Gas-phase experiments in combination with electronic structure calculations have been extremely successful in unraveling the structure and applications of nanoclusters. This tutorial review provides an overview about the recent developments in the structure and applications of noble metal clusters of gold, silver and copper. We start with a brief introduction about the definition of metal clusters and their size specific properties. We next discuss in detail about the advances made in the structural determination of noble metal clusters and finally conclude the review by providing a brief account about the different applications of these clusters.
Keywords: Metal Clusters, Structural Characterization, Electronic structure, Biodetection, Catalysis
Nanotechnology has received tremendous interest since the beginnings of 21st century although; it was Michael Faraday on the 1850s,  who started these studies on metal colloidal particles. Nanotechnology particularly focuses on the synthesis, characterization, design, applications and manipulation of the matter at low levels, including: “nanoparticles” and “metal clusters”.
Owing to their unique physical and chemical properties, metal clusters have become an exciting area of research in recent years. Clusters show intermediate properties between the isolated atom and the bulk metal and represent the most elemental building blocks in nature (after atoms). They are characterized by their size, and act as a bridge between atomic and nanoparticle behaviors, with properties entirely different from these two size regimes. The percentage of atoms present on the surface of clusters increases with a decrease of the core size, which could strongly affect their properties. As can be seen in Figure 1, bulk metal has a continuous band structure in which free electrons oscillate. However, in sharp contrast on reduction of the size to the nanoparticles regime, a splitting of the energies at the Fermi level is observed.
Therefore the valence density of states and the conduction band will be affected which leads to changing from a continuous density of states (on the bulk metal) to discrete energy levels. As the size becomes smaller and approaches the nanoscale, the wave character becomes more important and quantum mechanics becomes necessary to explain its behavior. The metal clusters dramatically exhibit size specific unique electronic and optical properties, such as molecule-like energy gaps  , strong photoluminescence  and high catalytic properties .
task in the cluster science due to the lack of direct experimental probes. Size selected bare clusters are generally produced in a molecular beam with a very low number density and thus cannot be characterized structurally by standard microscopic or diffraction techniques. However, recent advances in the physical characterization techniques in combination with high level quantum chemical calculations have lead to a significant success in determining the size dependent structural and electronic properties of a number of metal clusters with substantial degree of credence. The different experimental techniques involved in the structural characterization of metal clusters are: (i) ion mobility spectrometry (IMS) [5-6] (ii) photoelectron spectroscopy (PES) [7-13] (iii) trapped ion electron diffraction (TIED [14-15] and (iv) infrared multi-photon dissociation (IRMPD) spectroscopy [16-17]. For a given cluster, each of the above mentioned techniques measures a property which can be mapped with the help of the quantum mechanical calculations. In light of these advances, it has been now possible to address two old questions in the field of silver and particularly gold clusters: (i) how and why do the properties of silver and gold clusters change with the number of atoms and (ii) what is the effect of charge on the cluster properties.
Ion mobility measurements in combination with quantum mechanical calculations by Kappes and co-workers showed that cationic silver clusters tend to from 3D structures at n = 5 atoms .Further, theoretical calculations reveal planar structures up to n = 5, 6 and 7 atoms for the cationic, anionic and neutral silver clusters respectively. Systematic structural determination of cationic gold clusters for 4 ≤N ≤13 was also carried out by research group of M. M. Kappes  by comparing the measured collision cross sections in an ion mobility experiment with the theoretical (geometrical) cross sections for a large number of relaxed cluster isomers. As can be seen from Figure 2, a good match was observed for planar structures between the experimental and theoretical cross sections up to a size of 10 atoms. The surprising result that gold clusters retain planar structures up to large size range lead to further studies from the Kappes group on the anionic gold clusters. Around the same time, Pacific Northwest LabAtlanta investigation using PES and density functional theory (DFT) studies was also set up to probe the structure of anionic gold clusters up to a size of 14 atoms. The Kappes work5 and the Pacific Northwest Lab-Atlanta investigation  convincingly set the 2D-3D transition for a size of N = 12. The calculated lowest energy structures obtained by the Pacific Northwest Lab-Atlanta investigation using photoelectron spectroscopy and density functional studies are shown in Figure 2. Häkkinen et al. subsequently attributed the unusual stabilization of planar structures to the enhanced relativistic effects in the bonding of gold, which reduces the 5d-6s energy gap and thus enhances the s-d hybridization .
