Ligand plays one of the most important roles in the transition metal catalysis. During the last few decades, many sophisticated ligands which enable unprecedented transformations with high efficiency have been developed. Except for serendipity, development of such ligands depends on rational ligand engineering. Ligand engineering is a process where a molecular structure of a ligand is optimized to maximize reaction yield, selectivity and/or rate. To streamline this process, various electronic and steric parameters which describe inherent properties of ligands have been introduced, and correlation between these parameters and outcomes of the reaction have been investigated (Figure , left). For historical example, Tolman and coworkers have conducted a pioneering work in this field, where Tolman's electronic parameter (νCO) and the cone angle (θ) were introduced as metrics for electronic and steric properties of monodentate phosphorous(III) ligands. They revealed that, by plotting a measurable function F (i.e., reaction yield) against these parameters (so-called Tolman's plot), the electronic and steric characters of the reaction, which are used as the guidelines for designing optimal ligands, can be understood as the slope of the function with respect to each parameter (ΔF/ΔνCO and ΔF/Δθ). Their research has established the fundamental strategy of ligand engineering, and most of recent ligand discoveries have been achieved by (at least unconsciously) analyzing reaction outcomes in terms of ligand parameters (i.e., ΔF/Δp, where p is an arbitrary parameter). Notably, many advanced electronic/steric parameters have been recently developed, largely owing to the emergence of computational tools, enabling highly sophisticated design of ligand molecules. However, regardless of the simplicity of its fundamental strategy, ligand engineering is still a time-consuming and labor-intensive process. This stems from the difficulty in evaluating the effect of a single ligand parameter on a reaction outcome (Figure 1a, right). Because all electronic and steric parameters are inherently determined by the molecular structure of a ligand, modification of the molecular structure would perturb all parameters, rather than a single parameter of interest. Hence, even if structures of ligands are systematically modified (e.g., PEt3, P i Pr3 and P t Bu3), what is observed from experimental results is not the effect of a single parameter of interest but the sum of contributions of all parameter changes (ΔF). In other words, it is not possible to directly evaluate the slope of the objective function because none of parameters (p) can be treated as an independent variable. Therefore, the slope needs to be guessed by comprehensively analyzing reaction outcomes obtained from evaluation of many ligand molecules. It should be noted that correlation between F and p is not always simple, and hence a lot of time and resources are often required to collect a plenty amount of experimental data for understanding. Therefore, informatics techniques including regression analysis to rapidly capture important parameters for a given reaction are becoming promising tools in this field. Herein, we report the virtual ligand-assisted optimization (VLAO) method, a fundamentally new in silico approach for ligand engineering (Figure ). In this method, the electronic and steric characters of the reaction are estimated based on quantum chemical calculations and the following simple mathematical operations, rather than regression analysis of experimental data. This computational method is based on the use of the virtual ligand (VL), which was introduced in our previous study about the virtual ligand-assisted screening (VLAS). A VL is a dummy ligand for quantum chemical calculations to approximate electronic and steric properties of a real ligand. Whereas electronic and steric parameters of a real ligand are inherently determined by its chemical structure (see above), parameters in a VL (pVL) can be independently tuned. In the VLAS method, this feature of VLs was exploited to systematically investigate the entire parameter space to find an optimal parameter for the reaction of interest. On the other hand, the VLAO method takes advantage of this feature to mathematically analyze electronic and steric characters of a reaction. As shown in Figure (left), energies of an equilibrium structure (EQ) and transition state (TS) calculated using VLs can be differentiated in terms of parameters in the VLs (𝑑𝐸 ! /𝑑𝒑 "# ). Given that a reaction outcome such as reaction yield, selectivity or rate can be described as a function of energies of EQ and TS, we can calculate derivative values of such an objective function in terms of VL parameters (𝑑𝐹/𝑑𝒑 "# ) using 𝑑𝐸 ! /𝑑𝒑 "# . This value is exactly the extreme forms of ΔF/Δp, which is pursued in typical ligand engineering study. Hence, this would suggest a rational direction in which VL parameters should be tuned to maximize (minimize) the objective function (F). Then, we report a gradient-driven optimization of ligands within the VL parameter space (Figure , right). Based on calculated derivative values (𝑑𝐹/𝑑𝒑 "# ), the parameters in a VL are optimized by conjugate gradient (CG) method to maximize (minimize) the objective function F. This results in a VL with optimal parameters to achieve the target reaction most efficiently, which can be used as a rational guideline for designing optimal ligand molecules. The VLAO strategy was firstly demonstrated in three reported examples of ligand engineering, where monodentate, bidentate or asymmetric phosphine ligands are optimized. Then, the VLAO strategy was employed to experimentally find a highly selective ligand for the α-selective hydrogermylation of a terminal ynamide.