1 Introduction

Thermal elimination reactions are the most universal strategy for the stereoselective formation of unsaturated C=C systems. For this purpose, processes of the decomposition of amine N-oxides (Cope reaction) [1, 2], ammonium hydroxides (Hoffman reaction) [1], xanthates (Chugaev reactions) [1, 3, 4], alkyl carboxylates [5, 6], nitrocompounds [7, 8] as well as fluoroazoxy compounds [9, 10] can be applied. In the academic literature, it is generally assumed that these types of processes proceed according to the “concerted” mechanism via six- or five-membered, pericyclic transition state. However, the last discoveries in the field of molecular mechanisms of organic reactions undermine this insight [11]. For example, the comprehensive exploration in the framework of the MEDT study [12] shows without any doubts that the benzoic acid elimination from nitroalkyl esters should be treated as the one-step, multistage pseudocyclic reaction [13, 14]. For similar conclusion, is provided in the quantum chemical studies of nitrous acid [7, 8] and fluorodiazo acid [10] eliminations. On the other hand, in thermal conditions, any ionic mechanism may not compete with the one-step mechanism. For this purpose, the presence of Lewis acids [15, 16] or cations of the ionic liquids [17] is necessary.

Recently, Ioffe and co-workers [18] described interesting strategy for the preparation of five-membered, internal nitronic esters which is based on the elimination of the trimethylsilyl bromide (2) from 2-(trimethylsilyloxy)-3-bromo-3-methyl-isoxazolidine systems (1a–d).

This process is realized under relatively mild conditions and without intervention of toxic reagents. So, it may be attractive alternative for traditional protocol for preparation of five-membered, internal nitronic esters based on the transformations of mercuric nitroform salts [19,20,21,22]. Unfortunately, the molecular mechanism of the transformation described by Ioffe [18] is unknown. Therefore, we decide to shed light on the nature of the mentioned elimination. This can be better understand the factors, which may be determined scope of the applications of title reaction, and, in the consequence more optimal planning of organic syntheses if widely range of five-membered, internal nitronates.

In order to understand the energetics as well as molecular mechanistic aspects of the elimination, a MEDT study [12] of the title reaction was carried out at the M06-2X(PCM)/6-31+G(d) computational level, in which a combination of: (i) a DFT study of molecular mechanism of elimination of trimethylsilyl bromide (2) from 2-(trimethylsilyloxy)-3-bromo-3-methyl-isoxazolidines (1a–d) (Scheme 1), (ii) ELF topological analysis of 2-(trimethylsilyloxy)-3-bromo-3-methyl-isoxazolidine (1a) and (iii) a BET analysis of the elimination reaction of trimethylsilyl bromide (2) from 1a, was employed. This approach, as we have proved, is effective tool for studying the molecular mechanism of various types of reactions [13,14,15,16,17].

Scheme 1
scheme 1

General scheme of elimination trimethyl bromide (2) from 2-(trimethylsilyloxy)-3-bromo-3-methyl-isoxazolidines (1a–d)

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2 Computational details

All calculations associated with the elimination of trimethylsilyl bromide (2) from 2-(trimethylsilyloxy)-3-bromo-3-methyl-isoxazolidines (1a–d) were performed using the Gaussian 16 package [23] in the Prometheus computer cluster of the CYFRONET regional computer centre in Cracow. The geometries of all reactants, transition state structures (TSs) and products of the reactions were fully optimized using the M06-2X functional [24] together with the 6-31+G(d) basis set. This computational level has already been successfully used for the exploration of a reaction involving several different nitrocompounds and others [25,26,27]. Critical points were characterized by frequency calculations. All reactants and products had positive Hessian eigenvalues. All TSs had only one negative eigenvalue in their diagonalized Hessian matrices, and their associated eigenvectors were confirmed to correspond to the motion along the reaction coordinate under consideration. TSs were located using the (QST2) algorithm. Intrinsic reaction coordinate (IRC) calculations [28] were performed in all cases to verify that the located TSs are connected to the corresponding minimum critical points associated with reactants, products and intermediates. The polarity of the reaction environment was simulated using a relatively simple self-consistent reaction field (SCRF) [29, 30] based on the polarizable continuum model (PCM) of Tomasi’s group [31, 32]. The values of enthalpies, entropies and Gibbs free energies were calculated with the standard statistical thermodynamics at 25 °C and 1 atm [33].

