A theoretical study of DABCO and PPh₃ catalyzed annulations of allenoates with azodicarboxylate

Abstract

Previous experiments have shown that DABCO-catalyzed annulation of 2,3-butadienoate and diethylazodicarboxylate leads to 1,2-diazetidine (reaction (1)), whereas PPh₃-catalyzed 2-benzyl-2,3-butadienoate and diethylazodicarboxylate gives pyrazoline (reaction (2)). To understand the difference, the mechanisms of the two reactions have been studied using density functional theory (DFT) calculations. The calculated results indicate that the two reactions follow different reaction sequences. The favorable mechanism of reaction (1) includes four steps: (i) the nucleophilic attack of DABCO on 2,3-butadienoate forms a zwitterionic intermediate, (ii) the γ-addition of the zwitterionic intermediate to diethylazodicarboxylate, (iii) the intramolecular 4-exo-trig cyclization, and (iv) the catalyst DABCO liberation gives the final product, with Z-1,2-diazetidine being the main product. As for reaction (2), the first step is the formation of a zwitterionic intermediate via the addition of PPh₃ to diethylazodicarboxylate. The second step is the addition of the zwitterionic intermediate to the β-carbon atom of 2-benzyl-2,3-butadienoate, followed by the intramolecular cycloaddition. Finally, the elimination of triphenylphosphine oxide OPPh₃ affords pyrazoline. Our calculation results are in good agreement with experimental findings. The present study may be helpful not only for rational design of high-efficiency catalysts but also for understanding the reaction mechanism of similar reactions.

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1. Introduction

Cycloaddition provides a simple and convenient way to synthesize cyclic compounds from easily available building blocks. Allenes, which have unique structural properties and reactivities, are widely used in organic synthesis.¹ In 1995, Lu et al. published the first phosphine-catalyzed [3 + 2] cycloaddition reaction of allenoates with activated olefins.² Since then, Lewis base (such as phosphines and amines) and enzyme catalyzed annulation reactions of allenoates have became a powerful tool for the construction of carbo- and heterocycles.^3–16 For reviews, see ref. 17–20.

To date, under the catalysis of Lewis base, a large number of annulations of allenoates with imines and various species, which contain polarized C=X (X = C, O, N, S) bonds have been investigated either experimentally or theoretically. For example, Lewis based-catalyzed cycloaddition reactions of allenoates with activated alkenes,^21–24 imines,^25–34 aldehydes,^35,36 ketones,^37,38 ketimines,^39–44 oxadiene,⁴⁵ enynols,⁴⁶ and dithioester⁴⁷ have been extensively investigated experimentally. The potential applicability of these annulation reactions in the synthesis of natural products and pharmaceuticals have also been documented.^48–59 Moreover, there have been numerous theoretical studies on the Lewis based-catalyzed annulations of allenoates with activated alkenes,^60–63 ketones,^64,65 and aldehydes.^66–68

Among the various annulation reactions of allenoates, those using the electrophilic N=N bonds as reaction partners have been relatively much less explored.^69–71 Recent research from Tang and coworkers reported that the divergent amine-catalyzed cycloaddition of 2,3-butadienoate and diethylazodicarboxylate can form 1,2-diazetidine in moderate yields with high Z/E- and regio-selectivity (e.g. eqn (1) in Scheme 1).⁷¹ 1,2-Diazetidines, which contains two adjacent nitrogen atoms within a four-membered ring, are very important compounds because of their biological and pharmacological properties.^72–75

Scheme 1 DABCO and PPh₃-catalyzed annulations of allenoates and diethylazodicarboxylate.

In previous experimental studies, Nair et al. disclosed the phosphine-promoted annulation reaction of 2-benzyl-2,3-butadienoate with dialkylazodicarboxylate to form functionalized pyrazoline (e.g. eqn (2) in Scheme 1).⁶⁹ Pyrazolines are important heterocyclic compounds because they are widely used in numerous pharmaceutical and agrochemical industries.^76–81 Comparing eqn (2) reaction to eqn (1) reaction, it can be seen that under the catalysis of DABCO, the annulation of 2,3-butadienoate and diethylazodicarboxylate gives the four-membered ring product 1,2-diazetidines (eqn (1)), whereas using PPh₃ as catalyst similar substrates (2-benzyl-2,3-butadienoate and diethylazodicarboxylate) gives pyrazoline (eqn (2)). That is to say, under the catalysis of DABCO or PPh₃, similar substrates would lead to different products.

