. 4
figure 4

M06-2X-D3/6-311G(d,p) ELF localization domains and the positions of the TS1 and TS2 attractor basins. Monosynaptic basins are shown in red, protonated basins in blue, disynaptic basins in green, and attractor positions in purple

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Additionally, the ELF analysis of TS1 and TS2 revealed the presence of a single disynaptic basin, wherein 2.92e and 3.23e are combined from the C4–C5 bonding area.

Mechanistic implications along the stereoisomeric channels of 32CA reaction from the bonding evolution theory (BET)

The bonding evolution theory (BET), formulated by Krokidis [50] through the utilization of ELF topological analysis and Thom’s catastrophe theory [59], examines the successive alterations in bonding along a given reaction pathway. This provides mechanistic implications for understanding the reaction mechanism. Table 3 presents the populations of ELF basins at the specific sites where the reaction between nitronate 1 and dimethyl maleate 2 occurs during cyclisation, following the stereoisomeric route of TS1. Examination of the ELF basins identified six distinct topological phases belonging to the exo pathway. The ELF structure of the initial point S1 bears a resemblance to the bonding patterns seen in the individual compounds, as indicated in Fig. 1. The ELF studies conducted at the TS1 reveal the presence of a V(N1) monosynaptic basin, which integrates a population of 1.35e at S2, related to the N2 nitrogen lone pair. Pseudoradical centers are observed at carbon atoms C3 and C4 in the S3, leading to the creation of monosynaptic basins V(C3) and V(C4). TS1 belongs to Phase III, as shown in Fig. 5. In this phase, the formation of the single bonds O1–C5 and C3–C4 has not yet occurred. During Phase IV, pseudoradical centers emerge specifically at the carbon atom located at position 5 (C5), resulting in the creation of monosynaptic basins denoted as V(C5). In Phase V, the initial formation of single bonds occurs between carbon atoms C3 and C4. Phase VI witnesses the commencement of forming initial single bonds between atoms O1 and C5, evidenced by the emergence of the disynaptic basin V(C3,C4).

Table 3 ELF valence basin populations and distances of the forming bonds of the IRC structures S1–S5 that define the six phases characterizing the TS1. Distances are given in angstroms, Å, and GEDTs are given in average number of electrons
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Fig. 5
figure 5

M06-2X-D3/6-311G(d,p) IRC profile of TS1 for the 32CA reaction of nitronate 1 and dimethyl maleate 2

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Topological analysis of the AIM at the TSs

The topological analysis of the atoms-in-molecules (AIM) method, as developed by Bader and co-workers [29, 60], is employed to analyze interatomic interactions at the transition states. The values of the total electron density (ρ) and the Laplacian of electron density \({\nabla }^{2}\uprho ({\text{r}}_{\text{c}})\) at the bond critical points (BCP1 and BCP2) corresponding to the formation of O1-C5 and C3-C4 bonds are presented in Table 4. In both instances, the overall electron density is below 0.1 atomic units, in accordance with the topological analysis of ELF. Additionally, the empirical evidence suggests that the interatomic distance required for bond formation exceeds 2.0 Å. This information is further supported by the NCI gradient isosurfaces in Fig. 6 and the reduced density gradient (RDG) plot in Fig. 7. A continuous color-coding scheme based on the second eigenvalue of the Hessian is used, where strong, attractive interactions are represented in blue, weak interactions in green, and strong repulsive interactions in red.

Table 4 Total electron density, ρ (a.u.), and Laplacian of the electron density \({\nabla }^{2}\uprho ({\text{r}}_{\text{c}})\) (a.u.) of the critical points in the transition states associated with the 32CA reaction of nitronate 1 and dimethyl maleate 2
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Fig. 6
figure 6

NCI gradient isosurfaces of the transition states TS1 and TS2 for 32CA reaction of nitronate 1 and dimethyl maleate 2

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Fig. 7
figure 7

The reduced density gradient and gradient isosurfaces of TS1 and TS2

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Molecular docking against SARS-CoV-2

To elucidate the mode of action of the tested cycloadducts (3 and 4), a molecular docking analysis was employed to ascertain their binding modes against the main protease of SARS-CoV-2, a crucial target for the development of anti-SARS-CoV-2 drugs. The selection of these targets was based on their important involvement in viral protein synthesis. Consequently, directing therapeutic efforts towards these proteins offers prospective benefits in terms of virus eradication. The reliability of the docking parameters and procedures was validated by re-docking the co-crystallized ligand, which accurately reproduced the position and orientation observed in the crystal structure (RMSD = 1.34 Å).

The co-crystalized ligand engaged in interactions with the active site of the protein through the formation of five hydrogen bonds, with a corresponding free binding energy of − 7.5 kcal.mol−1, as shown in Table 5. Comparatively, compound 3 exhibited a more favorable binding affinity than the co-crystalized ligand, with a free binding energy of − 7.7 kcal.mol−1, while compound 4 exhibited a lower binding affinity with a value of − 7.2 kcal.mol−1. These findings are visually depicted in Fig. 8.

Table 5 Docking affinities of compounds 3, 4, and co-crystal ligand in kcal.mol−1 for the SARS-CoV-2 main protease
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Fig. 8
figure 8

3D and 2D interactions between tested compounds 3 and 4 with 6LU7 protein

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Conclusions

The 32CA reaction of nitronate 1 and dimethyl maleate 2 at the M06-2X-D3/6-311G(d,p) level of theory was investigated. The examination of the CDFT indices predicted the nucleophilic nature of nitronate 1, while dimethyl maleate 2 exhibited electrophilic behavior. The 32CA reaction is found to be polar zwitterionic type and proceeds through one-step mechanism with asynchronous TSs. According to the bonding evolution theory, the pseudoradical center at C3 and C4 formed earlier in the reaction, with the C3-C4 bond forming earlier as well, outweighing the significance of the two-center interaction between the most electrophilic and most nucleophilic centers. The two 32CA reaction variants studied were kinetically controlled and exhibited a one-step mechanism. The activation enthalpies for these reactions in benzene were 2.2 and 4.4 kcal.mol−1 for exo and endo paths, respectively, with activation free energies of 13.5 and 14.9 kcal.mol−1. The initial transition states did not exhibit the creation of C3-C4 and O1-C5 bonds, as indicated by the analysis of geometric parameters and the examination of the ELF and QTAIM. The transition states’ activation free energies derived using M06-2X calculations were in concurrence with the experimental data, suggesting significant diastereoselectivity in the reaction. The analysis conducted by BET indicated that the reaction mechanism followed a one-step mechanism.

Furthermore, the molecular docking simulations provided significant insights into the binding interactions between ligands 3 and 4 and the main protease (6LU7) of the SARS-CoV2 virus. The docking affinity values revealed variations in binding strength, with the cycloadduct 3 (− 7.7 kcal.mol−1) demonstrating the highest affinity, followed by co-crystal ligand (− 7.5 kcal.mol−1), and then cycloadduct 4 (− 7.2 kcal.mol−1). According to the results, the isoxazolidine ring enhances the affinity of the cycloadducts 3 with the SARS-CoV2 compared to the co-crystal ligand.