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Use of the Greek prefix η (eta) accompanied by a superscript number (e.g. η 4) describes the number of atoms in a ligand that are considered formally to be bonded to the metal atom. This is the hapticity of the ligand.
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For example, (η 3-Allyl)-(η 4-butadiene)-(η 5-cyclopentadienyl)-molybdenum(ii) (CSD refocde RATQUY), shown below.
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Cotton illustrates the notation using 16 examples. If you have full access to the Cambridge Structural Database (CSD) then, as an additional exercise, use ConQuest to find structure entries which match the 16 examples. Which of the 16 have CSD entries which exactly match the structures as depicted by Cotton? Which, if any have matching formulas, but are structurally different than depicted by Cotton? For those examples that lack exact formula matches, find the CSD entries which are most similar. In each case, give the name, according to Cotton's nomenclature, that correctly describes each molecule.
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