Combined PES/DFT investigation on the anionic gold clusters in the size range of 16-19 atoms in 2006 showed that the dominant ground state isomers form cage type structures. Au16- was found to be highly symmetric with Td symmetry where as the Au17- and Au18- cages were found to have C2V symmetry. Following this, global minimum calculations were carried to gain information about the structural features of neutral clusters in the 16-19 atom size range. It was shown that the neutral clusters are also dominated by cage type structural motifs in the 16-19 atom size range. Several studies[14,23-25] also revealed that Au19- has a pyramidal structure like that of tetrahedral Au20- but with a missing apex atom. The unique tetrahedral structure of Au20- was discovered much earlier than the above mentioned cage type structures using PES . Further, Lechtken et al. showed using TIED measurements  that Au20- is indeed tetrahedral whereas Au20+ contains a mixture of tetrahedral and deformed icosahedral conformers.
The tetrahedral structure of neutral Au20 cluster with a large HOMO-LUMO gap was confirmed by Gruene et al. using FIR-MPD  spectroscopy. The Td structure of Au20 has also been validated by a number of theoretical studies and relativistic effects are known to play an important role in its stabilization [27-32].
Structure determination of medium sized gold clusters becomes exceedingly difficult due to competition between the large numbers of possible isomers for the ground state in this size range. Very few structural studies have been carried experimentally beyond 20 atoms particularly for the cationic and neutral gold clusters. For the anionic gold clusters beyond 20 atoms, Xing et al. proposed an elongated cage structure for Au21- and a tube like structure for Au24- using TIED/DFT studies .However, Zeng and co-workers in a systematic PES/DFT  study on the gold clusters with 21 to 25 atoms revealed that the low energy isomers of Au21-are dominated by pyramidal structures. In case of Au22- and Au23-, pyramidaland double layer structures are found to be competitive. Au24- was found to have a tube like structure in line with the earlier study of Xing et al. The authors pointed out the possibility of multiple isomers for the anionic gold clusters with 21 to 24 atoms due to lack of consistency between the experimental and simulated results in this size range. Au25- was found to have a core-shell structure with a single atom-core and 24-atom shell. Au27- , Au28- and Au30- have also been shown to possess coreshell type structures with a single atom-core . Johansson et al. theoretically  predicted neutral Au32 to be “a 24-carat golden fullerene” with a highly stable and symmetrical (icosahedral) cage structure. However, the golden fullerene structure of Au32 has not been verified experimentally up to date. For the anionic Au32 cluster,[35,37-38] a low symmetry (C1) compact core-shell structure with a triangular three atom-core was proposed using PES/DFT studies. Earlier reports [39-40] on the structure of Au34- revealed a chiral structure with C3 symmetry which consists of a four-atom tetrahedral core and 30-atom shell using either or a combination of TIED, PES and DFT studies. However, Wang and co-workers [35,41] unequivocally confirmed a C1 core shell structure with fouratom core to be the global minimum structure for Au32 - using PES and DFT based studies. It was also shown that the structure of Au35- can be derived by attaching one gold atom to the surface of Au34-. Further, recently Zeng and coworkers  in a joint PES/DFT report concluded that anionic gold clusters with 36, 37 and 38 atoms exhibit core-shell type structure with a robust four-atom core.
