Many-atom interactions in solids

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Abstract
Computer simulation of complex processes in condensed matter comprises a large and broad research effort. These require good models of the interatomic interactions, valid over a wide range of circumstances. In most processes of interest, the crucial atoms are in positions far from standard bonding patterns, at least temporarily: at surfaces and defects, in clusters and in open structures like silicates, the coordination number varies widely. The difficulty of modelling interatomic interactions in such circumstances arises from the existence of strong many-atom forces, originating from the uncertainty principle and the variational principle of quantum mechanics. Some theory of many-atom interactions, and some evidence for them, will be reviewed briefly. In particular a series based on two-, three-, four-atom, etc., interactions is almost certainly not convergent in some cases. In recent years several empirical and semi-empirical, broadly similar approaches to modelling many-atom interactions have come into use, though there are few hard tests of how good they are. An alternative approach, requiring the largest computations possible, involves the Schrödinger equation for the whole simulation to a high relative accuracy.