Abstract:Skeletal numbers of elements have been introduced as derivatives of the 4n series method. They are based on the number of valence electrons present in the skeletal element. They are extremely useful in deducing possible shapes of skeletal elements in molecules or clusters especially the small to medium ones. For large skeletal clusters, the skeletal numbers may simply be regarded as identity numbers. In carbonyl clusters, they can be used as a guide to facilitate the distribution of the ligands such as CO, H a… Show more
“…The existence of cluster series was also detected and implied through the work of Wade (Wade, 1976), Mingos (Mingos, 1987) and the correlation of cluster symmetries by Rudolph (Rudolph, 1976). This is confirmed by the current work of applying skeletal numbers derived from the 4n series method (Kiremire, 2015b) which clearly indicate the existence of a whole vast universe of clusters linking up naked metallic elements to metal carbonyls (Kiremire, 2016b), metalloboranes (Kiremire, 2016c), Zintyl ions (Kiremire, 2016d), carboranes and other heteroboranes, boranes, and main group element clusters (Kiremire, 2017c). Using the skeletal numbers, a cluster comprising of a mono-skeletal element to a giant one of several hundred skeletal elements can readily be decomposed and represented by a single number now referred to as a cluster number Kor [K(n)parameter] (Kiremire, 2017b).…”
Section: Brief Backgroundsupporting
confidence: 64%
“…This concept has been applied in many examples in this paper. Other examples can be found in literature (Kiremire, 2016b(Kiremire, , 2017.…”
Section: Ligand Distributionsmentioning
confidence: 99%
“…The method regards all clusters comprising of skeletal elements from the main group and transition metals as interrelated and can be categorized by the 4n series method. The method uses skeletal numbers to analyze and categorize clusters (Kiremire, 2016a(Kiremire, , 2016b(Kiremire, , 2017a(Kiremire, , 2017b(Kiremire, , 2017c). …”
The recent introduction of skeletal numbers has made it much easier to analyze and categorize a wide range of many chemical clusters. In the process, it has been found that a large number of transition metal clusters with and without ligands are capped and do possess closo nuclear clusters. On the basis of the nuclear index, the clusters have been categorized into groups. The categorization of the clusters will greatly assist in promoting deeper understanding and the synthesis of novel clusters and their applications. A simple concept of graph theory of capping clusters has been introduced.
“…The existence of cluster series was also detected and implied through the work of Wade (Wade, 1976), Mingos (Mingos, 1987) and the correlation of cluster symmetries by Rudolph (Rudolph, 1976). This is confirmed by the current work of applying skeletal numbers derived from the 4n series method (Kiremire, 2015b) which clearly indicate the existence of a whole vast universe of clusters linking up naked metallic elements to metal carbonyls (Kiremire, 2016b), metalloboranes (Kiremire, 2016c), Zintyl ions (Kiremire, 2016d), carboranes and other heteroboranes, boranes, and main group element clusters (Kiremire, 2017c). Using the skeletal numbers, a cluster comprising of a mono-skeletal element to a giant one of several hundred skeletal elements can readily be decomposed and represented by a single number now referred to as a cluster number Kor [K(n)parameter] (Kiremire, 2017b).…”
Section: Brief Backgroundsupporting
confidence: 64%
“…This concept has been applied in many examples in this paper. Other examples can be found in literature (Kiremire, 2016b(Kiremire, , 2017.…”
Section: Ligand Distributionsmentioning
confidence: 99%
“…The method regards all clusters comprising of skeletal elements from the main group and transition metals as interrelated and can be categorized by the 4n series method. The method uses skeletal numbers to analyze and categorize clusters (Kiremire, 2016a(Kiremire, , 2016b(Kiremire, , 2017a(Kiremire, , 2017b(Kiremire, , 2017c). …”
The recent introduction of skeletal numbers has made it much easier to analyze and categorize a wide range of many chemical clusters. In the process, it has been found that a large number of transition metal clusters with and without ligands are capped and do possess closo nuclear clusters. On the basis of the nuclear index, the clusters have been categorized into groups. The categorization of the clusters will greatly assist in promoting deeper understanding and the synthesis of novel clusters and their applications. A simple concept of graph theory of capping clusters has been introduced.
“…Relatively recently, the 4n series method was developed and has further been refined for rapid application to analyze and characterize clusters with great success (Kiremire, 2016a(Kiremire, , 2016b. Golden clusters portray a wide range of fascinating shapes and have attracted increased intensity in research (Cotton and Wilkinson, 1980;Mingos, 1984Mingos, , 1987Greenwood and Earnshaw, 1998;Pauling, 1977;Pivoriũnas, 2005;Gimeno, 2008;Konishi, 2014).…”
Section: Introductionmentioning
confidence: 99%
“…It became tempting to try and analyze the golden clusters using the skeletal numbers derived from 4n series method. This paper presents an analysis and categorization of selected number of golden clusters using the newly introduced skeletal numbers and the conservation of cluster skeletal linkages principle (Kiremire, 2016b).…”
Golden clusters have been analyzed and categorized using the series method. They have been found to be intensely capped. The complexity of capping is likely responsible for the unique shapes of clusters. The predicted structures of the golden clusters with one or two nuclear indices have been found to be in agreement with the observations from structural determinations. According to the series, the golden clusters have tendency of occurring in an overlapping area which is normally dominated by naked metal clusters. The series approach method is easy and very reliable in analyzing and characterizing clusters. A brief background to the series method was included to ease readability of the paper.
More than forty transition metal carbonyls mainly bimetallic ones have been categorized using skeletal numbers. Their cluster valence electrons (CVE) were calculated using six different equations which had been discovered and consolidated during the course of the studies on chemical clusters over a period of time. These equations were easy to formulate after the discovery that chemical clusters form natural series which follow arithmetic progressions. With more scrutiny, it will be possible to find other equations which would help in calculating CVE. The categorization parameter, K*=C y +D z is a useful concept in analyzing clusters. Regardless of how it was arrived at for transition metals or main group elements, it conveys vital information. From, you can know how many skeletal elements are in a cluster, the cluster valence electrons can be calculated, the type of series and clan of the cluster can be determined and the possible geometrical skeletal structure of the cluster can be predicted, among others. The isomeric and graphical skeletal structures of some of the clusters were constructed.
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