1 Introduction

Diazo compounds have been extensively studied during the last few decades, and their value in organic synthesis is well known [1–5]. Transition-metal carbenoids derived from reactions of diazo compounds with a variety of metal complex are versatile intermediates in organic synthesis [6]. For several years, the rhodium-catalyzed reactions of donor/acceptor-substituted carbenoids have been explored, and the results showed that those carbenoids display much greater chemoselectivity when compared to the more conventional acceptor-substituted carbenoids [7–10]. A clear example of this effect is seen in a Hammett study of intermolecular cyclopropanation of para-substituted styrenes (Scheme 1) [11]. Electronic character of styrenes [ρ value of −0.9 (σ + scale)] can strongly affect the relative rates of reaction of methyl phenyldiazoacetate with various styrenes, while ethyl diazoacetate shows virtually no selectivity [11]. The greater chemoselectivity of the donor/acceptor carbenoids has opened up a number of reactions that were previously not viable with conventional carbenoids. In particular, vinylcarbene intermediates derived from vinyldiazoacetates exhibit a high level of selectivity in cyclopropanation [12–14] and carbon–hydrogen insertion reaction [15–17] and can participate in a diverse array of more elaborate transformation [15, 18, 19], such as the combined C–H insertion/cope rearrangement [18], and the ylide formation/[2,3]-sigmatropic rearrangement/oxy-cope rearrangement/ene reaction cascade sequence [19]. Furthermore, their propensity for formal [3+2] [20–22] and [4+3] [23–26] cycloaddition reactions has been demonstrated.

Scheme 1
scheme 1

Competition reaction with styrene. Using metal carbenoids. Reproduced with permission from Ref. [11] Copyright 2000, ScienceDirect

Full size image

Recently, Doyle et al. reported an efficient and highly regioselective cycloaddition reaction between the vinylcarbene from methyl 2-diazo-3-butenoate 1 and diverse nitrones catalyzed by rhodium octanoate [Rh2(Oct)4] (Scheme 2) [27]. The dirhodium vinylcarbene induced nitrone cycloaddition with subsequent cascade carbenoid aromatic cycloaddition/N–O cleavage, and rearrangement (CACR) gave products which have both oxygen and nitrogen-fused rings and a quaternary carbon in the middle. The compound structure obtained by X-ray diffraction of a single crystal reveals that extensive rearrangement has occurred, and the carboxylate group from the vinyldiazoacetate is bound to the quaternary carbon that connects the tricycle. Even though the reactions were carried out at room temperature, the products of the process were formed with remarkable specificity, and this type of reaction can be used as a general and selective method for preparation of multi-functionalized tricyclic heterocycles through an abnormal cascade process. A further surprising feature of the reactions is that, with meta- and ortho-substituents on the N-aryl group, cyclopropanation could have occurred on either side of the N-aryl bond, which would have led to the formation of two regioisomers; however, only a single regioisomer was formed in high yields. Therefore, this multi-step cascade process occurred with very high regiocontrol. This class of reaction has already become a standard method for laboratory and is being considered as a promising protocol for commercial process [28–30].

Scheme 2
scheme 2

Dirhodium vinylcarbene-induced nitrone cycloaddition with subsequent cascade carbenoid aromatic cycloaddition/N–O cleavage and rearrangement (CACR)

Full size image

In light of the experimental results and for further development of the CACR chemistry, it was felt that the deeper understanding of the reaction mechanism, in particular the origins of the observed selectivity on the molecular scale, was indispensable. We report herein the pathways of the rhodium-catalyzed reactions of methyl 2-diazo-3-butenoate and nitrone by using the density functional calculations, which provide the first qualitative account of the experimental data, as well as the structures of important intermediates and transition states involved in the catalytic cycle. The calculations explain how the CACR happens and disclose the reason why the reaction can have such high regioselectivity. It is worthwhile to mention that this is the first report on reaction mechanism for the CACR reaction in detail. The theoretical analysis of the properties of intermediates and transition states revealed unique roles of the rhodium carbene. The studies and mechanistic insights obtained herein can ultimately provide value in accelerating the design and optimization of catalytic processes of transition-metal-catalyzed carbene procedures.