To the best of our knowledge, the mechanisms of the above two reactions have not been investigated until now. Particularly unclear issues concerns the following questions: (1) how does the reactions take place in detail? (2) Does the two reactions share the same mechanism? (3) Why similar substrates in the two reactions show different reactivity? With these questions in mind, we herein carry out a systematic theoretical study. We aim to provide detailed mechanistic information for the above two reactions and rationalize previous experimental findings. The calculated results are expected to provide useful insights into these kinds of annulation reactions.

The remainder of this paper is organized as follows: we first describe the computational methods in Section 2. The reaction mechanism and Z/E-selectivity of the eqn (1) reaction are presented in Section 3.1 and Section 3.2, respectively. The reaction mechanism of the eqn (2) reaction is presented in Section 3.3, followed by further discussions of the two reactions in Section 3.4. Finally, some concluding remarks are drawn in Section 4.

2. Computational methods

All calculations presented herein were carried out with Gaussian 09 program package.⁸² Geometry optimizations were performed using the M06-2X method⁸³ in conjunction with the 6-31+G(d) basis set. Previous studies have shown that M06-2X functional can better describe the kinetics and thermodynamics.^84–89 Frequency calculations were carried out at the same level of theory, to characterize whether the obtained species was a minimum (with all real frequencies) or a transition state (with only one imaginary frequency), as well as to get thermodynamic corrections. Intrinsic reaction coordinate (IRC) calculations were also performed to confirm the transition states indeed connect two relevant minima.⁹⁰ To get more accurate energies, the single-point energy calculations were carried out at the M06-2X/6-311++G(d,p) level with the solvent effects included. The solvation effects of 1,4-dioxane (eqn (1)) and tetrahydrofuran (THF, eqn (2)) were considered by using the Cramer–Truhlar continuum solvation model SMD with default convergence criteria.⁹¹ Natural bond orbital (NBO) analyses were performed at the M06-2X/6-311++G(d,p) level to assign the atomic charges and Wiberg bond indices.^92–94 Unless otherwise specified, the calculated solvation-corrected relative free energies were used in our discussion throughout.

3. Results and discussion

3.1 Reaction mechanism of the eqn (1) reaction

On the basis of previous experimental study⁷¹ and our calculation results, the detailed mechanism for DABCO-catalyzed annulation of 2,3-butadienoate R1-(1) and diethylazodicarboxylate R2-(1) is outlined in Schemes 2–4. The corresponding free energy profiles are shown in Fig. 1–4. In the following part of this section, we detail the reaction mechanisms step by step. To make our discussion easier, the suffix -(1) was used to denote the structures involved in the eqn (1) reaction, whereas -(2) was used to denote the structures involved in the eqn (2) reaction (see Section 3.3).

Scheme 2 Possible mechanisms associated with 1.

Scheme 3 The two attack modes of 1 to R2 in the eqn (1) reaction (the hydrogen atoms are omitted).

Scheme 4 Possible mechanisms associated with 1a.

Fig. 1 Free energy profiles for the coupling of DABCO with 2,3-butadienoate. The solvation-corrected relative free energies at SMD (1,4-dioxane)/M06-2X/6-311++G(d,p) level are given in kcal mol⁻¹.

Fig. 2 Free energy profile of the reaction channels proceeded via 1 (the eqn (1) reaction). The solvation-corrected relative free energies at SMD (1,4-dioxane)/M06-2X/6-311++G(d,p) level are given in kcal mol⁻¹.

Fig. 3 Free energy profile of the reaction channels proceeded via 1a (the eqn (1) reaction). The solvation-corrected relative free energies at SMD (1,4-dioxane)/M06-2X/6-311++G(d,p) level are given in kcal mol⁻¹.

