# Relative Stability of Small Silver, Platinum, and Palladium Doped Gold Cluster Cations
## 5 Conclusions  
In this work, the relative stability of small cationic Ag, Pt, and Pd doped \(\text{Au}_{\text{N}}\)+ (\(N=2\)-7) clusters were investigated using a combination of photofragmentation experiments and density functional theory calculations. Mass spectra revealed a pronounced odd-even pattern in the abundances of \(\text{Au}_{\text{N}}\)+ and \(\text{AgAu}_{\text{N-1}}\)+, which can be rationalized by considering the delocalization of the \(s\)-valence electron of each atom in the cluster, including the Ag dopant. Clusters composed of an odd number of atoms possess an even number of delocalized electrons, closing superatomic electronic shells and gaining stability. Dissociation energies calculated for these clusters agree well with this picture, since the  
Figure 5: Total density of states of the clusters composed of \(N=4\) atoms. Projections into atomic states are presented in black for Au(d), in red for Au(sp), in blue for \(M\)(d), and in green for \(M\)(sp). The molecular orbitals of delocalized character extending over the entire cluster volume are plotted and labeled based on their nodal character (1S and \(1\text{P}_{\text{x,y}}\)). The HOMO-LUMO gap is labeled. In the case that the cluster is open-shell, both \(\alpha\) and \(\beta\) orbitals are plotted.  
Figure 6: Total density of states of the clusters composed of \(N=5\) atoms. Projections into atomic states are presented in black for Au(d), in red for Au(sp), in blue for \(M\)(d), and in green for \(M\)(sp). The molecular orbitals of delocalized character extending over the entire cluster volume are plotted and labeled based on their nodal character (IS and \(1\text{P}_{\text{x,y,z}}\)). The HOMO-LUMO gap is labeled. In the case that the cluster is open-shell, both \(\alpha\) and \(\beta\) orbitals are plotted.  
preferred fragmentation channels always produce the more stable fragments: Au\({}_{3}\)+, Au\({}_{5}\)+, AgAu\({}_{2}\)+, and AgAu\({}_{4}\)+. The Pt and Pd doped clusters, however, behave very differently. Experimentally, PtAu\({}_{2}\)+ and PdAu\({}_{2}\)+ correspond to intensity maxima, but PtAu\({}_{4}\)+ and PdAu\({}_{4}\)+ do not. The calculated dissociation energies of these clusters reveal a competition between channels that produce fragments of different sizes, especially in the \(N=4\)-\(6\) size range, explaining the smeared out odd-even pattern in their size-to-size dependent abundances. Analysis of the density of states of the clusters in the \(N=3\)-\(5\) size range reveals an unexpected behavior. At \(N=3\), both Pt and Pd delocalize one valence electron in order to close the 1S superatomic electron shell. At \(N=4\), though, the valence electrons of both dopants remain localized, which also allows the closing of the clusters' 1S shells. Finally, at the size \(N=5\), Pt and Pd again delocalize one electron, closing the 1S and 1P\({}_{x}\) shells. Overall, these results illustrate that it is difficult to predict a priori how doping would affect the electronic structure of clusters, even at the very smallest sizes.  
Conceptualization, P.F. and E.J.; formal analysis, P.F.; investigation, P.F. and E.J.; resources, P.F. and E.J.; writing--original draft preparation, P.F.; writing--review and editing, P.F. and E.J.; project administration, E.J.  
This research was funded by the Research Foundation-Flanders (FWO) (grant number G0B41.15N) and by the KU Leuven Research Council (grant number C14/18/073).