Origins of the universal binding-energy relation

Abstract

The universality of the relation between binding energy and interatomic separation occurs for metallic and covalent bonds in a wide range of situations, spanning diatomic-molecule energetics, chemisorption, bimetallic adhesion, cohesion in solids, and even interactions in nuclear matter. This has intrigued physicists for some time, and here we provide some insights into its origin. We considered the electron density distribution as the variable linking the total energy and interparticle separation. In the spirit of effective-medium theory, a host electron density as seen by each atom was computed. We found that in every case (cohesion, chemisorption, and diatomic molecules), the host electron density was, to a good approximation, a simple exponential function of interparticle separation. This arises primarily because of the essentially exponential decay of the electron density into vacancy sites, into interstitial regions, into the vacuum from surfaces, or into the vacuum from isolated atoms. This suggested a scaling of the electron density which provides a universal relationship between the scaled interatomic separation and the scaled electron density.This density scaling is key. We applied the scaling of the electron density to impurity-binding-energy--host-electron-density curves computed via the effective-medium approximation. A universal energy--electron-density relationship resulted. This could be combined with the previously noted universal relation between scaled electron density and interparticle separation to yield the universal binding-energy--distance relation. First-principles values of cohesive energies of solids and the energetics of certain diatomic molecules were also correlated with host electron densities, despite the fact that these types of energies are fundamentally different from each other and from impurity binding energies. We found a universal relationship between energies and host electron densities for cohesion and certain diatomic molecules which was the same as the one discovered for impurity binding energies. This, together with the universal relationship between electron density and interatomic separation, helps one to understand how a single energy-distance relation could describe chemisorption and cohesion as well as diatomic energetics.