2 Computational methods

2.1 Models

In the present work, we have studied a catalytic model reaction between vinylcarbenoid complex 2 and nitrone 3 to form two different products 4 and 5 using dirhodium tetrakis (formate), Rh2(O2CH)4, as a model of a common catalyst [31–34] (Scheme 3). Product 4 is in accord with the actual synthetic compound. The reaction to generating product 5 has not been reported in the literature and was investigated herein for comparison in regioselectivity. These model reactions serve to investigate the fundamental properties of the dirhodium carbene complex, as well as the mechanism and regioselectivity of CACR reactions. The vinylcarbenoid model 2 has been described in previous computational studies on cyclopropanation chemistry [31, 34]. This study is focused on an analysis of how the rhodium carbenoid reacts with the nitrone. For detailed discussions on the formation of the reactive vinylcarbenoid complex, see Refs. [31, 34].

Scheme 3
scheme 3

Model reactions for the computational studies

Full size image

2.2 Computational details

All of the calculations were performed with the Gaussian 09 software package [35]. Density functional theory (DFT) was employed using the three-parameter hybrid functional B3LYP [36, 37] to locate stationary points on the potential energy surface (PES). Structures were optimized with a basis set consisting of the 1997 stuttgart relativistic small-core effective core-potential and basis set [Stuttgart RSC 1997 ECP] [38–40] for Rh, augmented with a 4f-function (ζ f (Rh) = 1.350) [31] and the split valence basis set 6-31G(d,p) for all other atoms (C, H, N, Cl and O). The method and the basis sets used here are known to give reliable results for rhodium (carbene) reactions [5]. This composite basis set is abbreviated 6-31G(d,p)[Rh-RSC+4f]. The main discussion is based on single-point energies calculated at the B3LYP/6-311+G(2d,2p)[Rh-RSC+4f]//B3LYP/6-31G(d,p)[Rh-RSC+4f] level of theory, with zero-point energy corrections calculated at the B3LYP/6-31G(d,p)[Rh-RSC+4f] level and Gibbs free energies calculated at the B3LYP/6-31G(d,p)[Rh-RSC+4f] level of theory. Heavy-atom basis set definitions and corresponding pseudopotential parameters were obtained from the EMSL basis set exchange library [41, 42]. Each stationary point was adequately characterized by normal coordinate analysis (only one imaginary for a transition state and no imaginary frequencies for an equilibrium structure). The intrinsic reaction coordinate (IRC) analysis [43] was carried out throughout the reaction pathways to confirm that all stationary points are smoothly connected to each other.

To evaluate the effect of the solvent polarity on the energetics of CACR reactions, a single-point energy calculation was performed with self-consistent reaction field (SCRF) method [based on the SMD model [44], ε = 10.125 for dichloroethane (DCE)]. Natural population analysis and natural bond orbital (NBO) analyses were carried out at the same level as the one used for geometry optimization [45, 46]. All charge distribution analyses discussed throughout this article are made on the basis of the nature population analysis.

3 Results and discussion

3.1 Reaction to produce the real product 4

First, we investigated the reactions of 3 with vinylcarbenoid complex 2 to generate product 4 as a basic model reaction. Scheme 4 shows the reaction course that the catalytic cycle involves five steps. The free energy profile of this CACR reaction in the gas phase is given in Fig. 1. First, 3 and 2 interact through a stepwise [3+2] cycloaddition to form the complex III. The formation of C–O bond proceeds via TSI with an activation free energy of 2.8 kcal/mol, which is followed by the formation of C–C bond with the activation free energy barrier of 4.5 kcal/mol. Subsequent intramolecular cyclopropanation by the rhodium carbene on the nitrogen-bound aryl group is proposed to form intermediate V via two transition states TSIII and TSIV with the free energy barriers of 10.2 and 7.6 kcal/mol, respectively, and the catalyst is regenerated. The next step toward the final product first involves an electrocyclic opening of the cyclopropane ring (aromatic cycloaddition) to form intermediate VI via TSV with a free energy barrier 4.5 kcal/mol. Unexpected and unique N–O bond cleavage and [1,7]-oxygen migration then take place through TSVI with the largest free energy barrier of 22.2 kcal/mol followed by a downhill path to the final product with large exothermicity (64.7 kcal/mol). In TSVI, the cleavage of N–O bond and migration of oxygen to conjugated olefinic carbon atom take place simultaneously in a single step. No intermediates were located near TSVI along the intrinsic reaction coordinate.

