A Virtual Model for Describing Organophosphorus Reactivity: Validation and Application to Virtual Molecule-Assisted Optimization.

Optimizing reagent and catalyst molecules remains a fundamental yet resource-intensive task in organic chemistry, which our group previously streamlined by developing the "virtual ligand strategy." This in silico optimization framework approximates the electronic and steric effects of phosphine ligands using a mathematical model that enables rational-design principles to be extracted by numerically optimizing the corresponding parameters. Herein, this concept is extended and a new model that accounts for the reactivities of phosphines as reagents or organocatalysts is developed. The model reproduces substituent effects using distinct electronic and steric parameters and successfully captures changes in the valence state and coordination number of the phosphorus center that occur during a reaction. This approximation accurately reproduces the reactivities and structural features of real phosphines, with the Wittig reaction as a representative example. Furthermore, numerically optimizing the model parameters facilitates designing phosphines that minimize the activation barriers associated with the catalytic Staudinger amidation reaction.