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What is the key thing to look at when determining if a molecule is monodentate, bidentate, etc.?
The surest way to determine this is to look at the lewis structure. The atoms with lone pairs on them and still able to bond (ie, they can turn the lone pairs into a covalent bond to fulfill their octect or, expand the octet in the case of d-orbital containing elements) are the elements most likely to bond. For example, a Nitrogen with three covalent bonds and a lone pair is likely to be a site of bonding. Also, an Oxygen with that has a single bond is likely to turn two of the remaining six lone pair electrons into a covalent bond with a transition metal. Also, the shape of the molecule, which determines how close such elements are to one another, will determine if the ligand can bond in multiple places to the same transition metal. The closer they are to one another, the more likely the bonding sites are to attach to the same transition metal. Also beware of the ability of ligands to rotate about their sigma bonds, which alters the shape, thus changing how close the binding sites are to one another. A great example of this is edta, with six binging sites. Drawn out in the lewis stucture, the binding sites are far from one another. But in the actual 3d shape, the six binding sites attached to the same transition metal produces an octahedral geometry at the center of edta.
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