The topological analyses of the electron localization function (ELF) were performed with the TopMod [34] program using the corresponding M06-2X/6-31+G(d) monodeterminantal wave functions. ELF calculations were computed over a grid spacing of 0.1 a.u. for each structure, and ELF localization domains were obtained for an ELF value of 0.75. For the BET [35] studies, the corresponding reaction paths were followed by performing the topological analysis of the ELF for at least 76 nuclear configurations along the IRC paths.

3 Results and discussion

The MEDT study has been shared in three sections: In Sect. 3.1, the reaction profiles associated with the elimination of trimethylsilyl bromide (2) from 2-(trimethylsilyloxy)-3-bromo-3-methyl-isoxazolidines (1a–d) are analyzed, in Sect. 3.2, the ELF analysis of 2-(trimethylsilyloxy)-3-bromo-3-methyl-isoxazolidine (1a) is performed and in Sect. 3.3, a BET analysis of the elimination of trimethylsilyl bromide (2) from 2-(trimethylsilyloxy)-3-bromo-3-methyl-isoxazolidine (1a).

3.1 Study of the reaction path associated with the elimination of trimethylsilyl bromide (2) from 2-(trimethylsilyloxy)-3-bromo-3-methyl-isoxazolidines (1a–d)

From formal point of view, the most probable scenario of elimination of trimethylsilyl bromide (2) from 2-(trimethylsilyloxy)-3-bromo-3-methyl-isoxazolidine (1a) is a one-step mechanism (Scheme 2, path A), which may be realized via synchronical or non-synchronical transition state. However, ionic E1-type (path B) or E1cb-type (path C) mechanisms theoretically are also possible in some degrees. Therefore, all of these possibilities have been explored.

Scheme 2
scheme 2

Theoretically possible mechanisms for elimination of 2 from 2-(trimethylsilyloxy)-3-bromo-3-methyl-isoxazolidines (1a)

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In our study, we started from the analysis of reaction profile of elimination from parent N-oxide 1a. Unexpectedly, all attempts for optimization of the TS which may be connected with the transition state in the channel A were not successful. The DFT simulations show without any doubts that between valleys of starting molecule and products exist, not one, but three critical points, which can be connected with two transition states (TS1a and TS2a) and intermediate (IPa), respectively (Fig. 1).

Fig. 1
figure 1

M06-2X/6-31 +G(d) geometries of TSs and intermediate associated with the elimination of trimethylsilyl bromide (2) from 2-(trimethylsilyloxy)-3-bromo-3-methyl-isoxazolidine (1a)

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The conversion of starting molecule leads in the first reaction stage to the energetic maximum one, which can be connected with the TS1a structure. This is accompanied with increasing Gibbs free energy about 7 kcal/mol and slight reduction of the entropy (Table 1). Within the TS1a, the C1–Br2 single bond is broken and the rehybridization on the C1 carbon atom is observed. In the consequence, the N2–C1 bond decreases to 1.32 Å. So, the localized transition state should be connected with the E1-type mechanism according to the channel B (Table 2).

Table 1 Key energetical parameters of trimethylsilyl bromide (2) elimination from isoxazolidines (1a–d) according to M06-2X(PCM)/6-31+G(d) calculations
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Table 2 Key geometrical parameters of trimethylsilyl bromide (2) elimination from isoxazolidines (1a–d) according to M06-2X(PCM)/6-31+G(d) calculations
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Further conversion of the reaction system leads to the valley of the intermediate IPa. This intermediate is non-stable from thermodynamic point of view, because its Gibbs free energy is higher about 6 kcal/mol than in the case of the starting molecule. Within the IPa, the distance C1–Br2 is equal to 3 Å, whereas the N5–C1 connection exhibits nature of double bond (1.283 Å). The analysis of population of the Mulliken charges shows that this intermediate can be considered as the ionic pair. Its further conversion proceeds via second transition state TS2a. This requires increasing Gibbs free energy about 21.1 kcal/mol. Within this transition state, the Si3–O4 single bond is broken. At the same time, the new Br2–Si3 single bond is formed. The IRC calculations connect this critical point with the valleys of IPa (from the first side) and products (from the second side) (Tables 1 and 2).