Fig. 4 Free energy profile for the formation of Z- and E-1,2-diazetidine (the eqn (1) reaction). The solvation-corrected relative free energies at SMD (1,4-dioxane)/M06-2X/6-311++G(d,p) level are given in kcal mol⁻¹.

3.1.1 Addition of DABCO to R1-(1). Two conformers of R1-(1) are considered in the present study, the trans conformer trans-R1-(1) is slightly more stable than the cis conformer cis-R1-(1) (ΔΔG = 0.4 kcal mol⁻¹, as shown in Fig. 1). The nucleophilic attack of the N1 atom of DABCO to the C2 atom of cis-R1-(1) forms two zwitterionic intermediates 1-(1) and 1a-(1), which depending on the orientation of DABCO to cis-R1-(1). The corresponding transition states are TSR1/1-(1) and TSR1/1a-(1), respectively. The distance of N1–C2 shortens from 1.945 Å in TSR1/1-(1) and 1.941 Å in TSR1/1a-(1) to 1.511 Å in 1-(1) and 1.535 Å in 1a-(1). Moreover, NBO charge analyses indicate that the Wiberg bond indices change from 0.3841 in TSR1/1-(1), and 0.3873 in TSR1/1a-(1) to 0.8349 in 1-(1), and 0.8102 in 1a-(1). The above results demonstrate that the N1–C2 bond has formed in intermediates 1-(1) and 1a-(1). NBO charge analyses also indicate that the charges distributed on the DABCO- and R1-moieties in TSR1/1-(1) (TSR1/1a-(1)) are 0.325 e and −0.325 e (0.323 e and −0.323 e), respectively, indicating there is a charge transfer process from DABCO to R1-(1). As depicted in Fig. 1, the free energy barrier was calculated to be 21.4 kcal mol⁻¹ for TSR1/1-(1), and 22.1 kcal mol⁻¹ for TSR1/1a-(1). Formation of the zwitterionic intermediates 1-(1) and 1a-(1) is endergonic by 14.3 kcal mol⁻¹ and 14.7 kcal mol⁻¹, respectively, implying the nucleophilic addition step is not thermodynamically favorable. The addition of DABCO to trans-R1-(1) takes place via a similar pathway leads to intermediates 1-1-(1) and 1a-1-(1). The association of DABCO with trans-R1-(1) is endergonic by 21.5 kcal mol⁻¹ and 21.4 kcal mol⁻¹, and the free energy barrier of this step is 22.9 kcal mol⁻¹ for TSR1/1-1-(1) and 23.4 kcal mol⁻¹ for TSR1/1a-1-(1).

As shown in Fig. 1, TSR1/1-(1) and TSR1/1a-(1) are slightly lower than TSR1/1-1-(1) and TSR1/1a-1-(1). Moreover, 1-(1) and 1a-(1) are much more stable than 1-1-(1) and 1a-1-(1). Clearly, formation of 1-(1) and 1a-(1) is much more competitive than formation of 1-1-(1) and 1a-1-(1). Therefore, we focus on the reaction pathways starting from 1-(1) and 1a-(1) in the following discussion. The dipole moment of 1-(1) and 1a-(1) are 5.77 D and 9.73 D, respectively, demonstrating they have zwitterionic characteristics.

3.1.2 Reaction pathways starting from 1-(1). Once the zwitterionic intermediate 1-(1) is formed, two attack patterns of 1-(1) on R2-(1) are considered. One is the γ-addition mode, i.e. the γ-carbon (C4) atom of 1-(1) nucleophilically attack the N5 atom of R2-(1). It should be noted that both the upside and downside of R2-(1) can be approached by 1-(1), two attack modes can thus be located, which are labeled as “up attack mode” and “down attack mode”. To explain this issue clear, the two attack modes of 1-(1) to R2-(1) are shown in Scheme 3. On the basis of our calculations, the “down attack mode” is more favorable than the “up attack mode”. For simplicity of presentation, the results associated with “up attack mode” are provided in the ESI,† and we focus only on the discussion of the favored “down attack mode”. As shown in Fig. 2, the favored down attack lead to intermediate γ-2-(1) via γ-TS1/2-(1). The free energy barrier for this step is 8.3 kcal mol⁻¹ and this step is an exergonic process because the energy of γ-2-(1) is 21.1 kcal mol⁻¹ lower than that of 1-(1) + R2-(1). The gradually shortened C4–N5 distances (2.278 and 1.450 Å for γ-TS1/2-(1) and γ-2-(1), respectively) demonstrating the C4–N5 bond has formed in γ-2-(1). The negative charge values on N6 increased from −0.173 e in R2-(1), to −0.327 e in γ-TS1/2-(1), then to −0.594 e in γ-2-(1), demonstrating the coupling of 1-(1) with R2-(1) increases the charge on N6, and thus facilitate the subsequent intramolecular cycloaddition of N6 to C2.

