# Relative Stability of Small Silver, Platinum, and Palladium Doped Gold Cluster Cations
## 4 Discussion  
The electronic structure of the clusters composed of \(N\) = 3-5 atoms was analyzed for the different pure and doped clusters via calculations of total density of states (DOS) in order to understand their relative stability. Figure 4 presents this analysis for the clusters composed of three atoms. In the left panel, the DOS of Au\({}_{3}\)\({}^{+}\) is shown, which is projected into atomic \(d\)-(black) and \(sp\)-states (red). Due to the very small size of the cluster, the DOS is composed of molecular-like states with a strong \(d\)-character below the HOMO state. Within this dense region of occupied \(d\)-states, one state has a higher \(sp\)-character (although with an overall low intensity). A plot of the molecular orbital (MO) of this state  
\begin{table}
\begin{tabular}{c c c} \hline \hline \multicolumn{2}{c}{**Dissociation Channel**} & \(D_{N}\)**/eV** \\ \hline Au\({}_{3}\)\({}^{+}\) & \(\rightarrow\) Au\({}_{1}\)\({}^{+}\) + Au\({}_{2}\) & 4.14 \\ Au\({}_{4}\)\({}^{+}\) & \(\rightarrow\) Au\({}_{3}\)\({}^{+}\) + Au\({}_{1}\) & 2.25 \\ Au\({}_{5}\)\({}^{+}\) & \(\rightarrow\) Au\({}_{3}\)\({}^{+}\) + Au\({}_{2}\) & 2.58 \\ Au\({}_{6}\)\({}^{+}\) & \(\rightarrow\) Au\({}_{5}\)\({}^{+}\) + Au\({}_{1}\) & 2.71 \\ Au\({}_{7}\)\({}^{+}\) & \(\rightarrow\) Au\({}_{5}\)\({}^{+}\) + Au\({}_{2}\) & 3.20 \\ AgAu\({}_{2}\)\({}^{+}\) & \(\rightarrow\) Au\({}_{1}\)\({}^{+}\) + AgAu\({}_{1}\) & 4.69 \\ AgAu\({}_{3}\)\({}^{+}\) & \(\rightarrow\) AgAu\({}_{2}\)\({}^{+}\) + Au\({}_{1}\) & 2.18 \\ AgAu\({}_{4}\)\({}^{+}\) & \(\rightarrow\) AgAu\({}_{2}\)\({}^{+}\) + Au\({}_{2}\) & 2.44 \\ AgAu\({}_{5}\)\({}^{+}\) & \(\rightarrow\) AgAu\({}_{4}\)\({}^{+}\) + Au\({}_{1}\) & 2.51 \\ AgAu\({}_{6}\)\({}^{+}\) & \(\rightarrow\) AgAu\({}_{4}\)\({}^{+}\) + Au\({}_{2}\) & 3.41 \\ PtAu\({}_{2}\)\({}^{+}\) & \(\rightarrow\) Pt\({}_{1}\)\({}^{+}\) + Au\({}_{2}\) & 3.97 \\ PtAu\({}_{3}\)\({}^{+}\) & \(\rightarrow\shows a wavefunction that is delocalized over the entire cluster, with a nodal character resembling that of the 1S eigenstate of a particle confined in a 2-dimensional potential well [21]. This doubly occupied MO is the only one of delocalized character below the HOMO, showing that Au\({}_{3}\)+ has two itinerant electrons as anticipated. Each of the three Au atoms delocalizes its 6s electron, of which one is removed during ionization. The DOS also reveals the presence of two, almost degenerate, unoccupied MOs resembling the 1P\({}_{\mathrm{x}}\) and 1P\({}_{\mathrm{y}}\) cluster orbitals, which are higher in energy. The second panel of Figure 4 presents the case of AgAu\({}_{2}\)+, in which the DOS is also projected into the \(d\)-(blue) and the \(sp\)-states (green) of the silver dopant. The DOS of this cluster is very similar to that of Au\({}_{3}\)+, with the region close to the HOMO state having a higher Au than Ag character. This is a consequence of the relativistic nature of gold, which reduces the \(s\)-\(d\) energy separation [28]. As the figure reveals, this cluster also has only one doubly occupied MO of delocalized character (1S symmetry). Therefore, as expected, Ag is delocalizing its 5s electron. The PtAu\({}_{2}\)+ and PdAu\({}_{2}\)+ cases, which are presented in the right panels, are different. In both cases the DOS near the HOMO state is dominated by the \(d\)-states of the dopant atom, and, as for Au\({}_{3}\)+ and AgAu\({}_{2}\)+, only one MO of delocalized character is found to be doubly occupied. This indicates that PtAu\({}_{2}\)+ and PdAu\({}_{2}\)+ are also clusters with closed electronic shells, which is not trivial considering the electronic configuration of these dopant atoms. Therefore, at \(N=3\) the Pt dopant delocalizes its 6s electron ([Xe] 4\(f^{14}\) 5\(d^{9}\) 6s\({}^{1}\)), whereas the Pd dopant ([Kr] 4\(d^{10}\)) promotes one of its 4\(d\) electrons to an electronic configuration of [Kr] 4\(d^{9}\) 5s\({}^{1}\), which then delocalizes over the entire cluster. This leaves both dopant atoms with an open atomic \(d\)-shell.