Unraveling chemical bonding mechanisms through dipole moment variations under external electric fields

In a recent study [<i>Angew. Chem., Int. Ed.</i><b>62</b>, e202312078 (2023)], it was suggested that the maxima of the dipole polarizability along the bond dissociation coordinate can be used to define chemical bond cleavage. In this work, we systematically analyze this hypothesis by performing a spatial partitioning of the local derivatives of the electronic densities and dipole moments with respect to the external field along the bond axis, considering a set of chemically bonded and non-covalently bonded systems. Through this decomposition, we associate the behaviours of the polarizability and bond stretching with the intra- and/or extra-bond remodulations of the charge and of the fragments' local dipole. In particular, the remodulations are used to characterize the three interaction regions: (I) the bonded region, where the system responds to the field as a single molecular entity; (II) the bond-breaking region, characterized by the additional formation of a dipole moment, in between the atoms participating in the bond, that opposes the total molecular dipole; and (III) the dissociated state, corresponding to the sum of independent dipoles. Furthermore, our decomposition allows us to identify one critical point that might be used to roughly mark the transition between regions (II) and (III) and provides a more exhaustive understanding of the second region within a first principles framework, unravelling the nature of a bond by its electronic response properties, rather than by analyzing the hybridization of the electronic structure. Finally, we complemented this discussion by comparing the polarizability curve against standard methodologies to characterise chemical bonds, finding an alignment between the inflection points of bond order curves with the maxima of the molecular polarizability for covalent bonded systems, thus confirming the start of the bond-breaking.