Subsequent to its formation, γ-2-(1) can undergo [2 + 2] cycloaddition to form intermediate γ-3-(1) via γ-TS2/3-(1) (path 1a, as shown in Fig. 2). The free energy barrier for this step is 9.4 kcal mol⁻¹. It is noteworthy that this step is also an endergonic process since the energies of intermediate γ-3-(1) is 7.8 kcal mol⁻¹ higher than γ-2-(1). The C2–N6 bond is gradually shortened from 1.809 Å in γ-TS2/3-(1) to 1.618 Å in γ-3-(1).

At last, catalyst DABCO releases from γ-3-(1) gives the final product γ-P1-(1). As shown in Fig. 2, the free energy barrier for this step is −0.6 kcal mol⁻¹, which indicates that this step could happen very easily and DABCO is a very good leaving group. The final product γ-P1-(1) is 22.6 kcal mol⁻¹ lower that of γ-3-(1), demonstrating this step could happen irreversibly. The bond distance of C2–N1 is elongated from 1.618 Å in γ-3-(1) to 1.772 Å in γ-TS3/P1-(1). Meanwhile, the C2–C3 bond is gradually shortened from 1.445 Å in γ-3-(1), to 1.417 Å in γ-TS3/P1-(1), then to 1.342 Å in P1-(1). The above results demonstrate that with the elimination of DABCO, the C2–C3 bond becomes a double bond.

Besides the [2 + 2] cycloaddition discussed above, the alternative [3 + 2] cycloaddition of γ-2-(1) to give the five-membered ring intermediate γ-4-(1) was also studied (path 1b as shown in Fig. 2). The energy barrier calculated for [3 + 2] cycloaddition is 17.3 kcal mol⁻¹, and this step is endergonic by 12.4 kcal mol⁻¹, indicating formation of γ-4-(1) is energetically unfavorable.

The other attack pattern of 1-(1) on R2-(1) is the α-addition mode. The α-carbon (C3) atom of 1-(1) can also attack N5 from both upside and downside of R2-(1). For the sake of simplicity, only the favored upside attack affording α-2-(1) is discussed. The results for the downside attack mode are also provided in ESI.† As shown in Fig. 2, the α-addition step is exergonic by 20.8 kcal mol⁻¹ and the free energy barrier via α-TS1/2-(1) is 8.9 kcal mol⁻¹. The distance of C3–N5 bond is shortened from 1.984 Å in α-TS1/2-(1) to 1.445 Å in α-2-(1), indicating the C3–N5 bond is formed. Similar to γ-2-(1), α-2-(1) can undergo either [2 + 2] cycloaddition followed by DABCO elimination to generate α-P1-(1) (path 1c) or [3 + 2] cycloaddition to form α-4-(1) (path 1d), as depicted in Fig. 2. The free energy barriers calculated for [2 + 2] and [3 + 2] cycloadditions are 39.4 kcal mol⁻¹ (via α-TS2/P1-(1)) and 24.0 kcal mol⁻¹ (via α-TS2/4-(1)), respectively.

