In this work, we demonstrated that the D3 dispersion correction models can exhibit bumps and unphysical minima on the PES, leading to incorrect estimations of binding energies and thermodynamic properties of the systems considered. We showed that the problem originates from the way that C6 AB coefficients are computed in the D3 scheme. To address this issue, we redefined the k3 parameters, by introducing k3 AB coefficients that are specific to the identity of each atomic pair considered. The new scheme, named D3S, smooths the dispersion energy PES and alleviates the presence of unphysical local minima.