The work which was started more than ten years ago was to discern the possibility of an order within known carbonyl cluster formulas. It was subsequently discovered that the carbonyl clusters strictly follow the series given by S = 4n + q, where n represents the number skeletal elements in the cluster and q is a numerical variable. With the knowledge of the series formula, it was possible to categorize a given cluster formula into a categorization formula K_ =Cy + Dz where y + z = n. The parameter Dz represented the clan of the series while the Cy represented the family of the clusters. Relatively recently with the help of skeletal numbers of elements represented by K, it was discovered that an intrinsic generating function given by R = n (K -1)+1 could generate all possible fragments and clusters from a precursor skeletal fragment of n skeletal elements. This great discovery of intrinsic generating functions R, generates all possible fragments and clusters including all known and unknown stable chemical clusters.