Figure 4.

Mechanistic investigation by multidimensional regression modeling. A) Data from the arylation of 20 was used. [PdL] is the precatalyst as shown in Figure 3 with varying ligands. B) Regression model containing all 24 ligands of this data set. E_{σ*(P−C)avg} ^Boltz: Boltzmann-weighted average across the conformers of the average energies of the three P−C σ* antibonding orbitals in each phosphine. E_LP(P) ^Boltz: Boltzmann-weighted average of the energy of the phosphorus lone pair orbital. Sterimol B₁ ^Boltz is the least width and Sterimol L^minconf is the length of the lowest-energy conformer as seen from opposite the P substituents. Red points in the diagram: validation data (EV) not used in the model training. LOO = leave-one-out cross validation score. K-fold: average leave-three-out cross-validation score. C) Illustration and interpretation of the model terms. D) Regression model after removing the four smallest ligands in this data set to exclude the influence of competitive β-hydride elimination on the data.