Origins of the universal binding-energy relation

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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.