Linking Virtual and Real Worlds: Mathematical Framework to Identify Optimal Molecule based on Virtual Ligand Strategy

Identifying molecular entities with desired properties from a vast pool of potential candidates is a fundamental challenge in organic chemistry. In particular, ligand engineering—designing optimal ligands for transition metal catalysis—has been extensively studied over the past few decades. To address this challenge, we previously proposed the virtual ligand (VL) approach, a computational method that introduces a mathematical model to approximate ligand molecules within quantum chemical calculations. This model is then optimized to identify the electronic and steric properties most suited for a given reaction. However, the interpretability of the resulting VL parameters remained elusive, limiting predictions to a qualitative level. In this study, we establish a mathematical framework that links real molecules to the VL parameters, thereby enabling rapid and quantitative prediction of optimal ligands. The prediction algorithm was validated across four different reactions, and its accuracy, limitations and potential improvements are discussed.