Figure shows the ligand interaction energy (U 12 ) between a pair of NCs at the equilibrium touch distance, where U 12 represents the potential energy between ligands on different NCs, rather than between ligands on the same NC. Systems with attractive interactions, such as OD and ligands modified at the distal position, exhibit significantly lower U 12 values compared to repulsive systems. However, these differences are less pronounced at the lock distance (Figure ). Importantly, the interactions between NCs in solution are influenced not only by U 12 but also by complex ligand-solvent and solvent-solvent interactions. Comparing NCs in touch and lock modes with those in separated states, we found that solvent displacement significantly contributes to the attractive PMF in systems with attractive interactions (see Supplementary Notes).