Unification and Expansion of Wade-Mingos Rules with Elementary Number Theory

2018

IJC

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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.

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

2018

IJC

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The Main Group Elements, Fragments, Compounds and Clusters Obey the 4n Rule and Form 4n Series: They are Close relatives to Transition Metal Counterparts via the 14n Linkage

2016

IJC

The paper presents numbers which were derived from 4n-based series in a matrix table. The numbers agree precisely with the total number of valence electrons surrounding the respective skeletal elements. The series approach focuses mainly on the number of skeletal elements and their respective number of valence electron content regardless of the origin of the electrons and the type of skeletal elements. For instance, any 6 skeletal elements of transition metal carbonyls surrounded by 86 valence electrons coded as (6,86), series S = 14n+2 normally adopt an octahedral geometry whereas (6,26) series S = 4n+2 for main group elements also tend to adopt an octahedral shape. The transition metal carbonyl cluster series were extensively covered in our previous articles. This paper demonstrates that the main group fragments, clusters and molecules which we normally explain by terms such as valency, valence electrons and octet rule also obey the 4n-based series. The fragments, molecules and clusters of the main group elements correspond well to those of respective transition metal clusters especially the carbonyls if the masking electrons are removed from them. Hence, the series approach is a qualitative method that acts as a unifier of some transition metal clusters with some main group elements clusters.

Carbonyl Chalcogenides Clusters Existing as Disguised Forms of Hydrocarbon Isomers

2016

IJC

The 4n Series Method has been utilized to categorize, analyze and predict structures for transition metal carbonyl, borane, hydrocarbon and Zintl ion clusters. The method is being extended to study carbonyl chalcogenide clusters. Adequate examples have been given to demonstrate the application of the 4n series method to categorize clusters and where possible predict their possible skeletal structures. In this paper, the method is being applied to the study of carbonyl chalcogenide cluster complexes. What has been found is the striking structural similarity of a wide range of carbonyl chalcogenide clusters to those of corresponding hydrocarbon clusters. It was observed that when a derived hydrocarbon from a cluster, F CH = C n H q , is such that nq, the "hydrocarbon character" becomes reduced and the typical cluster tendencies increase. When n = q, the situation becomes more or less a borderline case. When q=0, then F CH = C n . When the series becomes bi-capped or more, then the equivalent carbon cations are obtained.