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Q5.15(i):
Discuss the nature of bonding in the following coordination entities on the basis of valence bond theory: \([Fe(CN)_{6}]^{4-}\)

Solution :

Step 1: Determining the Oxidation State of the Central Metal Ion

To analyze the bonding, we first identify the oxidation state of the iron ($Fe$) atom in the coordination entity $[Fe(CN)_{6}]^{4-}$.

Let the oxidation state of $Fe$ be $x$. The cyanide ion ($CN^-$) carries a charge of $-1$.

$x + 6(-1) = -4$

$x - 6 = -4 \implies x = +2$

[Per the rules of oxidation state determination in complex ions]. The iron exists as $Fe^{2+}$ ion.

Step 2: Electronic Configuration of Iron

  • Atomic number of $Fe (Z) = 26$.
  • Ground state configuration: $[Ar] 3d^6 4s^2$.
  • Electronic configuration of $Fe^{2+}$: $[Ar] 3d^6 4s^0$.

The $3d$ orbitals contain 6 electrons. According to Hund's Rule and the Pauli Exclusion Principle, the electrons are distributed as: $d_{xy}^2, d_{yz}^1, d_{zx}^1, d_{x^2-y^2}^1, d_{z^2}^1$.

Step 3: Effect of the Ligand Field

The ligand $CN^-$ is a strong field ligand [Per the Spectrochemical Series]. Consequently, it forces the electrons in the $3d$ orbitals to pair up to facilitate hybridization.

Before pairing: $3d$ (6 electrons distributed in 5 orbitals with 4 unpaired electrons).

After pairing (due to $CN^-$): The 6 electrons occupy the three lower $t_{2g}$ orbitals (in octahedral terminology), leaving the two $e_g$ orbitals vacant.

Step 4: Hybridization and Geometry

To accommodate the 6 pairs of electrons donated by the 6 $CN^-$ ligands, the metal ion utilizes two $3d$, one $4s$, and three $4p$ vacant orbitals. This results in $d^2sp^3$ hybridization.

3d Orbitals (Fe²⁺ paired) 4s 4p Hybridized Orbitals: (d²sp³)

Step 5: Magnetic and Electronic Properties

Property Result
Magnetic Nature Diamagnetic (all electrons are paired)
Magnetic Moment ($\mu$) $\sqrt{n(n+2)} = \sqrt{0(0+2)} = 0 \text{ B.M.}$
Complex Type Inner-orbital complex (or low-spin complex)
Geometry Octahedral

Final Solution: The complex $[Fe(CN)_{6}]^{4-}$ undergoes $d^2sp^3$ hybridization, resulting in an inner-orbital octahedral geometry that is diamagnetic due to the pairing effect of the strong-field cyanide ligands.


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