2G potentials under various grid sizes h (Figure ) reveals deviations from the target potential V G 2G due to the effect of the grid. When bead positions align precisely with the grid, the potential closely replicates the target potential, mimicking an infinitely dense grid scenario. However, as positions deviate from the grid, the potential weakens and the central grid positions experience the greatest disparity. This effect is amplified by larger grid sizes. In particular, h = 0.02 exhibits a minimal grid effect. To balance computational efficiency and accuracy, we chose a grid size of h = 0.04 for all HhPF simulations. Note that this value is exceptionally small compared to the typical values used for hPF simulations. This small value is needed because of the narrow repulsive Gaussian filter σ H1 = 0.1 nm. This aligns with our empirical observation that the optimal grid size is typically slightly less than half of the smallest characteristic distance in the simulated system. This finding highlights a potential limitation of the HhPF methodology: its challenge in accurately reproducing smaller spatial scales while maintaining computational efficiency.