Universal binding-energy-distance

When it comes to the metal-metal interactions (such as Fe-Fe and Al-Al), a whole group of empirical force fields are known from the literature. One of the most intuitive is the universal binding-energy-distance relationship [329,330] which simply reads... 

Several approaches have been used for determining functional forms for the pair sum Eq. [12]. Once the Hamiltonian matrix elements had been specified, Chadi, for example, used a near-neighbor harmonic interaction for covalent materials where the force constants and minimum energy distances were fit to bulk moduli and lattice constants, respectively. This expression was then used to predict energies and bond lengths for surfaces and related structures. More recently. Ho and coworkers have fit the pair sum to the universal binding energy relation. This reproduces not only lattice constant and bulk modulus, but also ensures reasonable nonlinear interatomic interactions that account for properties like thermal expansion. 

In an alternative microscopic model,a universal relation between binding energy and interatomic distance is presumed. The validity of this assumption was demonstrated for interfaces between metals, gases absorbed on metals and finally pure metals. The interdependence of binding energy ii(a) and distance a can be decomposed into a product of a function E a) and the cohesion energy Eq at equilibrium distance oq-... 

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