Although there is a clear preference for 3D morphology in Cu 3 /Cu 4 relaxations, the difference in stability between 2D and 3D clusters is not significant at this cluster size. Rather, the preference for 3D morphology is evident from the number of 3D structures after relaxation, and the larger magnitude of metal-metal interaction energies compared to metal-surface energies. For example, all Cu 3 which have 3 Cu atoms in a single cluster have very similar binding energy, regardless of whether they are 2D or 3D (typically less than 0.20 eV difference). This is due to the fact that these configurations form the same copper triangle structure. These configurations then have the same metal-metal interaction energy of about -1.24 eV. As discussed, the metal-metal interaction energy is the largest contributor to binding energy and so overall there will not be any significant differences in stability for these clusters whether adsorbed 2D or 3D on WX 2 . Although, as discussed in the introduction a metal-metal interaction energy which is larger than the metal-surface interaction energy, will contribute to 3D growth..It should be noted that this triangular structure takes a C 2v symmetry structure, which is the ground state configuration of a neutral three atom Cu cluster in the gas phase . The weaker metal-surface interaction presumably permits this cluster structure to be particularly stable.