Computational study on the mechanism and enantioselectivity of Rh₂(S-PTAD)₄ catalyzed asymmetric [4+3] cycloaddition between vinylcarbenoids and dienes

Abstract

In this paper, the mechanism of chiral rhodium-catalyzed [4+3] cycloaddition between a vinylcarbenoid and a diene to form cycloheptadiene has been studied using a two-layer ONIOM methodology consisting of density functional theory and semiempirical PM6. The mechanism involves the formation of vinylcarbenoid via nitrogen extrusion, cyclopropanation to form a divinylcyclopropane through removal of the catalyst, followed by Cope rearrangement of the resulting cis-divinylcyclopropane to form a cycloheptadiene. In this study calculations were carried out on tandem reactions of vinyldiazoacetate and siloxyvinyldiazoacetate with the consideration of geometric isomerism. Through the analysis of thermodynamics and kinetics the Cope rearrangement involving a boat transition state was determined as the rate-controlling step. The computational results indicated that siloxy substituted vinylcarbenoid displays a higher energy barrier and obtains reasonably higher enantioselectivity than for cyclopropanation of unsubstituted vinylcarbenoid, thus it has a critical influence on the favored product of ring extension and the chemical activity. Besides, the geometric isomerism of the substrates and the trapping approach were predicted to have full control over the stereogenic center of the final product rather than the enantioselectivity. Moreover, a desired relationship between the properties of the substrates and reaction energies has been established to understand the reactivity trend by activation strain model (ASM). Finally, an energy span model and AUTOF program were used to create a link between the catalytic cycles and the properties of the substrates.

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1. Introduction

Seven-membered rings that widely exist in useful natural and unnatural products have a long history of being explored and it is still a very active field.^1–4 Up to now many synthetic methods for functionalizing seven-numbered rings have been developed, while the tandem [4+3] cycloaddition between vinylcarbenoid and diene developed by the Davies group has been a general method with high stereoselectivity.^5,6 This model begins with a concerted but asynchronous^7,8 cyclopropanation of a metal vinylcarbenoid with a suitable diene trap to generate a slight preference for cis-type divinylcyclopropane with loss of the metal catalyst,⁹ and this step is proposed to preferentially occur on the side of the electron withdrawing group.¹⁰ Moreover, the carbenoid can be sensitive to the environment of the alkene trap, the electronic nature of the trapping agents can influence the reaction rate of cyclopropanation,⁹ and the alkene traps will only be the monosubstituted alkene, 1,1-disubstituted alkenes, and cis 1,2-disubstituted alkenes.¹⁰ This is subsequently followed by a Cope rearrangement to form a cycloheptadiene through a boat transition state with full control of the relative stereochemistry.¹¹ A donor/acceptor carbenoid has been widely demonstrated for the high enantioselectivity in the transformation through the comparison with an acceptor carbenoid in experimental and computational studies as well as kinetic isotope effects.^11–18 As shown in eqn (1)–(3),^19–23 in practical experiments the stable phenylcarbenoid obtains a relatively high level of diastereoselectivity. Consistently, the computed phenylcarbenoid displays a 4.5 kcal mol⁻¹ energy barrier while methyl carbenoid is almost enthalpically barrierless.²⁴ Furthermore, the carbenoid intermediate with a donor siloxy group tends to favor the formation of the target product with high enantioselectivity.^25–29

The chiral catalyst used in the carbenoid reaction possibly leads to a significantly higher diastereoselectivity.^30–33 Specific metal–ligands combinations can lead to a high asymmetric induction because the given metal carbenoid intermediates can distinguish between the potentially competing carbenoid reactions and/or the paths to different stereoisomers.³⁴ For instance, the adamantyl variant Rh₂(S-PTAD)₄ is rather favorable for Cope rearrangement with high chemoselectivity compared to other carbenoid reactions.^29,35 Dirhodium(II) tetracarboxylates incorporating N-phthaloyl-(S)pathalimido have been presented as high-efficiency catalysts for carbenoid reactions and there are two general symmetric conformations with different arrangements of the pathalimido groups.^2,13,36 One is Rh₂(S-PTPA)₄ developed by Hashimoto's group³⁷ which has a C₂ symmetric conformation with the pathalimido groups aligned in a “down-down-up-up” arrangement, and the other is Rh₂(S-PTTL)₄ presented by Fox's group which adopts a “chiral crown” conformation, and the pathalimido groups are in an “all-up” arrangement with a considerably distorted C₄ symmetry.^38–40 Recently the latter model was broadly utilized in relevant catalysts by other groups.^41–45 Besides, in cyclopropanation the donor/acceptor carbenoid was predicted to prefer the staggered arrangement rather than the eclipsed conformation that is adopted by the acceptor carbenoid.^10,24 In order to avoid steric hindrance of the bulky carbenoid, the alkene tends to trap the rhodium carbenoid in an end-on way^46,47 and the C–C bond of the diene aligns parallel to the Rh–C bond.^48,49