Now let us compare the feasibility of the γ- and α-addition modes, which can be rationalized by analyzing the potential energy surface associated with these processes. As shown in Fig. 2, γ-TS1/2-(1) is 0.6 kcal mol⁻¹ lower than α-TS1/2-(1), and γ-2-(1) is slightly more stable than α-2-(1). Moreover, the γ-addition transition states γ-TS2/3-(1) (2.6 kcal mol⁻¹, path 1a) and γ-TS2/4-(1) (10.5 kcal mol⁻¹, path 1b) are much lower than those associated with α-addition (32.9 kcal mol⁻¹ for α-TS2/P1-(1) in path 1c and 17.5 kcal mol⁻¹ for α-TS2/3-(1) in path 1d). It is clear that, the γ-addition is much more favorable than the α-addition, which is in good agreement with experimental results that only the γ-addition product was observed. As for the γ-addition pathways path 1a and path 1b, the [2 + 2] cycloaddition transition state γ-TS2/3-(1) is 7.9 kcal mol⁻¹ lower than the [3 + 2] cycloaddition transition state γ-TS2/4-(1). Consequently, the [2 + 2] cycloaddition via path 1a is much more competitive than the [3 + 2] cycloaddition via path 1b.

3.1.3 Reaction pathways starting from 1a-(1). The reaction pathways starting from 1a-(1) are very similar to those proceeded via 1-(1). The γ-carbon (C4) atom of 1a-(1) can also attack the N5 atom from the upside and downside of R2-(1) leads to intermediates γ-2a-(1) and γ-2a′-(1). Herein, we just discuss the reaction pathways proceeded via γ-2a-(1), and the results for γ-2a′-(1) are also collected in ESI.† The gradually shortened C3–N5 bond (2.330 Å in γ-TS1a/2a-(1), and 1.457 Å in γ-2a-(1)) indicates the C3–N5 bond has formed in γ-2a-(1). The negative charge values on N6 increased from −0.173 e in R2-(1), to −0.337 e in γ-TS1a/2a-(1), then to −0.575 e in γ-2a-(1), demonstrating the coupling of 1a-(1) with R2-(1) increases the charge on N6, and thus facilitate the subsequent intramolecular cycloaddition of N6 to C2. The free energy barrier associated with γ-addition of 1a-(1) to R2-(1) is 8.7 kcal mol⁻¹, and the reaction energy is 19.4 kcal mol⁻¹ (with respect to 1a-(1) + R2-(1)).

Subsequent to its formation, γ-2a-(1) undergoes a concerted N6–C2 bond formation and C2–N1 bond cleavage process affords the four-membered ring product γ-P2-(1) (path 2a as shown in Fig. 3). The distance of N6–C2 is shortened from 2.330 Å in γ-TS2a/3a-(1) to 1.457 Å in γ-3a-(1). In the meantime, the distance of C2–N1 is elongated from 1.511 Å in γ-2a-(1), to 1.555 Å in γ-TS2a/3a-(1), then to 3.125 Å in γ-3a-(1), and the C2–C3 bond is shortened from 1.389 Å in γ-TS2a/3a-(1) to 1.339 Å in γ-3a-(1). These results indicate that with the formation of γ-P2-(1), the catalyst DABCO regenerates and the C2–C3 bond becomes a double bond. The free energy barrier is 8.8 kcal mol⁻¹, and the reaction energy is −29.0 kcal mol⁻¹, which means this process could happen irreversibly. Alternatively, γ-2a-(1) can transform to γ-4a-(1) via the five-membered ring transition state γ-TS2a/4a-(1) (path 2b as shown in Fig. 3). The free energy barrier of this step is 13.6 kcal mol⁻¹ and the reaction energy is 1.1 kcal mol⁻¹, indicating an endoergic process.

Besides the γ-addition of 1a-(1) to R2-(1) discussed above, we also examine the α-addition of 1a-(1) to R2-(1). As depicted in Fig. 3, the free energy barrier of α-addition is 7.8 kcal mol⁻¹ for α-TS1a/2a-(1), and formation of α-2a-(1) is exergonic by 15.8 kcal mol⁻¹ relative to 1a-(1) + R2-(1). Once α-2a-(1) is formed, two processes are possible. One is formation of the N6–C2 bond via the five-membered ring transition state α-TS2a/3a-(1) (path 2c). The other is formation of the N6–C4 bond via the four-membered ring transition state α-TS2a/P2-(1) (path 2d). The free energy barriers for the above two processes are 14.4 kcal mol⁻¹ and 29.1 kcal mol⁻¹, respectively.

