where 𝑅 and 𝑇 are the gas constant and the temperature, respectively. The temperature was set to be 233.15 K. The 𝐸 6 ‡ is the electronic energy of a TS corresponding to the route i. In this case, the VL with the 2,3-bis(dichlorophosphino)quinoxaline moiety was used to reproduce quinoxaline-based diphosphine ligands. As shown in Figure (middle), the electronic and steric parameters of each substituent were set independently, with those of the Me group (pVL Me ) for R 1 and those of the t Bu group (pVL tBu ) for R 2 -R 4 , to reproduce (S)-quinoxt Bu3 as a whole. It should be noted that, considering high symmetry of Me and t Bu groups as well as the potential difficulty in optimizing many independent parameters, steric parameters corresponding to width and thickness of each substituent were set to be symmetric (i.e., a1 = a2 and b1 = b2 in each substituent). Geometry optimizations of eight TSs using thus-prepared VL were performed, and the branch selectivity and the enantiomeric excess were calculated to be 97.9% and 82.9%, respectively. These values are reasonably consistent with the experimental results (bs = 72% and ee = 87%) though the branch selectivity is slightly overestimated. With the optimized structures of eight TSs in hand, we then calculated the derivative values of the branch selectivity and the enantiomeric excess in terms of VL parameters (see SI for the detailed formulation). The derivative values with respect to steric parameters corresponding to width and thickness of each ovoid were shown in Figure (right). In this table, the a1-i and b1-i represent the width and thickness parameters for the i-th ovoid (R i ). As for the derivative values of R 1 (a1-1 and b1-1), whose effect was not discussed in Ito's report, intuitive results were obtained: An increasing steric bulk of R 1 increases the branch selectivity and decreases of the enantiomeric excess. If the Me group in (S)-quinoxt Bu3 is replaced with a bulkier substituent, steric repulsion between the ligand and the alkyl chain in the olefin would increase, thereby resulting in the selective formation of the branched product through routes Ab, Bb, Cb or Db. On the other hand, because the Me group is the only substituent which breaks symmetry of the ligand, replacing it with larger substituents would make the whole ligand (pseudo) C2 symmetric, resulting in the decreased enantioselectivity. Regarding the effects of R and) on the enantioselectivity (𝑑ee/𝑑𝑝), the calculate derivative values were consistent with the trend reported by Ito et. al.: The enantioselectivity is mainly determined by the size of R 2 and R 3 , and contribution of R 3 is greater than that of R 2 (see the magnitude of the derivative values). On the other hand, the effect of these substituents on the regioselectivity was relatively small comparing to those on the enantioselectivity and was not entirely consistent with the reported trends. Whereas Ito and coworkers reported that the regioselectivity is affected by the bulk of R 2 and R 4 , the derivative values (𝑑bs/𝑑𝑝) imply that not only these substituents but also R 3 have contribution to the regioselectivity. To see the origin of this contribution, steric interactions between the ovoid corresponding to R 3 and substrates (i.e., 1butene and Bpin) in the TS for the route Al, which is the most favorable reaction path to give the linear product 8, were analyzed (Figure , left). As a result, it was found that the strongest interaction is the repulsion between the ovoid and the hydrogen atom at the olefin (H26). Thus, increasing bulk of R 3 (a1-3 or b1-3) would enhance this repulsive interaction, destabilizing the corresponding TS. This will in turn cause the selective formation of the branched product, resulting in the positive derivative values for a1-3 and b1-3. Actually, this interaction was also found in the optimized structure for the corresponding TS reported by Ito and coworkers. The shortest interatomic distance between the hydrogen atom and the t Bu group corresponding to R 3 was calculated to be 2.34 Å (Figure , right). This value is comparable to the shortest interatomic distances between the Bpin moiety and the t Bu groups corresponding to R 2 or R 4 , on which the importance of R 2 and R 4 was discussed based. Because C1-symmetric quinox-type ligands which have different substituents at R 3 and R 4 positions are synthetically unavailable, the importance of R 3 could have been masked by that of R 4 and overlooked. Hence, the VLAO approach which enables systematic analyses of ligand effects can be a powerful tool for identifying unapparent but valuable factors for ligand engineering. To evaluate overall importance of each substituent, the derivative values of the sum of the branch selectivity and enantioselectivity were calculated (𝑑(bs + ee)/𝑑𝑝). Based on this result, criteria for each substituent to improve both regio-and enantioselectivity are suggested: R 1 should be smaller than Me group, R 2 and R 3 should be larger than t Bu group, and R 4 has the smallest impact on the selectivity. As Me group is the smallest alkyl group, and R 4 must be the same substituent as R 3 (see above), these criteria would be consistent with the ligand engineering by Ito and coworkers, where (S)-quinoxt Oc-tAd2 was identified as the optimal ligand, considering the synthetic accessibility of ligands.