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Twenty five years of Finnis–Sinclair potentials

In 1984, the paper, entitled A simple empirical N-body potential for transition metals by M.W. Finnis and J.E. Sinclair appeared in Philosophical Magazine A [1]. Twenty five years later, with more than 1500 citations, it is the most cited article in the Philosophical Magazine A series (1978–2002). In this Special Issue, to celebrate 25 years of Finnis–Sinclair potentials, we have invited papers that illustrate the range of simulations these potentials have enabled, as well as reviewing more recent developments in large-scale simulations in metals. Why have ‘Finnis–Sinclair potentials’ had such an enormous impact? Prior to 1984, atomistic simulations of metals almost invariably used pair potentials to describe atomic interactions. In nearly-free-electron metals, such as the alkalis and aluminum, pair potentials representing effective interactions between screened ion cores could be derived from second-order perturbation theory. However, these potentials accounted only for 10% of the cohesive energy of the metal and could even be anti-cohesive, as in the case of aluminum; the remainder was in a densitydependent, structure-independent energy. The potentials themselves were also dependent on density. If there were large local changes in density, such as at a free surface or even at a vacancy in a high-electron-density metal such as aluminum, there was little justification for ignoring the density dependence of the potentials. The use of potentials dependent on the local density was considered problematic, not least due to the difficulty in rigorously defining a local density. In transition metals, where no theoretical justification could be given to pair potentials, they were nevertheless constructed by fitting them to experimental data. If all the cohesion is represented by a sum of density-independent pair potentials, then the Cauchy relation is obeyed in cubic metals: c121⁄4 c44. This is not obeyed by any real metal – a fact that highlights the inadequacy of the pair-potential model. Although there were some earlier attempts to deal with the local density dependence of atomic interactions in metals, until 1984 almost all large-scale atomistic simulations in metals used pair potentials, many of which were constructed empirically. Finnis–Sinclair potentials solved the local density dependence of atomic interactions in metals at a stroke. The binding energy of the solid is described by two terms. The first is a short-range repulsive interaction described by a pair potential acting between neighboring atoms – nothing new there. However, the attractive interaction is now described by the square root of a sum of pair interactions to neighbors, centered on each atom in the solid. The novelty is entirely in the square root. The square root captures the dependence of atomic interactions on the local density: as the number of neighbors of an atom decreases, the strength of the remaining bonds increases. This immediately predicts an inward relaxation at