It was noted that, in the development of empirical potentials, it was assumed that atoms which were separated by more than a certain cut-off distance exerted negligible interatomic forces and could therefore be safely ignored in force calculations. This force truncation was ad hoc and was not based upon the physics of the situation. By using fast computers and accurate first-principles calculations, it was feasible to determine what the cut-off distance should be. A first-principles calculation, based upon density functional theory and the local density approximation, was used here to determine the extent of the interatomic forces in Al which were caused by various defect types. The forces on the neighbours of these defects, as deduced from first-principles calculations, were then compared with the corresponding values deduced from published short-range and long-range semi-empirical potentials. It was found that none of these semi-empirical potentials could quite reproduce the local density approximation results. The results also indicated that nearest-neighbour forces predominated for zero-dimensional and 1-dimensional defects. Only in the case of a free surface was it found that the forces at more distant neighbours were comparable in magnitude. By using new local density approximation force data for the single vacancy, a published potential was modified so as to improve significantly the agreement with first-principles calculations.

Determining the Range of Forces in Empirical Many-Body Potentials Using First-Principles Calculations. M.I.Baskes, M.Asta, S.G.Srinivasan: Philosophical Magazine A, 2001, 81[4], 991-1008