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15.2.1: Extensions of the Analogy

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    The isolobal analogy has applications beyond simple octahedral complexes. It can be used with a variety of ligands, charged species and non-octahedral complexes.

    The isolobal analogy can also be used with isoelectronic fragments having the same coordination number, which allows charged species to be considered. For example, \(\ce{Re(CO)5}\) is isolobal with \(\ce{CH3}\) and therefore, \(\ce{[Ru(CO)5]^+}\) and \(\ce{[Mo(CO)5]^−}\)are also isolobal with \(\ce{CH3}\). Any 17-electron metal complex would be isolobal in this example.

    In a similar sense, the addition or removal of electrons from two isolobal fragments results in two new isolobal fragments. Since \(\ce{Re(CO)5}\) is isolobal with \(\ce{CH3}\), \(\ce{[Re(CO)5]^+}\) is isolobal with \(\ce{CH3^+}\).

    The analogy applies to other shapes besides tetrahedral and octahedral geometries. The derivations used in octahedral geometry are valid for most other geometries. The exception is square-planar because square-planar complexes typically abide by the 16-electron rule. Assuming ligands act as two-electron donors the metal center in square-planar molecules is \(d^8\). To relate an octahedral fragment, MLn, where M has a dx electron configuration to a square planar analogous fragment, the formula MLn−2 where M has a dx+2 electron configuration should be followed.

    Octahedral MLn Square Planar MLn
    \(d^6: \quad \ce{Mo(CO)5}\) \(d^8: \quad \ce{[PdCl3]^-}\)
    \(d^8: \quad \ce{Os(CO)4}\) \(d^10: \quad \ce{Ni(PR3)2}\)

    Further examples of the isolobal analogy in various shapes and forms are shown

    Figure \(\PageIndex{1}\): Examples of extensions of the isolobal analogy. (Public Domain; Chem507f10grp5via Wikipedia)


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