# Relative Stability of Small Silver, Platinum, and Palladium Doped Gold Cluster Cations
## 3 Results
### Theoretical Results  
The computed lowest energy structures of Au\({}_{N}\)\({}^{+}\) and \(M\)Au\({}_{N-1}\)\({}^{+}\) (\(N=2\)-7, \(M=\) Ag, Pt, and Pd) clusters are shown in Figure 3. The lowest energy structures of cationic Au\({}_{N}\)\({}^{+}\) clusters are planar up to \(N=7\) (although Au\({}_{7}\)\({}^{+}\) has a slight out-of-plain distortion), according to ion mobility experiments [16]. In many DFT studies, however, it is predicted that the 2D to 3D transition takes place at \(N=8\), although the planar and 3D isomers of Au\({}_{8}\)\({}^{+}\) are close in energy [35; 55]. The source for this discrepancy can be related to the lack of implicit relativistic effects in most DFT studies on gold clusters, although that question goes beyond the scope of this study. In the \(N\leq 7\) size range, theory and experimental results agree that all Au\({}_{N}\)\({}^{+}\) clusters are two-dimensional. Upon Ag doping, the 2D-3D transition size is modified. AgAu\({}_{4}\)\({}^{+}\) adopts a 3D twisted X-structure, indicating a decrease of the transition size to \(N=5\), but AgAu\({}_{5}\)\({}^{+}\) is again a two-dimensional cluster. Pure Ag\({}_{N}\)\({}^{+}\) clusters are known to become three-dimensional at \(N=5\), as determined recently by far-infrared multiple photon dissociation spectroscopy measurements in conjunction with DFT calculations [56]. Upon Pt doping, calculations predict the 2D-3D transition at the lowest possible size, i.e., at \(N=4\), with PtAu\({}_{3}\)\({}^{+}\) adopting a tetrahedral geometry. Combined far-infrared multiphoton dissociation spectroscopy and DFT calculations have determined that pure Pt\({}_{N}\)\({}^{+}\) clusters become three-dimensional at \(N=4\) as well [57], showing the strong tendency of platinum to form 3D structures. For \(N>4\), all cationic Pt doped gold clusters adopt 3D configurations, except for \(N=7\), which maintains the Au\({}_{7}\)\({}^{+}\) structure substituting the central Au atom by the Pt dopant (however with a larger out-of-plane distortion). Finally, the case of Pd doping is similar to that of Pt, with 3D geometries from the lowest possible sizes of \(N=4\) onward. For most sizes, except \(N=5\) and 7, the structures of PdAu\({}_{N-1}\)\({}^{+}\) and PtAu\({}_{N-1}\)\({}^{+}\) are similar. At \(N=5\), both clusters adopt a 3D twisted X-structure, but the Pt dopant takes the central position of the cluster, whereas the Pd atom is at a side. At \(N=7\) the Pd dopant sits on top of an Au\({}_{6}\) triangular structure which is similar to AgAu\({}_{6}\)\({}^{+}\). The structures of pure Pd\({}_{N}\)\({}^{+}\) clusters have not been characterized experimentally. Nevertheless, DFT calculations predict 3D structures from the tetrameric cluster onward, showing also the strong tendency of palladium to adopt 3D configurations [58]. The computed lowest-energy dissociation channels and the corresponding dissociation energies of Au\({}_{N}\)\({}^{+}\) and \(M\)Au\({}_{N-1}\)\({}^{+}\) (\(N\) = 2-7, \(M\) = Ag, Pt, Pd) are listed in Table 1. As is known for Au\({}_{N}\)\({}^{+}\), the preferred dissociation channel oscillates between neutral monomer and neutral dimer evaporation, with even(odd)-\(N\) clusters preferentially emitting a neutral monomer(dimer) fragment [35; 59]. This demonstrates the higher relative stability of Au\({}_{3}\)\({}^{+}\) and Au\({}_{5}\)\({}^{+}\) since they are in the investigated size range of the preferred daughter clusters. This observation agrees with the interpretation of stability patterns based on valence electron delocalization and electronic shell closing; Au\({}_{3}\)\({}^{+}\) has two itinerant electrons, closing the 1S shell, whereas Au\({}_{5}\)\({}^{+}\) has four delocalized electrons, closing the 1S shell and the 1P\({}_{\rm x}\) subshell. The odd-even trend has also been found in experimentally determined dissociation energies of larger Au\({}_{N}\)\({}^{+}\) clusters [39]. In Reference [39], \(D_{N}\) values were determined for \(N\) = 7-27.