In this study, the first section gives a brief summary of the mechanism of the asymmetric [4+3] cycloaddition reaction. Based on the reported unusual donor/acceptor carbenoid, in the second section we extend the computational study to the tandem reactions of siloxy substituted vinyldiazoacetate and unsubstituted vinylcarbenoid to understand the influence of the siloxy group on the reactivity and enantioselectivity using the metal catalyst Rh₂(S-PTAD)₄ with the “chiral crown” conformation. In the third section further studies on tandem reactions of geometric isomers of substrates are presented and the relevant calculations estimate the main factors resulting in the final product with the specific stereogenic center. This is followed by analysis of the decomposition of the potential barriers using the activation strain model (ASM) to provide a causal relationship between the chemical reactivity and the nature of the substrates and indicates that in the transformation the interaction energies of the siloxy species between the deformed reactants are reasonably higher. In the final section, the influence of the substituent and geometric isomerism of the substrates on the catalytic activity is estimated using the AUTOF program.

2. Computational methods

All calculations were performed using the Gaussian'09 software package.⁵⁰ For fear of taking up considerable computational time the calculations on the rhodium system were carried out with a two-layer ONIOM methodology.⁵¹ As shown in Fig. 1, the substrates and dirhodium(II) carboxylates were in the high level layer and subjected to geometry optimization with a DFT/B3LYP^52,53 level of theory that included the LANL2DZ basis set (aliased and denoted [Rh-LA2] in the following) for Rh and the 6-31G(d) basis set for smaller atoms.^54–56 The ligands including adamantyl variants and pathalimidos were in the low level layer and semiempirical PM6 was used.⁵⁷ Heavy-atom basis set definitions and corresponding pseudopotential parameters were obtained from the EMSL basis set exchange library.^58,59 Vibrational contributions to the Gibbs free energy were calculated at the same level of optimization to obtain ZPVE and thermal corrections to the Gibbs energy (298.15 K and 1 atm). Equilibriums were confirmed to have zero imaginary vibrational modes and only one imaginary vibrational mode for each transition state was estimated.⁶⁰ Transition states were further characterized using intrinsic reaction coordinate (IRC) analysis with the EulerPC algorithm for the Rh system and the HPC algorithm for small systems to affirm that the stationary points were smoothly connected to either direction.^61–66 Solvent energies were evaluated using the self-consistent reaction field (SCRF) method based on the CPCM model^67,68 in toluene (ε = 2.37), solvation calculations were carried out at the higher B3LYP/6-311+G(d,p) level for the small atoms in the high-level layer using gas phase optimized structures. All discussed relative energies in the main text and ESI† refer to the Gibbs free energies in toluene with thermal corrections, unless specifically mentioned.

Fig. 1 The side and top views of Rh₂(S-PTAD)₄ in the ONIOM model.

The ASM is a computational approach which provides insight into the physical factors which govern the potential activation barriers among the competing pathways in a quantitative and qualitative way.^69–72 This method creates a causal link between the reaction barriers and the nature of the reactants as well as the characteristics of the chemical mechanism to understand the reactivity trend. For a method that is a fragment approach to predict the corresponding influence of various species on the activation barriers,⁷³ in the ASM along the reaction coordinate ζ the potential energy surface ΔE(ζ) can be decomposed into two portions, one is the strain energy ΔE_strain(ζ) that comes from the distortion of the reactants during the equilibrium geometry transformations corresponding to the transition state, and the other is the interaction ΔE_int(ζ) that is derived from the electronic structure and the mutual interaction between the increasingly deformed reactants:

ΔE(ζ) = ΔE_strain(ζ) + ΔE_int(ζ) (4)

In a catalytic reaction the turnover frequency (TOF), the number of cycles performed per unit time and catalyst concentration, is used to measure the efficiency of a catalyst. The energetic span model^74–79 significantly allows the estimation of the TOF of a catalytic reaction from the energy profile using eqn (5), and makes a correlation between the results of computational and experimental chemistry.

The “degree of TOF control” (X_TOF) is the quantification of the influence of all intermediates and transition states on the TOF performed using the energetic span model to determine the TOF determining intermediate (TDI) and the TOF transition state (TDTS). In addition, based on the degree of rate control the X_TOF was developed to measure the variation from a small change in a transition state or intermediate energy.^80–82 Once the TDI and TDTS have been estimated, the representation of TOF can be simplified to eqn (6):⁷⁵

with
δE is the energetic span as well as the apparent activation energy of the full cycle. Moreover, the simplified approximation is valid only when one intermediate and one transition state is estimated with X_TOF > 0.00. The AUTOF program was used to assess TOF and degrees of TOF control by calculating the complete model in a black box fashion.⁸³ Ultimately the kinetic information will be provided by the energetic span model and the AUTOF program to understand the critical factors of the computational catalytic cycles.

