DFT Case Study on the Comparison of Ruthenium-Catalyzed C–H Allylation, C–H Alkenylation, and Hydroarylation

Density functional calculations at the B3LYP-D3+IDSCRF/TZP-DKH(-dfg) level of theory have been performed to understand the mechanism of ruthenium-catalyzed C–H allylation reported in the literature in depth. The plausible pathway consisted of four sequential processes, including C–H activation, migratory insertion, amide extrusion, and recovery of the catalyst, in which C–H activation was identified as the rate-determining step. The amide extrusion step could be promoted kinetically by trifluoroacetic acid since its mediation lowered the free-energy barrier from 32.1 to 12.2 kcal/mol. Additional calculations have been performed to explore other common pathways between arenes and alkenes, such as C–H alkenylation and hydroarylation. A comparison of the amide extrusion and β-H elimination steps established the following reactivity sequence of the leaving groups: protonated amide group > β-H group > unprotonated amide group. The suppression of hydroarylation was attributed to the sluggishness of the Ru–C protonation step as compared to the amide extrusion step. This study can unveil factors favoring the C–H allylation reaction.


Table of Contents
. Cartesian coordinates of the stationary points involved in the main C-H allylation reaction. …… S3 Table S2. Cartesian coordinates of the stationary points involved in the formation of the ruthenium-(η 3 -allyl) complex and in the reaction pathway without the promotion of HOTFA. …… S32 Table S3. Cartesian coordinates of the stationary points involved in the β-H elimination processes. …… S45 Table S4. Cartesian coordinates of the stationary points involved in the protonation-demetalation processes. …… S55 Table S5. Electronic energies (in a.u.), solution entropies (in cal·mol -1 ·K -1 ) and Gibbs free-energies (in a.u.) of all the main stationary points. …… S72 Table S6. Imaginary frequencies (in cm -1 ) of the main transition states. …… S74  Table S1. Cartesian coordinates of the stationary points involved in the main C-H allylation reaction, optimized at the B3LYP-D3+IDSCRF/TZP-DKH(-dfg) level of theory.  Table S2. Cartesian coordinates of the stationary points involved in the formation of the ruthenium-(η 3 -allyl) complex and in the reaction pathway without the promotion of HOTFA, optimized at the B3LYP-D3+IDSCRF/TZP-DKH(-dfg) level of theory.

Names Cartesian Coordinates
INT-3-2-NA   Table S6. Imaginary frequencies (in cm -1 ) of the main transition states, determined at the B3LYP-D3+IDSCRF/TZP-DKH(-dfg) level of theory. kcal/mol, respectively. Obviously, the former path corresponding to the C−C bond coupling at the terminal olefinic carbon is kinetically more competitive, which is in S76 good agreement with the experimental observation. Additionally, the thermodynamic aspect favors the former pathway as well. The steric repulsion between the secondary amide group and the phenyl group should be responsible for the observed regioselectivity.  Figure S2. Migratory insertion pathways and free-energy variations (in kcal/mol), calculated at the B3LYP-D3+IDSCRF/TZP-DKH(-dfg) level of theory. We have tested the explicit solvation effect of TCE (see Figure S3). The last step of the main pathway, INT-7 → P + CAT, has the free-energy change of +3.1 kcal/mol, indicating that the product may not easily separate from INT-7, possibly due to the presence of an intramolecular hydrogen bond in INT-7. The difficulty in the product separation might lead to the deactivation of the catalyst. However, a TCE molecule is able to form a hydrogen bond with the product carboxyl group, and the participation of only one TCE makes the final step near free-energy neutral (∆G = 0.5 kcal/mol), which facilitates the separation of the product from the ruthenium center.

Discussion on the Explicit Solvation Effect
We also found that the explicit solvation effect of TCE may help to control the correct reaction direction, because the protonation of the side product (C 2 H 5 ) 2 NH by HOTFA could be effectively prevented, as follows.
The catalytic reaction produces the secondary amine (C 2 H 5 ) 2 NH, which could be protonated by HOTFA and thus might prevent the protonation of R2 by HOTFA.
DFT calculations predict that protonation of (C 2 H 5 ) 2 NH by HOTFA is 0.6 kcal/mol more favorable thermodynamically than that of R2 by HOTFA. If the explicit solvation effect of TCE is considered (TCE forms an H-bond with each amine), however, the former process is computed to be 0.7 kcal/mol less favorable thermodynamically than the latter process. Since the protonation of R2 is crucial for S78 promoting the β-amide elimination step, this solvation effect should be important for controlling the correct reaction direction. The present arguments on the solvent effect are only for qualitative reference.
In addition, we tested the explicit solvation effect on the C-H activation process.
We attempted to introduce one or two TCE molecules to form H-bonds with the oxygen atoms, but we found that the relative free energies varied not evidently (see Figure S4).