Judging from the magnitude of derivative values, it turned out that the parameters for thickness (b1, b2) and length (c2) of the ovoid has larger impacts on the exo selectivity. As for the electronic parameter (r0), a small negative derivative was obtained. Because an increase of 𝑟 7 value makes the VL electron-deficient (see Figure ), this result implies that electron-donating ligands would increase the exo selectivity. Because Cy group is apparently thicker and more electrondonating than Ph group, these results are qualitatively consistent with ligand engineering by Overman et. al., where the exo selectivity was improved by the use of PCy3. Then, we have performed the optimization of VL parameters (Figure ). In this case, the objective function (F) was set to be the exo selectivity (𝜉 LMN ) corrected by an additional penalty function (P) to constrain the ranges of parameters (see below), and seven VL parameters (r0, a1, a2, b1, b2, c1 and c2) were optimized to maximize F. The parameter set which reproduce PPh3 (pVL Ph ) was used as the initial parameter. The penalty function P constrains VL parameters to be optimized within "realistic" ranges. For example, the range of electronic parameter 𝑟 7 was set to be 1.2-2.4 Å, which covers the electronic effect between P t Bu3 and P(CF3)3. When the 𝑟 7 value approaches to the lower or upper limit, a positive penalty was subtracted from the objective function because real ligand molecules with such a high electron-donating or electron-withdrawing ability are rarely found (see Figure for the detailed formulation of P). Similarly, the ranges of steric parameters were set to be 1.0-6.0 Å for a1, a2, b1, b2 and c1, and 1.0-3.514 Å for c2. The upper limit of c2 (3.514 Å) was set considering the steric parameter d (3.214 Å). The parameter optimization was performed by the CG method. At each iteration, the VL parameters were updated based on the CG calculated using the derivative value of F ( 𝑑𝐹/𝑑𝒑 "# ), and geometry optimizations of (exo)-TS and (endo)-TS were performed. The exo selectivity (𝜉 LMN ) as well as the objective function (F) were then computed and plotted in Figure (crosses and open circles, respectively) along with corresponding VL parameters (dotted lines). After each line search, the maximum absolute values among the gradient components and the displacement components were calculated, and the convergence was determined when each of these values was less than 1 Å -1 and 0.1 Å, respectively. In addition, the objective function (F) was monitored at each iteration, and the calculation was terminated when the F value exceeds 99%. This criterion was set to prevent VL parameters from vibrating in a subspace where the F value is close to its upper limit (100%). As a result, the calculation was converged at after 17 iterations, and the F value was improved from 32.5% to 99.7%. The ovoid in the VL at the first and last iterations (ITR. 0 and ITR. 17) were visualized on Figure (middle). While the electronic feature (expressed by the color of the ovoid) has been slightly changed, the thickness of the ovoid was increased significantly (about 0.8 Å in total). To check how this steric change affects the exo selectivity, steric interactions between each ovoid in the VLs and methacrylonitrile 2 were analyzed. In (endo)-TS, two repulsive interactions (Int-1 and Int-2) were found: Int-1 is the repulsion between the hydrogen at the terminal olefin (H36) and the ovoid 1, and Int-2 is that between the nitrogen at the nitrile group (N42) and the ovoid 2. As summarized in the table, these repulsive interactions increased as the VL became bulkier. In particular, Int-2 increased by 0.32 kcal/mol before and after optimization (0.05 kcal/mol at ITR. 0 and 0.37 kcal/mol at ITR. 17). Similar two repulsive interactions were also found in (exo)-TS: One is the repulsion of the hydrogen at the terminal olefin, and the other is that of the hydrogen at the methyl group. However, these repulsive interactions did not increase as much as Int-2 did in the (endo)-TS when the VL became bulkier. Indeed, the repulsion of the hydrogen at the terminal olefin or the methyl group were calculated to be 0.14 and 0.06 kcal/mol even after optimization of VL parameters (ITR. 17). Thus, the steric change in the VL effectively destabilized only (endo)-TS, resulting in the increase of exo selectivity. This result is fully consistent with the ligand engineering by Houk and Overman et. al.