By the above, we have presented and discussed four pathways (path 2a–2d) associated with 1a-(1). As shown in Fig. 3, γ-TS1a/2a-(1) is only 0.9 kcal mol⁻¹ higher than α-TS1a/2a-(1), while γ-2a-(1) is 3.6 kcal mol⁻¹ lower than α-2a-(1), indicating formation of γ-2a-(1) and α-2a-(1) are competitive processes. The free energy barriers calculated for γ-TS2a/3a-(1) (path 2a), γ-TS2a/4a-(1) (path 2b), α-TS2a/3a-(1) (path 2c) and α-TS2a/P2-(1) (path 2d) are 8.8 kcal mol⁻¹, 13.6 kcal mol⁻¹, 14.4 kcal mol⁻¹ and 29.1 kcal mol⁻¹, respectively. We can easily conclude that formation of the four-membered ring product via path 2a is the most favorable channel.

3.2 Z/E stereoselectivity

On the basis of experimental results,⁷¹ DABCO-catalyzed [2 + 2] annulation of 2,3-butadienoate with diethylazodicarboxylate exhibits high Z/E selectivity, the major product being the Z-3-alkylidene-1,2-diazetidine (Z : E = 20 : 1). However, the reason for the high Z/E-selectivity is still lacking. According to our calculations, the Z- and E-3-alkylidene-1,2-diazetidine, corresponding to γ-P1-(1) and γ-P2-(1) in our results, result from the γ-addition of 1-(1) and 1a-(1) with R2-(1), respectively. For the purpose of comparison, the reaction pathways for the formation of γ-P1-(1) and γ-P2-(1) are collected in Fig. 4. As depicted in Fig. 4, the Z/E-selectivity-determining transition states are γ-TS1/2-(1) for path 1a (relevant to the formation of Z-product) and γ-TS1a/2a-(1) for path 2a (relevant to the formation of E-product). It is noteworthy that γ-TS1/2-(1) is 0.8 kcal mol⁻¹ lower than γ-TS1a/2a-(1), and γ-2-(1) is 2.1 kcal mol⁻¹ more stable than γ-2a-(1), indicating path 1a is both kinetically and thermodynamically much more competitive than path 2a. Consequently, the reaction would mainly give the Z-product via path 1a, consistent with experimental observations.⁷¹

Moreover, to better understand the Z- versus E-selectivity of the current [2 + 2] cycloaddition reaction, we calculated the HOMO–LUMO gap for the Z/E-selectivity-determining transition states, i.e. γ-TS1/2-(1) (associated with Z-product) and γ-TS1a/2a-(1) (associated with E-product). The results show that the HOMO and LUMO energies of γ-TS1/2-(1) are −0.22785 and −0.04229 a.u., respectively, while those of γ-TS1a/2a-(1) are −0.22601 and −0.03699 a.u., respectively. Therefore, the absolute energy difference between E_HOMO and E_LUMO for γ-TS1/2-(1) (5.05 eV) is smaller than that for γ-TS1/2-(1) (5.14 eV), which may accounts for the preferred formation of Z-isomers in experiments.

3.3 Reaction mechanism of the eqn (2) reaction

As shown in Scheme 1, the reactants of the eqn (1) reaction are similar to those of the eqn (2) reaction. However, under the catalysis of DABCO (eqn (1)) and PPh₃ (eqn (2)), the two reactions lead to different products. To better understand why similar reactants exhibit different reactivities, we carried out DFT calculations on the PPh₃-catalyzed annulation reaction of diethylazodicarboxylate R1-(2) with 2-benzyl-2,3-butadienoate R2-(2) in THF as the solvent (the eqn (2) reaction). The detailed mechanism is presented in Scheme 5. The corresponding free energy profile is shown in Fig. 5.

Scheme 5 Possible mechanisms for the eqn (2) reaction.

