Generating Functions of Cluster Formulas

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The book explores the mathematical rules governing chemical clusters through the 4N series method, enabling the design of cluster formulas for both known and unknown elements. It highlights the use of generating functions, such as F=14n+0 for osmium, rhodium, rhenium, and palladium, and K(N) for gold. The decomposition of cluster formulas into fragments and series is discussed, allowing predictions of geometrical shapes. Additionally, it examines the unique properties of golden clusters and introduces skeletal numbers for determining ligand distribution in cluster structures.