Functional effects, basis set effects and solvent effects were evaluated detailedly and are illustrated in the ESI.† We point out here that, the energy barriers of the sample reaction using M06L⁸⁴ and B3LYP-D3 (ref. 85) with the BJ-damping (-D3(BJ))⁸⁶ methods at the high level of the ONIOM methodology of this system are slightly higher than the original result and not more than 0.5 kcal mol⁻¹, while that using the M062X method⁸⁷ is lower than 1.4 kcal mol⁻¹. The inconformity between the functionals can be ascribed to the differences in describing the dispersion interactions in various ranges. On the other hand, in common practice for transition metal homogeneous catalysis, the ONIOM methodology with the B3LYP level in the high layer has allowed the selectivity and substituent effects to be computed with chemical accuracy for realistic experiments,^38,88–91 thus we chose this method to evaluate the present system. Besides, the discrepancies of the energy barriers for the example reaction, induced by higher basis sets or geometries optimization in the solvent, are not more than 0.1 kcal mol⁻¹ from the original result.

3. Results and discussion

Summary of the mechanism of [4+3] cycloaddition

The general pathway for the synthesis of the functional seven-membered ring in this study is shown in Scheme 1. The first step describes the formation of metal carbenoid 5 from the diazoacetate 2 catalyzed by metal–ligands 1. In this process the rhodium catalyst 1, as a Lewis acid, accepts the electron density from the carbene carbon of the vinyldiazoacetate 2, subsequently the back donation of electron density from the rhodium to the carbene carbon is considered and then the vinylcarbenoid intermediate 5 is formed with loss of nitrogen 4.³⁴ In the following concerted cyclopropanation step, the carbenoid carbon of vinylcarbenoid 5, an electrophilic reagent, accepts electron density from the trapping agent 6 and goes through a transition state 7 to generate a cis-type divinylcyclopropane 8 with removal of the catalyst 1. Ring extension of the resulting divinylcyclopropane proceeds easily in a stereoselective manner and has been used for stereoselective synthesis of various ring systems,³ thus in the eventual step the divinylcyclopropane 8 goes via a boat transition state 9 to form the cycloheptadiene 10 with full control of the relative stereochemistry at the stereogenic centers. At this point highly functionalized cycloheptadienes are finally obtained. For the geometric requirements of orbital overlap, the Cope rearrangement must occur on the same side, only in this way can the divinylcyclopropane go through a boat transition state state with a cis-type double bond. Otherwise the ring strain will be too large if the boat transition has a trans-double bond. Some rhodium amide¹⁹ and ruthenium catalysts^92–94 support the formation of trans-type cyclopropanes while the bulky catalysts lead to a slight preference for cis-type cyclopropanation.^95–98 In the following, the approach of diene traps from either the ester-group side or the ether-group side has been considered and in this case the generated divinylcyclopropanes with two stereogenic centers can be enantiomers of each other.

Scheme 1 Reaction pathway for the tandem reaction.

Substituent effects of the [4+3] cycloaddition reaction

All of the known donor/acceptor carbenoids are more stable than acceptor carbenoids. In addition, silylenol ether has a special structure which is specific to silyl-ether, and is often used as the auxiliary group to protect the carbonyl group in organic synthesis or as an intermediate to accomplish complicated reactions, such as regioselective synthesis. Silyl-ether is easily prepared and under mild conditions it is prone to hydrolysis. Thus vinyldiazoacetate with a siloxy group is hypothesized to make the metal carbenoid more stable, achieving higher enantioselectivity in cyclopropanation and playing a critical influence on the reactivity of this tandem reaction than unsubstituted vinylcarbenoid. In order to prove this assumption, this section reports the first series of computational studies on the tandem reactions of vinyldiazoacetate 2a-I (an isomer of vinyldiazoacetate 2a, C=C–C=N₂ s-cis) and siloxyvinyldiazoacetate 2b-I (an isomer of siloxyvinyldiazoacetate 2b, C=C–C=N₂ s-cis) with the trapping agent s-cis diene 6-I. The relative energies of the potential energy surface are shown in Fig. 2.

Fig. 2 The potential energy profiles for the calculated cycloaddition reactions of vinyldiazoacetate 2a-I (A) and siloxyvinyldiazoacetate 2b-I (B) with 6-I. The paths for the resulting R-cycloheptadiene are shown in red while those for S-cycloheptadiene are shown in blue.