As compared to the medium sized gold clusters, little attention has been paid towards the structural characterization of medium sized silver clusters. With the help of TIED experiments and theoretical calculations, [43-44] the research group of M. M. Kappes have investigated the structural features of certain cationic silver clusters in the size range 18 < n < 80 and Ag55- . Ag55+ is a Mackay icosahedrons, where as Ag55- shows a weak Jahn-Teller distorted icosahedral structure. The structure of clusters such as Ag19+ , Ag38+ , Ag59+ , Ag75+ and Ag79+ was also found to be based on the icosahedral motif. Similar technique was used to determine the structure of cationic silver clusters in the size range of 36 to 55 atoms .The structures of anionic gold and silver clusters in the size range of 55 to 64 atoms were studied recently using high resolution PES and DFT [46-48].It was observed that anionic silver clusters prefer structures based on the symmetrical icosahedral motifs, whereas, surprisingly anionic gold clusters were found to have low symmetry core shell structures in this size range. Further, it was shown that the preference of the anionic gold clusters for the core-shell structures in this size range is due to strong relativistic effects in the gold. Predictions of the geometrical structure of free copper clusters have been made by several ab initio studies. For sizes N < 10 first-principles based calculations have been developed , while Kabir et al. applied tight-binding methods  for sizes up to N = 55. Moreover, they calculated that most of the clusters in the size range 10 ≤ N ≤ 55 adopt an icosahedral geometry (Figure 3 B).
Thus, highly symmetric clusters may be viewed as geometric magicnumber clusters. Different theoretical studies have concluded on the planar geometry of small clusters with a copper atom number N≤5 ( Figure 3 A).Kabir  also found relative stability at Cu8, Cu18 and Cu20 (Figure 4) due to the electronic shell closing at N = 8, 18, and 20. This behavior corresponds to the magic number in electronic shell model besides a reversed even-odd alteration for N = 10−16 with maxima at odd sized clusters, Cu11, Cu13 and Cu15, which manifests the geometrical effect through icosahedral growth.
Over the last few years, the study of prediction models for ligand- protected gold clusters has been very important. The calculation has to combine different aspects at the same time : (1) the magic numbers required for electronic stabilization of the cluster, (2) the requirements for an electronically closed shell  formulated as (LS·ANXM)z: n* = NνA– M – z, where n* represents the number of electrons for shell-closing of the metallic core, which has to match one of the magic numbers corresponding to strong electron shell closures in an anharmonic mean-field potential giving rise to stable clusters; N stands for the number of core metal atoms (A); νA is the atomic valence; M is the number of electronlocalizing (or electron - withdrawing) ligands X, assuming a withdrawal of one electron per ligand molecule; and z represents the overall charge of the complex. The weak ligands represented by LS may be needed for completing the steric surface protection of the cluster core and (3) the fact that solution-phase clusters require a sterically complete protective ligand shell compatible with a compact atomic shell structure for the metallic core, the satisfying of all such conditions complicates the calculations of the structures enormously. Recently, research on the structure of metal clusters has mainly been focused on alkanethiolate-stabilized gold and silver clusters. However, due to the difficulty in synthesizing homogeneous and high-quality sub-nanometer sized crystals, only limited cluster systems have been investigated. For example: Jadzinsky et al.  reported the X-ray structure determination of an Au102(p-MBA)44(pMBA, p- mercaptobenzoic acid) single crystal. They found an Au49 core surrounded by two groups of 20 Au atoms face camping the Au49 and then 13 Au atoms dispersed without apparent symmetry. Zhu  and Heaven  proposed a similar Au combination for the Au25(SR)18 cluster: an icosahedral Au13 core plus the exterior 12 Au atoms in the form of six –RS–Au–RS–Au–RS– motifs. Besides this, Zhu et al. found that all the proposed Au25(SR)18 structure was independent of the employed ligands.
Exact simulation of the electronic structure of metal clusters is a very difficult task, particularly for smaller clusters in solution and protected by caping agents. Therefore, the use of simple models such as the Jellium model  (quantum mechanical model) gives a considerably good approximation, preserving many of the physicochemical characteristics of the clusters. The Jellium model was firstly developed for clusters in the gas phase and consists on the assumption that a metal cluster can be modeled by uniform, positively charged density spheres with the energy levels filled with free electrons in accordance with the Pauli principle. Hence, free valence electrons are assumed to move in a homogeneous spherical ionic background. Each time that filled electronic 7 shells appear, the corresponding cluster exhibits enhanced stability. The total energies as a function of cluster size, calculated by this model agree with the position of the peaks obtained by mass spectrometry of the clusters, related with the abundance of most stable clusters. Alkali metal clusters, NaN, were studied by mass spectrometry by Knight et al. showing unusual stability at specific cluster sizes N= 2, 8, 18, 34, 40…atoms. For instance, eight free electrons completely filled the 1s and 1p energy states forming a complete valence shell, thereby making Na8 cluster very stable. Besides this, the intensity distributions show that clusters with an even number of atoms are more stable than those with an odd number of atoms. These specific cluster sizes will be known as “magic numbers”. Most studied metal clusters as Au, Ag and valence Cu have an electronic configuration characterized by a closed d shell and a single s electron: [Cu: Ar(3d)10(4s)1], [Ag:Kr(4d)10(5s)1] and [Au: Xe(5d)10(6s)1] similar to the alkali metal clusters. Early experiments have established that AuN, AgN, and CuN clusters (N= 2, 8, 20, 34, 58...) are all electronic magic-number clusters  (Figure 5) observing that clusters carrying a simple positive charge (cation) should exhibit magic numbers that are shifted by one, being sizes with 9, 21, 41 being those which contain 8, 20, 40 valence electrons.
