Bøger af Enos Kiremire

The book presents two interrelated ways of categorizing chemical structures: the 4N and skeletal numbers methods, and their linkage to geometrical structures of clusters (symmetry). The skeletal numbers are derived from the 4N series. The application of the 4N method of categorization of clusters is demonstrated using palladium carbonyl clusters. The use of skeletal numbers to categorize clusters is illustrated using boranes, carboranes, metalloboranes and isolobal fragments. The K(n) cluster map is presented. The beauty and simplicity of skeletal numbers in predicting cluster symmetries is that a simple molecule or a giant cluster can be represented by a single whole number as in the case of C2H2(K=3) and Pd165L90(K =570). Such numbers form the basis of constructing their isomeric graphical shapes.

The book introduces the analysis and categorization of golden clusters using the 14N/4N method and its skeletal numbers for the first time. The application of skeletal numbers is quite easy, fast and precise. Initially the method which has been found to be very successful in categorizing clusters of other skeletal elements is well demonstrated using the osmium fragments and clusters. It is then applied to clusters of gold with some elements from the p-block elements. The analysis of the golden clusters with the series method reveals that the clusters obey the 4N series principle and are highly capped with nuclei comprising mainly of one or two elements in the nuclei. A small number of clusters indicate the absence of skeletal elements in the nucleus. A cluster with such a nucleus has been referred to as having a black-hole. With more understanding of the 4N series method a simple graph theory concept has been introduced to sketch isomeric graphical structures of the clusters as well as being utilized to hypothetically distribute the ligands around the skeletal elements.

The book introduces the concept of application of skeletal numbers to categorize skeletal elements, fragments, molecules and clusters into cluster series. It explains their origin from the series formulas S =4n+q and S=14n+q or the cluster valence electron equation Ve=8n-2K and 18n-2K. The capping concept and the K(n) parameter based on series are introduced and explained. The classification of clusters into [Mx] clans and S=4n+q families are introduced. The three major cluster series are identified. The ideal distribution of ligands and charges onto skeletal elements is explained. Categorization of Matryoshka clusters using the 4N series for the first time is also covered. A new formula for calculating cluster valence electrons Ve=4+2x+2(n-1) for main group elements and Ve=14+2x+12(n-1) for transition metal elements is introduced for the first time.

The analysis of transition metal and main group element clusters revealed that they strictly obey the series S=14n +q and 4n+q respectively where q is a numerical variable and n is the number of skeletal elements in a cluster. When q¿0, then the cluster is as a capped one. Due to the isolobal relationship between 14n+q and 4n +q series, it was decided that the 4n+q series be adopted for the categorization of all clusters from the main group and transition metal elements except when the calculation of cluster valence electrons is conducted. The evolution of the capping theory goes through the stage of using the discovered skeletal numbers and the genesis principle of clusters up to the finest level of calculating cluster valence electrons and the process of generating cluster formulas using the 12N capping theory. The capping theory is so precise in determining cluster valence electrons (CVE) and may be regarded as a natural law of chemical clusters.

The book uses a new approach to cluster theory by applying skeletal numbers rather than polyhedral skeletal electron pair theory (PSEPT) or cluster valence electron (CVE) counting approach. Zintl ions and matryoshka clusters may be regarded as being inter-related. The skeletal numbers are easy to use and therefore the categorization of any cluster is rapid. A cluster formula regardless of how complex and formidable it may look like is readily decomposed by skeletal numbers into a single whole number digit and by knowing the number of skeletal elements involved, the cluster is categorized. The categorization is expressed by a simple formula K=CyC[Mx], where y+x=n, the number of skeletal elements in the cluster, y represents the capping or de-capping skeletal elements of the outer shell of the cluster, and x represents the nucleus, the inner shell of the skeletal elements. With this information as a guide, a tentative cluster shape may be predicted. Furthermore, if needed, the cluster valence electrons can easily be calculated and compared with the numerical number of cluster valence electrons calculated using the conventional method.

The introductory section of the book provides examples of a selected method of how the skeletal numbers can be applied to analyze and categorize transition metal carbonyl clusters. It also puts a distinction between the skeletal number (K) of an element and the skeletal linkages (K) of two or more skeletal elements bound together in a cluster. The relationship between the empirical formula, K= ¿ [E-V] and V=18n-2K for transition metal clusters or V= 8n-2K for main group elements is illustrated. The six fundamental equations for calculating cluster valence electrons (CVE) are provided. There are four articles which analyze and categorize clusters using mainly skeletal numbers approach and three others which categorize clusters applying the 4N series approach when the skeletal numbers had not yet been discovered. All in all, the book equips the reader with powerful methods of analyzing and categorizing any cluster from the main group or transition metal elements.