In the first step of carbenoid formation, vinyldiazoacetate 2a-I undergoes an energy barrier of 12.1 kcal mol⁻¹, while siloxyvinyldiazoacetate 2b-I has a barrier of 6.8 kcal mol⁻¹. The former leads to an exothermic energy of −11.4 kcal mol⁻¹, and the reaction energy of the latter is −16.0 kcal mol⁻¹. In the same process, Davies' group reported that in the nitrogen extrusion step phenyldiazoacetate displays an energy barrier of 11.3 kcal mol⁻¹, whereas the barrier of methyl diazoacetate is 11.9 kcal mol⁻¹. An interesting finding above is that the diazoacetates with a stronger donor group have lower energy barriers. Also the reaction energies of the diazoacetates with a stronger donor group are more exothermic in the process of carbenoid formation, correspondingly the acceptor methyl diazoacetate has been predicted to be endothermic by +5.3 kcal mol⁻¹. This can be attributed to the electrophilic character of the donor/acceptor diazoacetates, and generally the diazoacetates with a stronger donor group will be more stable.

In the subsequent step of trapping the carbenoid, the actual diene 6-I can approach the vinylcarbenoid 5a-I from either the side of the ester group or the side of the ether group. Trapping from the ester-group side, vinylcarbenoid 5a-I undergoes a cyclopropanation through a transition state 7a-I with a barrier of 5.7 kcal mol⁻¹, and results in the formation of (S,S) divinylcyclopropane 8a-I which contains two stereogenic centers and has an exothermic energy of −34.8 kcal mol⁻¹. Conversely, the actual diene 6-I trapped from the ether-group side overcomes a barrier of 3.3 kcal mol⁻¹ to form the (R,R) divinylcyclopropane 8a-II, and this process is exothermic by −25.7 kcal mol⁻¹. For the C=C–C=N₂ s-cis siloxyvinylcarbenoid 5b-I, no matter from which side the actual diene traps, the energy barriers of cyclopropanation are both higher than that of vinylcarbenoid 5a-I. The approach of the trapping agent 6-II from the ester-group side of the carbenoid 5b-I via a boat transition state with a barrier of 9.6 kcal mol⁻¹ forms the (R,S) divinylcyclopropane 8b-I, and approaching from the ether-group side the carbenoid 5a-I overcomes a potential energy barrier of 11.3 kcal mol⁻¹ to obtain the enantiomer 8b-II. In this process, the former has an exothermic energy of −33.4 kcal mol⁻¹, and the latter process releases an energy of −29.4 kcal mol⁻¹. A previous study indicated that in cyclopropanation a phenylcarbenoid gains an energy barrier of −9.1 kcal mol⁻¹, while the transition structure of methylcarbenoid is located on the free energy potential surface. Similarly, for some other acceptor carbenoids it has been reported that the energy of the approximate transition state in cyclopropanation is lower than the metal carbenoid, thus this carbenoid is seen as enthalpically barrierless.^9,16 Compared with the barriers of the donor/acceptor carbenoids described above, we find that the siloxy substituted vinylcarbenoid gains a higher energy barrier in this carbenoid reaction. In a Hammett study for the cyclopropanation system with a series of styrenes, phenyldiazoacetate obtains a ρ value of −1.0, while methoxy phenyldiazoacetate gains a ρ value of −1.3. In this paper, the donor siloxy group imparts a much higher carbenoid stability and leads to the appearance of a relatively late transition state with a more stabilized positive charge build-up, and this result is consistent with the above. The main structures involved in the first series of calculations are shown in Fig. 3. The lengths between the vinylcarbenoid carbon and β-site carbon of the trapping agent marked in the trigonal transition states of the vinylcarbenoids range from 2.93 Å to 3.05 Å, and this observation suggests that this bond is slightly formed. Due to the bond length of the carbenoid carbon and the α-site carbon of the trapping agent ranging from 2.39 Å to 2.61 Å, a concerted but highly asynchronous transition state is estimated once again. In the cyclopropanation of vinylcarbenoid 5a-I with an ester-group approach, the Rh–C bond is elongated from 2.00 Å in the free carbenoid complex to 2.05 in the transition state 7a-I, for the same process with siloxyvinylcarbenoid 5b-I the Rh–C bond increases by 0.07 Å, which is consistent with the calculated later transition state 7b-I with a more stabilized positive charge build-up. Thus the vinylcarbenoid 5b-I has been estimated to have a higher level of enantioselectivity and this is consistent with the practical experiment.¹³

Fig. 3 Structural views of the transition states for the cycloaddition reaction of vinyldiazoacetate 2a-I and siloxydiazoacetate 2b-I with trapping agent 6-I, catalyzed by Rh₂(S-PTAD)₄.