Scheme 4
scheme 4

Pathway of the Rh2(O2CH)4-catalyzed CACR reaction of 2 and 3 to produce 4

Full size image
Fig. 1
figure 1

Free energy profile of the Rh2(O2CH)4-catalyzed CACR reaction of 2 and 3 to produce 4 at the B3LYP/6-311+G(2d,2p)[Rh-RSC+4f]//B3LYP/6-31G(d,p)[Rh-RSC+4f] level. The result of the free energies in gas phase is given in red, and the result of the free energies in DCE is shown in blue

Full size image

To probe the solvent effect on the reaction energetics, SCRF calculations (SMD model) were performed based on the gas-phase geometry. Dichloroethane (DCE, ε = 10.125) was investigated as the solvent because it is used for the CACR reaction in practice. The relative free energies of the stationary points on the potential energy surface in DCE are also given in Fig. 1 (in blue). The free energy profile did not change very much from the one in the gas-phase calculations. The N–O cleavage and [1,7]-oxygen migration processes have the largest free energy barrier (19.6 kcal/mol in DCE). Therefore, this step can be regarded as the rate-determining step (RDS). Moreover, the free energy barrier for TSVI has a small decrease, and the energy barrier for cyclopropanation has a slight increase. As compared to the free energy profile in gas phase, the [1,7]-oxygen migration step has the highest energy barrier, which suggests that how to overcome the energetic bottleneck for the [1,7]-oxygen migration becomes very crucial for accelerating the reaction rate.

The 3D structures of representative stationary points are shown in Fig. 2. The Rh1–Rh2 bond of I has no significant change toward the formation of the complex III (2.479 → 2.474 Å). The Rh1–C1 bond of I (2.036 Å) has a significant increase in first to form the intermediate II (2.103 Å) and then shortens through the C–C bond formation stage TSII (2.063 Å) to form the complex III (1.981 Å, 5.8 % decrease), which indicates that II barely has the character of carbene complex. To probe the function of the nuclear structure of the dirhodium catalyst, we analyzed the nature of the Rh–Rh–C π and σ-bond systems in II (carbene complex). Important orbital of II is shown in Fig. 3. LUMO of the complex II was found to be exactly what is expected and composed mainly of the carbene 2p orbital, which accepts rather small back-donation form the Rh1 4dxz orbital to form an extended π*-system that possesses a strongly electrophilic carbene carbon.

Fig. 2
figure 2

B3LYP/6-31G(d,p)[Rh-RSC+4f] structures of stationary points in CACR reaction of 2 and 3–4. The numbers refer to bond length (Å)

Full size image
Fig. 3
figure 3

Electronic structure and shape of the frontier electronic level (LUMO) of complex II

