So far our work concentrated mainly on potentials for metals. In the period 1983-1986 we developed the glue model, a formulation containing a density-dependent many-body term in addition to usual two-body interactions. This term allows to mimic quite effectively the "gluing" character of the cohesion due to conduction electrons in metals: ions have a low energy as long as they are immersed in the "electron sea", while the exact position of neighbouring ions is relatively unimportant. In turn, however, conduction electrons are brought into the system by the atoms themselves. This led us to write a Hamiltonian where a short-ranged "density function" is attached to atoms, so that for each atom in the system we can compute an effective coordination defined as the sum of all the density contributions coming from neighboring atoms. The energy of this atom will then depend non-linearly upon this effective coordination. The non-linearity of the energy dependence upon coordination essentially models this physical fact, ultimately a consequence of Pauli's principle: the strength of individual bonds decreases as the local environment becomes more crowded. In contrast, with two-body potentials the strength of individual bonds does not depend on the environment. This feature is crucial to capture the physics of bonding in metals. More details can be found in F. Ercolessi, M. Parrinello and E. Tosatti, Simulation of gold in the glue model, Philos. Mag. A 58, 213 (1988) (reprints available on request). For a general review on potentials, I recommend A. E. Carlsson, Solid State Physics 43, 1 (1990).Other schemes such as the Embedded Atom Method, the Finnis-Sinclair method and Effective Medium Theory are similar from the analytical point of view. However, potentials for the same element obtained by different schemes can exhibit different properties, particularly in geometries not considered during fitting (surfaces, liquid, etc.). In this respect, the philosophy of glue model implementations has always been that of trying to construct potentials that work reasonably well in a wide range of geometries, with special attention to surfaces, thermal properties and melting point. This has been basically achieved by giving up at the outset any pretension to obtain parts of the potentials analytically by first-principle considerations, which would unavoidably imply rather drastic approximations, as electrons formally disappear in a classical potential. Fits are done by considering all the functions constituting the potential as free to be determined, and are conducted with the sole goal of maximizing the accuracy of the model.
While rather successful potentials were constructed in this way for gold and lead, it is clear that the route of wholly empirical fits has severe limitations, and a good potential is often the result of craftmanship and patience rather than science. Moreover, ab initio methods are often capable of producing very accurate interactions, even if expensively. Why not use this information? This consideration led to the development of the Force-Matching Method, where (follow the link for details) the fit is driven not only by experimental data, but also by a large quantity of numerical data about the interactions obtained by first-principles. In this way, the shape of the functions constituting the classical potential is learnt by means of electronic structure calculations, rather then guessed. Rich parametrizations can be used, and accuracy improves greatly. Potentials for aluminum and magnesium were developed using this method. The Force-Matching Method is described in F. Ercolessi and J. B. Adams, Europhys. Lett. 26, 583 (1994) (reprints available on request).
You can download glue potentials for your own use. Select the material you are interested in. The link will bring you to a page containing the potential (returned as a set of Fortran subroutines) and a bibliography of some applications carried out with it.
See also: Force-Matching method