In the final Cope-rearrangement step, with two stereogenic centers disappearing and formation of one other stereogenic center, the (S,S) divinylcyclopropane 8a-I goes through a transition state 9a-I with a 24.3 kcal mol⁻¹ activation energy to generate the R-cycloheptadiene 10a-I. This reaction has a predicted exothermic energy of −13.2 kcal mol⁻¹. The enantiomer 8a-II undergoes a lower transition state 9a-II with a 21.1 kcal mol⁻¹ energy barrier, and renders the formation of the favored S-cycloheptadiene 10a-II releasing energy of −15.7 kcal mol⁻¹. In the same process, the (R,S) divinylcyclopropane 8b-I goes through the transition state 9b-I with a 27.0 kcal mol⁻¹ energy barrier and ultimately obtains the R-cycloheptadiene 10b-I with an exothermic energy of −9.5 kcal mol⁻¹. Meanwhile enantiomer 8b-II displays an energy barrier of 28.6 kcal mol⁻¹ and generates the S-cycloheptadiene 10b-II with an exothermic energy of −8.7 kcal mol⁻¹, thus the R-cycloheptadiene is favored in this tandem reaction.

In addition, for the highest activation energy of the Cope rearrangement of each substrate among the tandem reactions, this process was proposed as the rate-controlling step.

Geometry effects of the [4+3] cycloaddition reaction

The second series of calculations describe the tandem [4+3] cycloaddition reaction of C=C–C=N₂ s-trans vinyldiazoacetate 2a-II and C=C–C=N₂ s-trans siloxyvinyldiazoacetate 2b-II with s-trans actual diene 6-II. It is known that the chemical properties of cis-trans isomers with identical functional groups are basically similar, however, for some reactions that relate to the relative steric positions of certain atoms or atomic groups, the steric interactions of the cis-trans isomers are different, thus we hypothesized that the geometrical features can lead to a difference in the chemical reactivity for the vinyldiazoacetate isomers. Before this series of calculations, we tried to carry out a computational study on either C=C–C=N₂ s-cis vinyldiazoacetate 2a-I with the s-trans actual diene 6-II, and C=C–C=N₂ s-trans vinyldiazoacetate 2a-II with the s-cis actual diene 6-I, however none of these attempts were successful. The results of the same trials for siloxyvinyldiazoacetates were similar and the main reason is that the resulting divinylcyclopropanation is trans-type while the cis-type is strictly required in Cope rearrangement.

In the first step of the tandem [4+3] reaction, vinyldiazoacetate 2a-II is catalyzed by the rhodium system via a transition state 3a-II with a 8.8 kcal mol⁻¹ energy barrier to generate the vinylcarbenoid intermediate 5a-II, and has an exothermic energy of −9.4 kcal mol⁻¹. This barrier is lower than that of the isomer 2a-I by 3.3 kcal mol⁻¹. This implies that the carbenoid 5a-II derived from the isomer 2a-II is more unstable than carbenoid 5a-I. In the subsequent step, the actual diene 6-II traps from the ether-group side of the carbenoid intermediate 5a-II and undergoes a trigonal transition state 7a-III with a barrier of 2.1 kcal mol⁻¹, and this step is predicted to be exothermic by −30.5 kcal mol⁻¹, forming (R,R) divinylcyclopropane 8a-III. When approached from the ester side intermediate 5a-II goes through a barrier of 3.4 kcal mol⁻¹, and results in the formation of (S,S) divinylcyclopropane 8a-IV with a −25.9 kcal mol⁻¹ exothermic energy. Compared with similar paths of the isomer 5a-I, it can be seen that the isomer 5a-II has higher barriers and tends to generate the later transition state with a more positive charge build-up. In the final step of the ring extension, the divinylcyclopropane 8a-III overcomes an intractable potential energy barrier of 48.8 kcal mol⁻¹, and forms R-cycloheptadiene 10a-III with an endothermic energy of 17.7 kcal mol⁻¹. In the same process the enantiomer 8a-IV has a much lower barrier of 21.2 kcal mol⁻¹ and this transformation has a reaction energy of −14.7 kcal mol⁻¹. Obviously, generation of the S-cycloheptadiene 10a-IV is favorable in this cycloaddition reaction which is in good agreement with the results of the first series of calculations.

