Determining the range of forces in empirical many-body potentials using first-principles calculations

A computationally efficient and accurate description of interatomic interactions is indispensable to the fidelity of atomistic simulations. In the development of popular empirical potentials, it is assumed that atoms separated beyond a certain cut-off distance have negligible interatomic forces and hence may be safely ignored in the force calculations. This arbitrary, and yet common, practice of force truncation is undoubtedly ad hoc and is not grounded in the physics of the interactions. With the advent of fast computers and accurate first-principles calculations, it is now feasible to determine what this cut-off distance should be. In this work, employing a first-principles calculation based on density functional theory and the local density approximation (LDA) we probe the extent of interatomic forces in aluminium caused by a variety of defect types. The forces on neighbours to these defects, obtained from first-principles calculations, were then compared with the corresponding values from many short- and long-range semiempirical literature potentials. It is clear that none of these semiempirical potentials can reproduce the LDA results, although the newest potentials that use LDA force data for potential determination come close. The results also indicate that nearest-neighbour forces are dominant for zero- and one-dimensional defects. Only for a free surface did we find forces at more distant neighbours to be comparable in magnitude. Using the new LDA force data for the single vacancy, we modify a literature potential to improve significantly the agreement with the first-principles calculations.