A Comparison between the Cycloadditions of Allenyl- and Vinyl-Cyclopentanes Using Density Functional Theory and GRRM Program

Abstract

Cycloaddition catalyzed by transition metals such as rhodium (I) is an important way to synthesize functionalized molecules in medicinal chemistry. When the reagent has a saturated ring containing more than five carbons (or heavy atoms), the reaction can progress when the compound has an allenyl group, but not for a vinyl group. Here, we constructed two computational models for allenylcyclopentane-alkyne and vinylcyclopentane-alkyne, and obtained their reaction pathways using density functional theory (DFT). From the reaction pathways, we confirmed that the former model has a much lower reaction energy than the latter. We also found that the molecular orbitals of the transition state structure at the rate-controlling step contribute significantly to the difference in reactivity between the two models.

Introduction

Transition metals are frequently used in catalysts^1–3) to obtain functionalized molecules. Small cycloalkanes are critical for organic synthesis in medicinal chemistry,^4–6) and transition metal catalysts are sometimes utilized to obtain functional molecules from cycloalkanes as the starting point. Rhodium (I) catalyzes the cycloadditions^7–22) of vinyl- or allenyl-cycloalkanes. Reactants containing 3-membered, 4-membered, and 5-membered rings have been reported. For example, intramolecular [5 + 2] cycloadditions of vinylcyclopropane analogs^23–31) and [6 + 2] cycloadditions of vinyl cyclobutane-alkynes^32–34) catalyzed by Rh give 7- and 8-membered carbocycles, respectively.

In terms of mechanism, the Rh-catalyzed cycloadditions of vinyl cyclopropanes (3-membered reactants) are considered to be driven by the strain energy^35–38) via a cleavage pathway. However, for larger rings with lower strain energies, especially 5-membered rings, the metallocycle intermediates are considered to play important roles.³⁹⁾ Hereafter, the corresponding pathway will be called the “metallocycle pathway.”

Cycloaddition has been reported for vinylcyclopropane and vinylcyclobutane but not the vinylcyclopentane analogs. Recently, Mukai et al. used allenylcyclobutane-alkyne⁴⁰⁾ and allenylcyclopentane-alkyne⁴¹⁾ as substrates for Rh catalysts (Fig. 1). Those authors considered the allenyl group to play an important role in these reactions.^42,43) Nevertheless, no ab initio calculations of these reactions have been published. Therefore, the present theoretical calculation was carried out to clarify the difference between allenyl and vinyl groups in these reactions. This study is the first to investigate the driving force for the cycloaddition of allenylcyclopentane-alkyne by comparison with vinylcyclopentane-alkyne.

Fig. 1. RhI-Catalyzed Cycloadditions Reported by Mukai et al. (n = 1, 2)

Results and Discussion

To compare the effects of allenyl and vinyl groups on the Rh-catalyzed intramolecular cycloaddition reaction, two computational models (details in the Theoretical Calculation section) were constructed. Their reaction pathways were calculated and compared to each other.

Pathway of the Allenylcyclopentane-Alkyne Model

From the reaction pathway for the allenylcyclopentane-alkyne model (Fig. 2), the oxidative cyclization of Int1a to the important rhodacyclopentane intermediate Int2a via TS1a has an energy barrier of 18.1 kcal/mol and is slightly exergonic by 0.1 kcal/mol. After the formation of Int2a, β-carbon elimination occurs through the transition state TS2a, where the barrier is 19.0 kcal/mol higher than that in Int2a. The β-carbon elimination is exergonic from the calculation, and the intermediate Int3a is 8.2 kcal/mol lower in energy than Int2a. Then, intermediate Int3a goes through the C(sp³)–C(sp²) reductive elimination via TS3a and generates the intermediate Int4a, and the energy barrier of this step is 12.9 kcal/mol. Finally, the [7 + 2] cycloaddition is completed by removing the Rh-complex to give the product PDa, and Int1a is regenerated for the next catalytic cycle. The whole process of this [7 + 2] cycloaddition was calculated to be exergonic by 28.9 kcal/mol.

Fig. 2. Reaction Pathway of Rh-Catalyzed Intramolecular [7 + 2] Cycloaddition for the Allenylcyclopentane-Alkyne Model

All free energies are in kcal/mol.

Pathway of the Vinylcyclopentane-Alkyne Model

Similar to the allenylcyclopentane-alkyne model, reaction in the vinylcyclopentane-alkyne model also progresses in the order of oxidative cyclization→β-carbon elimination→reductive elimination (Fig. 3). However, the energy barrier at the step of oxidative cyclization is 32.4 kcal/mol, much higher than that in the allenylcyclopentane-alkyne model. This step was calculated to be endergonic, and the energy of Int2b is 19.7 kcal/mol higher than that of Int1b. The β-carbon elimination via TS2b exhibits an energy barrier of 23.5 kcal/mol compared to Int2b, and the energy of Int3b is 4.6 kcal/mol lower than Int2b. In the reductive elimination, the intermediate Int4b is generated from Int3b via TS3b, and there is an energy barrier of 10.2 kcal/mol compared to Int3b. Finally, the [7 + 2] cycloaddition is completed by removing the Rh-complex to give the product PDb, and Int1b is regenerated for the next catalytic cycle. The whole process of this [7 + 2] cycloaddition was calculated to be exergonic by 17.7 kcal/mol.

