Density functional theory has been employed to investigate the mechanisms of Rh-catalyzed intramolecular [2 + 2 + 2] cycloaddition reactions. The reaction starts with the coordination of a Rh center in the catalyst to the alkyne in reactant 1a firstly, and then to one of the double bonds in the allene, leading to the formation of the first six-membered ring. After that, there are two different reaction pathways, which result in the [2 + 2 + 2] and [2 + 2] products, respectively. For the [2 + 2 + 2] reaction pathway, the remaining alkene in reactant 1a will coordinate to the Rh center, and then there are two successive C-C couplings to make the second six-membered ring and one three-membered ring, which leads to the formation of the final product. At the same time, the broken Rh-Cl bond will be formed again to finish the recovery of the catalyst and the separation of the final product. It was deduced from the energy span model that the TOF-determining transition state (TDTS) and intermediate (TDI) are TS3 and INT2, and thus the activation free-energy barrier is 32.1 kcal mol~(-1) at the temperature of 383.75 K. The substituent effect and intermolecular interaction energy have also been addressed in this paper.
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