# 15.2.1: Extensions of the Analogy

• Wikipedia
$$\newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$ $$\newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$$$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}[1]{\| #1 \|}$$ $$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}[1]{\| #1 \|}$$ $$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$$$\newcommand{\AA}{\unicode[.8,0]{x212B}}$$

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

This page titled 15.2.1: Extensions of the Analogy is shared under a CC BY-SA 4.0 license and was authored, remixed, and/or curated by Wikipedia via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.