As shown in Fig. 4B, C=C–C=N₂ s-trans siloxyvinyldiazoacetate 2b-II goes through a barrier of 11.3 kcal mol⁻¹ and renders the carbenoid formation step exothermic by −7.0 kcal mol⁻¹. In the second step, when the s-trans actual diene 6-II is trapped from the ether-group side the intermediate 5b-II overcomes an energy barrier of 7.5 kcal mol⁻¹ and forms (S,R) divinylcyclopropane 8b-III, and this reaction has an exothermic energy of −30.9 kcal mol⁻¹. Approach from the opposite side of carbenoid 5b-II via a barrier of 12.0 kcal mol⁻¹ generates (R,S) divinylcyclopropane 8b-IV, with this process having a reaction energy of −30.4 kcal mol⁻¹. In the final step, complex 8b-III and the enantiomer 8b-IV display barriers of 26.7 kcal mol⁻¹ and 29.1 kcal mol⁻¹, respectively.

Fig. 4 The potential energy profiles for the calculated cycloaddition reactions of vinyldiazoacetate 2a-II (A) and siloxyvinyldiazoacetate 2b-II (B) with 6-II. The paths for the resulting R-cycloheptadiene are shown in red while those of S-cycloheptadiene are shown in blue.

As can be seen from Fig. 5, the difference in the two bond lengths that are formed in the carbenoid trapping step is at least 0.48 Å (for the TS 7a-III), and this observation once again demonstrates the characteristics of cyclopropanation being concerted and asynchronous. Besides, for the transition state 9a-III with a distinctly higher barrier, it is clear that the formed bond is shorter at least than others and the broken bond is relatively long, thus we infer that this could be the main reason which leads to the highest barrier among the similar reactions in this study.

Fig. 5 Structural views of the transition states for the cycloaddition reaction of vinyldiazoacetate 2a-II and siloxydiazoacetate 2b-II with trapping agent 6-II, catalyzed by Rh₂(S-PTAD)₄.

Table 1 shows the array of reactants, the trapping side of the dienes and the stereogenic centers of the products. According to the information in Table 1, the divinylcyclopropane 2 column indicates that the same approaches to the geometric isomers give the same stereogenic centers in the cyclopropanation step, while the stereogenic center of the final products in the Cope rearrangement is the opposite. This finding implies that the stereogenic center of the final product depends on the geometric isomerism of the substrates and the approach of the trapping agent. Secondly, for unsubstituted vinyldiazoacetate 2a-I and 2a-II the favored cycloheptadienes generated in the rate-controlling step are consistent for the S-type, and for siloxy vinyldiazoacetate the R-cycloheptadienes are the products with favored thermodynamics. This demonstrates that the favored stereogenic product of the ring extension step mostly depends on the carbenoid structure. Finally, in cyclopropanation approaches from the ester-group side of the unsubstituted vinylcarbenoids in Fig. 2A and 4A all have relatively high barriers and generate two of the same stereogenic centers in divinylcyclopropanes. For the cyclopropanation of siloxyvinylcarbenoids the approach of the actual diene from the ether side as shown in Fig. 2B has a higher energy barrier than that of the other side, while in Fig. 4B the relative energy comes from the approach from the ester-group side. Thus the trapping side has some influence on the chemical reactivity but is not decisive.

Table 1 The reaction components and the final product configuration of the ring extension

Entry	R1^a	Vinyldiazoacetate 2^b	Trapping agent 6^b	Approach side^c	Divinylcyclopropane^b	Cycloheptadiene^b
a The vinyldiazoacetate substituent.b Sterics of the complexes.c The approach of the trapping agent.
a	H	cis	cis	Ester	S,S	R
b	H	cis	cis	Ether	R,R	S
c	H	trans	trans	Ether	R,R	R
d	H	trans	trans	Ester	S,S	S
e	Siloxy	cis	cis	Ester	R,S	R
f	Siloxy	cis	cis	Ether	S,R	S
g	Siloxy	trans	trans	Ether	S,R	R
h	Siloxy	trans	trans	Ester	R,S	S

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Activation strain analysis

For further studies on the chemical reactivity of the tandem reaction influenced by the siloxy substituent and geometric isomerism, besides the computed reaction barriers in the last section, we performed potential barriers decomposition using ASM. According to similar reported methods^99–103 a useful set in ASM was chosen for fragment1 [ABC] and fragment2 [CDEFG] as shown in Fig. 6. The depicted fragment1 is transformed from vinyldiazoacetate 2 and the parent system of fragment2 is the trapping diene 6.

Fig. 6 Fragmentation process in the system of Cope rearrangement.

