A well-established principle in particle-mesh methods is that potentials derived from indirect computations through density projections onto numerical grids tend to be more diffuse than those calculated directly from pairwise distances. Our study provides further evidence for this phenomenon. By fitting the W H 2G potentials to a two-Gaussian model and analyzing their attractive components, we observe a clear trend: as the grid size h increases, the attractive component becomes wider and less pronounced. This effect is quantitatively demonstrated by the decreasing weight parameter a G2 and the increasing width parameter σ G2 in Figure . These findings highlight the importance of carefully considering grid resolution in particle-mesh methods, as it can significantly influence the effective interactions between particles, and consequently the overall system behavior.