These distributions reveal no clear trend in energy differences from additional correlation terms. Figure notably demonstrates that correlating spatially distant bond changes can sometimes significantly increase energy differences. This suggests that imposing correlations on uncorrelated pairs of atom pairs may increase energetic instability. These findings indicate that single pivot atom-mediated correlation terms are the primary contributors to reaction path improvement. Difference between patterns from eq 9 and eq 10. (b) Difference between patterns from eq 8 and eq 10.