Cope rearrangement is an intermolecular ring opening reaction 8 → TS9 → 10, along the reaction coordination ζ which is obtained from the IRC analysis with the steepest descent computation.¹⁰⁴ In the ASM, the potential energy barrier of the Cope rearrangement can be decomposed into the strain energy ΔE_strain(ζ) and the interaction ΔE_int(ζ).¹⁰⁴ According to this method the interplay between ΔE_strain(ζ) and ΔE_int(ζ) satisfies dΔE_strain(ζ)/dζ = −dΔE_int(ζ)/dζ, and the potential energy barrier ΔE^≠ = ΔE(ζ^TS) consists of the activation energy ΔE^≠_strain = ΔE_strain (ζ^TS) which is positive and destabilizing, in addition to the TS interaction ΔE^≠_int = ΔE(ζ^TS) which is negative and stabilizing. The activation strain analysis of the Cope rearrangement reaction is presented in Table 2. In addition, the C_A⋯C_G bond that is formed in Cope rearrangement is taken as the geometric parameter.

Table 2 Activation strain analysis of the Cope rearrangement reactions a–h

Entry	ΔE^≠^a	ΔER	ΔΔEint^b	ΔΔE^≠strain (frag1)	ΔΔE^≠strain (frag2)	ΔΔE^≠strain^c
Energy in kcal mol^−1 computed at the level of B3LYP/6-311+(d,p) with the Gibbs free energy correction.a Activation energy ΔE^≠ = [E(frag1 in geom of TS9) − E(frag1 in geom of 8)] + [E(frag2 in geom of TS9) − E(frag2 in geom of 8)].b Interaction ΔΔEint = ΔE^≠ − ΔΔE^≠strain.c Activation strain ΔΔE^≠strain = ΔΔE^≠strain (frag1 in geom of 8) + ΔΔE^≠strain (frag2 in geom of 8).
a	20.79(24.27)	−0.03	6.00	0.71	14.08	14.79
b	19.47(21.12)	−0.03	5.68	3.22	10.57	13.78
c	45.27(48.80)	0.02	−5.65	13.8	37.12	50.92
d	18.83(21.17)	−0.03	8.34	−3.18	13.66	10.49
e	26.50(27.04)	−0.02	16.67	−2.51	12.34	9.83
f	27.02(28.59)	−0.02	17.46	−2.63	12.19	9.56
g	24.56(26.67)	−0.02	19.24	−5.91	11.23	5.31
h	25.82(29.12)	−0.02	21.32	−2.79	7.29	4.49

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According to Table 2, comparison of the activation strain analysis in entries a–d derived from carbenoid 2a and entries e–h with the siloxy substituent shows that the latter displays relatively lower strain ΔE_strain(ζ) (ranging from 4.49 kcal mol⁻¹ to 9.83 kcal mol⁻¹) than that of the former (ranging from 10.49 kcal mol⁻¹ to 50.92 kcal mol⁻¹). The interaction ΔE_int(ζ) is enhanced to 16.67–21.32 kcal mol⁻¹, this obvious variation in the interaction ΔE_int(ζ) indicates that in the rate-controlling step the siloxy species have relatively higher interaction between these deformed reactants to counteract the destabilizing strain ΔE_strain(ζ). Secondly, entry c indicates that the Cope rearrangement of divinylpropane 8a-III presents a much higher activation strain ΔΔE^≠_strain of 50.92 kcal mol⁻¹. The chemical properties of the isomers are analogous, thus the notable height of the barrier can be ascribed to the steric hindrance of the geometrical deformation. This can be explained by the description in Fig. 4A, where the relevant bond length of C_A⋯C_G of the transition state 9a-III is 1.88 Å, while the corresponding bond length of the enantiomers is 2.48 Å. Furthermore observation of entry c presents that the main structural deformation comes from frag1 with a value of 37.12 kcal mol⁻¹. The reason could be that frag1 is transformed from the vinyldiazoacetate 2a-II leading to a major destabilizing factor with a great barrier height in the Cope rearrangement.

ASM is another method used to understand the reactivity trends of chemical reactions except by the measured or computed rates and energy barriers. In summary, when the substituent is the only variable, the stabilizing interaction cannot offset the strong destabilizing deformation of the fragment and thus leads to a higher potential energy barrier level in the rate-controlling step. For the geometric isomers of the substrate, the progress of the ring extension that follows the carbenoid trapping step for C=C–C=N₂ s-cis vinyldiazoacetate with a cis-type diene trap obtains a higher strain energy with a stabilizing interaction between the increasing deformation of the reactants.