In the next step, the influence of the polarity solvent on the reaction course has been examined. For this purpose, we compared key geometrical and energetical parameters of critical structures optimized in the simulation in the presence of benzene (ω = 2.271), acetone (ω = 20.493), nitromethane (ω = 36.562) and water (ω = 78.355) (Tables 1 and 2). It was found that independently of solvent polarity, the transformation of 1a molecule into 2 + 3a molecular system proceeds according to analogous mechanism. In all cases, three critical points between valleys of substrate and products have been identified. So, the nature of reaction profiles of considered processes is very similar. Their quantitative description is only different in some degrees. In particular, the Gibbs free energies of transition states in more polar solvent are slightly lower than in the benzene solution. On the other hand, the more polar solvents stabilize significantly the ionic intermediate IPa. In consequence, its Gibbs free energy in nitromethane is 1.3 kcal/mol lower than in the benzene solution.

Finally, other molecular systems (1b–d) including 2-(trimethylsilyloxy)-3-bromo-3-methyl-isoxazolidine moiety have been examined in similar type transformations (Tables 1, 2). It was found that the nature of the substituent stimulates in some degrees the quantitative description of critical point on reaction profile. In particular, the presence of electron-donating substituents decreases the first activation barrier and increases thermodynamical stability of ionic pair. On the other hand, the presence of electron-withdrawing substituents increases the first activation barrier, with decreasing of the thermodynamical stability of ionic pair. It should be underlined, however, that independently of the nature of substitution of 5 positions of heterocyclic system, the elimination of the trimethylsilyl bromide proceeds according to the same, stepwise, E1-type mechanism. Thus, the proposed molecular mechanism can be treated as general scheme for some range of 2-(trimethylsilyloxy)-isoxazolidine systems.

3.2 ELF topological analysis of 2-(trimethylsilyloxy)-3-bromo-3-methyl-isoxazolidine (1a)

First, we decided to analyze the electronic structure of reactant. For this purpose, a topological analysis of the ELF of 2-(trimethylsilyloxy)-3-bromo-3-methyl-isoxazolidine (1a) was performed. The ELF attractors, including the valence basin populations, ELF localization domains and the proposed Lewis structure from the ELF topological analysis for 1a, are shown in Fig. 2. ELF topological analysis of 1a shows the presence of four disynaptic basins: V(Si3,O4), V(N5,C1), V(C1,Br2) and V(O4,N5) with electron populations of 1.50 e, 2.11 e, 1.28 e and 1.04 e. We also find six monosynaptic basins: V(O4) and V′(O4), with electron populations of 2.35 e and 2.67 e and V(Br2), V′(Br2) and V″(Br2) with total population of 7.39 e and V(N5) with electron population of 2.45 e.

Fig. 2
figure 2

Representation of ELF attractors together with valence basin population, ELF localization domains and the proposed Lewis structure of 1a

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According to the Lewis structures, V(N5) monosynaptic basin, integrating 2.45 e is associated with lone pair. It is worth noting that two disynaptic basins V(C1,Br2) and V(O4,N5) with electron populations of 1.28 e and 1.04 e have low electron population and should be treated as partial single bond (Fig. 2).

3.3 BET study of the elimination of trimethylsilyl bromide (2) from 2-(trimethylsilyloxy)-3-bromo-3-methyl-isoxazolidine (1a)

The BET study of the elimination of trimethylsilyl bromide (2) from 2-(trimethylsilyloxy)-3-bromo-3-methyl-isoxazolidine (1a) indicates that this reaction is topologically characterized by seven different phases. The population of the most meaningful valence basins of the selected points of the IRC is included in Table 3. The attractor positions of the ELF for the important points along the IRC are shown in Fig. 3, while the basin population changes along the reaction path are graphically depicted in Fig. 4.

