Distinguishing between chemical bonding and physical binding using electron localization function (ELF)

To distinguish between chemical bonding and physical binding is usually simple. They differ, in the normal case, in both interaction strength (binding energy) and interaction length (structure). However, chemical bonding can be weak (e.g. in some metallic bonding) and physical binding can be strong (e.g. due to permanent electrostatic moments, hydrogen binding, etc) making differentiation non-trivial. But since these are shared-electron or unshared-electron interactions, respectively, it is in principle possible to distinguish the type of interaction by analyzing the electron density around the interaction point(s)/interface. After all, the former should be a contact while the latter should be a tunneling barrier. Here, we investigate within the framework of density functional theory typical molecules and crystals to show the behaviour of the electron localization function (ELF) in different shared-electron interactions, such as chemical (covalent) and metallic bonding and compare to unshared-electron interactions typical for physical binding, such as ionic, hydrogen and Keesom, dispersion (van der Waals) binding and attempt to categorise them only by the ELF and the electron population in the interaction region. It is found that the ELF method is not only useful for the characterization of covalent bonds but a lot of information can be extracted also for weaker types of binding. Furthermore, the charge integration over the interaction region(s) and tracing the ELF profile can reveal the strength of the bonding/binding ranging from the triple bonds to weak dispersion.