Kinetic information obtained from the energetic span model with the AUTOF program

In this section the AUTOF program was used to calculate the TOF of the catalytic reaction and the degree of TOF control. A previous study reported that the major factor for the efficiency of the catalyst is the state energies and followed by the concentration of the reactants and/or products,⁸³ in this study we take the computed state energies into account by entering an x for every concentration in the AUTOF program. The complete model of the cycloaddition reaction applied in the black box has three steps, in the first step vinyldiazoacetate and the rhodium catalyst enter and nitrogen leaves, subsequently the trapping agent enters and the metal catalyst leaves, and finally the cycloheptadiene leaves. The details of the input and output in the AUTOF program are included in the ESI.†

From the calculations with the AUTOF program, the X_TOF values of divinylcyclopropane 8 and the boat transition state 9 are all greater than 0.00 in each entry,⁸³ thus the cyclopropane 8 is marked as TDI and the transition state 9 that appeared after the TDI is determined as the TDTS. According to the energetic span approximation, the corresponding apparent activation energies of the full cycle are listed in Table 3. It can be seen that for the cyclic reaction of unsubstituted vinyldiazoacetates 2a, the apparent activation energies δE of entries b and d are lower than those of entries a and c which ultimately give the R-type cycloheptadienes. For the siloxyvinyldiazoacetates 2b, the δE of entries f and h are higher than that of entry e and entry g. As was learnt from the first section and second section the stereogenic center of the favored product derived from unsubstituted vinylcarbenoid 2a is S-type, while the stereogenic center of the favored product transformed from siloxyvinylcarbenoid 2b is R-type, thus the catalytic activities of these favored products are basically consistent with the reaction reactivities.

Table 3 δE and X_TOF for the cyclic reaction

Entry	TDI	TDTS	δE	TOF/h^−1
A	−46.2	−22	24.3	1.34 × 10^−2
B	−37.1	−16	21.1	3.94
C	−39.9	8.9	48.8	9.17 × 10^−21
D	−35.2	−14.1	21.2	4.84 × 10^−1
E	−49.4	−22.4	27	1.53 × 10^−4
F	−45.4	−16.1	28.6	1.06 × 10^−5
G	−37.9	−11.2	26.7	2.90 × 10^−4
H	−37.4	−8.3	29.1	4.28 × 10^−6

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Moreover, entry b for the transformation from vinyldiazoacetates 2a-I with an ether-group side approach has the highest TOF value of 3.94 h⁻¹ among the catalytic cycles, which predicted that using the chosen metal catalyst for the tandem reaction of vinyldiazoacetates 2a-I with an ether-group side approach has the highest catalytic activity, following on from going through the boat transition state which has the lowest potential barrier among the whole series of calculations. The other noteworthy result is entry c which has the minimal value of TOF, and that is consistent with the highest intractable potential barrier of divinylcyclopropane 8a-III. In summary, the catalytic activity is related to the chemical reactivity of the ring extension step to some degree and depends on the geometric isomerism and the trapping approach. Thus in practice some auxiliary groups, such as the siloxy group, can be used in an attempt to stabilize the carbenoid to improve the catalytic efficiency with the exception of obtaining high selectivity.

4. Conclusions

In the study described herein, the asymmetric [4+3] cycloaddition of vinyldiazoacetate and siloxyvinyldiazoacetate has been described in detail. According to the computational analysis of thermodynamics and kinetics, the rate-controlling step of cycloaddition was determined as the Cope rearrangement. Moreover, the uniquely stereogenic center of the functionalized cycloheptadienes depends on the cyclopropanation, with full control of the relative stereochemistry, that is the geometric isomerism of substrates and the approach of the trapping agent. In the cyclopropanation step the resulting energy barriers of siloxyvinylcarbenoids are higher than those of vinylcarbenoids, which can be ascribed to the more delocalized negative charge of the carbenoid carbon and ultimately the siloxyvinylcarbenoid has a higher level of enantioselectivity. Furthermore, through the analysis of the decomposition of the potential barriers with ASM, these siloxy species have been estimated to have stronger interactions between the deformed reactants in the transformation than the unsubstituted. The siloxy group is easy to remove in synthesis, thus this carbenoid has a high practical value in general synthesis. In addition, the favored final product of the cycloaddition derived from vinyldiazoacetate is S-cycloheptadiene while for the siloxyvinyldiazoacetate it is R-cycloheptadiene, this result is consistent with practical experiments. Finally, the catalytic reactivity of this cycloaddition has been predicted to mainly depend on the carbenoid structure.

Besides, the solvent effects in this system were tested with the considerations of a solvent model and solvent polarity, and as a result nonpolar solvent is demonstrated to be better for the rhodium carbenoid in this study. The two-layer ONIOM methodology performed in this study with the B3LYP functional in the high level and the [Rh-LA2] basis set for Rh displays efficient calculations to describe the rhodium system. In our future work we will improve the flexibilities of the functions on the metal system which cause the slight differences that exist between the tested functionals.

Acknowledgements

This work was supported by the State Key Program of Natural Science of Tianjin (Grant No. 13JCZDJC26800), MOE Innovation Team (IRT13022) of China, NSFC (21421001), and the State Key Program of National Natural Science Foundation of China (Grant No. 21433008).

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c5ra14815d

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