GATE 2026 CY – Question 41

Inorganic Chemistry · Organometallics: 18-Electron rule; metal-alkyl, metal-carbonyl, metal-olefin and metal-carbene complexes and metallocenes. Fluxionality in organometallic complexes. Types of organometallic reactions. Homogeneous catalysis – Hydrogenation, hydroformylation, methanol to acetic acid process, olefin metathesis and Wacker oxidation. Heterogeneous catalysis – Fischer-Tropsch reaction, Ziegler-Natta polymerization. · 2 marks · Multiple choice

The correct electronic configuration of central metal ion in ferrocene with z-axis passing through the centre of two C5H5 − rings and the metal ion is

$d_{xy}^2=d_{x^2-y^2}^2<d_{z^2}^2<d_{xz}^0=d_{yz}^0$
$d_{xz}^2=d_{yz}^2<d_{z^2}^2<d_{x^2-y^2}^0=d_{xy}^0$
$d_{xy}^2=d_{xz}^2=d_{yz}^2<d_{x^2-y^2}^0=d_{z^2}^0$
$d_{xy}^2<d_{xz}^2=d_{yz}^2<d_{x^2-y^2}^0<d_{z^2}^0$

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Correct answer: (A) $d_{xy}^2=d_{x^2-y^2}^2<d_{z^2}^2<d_{xz}^0=d_{yz}^0$

Explanation

Ferrocene, $\text{Fe(C}_5\text{H}_5)_2$, contains Fe(II), which is $d^6$, in a sandwich with the $z$ axis through the two ring centres. The 18-electron count is $6+2\times6=18$.

The five $d$ orbitals group by symmetry ($D_{5d}/D_{5h}$):
- $a_{1g}$ ($d_{z^2}$) and $e_{2g}$ ($d_{xy},d_{x^2-y^2}$): essentially non-bonding or only weakly interacting with the rings. These are the lowest of the $d$-based orbitals and take the six $d$ electrons.
- $e_{1g}$ ($d_{xz},d_{yz}$): interact strongly with the $\pi$ orbitals of the rings and are pushed up (antibonding), so they remain **empty**.

**Configuration:** $d_{xy}^2=d_{x^2-y^2}^2<d_{z^2}^2<d_{xz}^0=d_{yz}^0$ (option A).