Table 3 ELF valence basin populations, distances of the breaking and forming bonds for the structures of the IRC, 1a − 2 + 3a, defining the seven phases characterizing the molecular mechanism of the elimination of trimethylsilyl bromide (2) from 2-(trimethylsilyloxy)-3-bromo-3-methyl-isoxazolidine (1a)
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Fig. 3
figure 3

ELF attractor positions for the most relevant points along the IRC associated with the rupture of C1–Br2 bond and formation of double bond between N5 and C1 atoms during the elimination of trimethylsilyl bromide (2) from 2-(trimethylsilyloxy)-3-bromo-3-methyl-isoxazolidine (1a)

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Fig. 4
figure 4

ELF attractor positions and basins for the most relevant points along the IRC associated with the formation of the Br2–Si3 bond and rupture of the Si3–O4 bond during the elimination of trimethylsilyl bromide (2) from 2-(trimethylsilyloxy)-3-bromo-3-methyl-isoxazolidine (1a)

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Phase I, 3.79 Å ≤ d(C1–Br2) < 4.10 Å, 8.29 Å ≥ d(Br2–Si3) > 6.98 Å and 3.24 Å ≤ d(Si3–O4) < 3.28 Å ,begins at the P1. This point is the interrupt of the IRC from TS toward the isolated 2-(trimethylsilyloxy)-3-bromo-3-methyl-isoxazolidine (1a).The ELF picture of P1 represents small changes in ELF valence basin electron populations of 1a. ELF analysis of P1 shows slight increase in the population of V(Si3,O4), V(O4,N5), V(N5,C1) disynaptic basins. In other side, the population of V(C1,Br2) disynaptic basin progressively decreases.

Phase II, 4.10 Å ≤ d(C1–Br2) < 4.57 Å, 6.98 Å ≤ d(Br2–Si3) < 7.12 Å and 3.28 Å ≤ d(Si3–O4) < 3.33 Å, starts at P2. At this point, described by fold F catastrophe, the first noticeable topological change along the IRC occurs in this phase. In this phase, we observed the disappearance of the disynaptic basin V(C1,Br2). We also notice that a new V(C1) and V’’’(Br2) monosynaptic basins integrating 0.40e and 2.08 e are established at P2. This new V(C1) monosynaptic basin is associated with the pseudoradical center at the C1 carbon of the structure P2.

Phase III, 4.57 Å ≤ d(C1–Br2) < 5.14 Å, 7.12 Å ≤ d(Br2–Si3) < 7.28 Å and 3.33 Å ≤ d(Si3–O4) < 3.37 Å, which begins at TS1a, the next significant topological change along the reaction path takes place. In this point, described by fold F catastrophe, we observed the disappearance of a V(C1) monosynaptic basin, the disappearance of V(N5) monosynaptic basin achieved the smallest value 1.93e, and the V(O4) monosynaptic basin split into two V(O4) and V’(O4) monosynaptic basins, integrating 2.23 e and 2.66 e. In this phase, there is a first transition state (TS1a) of the elimination of trimethylsilyl bromide (2) from 2-(trimethylsilyloxy)-3-bromo-3-methyl-isoxazolidine (1a); d(C1–Br2) = 4.57 Å, d(Br2–Si3) = 7.12 Å and d(Si3–O4) = 3.33 Å (Table 3, Fig. 3).

Phase IV, 5.14 Å ≤ d(C1–Br2) < 5.52 Å, 7.28 Å ≤ d(Br2–Si3) < 7.71 Å and 3.37 Å ≤ d(Si3–O4) < 3.38 Å, starts at P3 and is featured by cusp C† catastrophe. In this phase, the next most important topological change along the reaction path takes place; the V(N5) monosynaptic basin disappears, and a new V’(N5,C1) disynaptic basin integrating 2.14e is formed. This new V’(N5,C1) disynaptic basin is associated with the formation of a double bond between N5 and C1 atoms.

