Mapping π-electron reorganization in the language of resonance: the differential bond delocalization function

We present ΔBDF_π, a first principles method designed to help chemists visualize and understand how π electron systems respond to structural and environmental perturbations. Derived from the recently developed Bond Delocalization Function (BDF_π), ΔBDF_π is a three dimensional differential function that quantitatively maps reorganization of the π electronic structure induced by substitutions, noncovalent interactions, and other perturbations, allowing these effects to be directly compared. ΔBDF_π provides an intuitive interpretation of complex changes in π-molecular orbital coherence in the language of resonance theory. Through examples including resonance assisted hydrogen and halogen bonding, intermolecular interactions, substituent effects, and solvation and redox transitions, we demonstrate the usefulness of ΔBDF_π in studying susceptibility of π-systems to diverse factors and explaining the underlying mechanisms.