Experimental evidences for the inert electronic shell structure in some copper clusters have been given by Winter et al.  who studied the chemical stability of CuN clusters by a reduced reactivity towards O2. Anomalously low intensities were observed for N=20, 34, 40, 58 and 92, concluding the reactivity of CuNCLs-O2 is inhibited by electronic shellclosing effects at these sizes.
Due to the unique physicochemical properties, metal clustershave already been applied in different fields, such as sensing, catalysis, biological labeling, biomedicine and electronics. Here, we will briefly summarize several important applications of metal clusters in biodetection, biological imaging and catalysis, which are the main topic applications.
Recognition-based biosensing of metal ions by metal clusters is being extensively studied nowadays .Many ions has been successfully detected by using fluorescence quenching of metal clusters as Pb, Cu, Co, Al, etc. Gold clusters can succesfully sense Hg2+ based on their fluorescence quenching through Hg (II)-induced aggregations of clusters (Figure 6) [59-60]. Fluorescent silver clusters have also been demonstrated satisfactory to detect mercury ions even at subnanomolar concentrations . As well, small biomolecules, such as cysteine , H2O2 , cyanide , etc has been also detected using metal
Metal clusters of gold with their bright emission, good biocompatibility and photostability are becoming attractive alternatives to conventional fluorophores (organic dyes or quantum dots) for bioimaging. In a recent study, Jao et al  synthesized gold clusters (photobleaching resistant) with dendrimer templates which can act as bio-trackers for intracellular targeting and tracking. In vivo 1st study of fluorescence imaging have been presented by Wu et al.  by using ultrasmall BSA-stabilized Au clusters. As shown in Figure 7, fluorescence images of the subcutaneously injected mice exhibited bright emission from different locations depending on the injected Au clusters dose.
The unusual catalytic activity of metal clusters has attracted more and more attention over the past years. Initially, clusters were dispersed on a solid support in order to prevent the clusters from aggregating during the catalysis reactions. Studies on supported metal clusters showed that in addition to the cluster size, the nature of the support materials also plays a key role for their catalysis performance. Harding et al. [65,67] studied the control and tunability of the catalytic oxidation of CO by Au20 clusters deposited on MgO surfaces. Catalysis of the oxidative dehydrogenation of propane by Pt clusters  or propene epoxidation catalysis  by gold clusters have been also studied. Another interesting example of the catalytic properties is the use of silver clusters to prevent pathologies, shuch as fetal alcohol syndrome . It has been demonstrated that some silver clusters (AgCLs) are able to electrocatalyze the oxidation of alcohols and prevent its cytotoxicity under physiological conditions at very low potentials, like those found on live cells (Figure 8).
This review has attempted to provide a valuable account about the structural characteristics of noble metal clusters. It is noted that the noble metal clusters form a wide range of form a variety of fascinating structures, including planar, cage-like, pyramidal, tube-like, core−shell, and fullerene-like structures. The unique geometrical structure of these clusters is reflected in terms of their electronic structure and gives rise to exciting applications in imaging, sensing, catalysis. Further studies must be carried out to tune the structure of these systems by changing factors such as composition of the cluster, nature of ligands, charge of the cluster and so on to obtained desired electronic and geometric structure for exciting applications.