The fundamental origin of the Pt 4 and Pt 7 thermodynamic stability is rooted in their physical and electronic structure. From a simple visual inspection of Pt 4 and Pt 7 isomers in Figure , we see that the GM structures for these two cluster sizes are much more crystalline than the other cluster sizes. Furthermore, there appear to be more under-coordinated Pt atoms in Pt 5 and Pt 6 compared to Pt 4 and Pt 7 . For a quantitative investigation of the Pt-Pt and Pt-support bonding, we used the LOBSTER program to obtain the ICOHP values for relevant atom pairs. The ICOHP values are then used to classify Pt-Pt and Pt-support bonds as strong and weak, and to count them (Figure ). What we find is that Pt 4 and Pt 7 GM structures have more bonds per Pt atom than any other cluster size and isomer, meaning that in gaining or losing an atom, the total number of bonding interactions would decrease. Interestingly this comes from different contributions; for Pt 4 , many of these bonds come from interactions with Al and O atoms of the support, while for Pt 7 it is mostly with other Pt atoms. We can also see the interplay between Pt-Pt and Pt-support interactions in the structures-more planar structures that interact more with the support have more negative ICOHP values for Pt-support interactions (Figure ). Thus, the unique stability of Pt 4 and Pt 7 arises from the regular, crystalline nature of their GM structures, which is reflected both in the number of Pt-Pt bonds and strong bonding with the support.