Fig. 5 Free energy profile of the eqn (2) reaction. The solvation-corrected relative free energies at SMD (THF)/M06-2X/6-311++G(d,p) level are given in kcal mol⁻¹.

The eqn (2) reaction starts with the attack of PPh₃ on R1-(2). To be specific, the P1 atom of PPh₃ attacks the N2 atom of R1-(2) leads to the zwitterionic intermediate 1-(2). The distance of P1–N2 bond is shortened from 2.408 Å in TSR1/1-(2), to 1.682 Å in 1-(2), which indicates that the P1–N2 bond has formed in 1-(2). The first step of the eqn (2) reaction is exergonic by 5.7 kcal mol⁻¹, and the energy barrier of this step is 19.5 kcal mol⁻¹.

Next, the N3 atom of intermediate 1-(2) attacks on the C6 atom of R2-(2) leads to intermediate 2-(2). The gradually shorten bond distance of N3–C6 (1.987 Å and 1.475 Å in TS1/2-(2) and 2-(2), respectively) indicates that the N3–C6 bond is formed. The NBO charge values of C7 increased from −0.210 e in R2-(2), to −0.461 e in TS1/2-(2), then to −0.793 e in 2-(2), demonstrating the association of 1-(2) and R2-(2) increases the negative charge of C7, which facilitate the addition of C7 on C4 in the next step. The energy barrier calculated for the association of 1-(2) and R2-(2) is 26.6 kcal mol⁻¹, and this step is endergonic by 7.6 kcal mol⁻¹ (with respect to 1-(2)).

Subsequently, intermediate 2-(2) undergoes an intramolecular cycloaddition of C7 to C4 generates intermediate 3-(2) via the five-membered ring transition state TS2/3-(2). The bond distance of C7–C4 is shortened from 3.277 Å in 2-(2), to 2.508 Å in TS2/3-(2), then to 1.618 Å in 3-(2), demonstrating the C7–C4 bond has formed in 3-(2). It should be noted that we are unable to locate the transition state connecting intermediates 3-(2) and 4-(2) despite numerous attempts. We examined the optimized structure of 3-(2) and compared with 4-(2), finding that the structures of these two intermediates are very similar. The differences are associated with the four-membered ring P1–N2–C4–O5. The distances of P1–N2/N2–C4/C4–O5/O5–P1 are 1.593/1.534/1.306/2.408 Å in 3-(2) and 1.896/1.440/1.413/1.712 Å in 4-(2). The transformation of 3-(2) to 4-(2) is exergonic by 1.1 kcal mol⁻¹.

The last step of the eqn (2) reaction is the elimination of OPPh₃ from 4-(2) leads to the final product P-(2). The distances of P1–N2 and C4–O5 are elongated from 1.896 Å and 1.413 Å in 4-(2), to 2.449 Å and 1.641 Å in TS4/P1-(2). Meanwhile, the N2–C4 bond is shortened from 1.440 Å in 4-(2), to 1.359 Å in TS4/P1-(2), then to 1.332 Å in P-(2). The above results indicate that with the elimination of OPPh₃, the N2–C4 bond becomes a double bond.

As shown in Fig. 5, the energy barrier calculated for the second step (1-(2) → TS1/2-(2)) is 26.6 kcal mol⁻¹, which is much higher than the other steps. Therefore, this step is the rate-determining step of the eqn (2) reaction.

3.4 Further discussion

On the basis of our calculations, the eqn (1) reaction initiates with the association of DABCO with 2,3-butadienoate leading to the formation of a zwitterionic intermediate, followed by γ-addition to diethylazodicarboxylate. In contrast, the eqn (2) reaction starts with the coupling of PPh₃ with diethylazodicarboxylate. That is to say, the eqn (1) and (2) reactions follow different reaction sequence. To better understand these differences, we explored the possible reaction pathways associated with the coupling of DABCO with diethylazodicarboxylate (Fig. 6a), and PPh₃ with 2-benzyl-2,3-butadienoate (Fig. 6b).

