# Relative Stability of Small Silver, Platinum, and Palladium Doped Gold Cluster Cations
## 1 Introduction  
Small metal clusters in the gas phase, produced under conditions where cluster-cluster and cluster-environment interactions are absent, are ideal model systems for a fundamental understanding of the different physical and chemical properties of matter. In a gas phase experiment, clusters are produced and characterized as a function of size, composition, and charge state with atomic precision, and their inherent small size allows for direct comparison with detailed quantum chemical calculations. Many examples in the literature can be found in which small clusters are used to elucidate intrinsic properties of matter, such as the stability of alloy complexes [1; 2], the reactivity and catalytic properties of metals [3; 4], the optical responses of matter [5; 6], and the magnetic coupling of different elements and their evolution from the atom to the bulk [7; 8]. In particular, small gold clusters have been intensively studied over the past few decades due to their fascinating properties. For example, at the nanoscale gold becomes reactive towards different molecules [9; 10; 11; 12], whereas in bulk it is one of the noblest elements [13]. Moreover, small gold clusters possess unique optical properties [6; 14] that are different from those of silver clusters, even though both elements have a similar electronic configuration. The structures of small gold clusters are also remarkable; for instance, Au\({}_{20}\) is known to adopt a highly symmetric pyramidal geometry [15], and smaller gold clusters remain planar up to surprisingly large sizes. The size at which clusters adopt three dimensional structures in their lowestenergy configuration depends on the charge state. Whereas cationic clusters are planar up to \(N=7\), according to ion mobility experiments [16], anions become three-dimensional at size \(N=12\)[17; 18; 19]. The size-dependent stability of small gold clusters is also of interest. In those small metal clusters, each atom delocalizes its 6s valence electron over the entire cluster volume. Electron confinement by the small size of the system results in the development of electronic shells with similar nodal character and degeneracy as those in single atoms [20]. Because of the different nature of the confining potential, however, electronic shells in clusters follow a different order, with no restrictions between quantum numbers [21]. The order of the so-called superatomic electronic shells depends on the exact shape of the confining potential, but in spherically symmetric potentials it follows the pattern: 1S, 1P, 1D, 2S, 1F, 2P,... [22; 23]. The filling of these shells explains the famous stability pattern of Na clusters, with intensity maxima at clusters composed of 2, 8, 10, 40,... atoms [24]. When a cluster has the precise number of atoms, or in this context of delocalized electrons, that close an electronic shell, stability is enhanced with a concomitantly larger energy separation between the highest occupied and lowest unoccupied molecular orbitals (the highest occupied molecular orbital (HOMO)-lowest unoccupied molecular orbital (LUMO) gap) [15]. Such patterns in stability, related to the cluster's electronic shell structure, have been observed mass-spectrometrically in numerous occasions for Au clusters, with a very pronounced size-by-size dependence, since the low-symmetric structures of the clusters lift all but the spin's degeneracy [25; 26; 27]. The size-dependency of cluster properties can be greatly altered by the introduction of dopant atoms. This holds for their reactivities [28; 29; 30], stabilities [2; 31; 32], optical properties [14; 33], and magnetism [34]. The changes in their properties can be related to an interplay between cluster geometry and electronic structure, both being affected by doping.