We have calculated the melting temperatures for Ne nanoclusters and bulk solid using two-body Hartree-Fock dispersion (HFD)-like potential by molecular dynamics simulations. To take quantum and many-body forces into account, a new simple and accurate empirical expression is used with the HFD-like potential without requiring expensive calculations. The results indicate that our effective HFD-like potential improves the prediction of the classical two-body results to get better agreement with experiment than an ab initio model. (C) 2014 Elsevier B.V. All rights reserved.