**1. Introduction**

Substances in our surroundings are composed of assemblies of atoms. For example, a metal is a conglomerate of a nearly infinite number of metal atoms. By contrast, certain substances are made up of a countable number of metal atoms. These substances are called "metal clusters" because their shape resembles grape clusters. Although no clear definition of metal clusters has been established, the term generally refers to an aggregate of two to several hundred metal atoms (**Figure 1**); most such aggregates have a superfine size of 2 nm or less.

The proportion of surface atoms in metal clusters differs substantially from that in bulk metals. Taking a metal cluster with an icosahedral structure as an example, a metal cluster with

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**Figure 1.** Relation of metal clusters discussed in this chapter to a single atom and the bulk metal.

55 atoms (**Figure 1**) has 42 surface atoms, corresponding to 76.3% of the total atom number. In the case of a 13-atom metal cluster (**Figure 1**), 12 atoms are on the surface, corresponding to 92.3% of the total atoms. In bulk metals (**Figure 1**), the proportion of surface atoms is only approximately 0.00001% in a cube of 1 cm3 . Thus, compared with bulk metals, metal clusters have a much higher proportion of surface atoms available to react with other substances. Moreover, in addition to these geometric features, metal clusters also exhibit particular characteristics related to their electronic structures. Bulk metals have an electronic structure in which the valence and conduction bands are connected. Conversely, discretization of the electronic structure occurs in metal clusters because of the small number of constituent atoms.

Because of these geometric and electronic features, metal clusters exhibit physical and chemical properties that differ from those of the corresponding bulk metals. For example, although bulk gold (Au) is an inactive metal, as its size decreases to the cluster level, Au exhibits high catalytic activity in various oxidation and reduction reactions [1, 2]. Furthermore, the sizespecific properties of clusters greatly vary depending on the number of constituent atoms. **Figure 2** shows a photograph of aqueous solutions of thiolate (SR)-protected Au clusters (approximately 1 nm in size) with 10–39 gold atoms [3]. The color of the cluster solutions differs substantially depending on the number of constituent atoms in the clusters. This diversity of colors can be attributed to the aforementioned discrete electronic structure of clusters.

As illustrated above, metal clusters exhibit physical and chemical properties that differ substantially from those of bulk metals despite being composed of the same elements. Furthermore, the properties of clusters vary greatly depending on the number of constituent atoms. Because of their very small size, clusters contribute to the miniaturization of materials and conservation of resources. Thus, metal clusters currently attract great attention in a wide range of fields as new nanoscale functional materials.

**Figure 2.** Photograph of aqueous solutions of glutathionate-protected Au*<sup>n</sup>* clusters [3].

In recent years, the atomically precise synthesis of metal clusters protected with organic ligands [4–19] and polymers [20, 21] has advanced dramatically. In addition, substantial knowledge about the size-specific physical/chemical properties exhibited by these metal clusters has been gathered. In this chapter, we describe the precise synthesis methods of the moststudied SR-protected Au clusters, Au*<sup>n</sup>* (SR)*m*, and their heteroatom-substituted clusters, which are called alloy clusters.
