To further investigate the preference for either 2D or 3D Cu n structures on the TMDs, CI-NEBs were performed to find the energy barrier when transitioning from 2D rhombic structures to a 3D tetrahedral structure, where both structures are adsorbed to the monolayer at X and a copper atom bound to the TMD migrates to the apex of the tetrahedral cluster. On WS 2 and WSe 2 the computed activation barriers are 0.30 eV and 0.37 eV. The activation barrier to transition from the 3D tetrahedral structure to the 2D rhombic structure, that is Cu migration onto the TMD, is 0.06 and 0.07 eV on the sulphide and selenide, respectively. This is consistent with the 2D rhombic cluster being more stable than the tetrahedral structure. Thus the activation barriers between different structures on these TMD monolayers are relatively small, consistent with the relatively weak copper-surface interactions. On the telluride monolayer, no transition state was found, implying that the tetrahedral structure is possibly a saddle point. It should be noted however that one configuration which began as a tetrahedral structure on WTe 2 , relaxed to a rhombic structure with three Cu atoms adsorbed to the surface (see figure ).