A Hypothetical Model for the Formation of Transition Metal Carbonyl Clusters Based upon 4n Series Skeletal Numbers

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 and charges onto the skeletal atoms. A naked skeletal cluster may be viewed as a reservoir for skeletal linkages which get utilized when ligands or electrons get bound to it. The sum of linkages used up by the ligands bound to a skeletal fragment and the remaining cluster skeletal numbers is equal to the number of the skeletal linkages present in the original "naked parent" skeletal cluster. The skeletal numbers can be used as a quick way of testing whether or not a skeletal atom obeys the 8-or 18-electron rules.

Graph Theory of Chemical Series and Broad Categorization of Clusters

“…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).…”

“…This concept has been applied in many examples in this paper. Other examples can be found in literature (Kiremire, 2016b(Kiremire, , 2017.…”

“…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 Golden Series and Clusters of Gold-unique Shapes and Bonding

“…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).…”

“…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).…”