Wade-Mingos’ rule

Wade also extended the application of his rules to transition metal clusters the further extension by D. M. P. Mingos mainly concerns the bonding in metal carbonyl and metal phosphane clusters, i.e. organometallic compounds (Wade-Mingos rules) these are beyond the scope of this book. 

The dianionic Ga8 cluster [Ga8(flu)8]2 453 (flu = fluorenyl) has been synthesized by salt metathesis reaction between a metastable Ga Br solution and fluorenyllithium.344 The eight Ga atoms form a square antiprismatic core. This is rather unexpected because 453, which is a z/oro-cluster according to the Wade-Mingos rules, was expected to adopt the dodecahedral structure as was observed for the corresponding boron clusters. However, computational calculations demonstrated that in the case of eight Ga atoms, the formation of a square antiprismatic structure is energetically favored (Figure 33). 

Polyhedral Skeletal Electron Pair Theory The Wade-Mingos Rules... 

Balakrishnarajan and Jemmis [32, 33] have very recently extended the Wade-Mingos rules from isolated borane deltahedra to fused borane ("conjuncto ) delta -hedra. They arrive at the requirement of n I m skeletal electron pairs corresponding to 2n + 2m skeletal electrons for such fused deltahedra having n total vertices and m individual deltahedra. Note that for a single deltahedron (i.e., m = 1) the Jemmis 2n + 2m rule reduces to the Wade-Mingos 2n I 2 rule. 

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. 

Keywords Jellium model Metal clusters Wade-Mingos rules Zintl ions Contents... 

Application of the Wade-Mingos Rules to Polyhedral Boranes ... 

Beyond the Wade-Mingos Rules The Jellium Model. 12... 

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 Relationship of Zintl Ions to Polyhedral Boranes The Wade-Mingos Rules and the Aromaticity of Clusters... 

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. 

Removal of two vertices from a deltahedron leads to arachno polyhedra having 2n + 6 skeletal electrons according to the Wade-Mingos rules [13-16]. Among the many theoretical possibilities for arachno polyhedra, the pentagonal antiprism, generated by removal of a pair of antipodal vertices from an icosahedron, is the most significant in bare post-transition metal cluster chemistry. 

Information on the numbers of skeletal electrons contributed by each cluster vertex is necessary to apply the Wade-Mingos rules [13-16] to bare clusters of the posttransition elements. The mles discussed above for polyhedral boranes can be adapted to bare post-transition metal vertices as follows ... 

The Wade-Mingos rules appear to be applicable to the above clusters when they are polyhedra in which each vertex has degree of at least 4 (e.g., the 9-vertex... 

The third DFT study [96] was motivated by the existence of the stable pentagonal antiprismatic cluster [93] Pd Biio" found in Bii4PdBri6. This cluster is an example of a cluster with an interstitial atom that obeys the Wade-Mingos rules [13-16]. Thus, the pentagonal antiprism is derived from an icosahedron by removal... 

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