Graph Theory of Capping Golden Clusters

2018

IJC

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Matryoshka clusters have been analyzed and categorized using skeletal numbers for the first time. They have been found to portray a unique way of capping by having the nuclear elements occupying the outer layer and what were supposed to be the capping elements on the outside taking the place of the nucleus. Hence they belong to a new type of cluster series. The different types of capping clusters have been identified. Isomeric graphical structures of the clusters can be constructed in accordance with the connectivity rule of the series. It appears that the elements with large skeletal numbers have a tendency of going inside and forming an icosahedral shape. The 4N series method is a useful hypothetical model for analyzing and categorizing clusters of the main group and transition metals.

Section: The Nucleus Inside the Capping Elementsmentioning

confidence: 99%

Inside out Capping Clusters: Matryoshka Series

2018

IJC

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“…Since clusters of the main group and transition metals are interrelated, it was proposed that they be categorized into cluster groups (Kiremire, 2018b). Furthermore, the closo baseline(S = 4n+2) was selected to be used as a reference point.…”

Section: S = 4n+qmentioning

confidence: 99%

“…More information on categorization of clusters including the golden ones can be found in the recently published work (Kiremire, 2018a(Kiremire, , 2018b…”

Section: F-16mentioning

confidence: 99%

Generating Cluster Formulas Using The Primary Clusters And The K(n) Parameters

2018

IJC

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The formulas of transition metal clusters can be regarded as multiples of their respective PRIMARY CLUSTERS and K(n) parameters. A primary cluster of a transition metal skeletal element can be defined as that cluster of a mono-skeletal element which obeys the 18 electron rule. Such clusters, among others include, Cr(CO)6, Fe(CO)5, Ni(CO)4, and Zn(CO)3 and the respective K values of the skeletal elements are 6, 5, 4 and 3. The selected K(n) series are given and the derived hypothetical golden clusters are given as examples for illustrations. Selected known golden clusters are also found to be multiples of K(n) parameters and the 18 valence fragment cluster, AuL3.5. The graphical representations of a few selected examples of golden clusters are given.

“…Some of the vital information the K(n) parameter contains was extensively covered in earlier work (Kiremire,2018a(Kiremire, ,2018b. Among others, it includes organizing CLUSTERS into CLANS as illustrated in Figure 1, and FAMILIES of clusters as indicated in Figures 2-6 and predicting the shapes of clusters.…”

Section: Information Derived From the K(n) Parametermentioning

confidence: 99%

The Cluster Valence Electrons (VE) Are Natural Numbers of Clusters Generated by K(N) Parameters: VE and K(N) Are Intertwined

2018

IJC

The paper presents a highly refined work on broad categorization of clusters using the series method with emphasis on cluster valence content. In this regard, the K(n) parameter plays a crucial role. The K(n) parameters are interrelated and have been utilized to generate a cluster map of clusters. The cluster map of skeletal elements and their clusters can be extended indefinitely. The elements refer to main group and transition metal elements. The inter-conversion of K(n) parameter map into a selected portion of cluster valence electron content map was done indicating the origin of the cluster valence electron numbers which are sometimes associated with certain characteristic geometries. The map indicates that the main group and transition metal elements and their clusters are all interlinked via either the K(n) map or the cluster valence electron content map.