Post-Transition Element Clusters

Abstract This chapter reviews the methods that are useful for understanding the structure and bonding in Zintl ions and related bare post-transition element clusters in approximate historical order. After briefly discussing the Zintl-Klemm model the Wade-Mingos rules and related ideas are discussed. The chapter concludes with a discussion of the jellium model and special methods pertaining to bare metal clusters with interstitial atoms. 

Modem work on these and related bare post-transition element clusters began in the 1960s after Corbett and coworkers found ways to obtain crystalline derivatives of these post-transition element clusters by the use of suitable counterions. Thus, crystalline derivatives of the cluster anions had cryptate or polyamine complexed alkali metals as countercations [8]. Similarly, crystalline derivatives of the cluster cations had counteractions, such as AlCLj, derived from metal halide strong Lewis acids [9]. With crystalhne derivatives of these clusters available, their structures could be determined definitively using X-ray diffraction methods. 

An essential feature of the Wade-Mingos rules [13-16] is the partitioning of the valence electrons of the cluster atoms into skeletal electrons and external electrons. For polyhedral boranes, the external electrons are used to form bonds to external groups, such as hydrogen atoms in the prototypical borane dianions However, for bare post-transition element clusters, these external electrons formally correspond to nonbonding electron pairs. Subsequent experimental and theoretical... 

The next development in the understanding of structure and bonding in the Zintl ions recognized their relationship to the polyhedral boranes and the isoelectronic carboranes. Then the Wade-Mingos rules [13-16], which were developed to understand the structure and bonding in polyhedral boranes, could be extended to isovalent Zintl ions and related post-transition element clusters. 

To understand the unusual structures found in bare post-transition element clusters and underlying reasons for differences in the structures between analogous boranes and post-transition element clusters, we carried out extensive density functional theory (DFT) studies of bare germanium clusters during the past decade [18-20, 69-72]. In three cases (Fig. 5), these studies predict lowest energy structures for Ge clusters that are different from the well-established structures of the isovalent boranes and carboranes C2B 2H . Thus, the lowest energy... 

Acknowledgment The author is indebted to the US National Science Foundation for support of this workunder Grant CHE-0716718. This article is dedicated to the memory of Prof. loan Silaghi-Dumitrescu (1950-2009) in recognition of the pivotal role that he played in density functional theory studies on bare post-transition element clusters. 

Cluster polyhedra as found in boranes, metal carbonyl clusters, coinage metal clusters, and post-transition element clusters... 

Whereas the transition-metal clusters are ligand-supported (in the typical case by carbonyls), the post-transition element clusters are most often unsupported and/ or destabilized by the interaction with ligands hence the use of the term ""naked cluster". 

The transition-metal clusters often display highly symmetrical metal frameworks, normally with symmetries derived from the platonic or archimedian solids or variations thereof. The post-transition element clusters, on the other hand, are not necessarily aflfected by such confinements. However, as will be explained in Sec. 1.29.4, relationships between the structure and the electron count do exist for the naked clusters, and regular, closed geometries are found for a rather large group of these species. For instance, the trigonal prismatic symmetry of the Rhf, framework in Fig. lA is also found in the naked tellurium cluster... 

Another term which will frequently be used is sub-valence . This term will hereafter be defined as it normally (but implicitly) is, namely as an unusually low, positive oxidation state, which generally will not be stable in aqueous solution. The two terms sub-valence and cluster are intimately connected in the sense that all naked, cationic post-transition element clusters are sub-valent species. 

To summarize, the naked post-transition element clusters normally present themselves in strongly Lewis-acidic solutions and in solid compounds, which are ionic in the sense that their structures contain large, weakly coordinating anions separated from the cluster cations at van der Waals or weakly bonding distances. The latter fact has given rise to the expression anti-coordination chemistry in connection with such cluster compounds. 

Table 3. Superacids which have been used in the synthesis of post-transition element clusters.

The determination of the ec of naked post-transition element clusters is generally very easy (as compared to the transition-metal case) because of the lack of occupied valence d orbitals, interfering ligands and interstitial atoms.The ec of... 

Table 4. Characterized, homoatomic post-transition element clusters with electron counts (ec) > 5n (excluding polychalcogenides).

Inter-cluster bonding between the post-transition element clusters is rather common. Both Hg4" and b chain fragments inter-connect, as already discussed in the Secs. 1.29.4.3 and 1.29.4.5, and the cationic cluster chemistry of tellurium has been shown to contain examples of similar, but more elaborate inter-cluster bond-ing [17.250] (Te8 )(WCl6 )2 the inter-cluster Te-Te distance is found to be short... 

The reaction chemistry of the naked post-transition element clusters is still a rather white spot on the map of cluster chemistry. To a large extent this is a consequence of experimental difficulties and the often extreme redox conditions. Thus, the reactions of anionic clusters are often trivial results of their strong reducing capac-ity[68] cationic counterparts are often exceedingly strong oxidizers. An... 

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