For the moment, there is no exact description of van der Waals (vdW) interactions. ACFD-RPA \cite{Gould1} is expected to better describe vdW bonding, but it is not exact. The PBE/DFT-D2 method is less satisfactory, however, its results are in good agreement with experimental data. Although our fitting technique may weaken (not neglect) the vdW interactions and produce interlayer potentials with weakened vdW, the obtained interlayer potentials reproduce energetics of graphite near the equilibrium interlayer distance very well, as shown in Ref. \cite{Chen}. If having inputs which fully include vdW interactions and having better fitting functions, we believe that interlayer potentials can also fully include vdW interactions in graphite system.
@article{arxiv.1407.3382,
title = {Replying "the comment on Interlayer interactions in graphites"},
author = {Xiaobin Chen and Fuyang Tian and Clas Persson and Wenhui Duan and Nanxian Chen},
journal= {arXiv preprint arXiv:1407.3382},
year = {2014}
}