Full size image

Analysis of the charge distribution during the reaction course was found to be informative and showed strong parallelism between this realistic model to form 4 (Fig. 4a), and the model to form 5 discussed later (Fig. 4b). The nitrone moiety releases negative charge (C4: +0.03 → +0.16, O6: −0.51 → −0.42) upon formation of II, and the negative charge moves largely into the vinylcarbene carbon C1 (+0.04 → −0.12) and the N5 atom (+0.09 → +0.01). In the C2–C4 bond formation stage (TSII), the nitrogen moiety becomes less positive (N5: +0.01 → −0.15, C4: +0.16 → −0.06), and the carbene carbon becomes cationic (−0.12 → +0.16).In the complex IV, the benzene ring attached to N5 atom significantly becomes more positive (C7: +0.15 → +0.31), because the negative charge moves largely from the p-type orbital of the C7 into the C1 atom. The Charge of the Rh1 and Rh2 atoms changes just a little during the C1–C8 bond formation (Rh1: +0.44 → +0.47; Rh2: +0.51 → +0.55).However, in the C1–C7 bond formation, Rh1 and Rh2 lose a lot of negative charge (Rh1: +0.47 → +0.68; Rh2: +0.55 → +0.68) and C7 becomes less positive (+0.31 → +0.13), which is in accord with the removing of the donation from carbene to Rh. In the electrocyclic reaction TS (TSV), the C1–C7 and C1–C8 bond significantly shorten (1.580–1.503 and 1.537–1.490 Å, respectively.), and C7 and C8 atom lose negative charge (C7: +0.13 → +0.20, C8: −0.26 → −0.19). The negative charge moves largely into the C1 atom (−0.16 → −0.22). In [1,7]-oxygen migration step, the C7–N5 bond shortens (1.449 Å → 1.282 Å), and the benzene ring attached to N5 loses negative charge (C7: +0.20 → +0.25, C8: −0.19 → +0.06). The nitrone moiety becomes negatively charged (N5 decrease by +0.21) because of forming of the C7–N5 π-bonding electrons. Some negative charge is also transferred to the O6 atom (−0.13).

Fig. 4
figure 4

Charge distribution along the reaction coordinate for a the reaction to 4 and b the reaction to 5

Full size image

3.2 Reaction to produce isomer 5

Furthermore, to prove the reasonableness of the mechanism proposed for the above catalytic system and gain insight into the influencing factors for highly regioselectivity for the present reaction, the other reaction of nitrone 3 with dirhodium vinylcarbene 2 to produce 5 was investigated. The free energy profile along the reaction progress is shown in Fig. 5. To make a concise expression, the detailed reaction mechanism to form 5 is shown in Fig. 6. The reaction pathway and the energetics obtained for this reaction are essentially the same as those of the reaction to form 4 (Fig. 1). The CACR reaction also starts with the [3+2]-cycloaddition. This step goes through stepwise mechanism via TSVII and TSVIII with low free energy barriers of 3.2 and 3.8 kcal/mol, respectively, in the gas phase. The charge distribution shows the same tendency as found for the reaction to form 4. In the next cyclopropanation step, carbene atom C1 reacts with C9 instead of C8 to form the intermediate IX. Unlike the result in the reaction to obtain 4, the C1–C9 bond formation step process via transition state TSIX with a significantly higher activation free energy (18.1 kcal/mol in gas phase). In the next electrocyclic opening of the cyclopropane ring, the free energy barrier for overcoming TSXI is much lower (∆G ≠ = 5.7 kca/mol). Downhill from TSXI, seven-membered ring intermediate XI is formed. Since the activation of the N–O bond is poor, the electrophile attack of O to C9 via a concerted transition state TSXII requires a higher Gibbs free energy of activation of 22.0 kcal/mol in gas phase, which is nearly identical with that of the reaction to form 4 (22.2 kcal/mol). When taking the solvent effect into consideration, the energy profile has a little different from that in gas phase. The step of [1,7]-oxygen migration also bears a large free energy barrier (19.2 kcal/mol), which indicates that the oxygen migration is also difficulty in all cases. However, in the reaction to form 5, the C1–C9 bond formation bears the largest energy barrier (19.8 kcal/mol) and the cyclopropanation step has become the rate-determining step (RDS).

Fig. 5
figure 5

Free energy profile of the Rh2(O2CH)4-catalyzed CACR reaction of 2 and 3 to produce 5 at the B3LYP/6-311+G(2d,2p)[Rh-RSC+4f]//B3LYP/6-31G(d,p)[Rh-RSC+4f] level. The result of the free energies in gas phase is given in red, and the result of the free energies in DCE is shown in blue

Full size image
Fig. 6
figure 6

B3LYP/6-31G(d,p)[Rh-RSC+4f] structures of stationary points in CACR reaction of 2 and 3–5. The numbers refer to bond length (Å)

