Ambimodal reactions involve a single transition state leading to multiple products. In such reactions, transition state theory gives no information about the ratio of products that are formed, and molecular dynamics must be performed to predict this ratio. Understanding the relationship between the transition structure and the product ratio is a long-standing problem in molecular dynamics. We have studied 15 ambimodal pericyclic reactions and investigated the relationship between the TS bond lengths in the saddle points and the product ratios from trajectory simulations. A linear correlation, ln(B:A) = -9.4(Bond 3 - Bond 2), is found with R = 0.92, where A and B refer to the products formed upon formation of bonds 2 and 3, respectively. The correlation shows that the ratio of products formed after the bifurcation is related to the partial bond lengths, and corresponding bond orders, in the transition state.

Transition-metal-catalyzed cross-coupling has emerged as an effective strategy for chemical synthesis. Within this area, direct C-H bond transformation is one of the most efficient and environmentally friendly processes for the construction of new C-C or C-heteroatom bonds. Over the past decades, rhodium-catalyzed C-H functionalization has attracted considerable attention because of the versatility and wide use of rhodium catalysts in chemistry. A series of C-X (X = C, N, or O) bond formation reactions could be realized from corresponding C-H bonds using rhodium catalysts. Various experimental studies on rhodium-catalyzed C-H functionalization reactions have been reported, and in tandem, mechanistic and computational studies have also progressed significantly. Since 2012, our group has performed theoretical studies to reveal the mechanism of rhodium-catalyzed C-H functionalization reactions. We have studied the changes in the oxidation state of rhodium and compared the Rh(I)/Rh(III) catalytic cycle to the Rh(III)/Rh(V) catalytic cycle using density functional theory calculation. The development of advanced computational methods and improvements in computing power make theoretical calculation a powerful tool for the mechanistic study of rhodium chemistry. Computational study is able to not only provide mechanistic insights but also explain the origin of regioselectivity, enantioselectivity, and stereoselectivity in rhodium-catalyzed C-H functionalization reactions. This Account summarizes our computational work on rhodium-catalyzed C-H functionalization reactions. The mechanistic study under discussion is divided into three main parts: C-H bond cleavage step, transformation of the C-Rh bond, and regeneration of the active catalyst. In the C-H bond cleavage step, computational results of four possible mechanisms, including concerted metalation-deprotonation (CMD), oxidative addition (OA), Friedel-Crafts-type electrophilic aromatic substitution (SAr), and σ-complex assisted metathesis (σ-CAM) are discussed. Subsequent transformation of the C-Rh bond, for example, via insertion of CO, olefin, alkyne, carbene, or nitrene, constructs new C-C or C-heteroatom bonds. For the regeneration of the active catalyst, reductive elimination of a high-valent rhodium complex and protonation of the C-Rh bond are emphasized as potential mechanism candidates. In addition to detailing the reaction pathway, the regioselectivity and diastereoselectivity of rhodium-catalyzed C-H functionalization reactions are also commented upon in this Account. The origin of the selectivity is clarified through theoretical analysis. Furthermore, we summarize and compare the changes in the oxidation state of rhodium along the complete reaction pathway. The work described in this Account demonstrates that rhodium catalysis might proceed via Rh(I)/Rh(III), Rh(II)/Rh(IV), Rh(III)/Rh(V), or non-redox-Rh(III) catalytic cycles.

DFT investigations into the mechanism of Ni-catalyzed alkylation of benzamides with alkyl halides are reported. Computational results show that the Ni(ii)–Ni(iv) catalytic cycle is favorable; meanwhile, the oxidative addition of alkylbromide forms a Ni(iv) intermediate and is the rate-determining step of the whole catalytic cycle.

Density functional theory method N12 was used to study the mechanism of the [Ir(cod)OH] 2 /Xyl−MeO−BIPHEP-catalyzed para-selective C−H borylation reaction. The results revealed that the use of a bulky diphosphine ligand such as Xyl−MeO−BIPHEP was unfavorable for the previously proposed iridium(III)/iridium(V) catalytic cycle because it resulted in considerable steric repulsion in the hepta-coordinated iridium(V) intermediate. Inspired by this steric effect, we have proposed a novel iridium(I)-/iridium(III)-based catalytic cycle for this transformation and shown that it can be used to account for the experimental results. The iridium(I)/iridium(III) catalytic cycle induced by this steric effect consists of several steps, including (i) the oxidative addition of the C−H bond of the substrate to an active iridium(I) boryl complex; (ii) the reductive elimination of a C−B bond; (iii) the oxidative addition of B 2 pin 2 to an iridium(I) hydride complex; and (iv) the reductive elimination of a B−H bond. Notably, the computed regioselectivity of this reaction was consistent with the experimental observations. The high para-selectivity of this reaction was also explained using structural analysis and a 2D contour model, which revealed that the strong steric repulsion between the diphosphine ligand and the meta-substituents resulted in a higher energy barrier for meta-C−H activation.

Density functional theory (DFT) method B3LYP with a dispersion term (B3LYP-D3BJ) has been used to clarify the regioselectivity of zinc mediated 1,3-dipolar cycloaddition of azides and alkynes. Computational results indicate that the dipolar cycloaddition takes place via a concerted five -membered-ring transition state, leading to a 1,5-disubstiuted 1,2,3-triazole product, which is consistent with the experiment reported by Greaney's group. The coordination of imidazole ligand to zinc is reversible, and the regioselectivity is irrelevant to the coordination of imidazole ligand. Moreover, substituent effect of alkynes has also been studied. Finally, distortion-interaction analysis along the reaction pathways and frontier molecular orbital theory are used to explain the reactivity and 1,5-regioselectivity.

Nitrones have been used for rhodium-catalyzed cyclization C-H bond activation and O atom transfer of arylnitrones with alkynes by Chang et al. ( J. Am. Chem. Soc. 2015 , 137 , 4908 - 4911 ). Density functional theory method has been used to study the mechanism, regio-, and diastereoselectivity of type reactions. The results elucidated that the reaction pathway for Rh(III)-catalyzed cyclization of N-arylnitrones with alkyne contains a C-H bond activation, an alkyne insertion into Rh-C bond, a reductive elimination to form a Rh(I) complex, an oxidative addition leading to N-O cleavage, an imine insertion into the Rh-C bond, and the final protonolysis to regenerate the products and the active catalyst. The regioselectivity of this reaction with asymmetric alkyne is controlled by the electronic effect in alkyne insertion type instead of steric effects. The distortion-interaction analysis is also used to explain the regioselectivity. The diastereoselectivity is controlled by the imine insertion step. In this step, the sterically less hindered transition state is favored, leading to stereoselective product formation.

Density functional M11 was used to study the mechanism and enantioselectivity of a binaphthophosphepine-catalyzed intramolecular [3 + 2] cycloaddition reaction. The computational results revealed that this reaction proceeds through nucleophilic addition of the phosphine catalyst to the allene, which yields a zwitterionic phosphonium intermediate. The subsequent stepwise [3 + 2] annulation process, which starts with the intramolecular nucleophilic addition of the allenoate moiety to the electron-deficient olefin group, determines the enantioselectivity of the reaction. This step is followed by a ring-closing reaction and water-assisted proton-transfer process to afford the final product with concomitant regeneration of the phosphine catalyst. Theoretical predictions of the enantioselectivity for various phosphine catalysts were consistent with experimental observations, and 2D contour maps played an important role in explaining the origin of the enantioselectivity. Moreover, on the basis of our theoretical study, new binaphthophosphepine catalysts were designed and that are expecting to afford higher enantioselectivity in this cycloaddition reaction.

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