On the importance and problems in the construction of many-body potentials

Abstract

A fundamental problem exists regarding the rigorous representation of the non-additive part of the many-body potential. This is illustrated by considering the contributions to the crystal binding energies at 0 K, E(0), of the rare gases (Ne, Ar, Kr and Xe) arising from reliable two-body potentials and a variety of non-additive terms including dispersion and first-order exchange energies. The non-additive contribution to the crystal binding energies, as defined by the difference ΔE(0) between the experimental results and those evaluated from the two-body potentials, is relatively large. It is shown that while this difference corresponds (in magnitude) to the contribution arising from the non-additive dispersion energies, there can be a significant cancellation between this contribution to ΔE(0) and that arising from the non-additive first-order three-body exchange energies with a resulting disagreement with experiment. Various possible non-additive interactions are considered in an attempt to resolve this discrepancy but, due to insufficient reliable data, no definite conclusions can be made on this point at the present time. The significance of these results regarding the understanding of the many-body potential and the evaluation of the properties of dense matter are discussed in a general way.