Full size image

Two reactions mentioned above affording 4 and 5 are two parallel. Based on our calculational results, although the free energy barrier of RDS to 5 is larger than that to 4, the difference between those two reactions is small. So the reaction dynamics is not the main factor responsive to the fact that the amount of product 4 dominates over 5 in DCE. We noted that an acidic additive 1,1,1,3,3,3-hexafluoro-2-propanol (HFIP) was used to capture the basic product in the experiment research [27]. So the proportion of alkaline dissociation equilibrium constant K b values of products 4 and 5 was also calculated in our study according to the Eqs. (1) and (2).

$$ {\text{B }} + {\text{ H}}^{ + } \, \overset {\Delta G_{B}^{\theta } } \rightleftharpoons {\text{ BH}}^{ + } $$
(1)
$$ \frac{{K_{b,4} }}{{K_{b,5} }} = \exp \left( { - \frac{{\Delta G_{4}^{\theta } -\Delta G_{5}^{\theta } }}{RT}} \right) = \exp \left( {\frac{{G_{4}^{\theta } - G_{{{\text{H}}4^{ + } }}^{\theta } - G_{5}^{\theta } + G_{{{\text{H}}5^{ + } }}^{\theta } }}{RT}} \right) $$
(2)

where ΔG θ4 and ΔG θ5 are the free energy changes of reactions corresponding to producing 4 and 5 in the standard state, respectively. R is mole gas constant, and T equals to 298.15 K. Table 1 lists the Gibbs free energies of product 4 and 5, as well as their corresponding protonated substances H4 + and H5 +. It is easy to find that the basicity of the product 4 is stronger than that of the product 5. As a result, HFIP more easily reacts with 4 than 5, and thus, the reaction equilibrium will move to the formation of product 4, which is consistent with the experimental results that the reaction between 1 and 3 has high regioselectivity.

Table 1 Gibbs free energy (in kcal/mol) of product 4 and 5, and their corresponding protonated substances H4 + and H5 + in DCE
Full size table

It is well known that rhodium carbenoids are Fischer-type carbenoids (see Fig. 7). From the charge distribution along the reactions, it is clear that the carbene C1 atom occurs electrophilic addition, along with a significant reduction of its charge. When there is an electron-withdrawing group such as chlorine at C10 of nitrone,the charge density of chlorine’s ortho-site decreases due to the negative inductive effect of chlorine. On the other hand, the electron density on C8 is slightly affected by the negative inductive effect of chlorine. Therefore, the electrophilic addition is more likely to occur at C8 site, rather than C9 site.

Fig. 7
figure 7

Fischer and Schrock-type carbenoids

Full size image

4 Conclusion

On the basis of our theoretical computations, we have developed a mechanistic proposal for the CACR reaction. The present studies have revealed, for the first time, the energetics, the electronic nature, and the 3-D structures of the intermediates and the transition states in the catalytic cycle of the dirhodium vinylcarbene-induced nitrone cycloaddition with subsequent cascade carbenoid aromatic cycloaddition/N–O cleavage and rearrangement. The reaction of vinyldiazoacetate-induced nitrone starts from the stepwise [3+2] cycloaddition. Subsequent intramolecular cyclopropanation and electrocyclic opening of the cyclopropane ring by the rhodium carbene on the nitrogen-bound aryl group take place to form a heptatomic ring intermediate. A [1,7]-oxygen migration to final product occurs via a concerted transition state. The reactions to form 4 and 5 have similar mechanisms, and the step of cyclopropanation is the regioselectivity determining step. With meta-substituent (Cl) on the N-aryl group, the charge density of chlorine’s ortho-site decreases due to the negative inductive effect of chlorine. Therefore, as compared to the electrophilic addition on the C8 atom, the electrophilic addition on the C9 site owns a significantly incensement on the energy barrier of cyclopropane (TSIII and TSIX). Since the basicity of the product 4 is stronger than that of the product 5, the acidic additive HFIP promotes the formation of product 4.

5 Supporting information

The optimized Cartesian coordinates and geometrical structures of all stationary points along the potential energy profiles. This material is available free of charge via the Internet at http://springerlink.lib.tsinghua.edu.cn/content/.