Fig. 3. Reaction Pathway of Rh-Catalyzed Intramolecular [7 + 2] Cycloaddition for the Vinylcyclopentane-Alkyne Model

All free energies are in kcal/mol.

Comparison of the Two Models

In both models, the rate-determining step is β-carbon elimination, and the total energy barriers are 19.0 and 43.2 kcal/mol for allenylcyclopentane-alkyne and vinylcyclopentane-alkyne, respectively. These results indicate that the allenyl-cycloaddition is more active than vinyl-cycloaddition, and the latter might require other driving forces (for example, distortion energy in the case of cyclopropane) to proceed.

Fig. 4. Energy Diagram of the Reaction Paths for Allenylcyclopentane-Alkyne and Vinylcyclopentane-Alkyne Models

To further compare the reactivity of allenyl- and vinyl-cycloadditions, we calculated the molecular orbitals of important transition states in each reaction (TS1a/b and TS2a/b, Figs. 5, 6. In the case of the allenylcyclopentane transition state TS1a, the d-orbital of Rh has the same phase as the C=C bond π orbital, i.e., they form a bonding orbital (Fig. 5a). On the contrary, in the highest occupied molecular orbital (HOMO) of the vinylcyclopentane transition state TS1b, the Rh d-orbital and C–C σ-bond orbital are anti-bonding (Fig. 5b). Similarly, in TS2a, the phase of the Rh d-orbital is the same as that of the ① C=C bond π-orbital, ② C–C bond σ-orbital, and ③ C–H bond σ-orbital (Fig. 6a). On the contrary, the HOMO-3 of TS2b shows that the d-orbital of Rh is opposite in phase to ④ C–C σ-bond orbital and the same as ⑤ the C=C π-orbital (Fig. 6b). The anti-bonding relation at ④ blocks the broad interorbital interactions such as those existing in TS2a. These differences in the molecular orbitals of key transition states might be responsible for the energy difference between the pathways of vinyl- and allenyl-cycloadditions, as well as the different reactivity observed between the allenyl and vinyl groups.

Fig. 5. HOMO Diagrams of a) TS1a and b) TS1b

Fig. 6. HOMO-3 Diagrams of a) TS2a and b) TS2b

Fig. 7. Constructed Reaction Models for the Calculation of a) Allenylcyclopentane and b) Vinylcyclopropane Including the Intermediates

Conclusion

We carried out DFT calculations for the reaction pathways of [Rh(CO)₂Cl]₂-catalyzed [7 + 2] cycloadditions from allenyl- and vinyl-cyclopentane-alkyne using the Global Reaction Route Mapping (GRRM) program. The results were used to explain the difference in reactivity between allenyl- and vinyl-cyclopentane. Previous studies³⁵⁾ only considered the reactivity of vinyl-cyclopropane-alkyne and attributed it to the release of distortion energy. For the first time, this study revealed that the overlap in p(π)–d(π)–p(π) orbitals, which partially originates from the allenyl substituent, can stabilize the reaction pathway and allow the cycloaddition to progress. As the next step, we are extending the calculation to similar reactions with other transition metal catalysts, in order to reveal why Rh has the best (or at least relatively better) catalytic activity among transition metal elements.

Theoretical Calculation

Model Construction

To compare the role of the vinyl and the allenyl groups during the reaction, we constructed two models with feasible sizes for the calculation (Fig. 6). We selected [Rh(CO)₂Cl]₂, which was used in Mukai’s study,⁴¹⁾ as the catalyst. The intermediates of the models were designed according to the original report^39,41) of the reactions.

Pathway Calculation

All DFT (B3LYP^44–46) and M06⁴⁷⁾) calculations were performed with Gaussian09⁴⁸⁾ and GRRM17^49–53) programs based on Gaussian09. Structure optimizations and frequency calculations were carried out with B3LYP/6-31G (d) (H, C, O, Cl) and Stuttgart–Dresden Effective Core Potential (SDD ECP) (Rh). The transition state (TS) structures were obtained from DS-AFIR calculation in GRRM17. Single point energy considering the solvent effect of toluene (Self-Consistent Reaction Field (SCRF) method using the Polarizable Continuum Model (PCM) model^54–56)) and the atomic radii used for the PCM calculations (specified using the UFF keyword) was obtained by the calculations of the B3LYP geometries with M06/6-311 + G (d, p) (H, C, O, Cl) and SDD ECP (Rh). Gibbs free energies (kcal/mol) were calculated based on the single point energies from M06 and the frequencies from B3LYP.

Conflict of Interest

The authors declare no conflict of interest.

Supplementary Materials

The online version of this article contains supplementary materials (details of computations).

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