While first-principles methods for computer simulation in condensed matter are rapidly improving in speed and accuracy, classical interatomic potentials continue to constitute the only way to perform Molecular Dynamics or Monte Carlo computations on systems with a very large size (millions of atoms) or for long simulation times (nanoseconds).
With the advent of massively parallel machines, simulations on the mesoscopic scale appear feasible, allowing us to address a whole new range of problems in the physics of defects, surfaces, clusters, liquids and glasses, and in molecular biology. However, obtaining accurate and realistic interatomic potentials constitutes a very challenging task.
There are two aspects to consider when developing an accurate potential:
However, pairwise interactions fail miserably to describe the most common materials we ordinarily deal with, such as metals and semiconductors. The basic reason is that in a two-body potential the strength of each bond is by definition dependent only on the distance between the two atoms involved: the positions of all the other atoms are not relevant. In practice, however, the strength of the bond between two atoms is affected by the environment as determined by the other atoms in the proximity. As a site becomes more crowded, the bond strength will generally decrease as a result of Pauli repulsion between electrons. The modeling of many important physical and chemical properties depends crucially on the ability of the potential to "adapt to the environment".
Research carried on in the last two decades has clearly shown that, by giving up the two-body approximation and working with more complex analytical forms, it is feasible to model metals and semiconductors using classical potentials. To do that, fairly elaborate analytical expressions--involving for instance density-dependent terms, angular forces, or moment expansions--are necessary for a realistic description under different conditions (geometries, structures, thermodynamic phases). A typical potential is thus constituted by a number of functions combined in a complex way, and often nested one into another. Such are, for instance, the glue and Embedded Atom potentials for metals, and the Abell-Brenner-Tersoff potentials for semiconductors.
The analytical form is however only the starting point: one has to fit it to the material at hand.
The goal of the Force Matching project was to set up a fitting procedure capable of dealing with the complexity of multifunction potentials and exploit effectively their modeling power, by making use of the richest source of information on the nature of atomic interactions: first-principles calculations.
This approach has been certainly stimulated by the fast progress of methods based on Density Functional Theory (DFT), notably on the Local Density Approximation (LDA), and on Tight-Binding (TB). These methods are now able to supply atomic forces (and perform dynamics) for a very large number of configurations, including different geometries such as defects, surfaces, clusters, molecules, liquids, but are still unable to handle systems with many thousands of atoms or long simulation times (ns). The large amount of information that can be obtained from LDA or TB techniques can however be used to construct better interatomic potentials, or to attack materials so far considered difficult to model.
The ``computational fitting'' scheme is aimed at obtaining better potentials with less human effort, avoiding the transferability problems that traditionally plague empirical potentials. The numerical engine is based on trying to match as closely as possible the first principles forces with those obtained from the potential, and for this reason it has been named Force Matching Method. The optimization is performed by carrying out a minimization in a relatively large parameter space (of the order of 100 parameters). By explicitly including different geometries and different temperatures (if data come from ab initio molecular dynamics), one can attack the transferability problem at its very heart. One can says that the potential is constructed by learning from first-principles.
The first application of this method resulted in a glue potential for Al, whose realism and accuracy surpass those of previously existing models. This work was presented and discussed in a paper published in Europhys. Lett. 26, 583 (1994). This potential is now extensively used for studies of surfaces and bulk defects. A potential for Mg has been presented in Modelling and simulation in materials science and engineering 4, 293 (1996), by X.-Y. Liu et al..
Current work is focused towards the exploration of new, rich analytical forms, suited for modelling a large variety of materials (including organic systems), whose complexity is such to make traditional fitting methods too cumbersome to carry out.
Among other notable applications, the method has been used by two different groups to construct effective interactions for hydrogen under pressure [J. Kohanoff and J.-P. Hansen, Phys. Rev. E 54, 768 (1996); B. Edwards, N. W. Ashcroft and T. Lenosky, Europhys. Lett. 34, 519 (1996)], and to parametrize a tight-binding model for silicon [T. J. Lenosky, J. D. Kress, I. Kwon, A. F. Voter, B. Edwards, D. F. Richards, S. Yang, and J. B. Adams, Phys. Rev. B 55, 1528 (1997)].
See also: Interatomic potentials