Back to the basics of coordination chemistry

If you already know about Sidgwick's EAN rule, scroll down to skip to the main problem.

The Sidgwick's rule of effective atomic number (EAN rule) states that in a number of metal complexes, the metal atoms tend to surround themselves with ligands in a way that their effective atomic number is numerically equal to the noble gas element found in the same period. Commonly most complexes are formed by the d-block elements, therefore the most frequently referred noble gases are Krypton(36), Xenon(54) and Radon(86).

The formula to compute the effective atomic number of the metal atom in a complex is given by:

$\begin{aligned} \text{Effective atomic number} &= \text{Atomic number of metal - Oxidation state} \\ &+ \text{Sum of number of electrons donated by ligands} \end{aligned}$

However, this rule was later ruled out when Crystal Field Theory was published years later which clearly stated the reasons for the stability of complexes.

---

The EAN rule is still, however, an interesting concept and is frequently a topic for problems in coordination chemistry.

Problem:

Assuming that EAN rule holds and the given metal (where metal atom belongs to the fifth period of the periodic table) complexes are stable, find the metal atoms in each complex and their oxidation states.

Let the atomic numbers of the metal atoms in each respective complexes $A,B,C$ and $D$ are $Z_1, Z_2, Z_3$ and $Z_4$ and their oxidation states are $O_1, O_2, O_3$ and $O_4$ respectively. Calculate $\displaystyle \sum_{i=1}^4 Z_i - \sum_{i=1}^4 O_i$ .

Details:

• The ligand $\text{PCy}_3$ is the tricyclohexylphosphine ligand.

• In figure C, the biphenyl group present in the figure connected by a bond joining metal atom to only one carbon atom of each benzene ring has only 2 participating electrons per bond .