# Relative Stability of Small Silver, Platinum, and Palladium Doped Gold Cluster Cations
## 3 Results  
### Abundances of Photofragmented Clusters  
The results of the photofragmentation experiments are summarized in Figure 2, which shows the cluster abundances (\(I_{N}\)) for (a) Au\({}_{N}\)\({}^{+}\), (b) AgAu\({}_{N-1}\)\({}^{+}\), (c) PtAu\({}_{N-1}\)\({}^{+}\), and (d) PdAu\({}_{N-1}\)\({}^{+}\) clusters, in the size range of \(N=2\)-6. The values of \(I_{N}\) were calculated by integrating the peak area of each corresponding cluster size in the mass spectra. In panel (a) the well-known odd-even oscillation in the abundances of Au\({}_{N}\)\({}^{+}\) is seen, with local maxima for clusters composed of an odd number of atoms [25; 27; 35]. As discussed, this pattern can be understood by the delocalization of each Au 6s valence electron over the cluster volume, which, due to quantum confinement, develops energy shells. The cluster has an enhanced stability if all shells are completely filled. Since these clusters are positively charged, an odd number of atoms corresponds to an even number of electrons, required to close the electronic shells due to spin degeneracy [20]. We point out, however, that this simplified model assumes a negligible influence of the Au 5\(d\) electrons on the relative stability pattern. Upon Ag doping, as presented in Figure 2b, the odd-even oscillation in the abundances of pure gold clusters was not significantly modified. Local maxima in \(I_{N}\) are found for AgAu\({}_{2}\)\({}^{+}\) and AgAu\({}_{4}\)\({}^{+}\), with an amplitude of the abundance oscillation similar to that for pure Au\({}_{N}\)\({}^{+}\). The simple explanation for this is that the silver atom, with an electronic [Kr] 4\(d^{10}\) 5s\({}^{1}\) configuration, delocalizes its valence electron for each cluster size. This observation is not surprising, since pure Ag clusters possess a very similar odd-even stability pattern as pure Au clusters [32], although it is slightly more pronounced due to the less influential \(d\)-states of the clusters in their electronic structure [28]. The effect of Pt doping on the Au\({}_{N}\)\({}^{+}\) abundances is shown in Figure 2c. As seen, the odd-even staggering is to some extent preserved upon Pt doping up to \(N=4\), with an intensity maximum at PtAu\({}_{2}\)\({}^{+}\). This pattern, however, changes at \(N=5\), because PtAu\({}_{4}\)\({}^{+}\) is not a local intensity maximum. Since the electronic configuration of the platinum atom is [Xe] 4\(f^{14}\) 5\(d^{9}\) 6s\({}^{1}\), the observed stability  
Figure 2: Abundances after photofragmentation for (**a**) Au\({}_{N}\)\({}^{+}\), (**b**) AgAu\({}_{N-1}\)\({}^{+}\), (**c**) PtAu\({}_{N-1}\)\({}^{+}\), and (**d**) PdAu\({}_{N-1}\)\({}^{+}\) clusters; these represent the relative stability of the different sizes. The values were calculated by integrating the area of the corresponding signal in the mass spectra. pattern suggests the delocalization of the Pt 6s valence electron in the \(N=2\)-4 size range, giving a total of two delocalized electrons in the PtAu\({}_{2}\)\({}^{+}\) cluster. This assumption is not trivial in view of the open \(d\)-shell configuration of Pt. An understanding of the modified pattern in the \(N=4\)-6 size range upon Pt doping requires further analysis. Finally, the abundances of the PdAu\({}_{N-1}\)\({}^{+}\) clusters are shown in Figure 2d. The stability pattern is very similar to that seen for the Pt doped case, with a relative intensity maximum at \(N=3\) but not at \(N=5\). For the Pt doped clusters, this pattern in the abundances suggests that Pd delocalizes one electron in PdAu\({}_{2}\)\({}^{+}\), even though this atom has a ground state electronic configuration with a full \(d\)-shell and no valence \(s\) electrons ([Kr] 4\(d^{10}\)). Photoelectron spectroscopy experiments on anionic PdAu\({}_{N}\)\({}^{-}\) clusters below \(N=6\) have shown that Pd can promote one of its 4\(d\) electrons to the 5s shell, which then participates in the bonding with Au [53].