At IPa, 5.52 Å ≤ d(C1–Br2) < 5.90 Å, 7.71 Å ≥ d(Br2–Si3) > 5.47 Å and 3.38 Å ≤ d(Si3-O4) < 3.53 Å, commences the Phase V, which is described by fold F catastrophe. At this phase, the V’’’(Br2) monosynaptic basin disappears. We find in this phase an intermediate (IPa) of the studied reactions; d(C1–Br2) = 5.52 Å, d(Br2–Si3) = 7.71 Å and d(Si3–O4) = 3.38 Å (Table 3, Fig. 3).

Phase VI, 5.90 Å ≤ d(C1–Br2) < 6.02 Å, 5.47 Å ≥ d(Br2–Si3) > 4.85 Å and 3.53 Å ≤ d(Si3–O4) < 3.89 Å, starts at P4. At this point, described by cusp C catastrophe, a new V(Br2,Si3) disynaptic basin appears with the population 0.62e as a consequence of the disappearance of a V’’(Br2) monosynaptic basin integrating 3.05e.

Finally, the last Phase VII, 6.02 Å ≤ d(C1–Br2) < 6.34 Å, 4.85 Å ≥ d(Br2–Si3) > 4.27 Å and 3.89 Å ≤ d(Si3–O4) < 5.38 Å, begins at TS2a, which is described by fold F catastrophe. At this point, the next significant topological change takes place; a V(Si3,O4) disynaptic basin integrating 1.36e disappears. This phase begins at second transition state (TS2a) of the analyzed reaction; d(C1–Br2) = 6.02 Å, d(Br2–Si3) = 4.85 Å and d(Si3–O4) = 3.89 Å (Table 3, Fig. 4). In products of reaction 2 + 3a, we also observed the formation of V’’(Br2) monosynaptic basin integrating 2.42e.

From the BET analysis of this elimination of trimethylsilyl bromide (2) from 2-(trimethylsilyloxy)-3-bromo-3-methyl-isoxazolidine (1a), some interesting conclusions can be drawn: (i) BET analysis allows to distinguish seven phases along the reaction path which have been grouped into four Groups A–D (Table 4); (ii) Group A, which includes Phases I–II, is associated with the rupture of the C1–Br2 bond of 2-(trimethylsilyloxy)-3-bromo-3-methyl-isoxazolidine (1a); (iii) the rupture of this bond leads to formation of two C1 and Br2 pseudoradical centers; (iv) Group B, containing Phases III–V, is mainly associated with the formation of the N5–C1 double bond; (v) Group C, including Phase VI, is related to formation of a new Br2–Si3 bond. It is worth noting that when the Br2–Si3 bond is formed, the Si3–O4 bond is not broken yet. (vi) The breaking of the Si3–O4 bond takes place in the last Phase VII, which is included in the last Group D. In this group, we also observed the formation of the products of reaction 2 and 3a.

Table 4 Sequential bonding changes takes place the elimination of trimethylsilyl bromide (2) from 2-(trimethylsilyloxy)-3-bromo-3-methyl-isoxazolidine (1a), showing the equivalence between the topological characterization of the different phases and the chemical processes occurring among them. Distances are given in angstroms, Å View full size image
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4 Conclusions

The reaction of elimination of trimethylsilyl bromide (2) from 2-(trimethylsilyloxy)-3-bromo-3-methyl-isoxazolidines (1a–d) has been studied using DFT methods at the M06-2X(PCM)/6-31+G(d) computational level through the combination of the exploration and characterization of the reaction profiles associated with the elimination of trimethylsilyl bromide (2) from 2-(trimethylsilyloxy)-3-bromo-3-methyl-isoxazolidines (1a–d) and analysis based on MEDT theory. The title elimination reactions of trimethyl bromide (2) from 2-(trimethylsilyloxy)-3-bromo-3-methyl-isoxazolidines (1a–d) become via a E1-type two-step mechanism. BET analysis of the elimination of 2 from 1a indicates that this reaction begins with rupture of the C1–Br2 bond. Successively, we observed the formation of N5–C1 double bond and next the bond between atoms Br2 and Si3. And the last stage of the reaction is the rupture of the Si3–O4 bond.