Fig. 6 Free energy profile for the coupling of DABCO with diethylazodicarboxylate (relevant to the eqn (1) reaction) and PPh₃ with 2-benzyl-2,3-butadienoate (relevant to the eqn (2) reaction). The solvation-corrected relative free energies at M06-2X/6-311++G(d,p) level are given in kcal mol⁻¹.

As can be seen from Fig. 6a, the free energy barrier for the reaction between DABCO and diethylazodicarboxylate is 16.6 kcal mol⁻¹, and this process is endoergic by 16.2 kcal mol⁻¹ indicating the reverse reaction (1c-(1) → TSR2/1c-(1)) is very easy to happen, thus the formation of 1c-(1) is highly unfavorable.

As for the coupling of PPh₃ with 2-benzyl-2,3-butadienoate, the free energy barriers are calculated to be 25.5 kcal mol⁻¹ for TSR2/1a-(2) and 25.9 kcal mol⁻¹ for TSR2/1a-1-(2) (Fig. 6b), which are much higher than that associated with the coupling of PPh₃ with diethylazodicarboxylate (19.5 kcal mol⁻¹ for TSR1/1-(2), see Fig. 1). Moreover, as depicted in Fig. 1 and 6b, 1a-(2) and 1b-(2) are much higher than 1-(2). Obviously, formation of 1-(2) is kinetically and thermodynamically much more favorable than formation of 1a-(2) and 1b-(2).

Based on the above results, DABCO prefers to attack allenoate over diethylazodicarboxylate, while PPh₃ preferentially couples with diethylazodicarboxylate. Our calculated results are consistent with experimental observations.^69,71

Moreover, we performed NBO charge analysis for DABCO, 2,3-butadienoate and diethylazodicarboxylate (involved in the eqn (1) reaction), as well as PPh₃, diethylazodicarboxylate and 2-benzyl-2,3-butadienoate (involved in the eqn (2) reaction). The NBO results show that the charges of N1 in DABCO, C2 in 2,3-butadienoate and N5 in diethylazodicarboxylate are −0.550 e, 0.163 e and −0.173 e, respectively, and the charges of P1 in PPh₃, N2 in diethylazodicarboxylate and C6 in 2-benzyl-2,3-butadienoate are 0.855 e, −0.173 e and 0.143 e, respectively. Therefore, the N1 atom of DABCO prefers to attack C2 of 2,3-butadienoate, while the P1 atom of PPh₃ prefers to attack N2 of diethylazodicarboxylate.

4. Conclusion

With the aid of density functional theory (DFT) calculations, we have investigated the mechanisms of the DABCO and PPh₃ catalyzed annulations between allenoates and diethylazodicarboxylate. The calculated results can be summarized as follows:

(1) For DABCO-catalyzed annulation reaction of 2,3-butadienoate R1-(1) with diethylazodicarboxylate R2-(1), the favorable reaction mechanism includes four steps: (i) the nucleophilic attack of DABCO to R1-(1) (step 1), (ii) the involvement of R2-(1) (step 2), (iii) the intramolecular cycloaddition (step 3) and the catalyst DABCO liberation gives the final product 1,2-diazetidine (step 4). The Z-isomer product is the main product, which is in good agreement with experimental findings. The second step is the rate-determining and Z/E-selectivity determining step, the energy barriers via transition state TS1/2-(1) is 22.6 kcal mol⁻¹.

(2) For PPh₃-catalyzed annulation of 2-benzyl-2,3-butadienoate R2-(2) with diethylazodicarboxylate R1-(2), the whole reaction proceeds through four steps: the first step is the coupling of PPh₃ with R1-(2), followed by the addition to the β-carbon atom of R2-(2), the third step is the intramolecular cycloaddition, and the last step is the OPPh₃ liberation leading to the final product pyrazoline. The second step is found to be rate-determining with a barrier of 26.6 kcal mol⁻¹.

Our calculation results are in good agreement with previous experimental findings. In summary, this work provides a detailed mechanistic understanding of the experimental observations.

Acknowledgements

This work is supported by the National Natural Science Foundation of China (No. 21403024), and National Supercomputing Center in Shenzhen.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c6ra19308k

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