draw a molecular orbital diagram for Cr(CO)6

draw a molecular orbital diagram for Cr(CO)6

The correct answer and explanation is :

Molecular Orbital Diagram for Cr(CO)₆

To construct the molecular orbital (MO) diagram for chromium hexacarbonyl, Cr(CO)₆, we must consider the interaction between the metal d-orbitals and the ligand group orbitals derived from the six CO ligands. Cr(CO)₆ is an octahedral complex, and the bonding is best understood using molecular orbital theory based on symmetry-adapted linear combinations (SALCs) of ligand orbitals.

1. Electron Configuration:

• Chromium in Cr(CO)₆ is in the 0 oxidation state.
• Atomic number of Cr = 24 → [Ar] 3d⁵ 4s¹ → in complex, 3d⁶ (after accepting 6 electrons from CO ligands).

2. Ligand Orbitals (CO):

Each CO ligand donates:

• One σ-donor orbital from the lone pair on carbon.
• One π-acceptor orbital via the empty π* orbitals.

For 6 ligands:

• 6 σ-donor orbitals form SALCs of a₁g, t₁u, eg symmetry.
• 6 π-acceptor orbitals form SALCs of t₂g, etc.

3. Metal Orbitals (Cr):

• 3d (t₂g + eg), 4s (a₁g), and 4p (t₁u) orbitals.

4. MO Interactions:

• σ-donation from CO fills lower-energy bonding orbitals.
• π-backbonding: metal t₂g electrons are donated into CO’s π* orbitals, stabilizing the complex and weakening the C≡O bond.

5. Electron Counting:

• Cr⁰ contributes 6 valence electrons.
• Each CO contributes 2 electrons × 6 = 12 electrons.
• Total = 18 electrons → follows the 18-electron rule.

Molecular Orbital Diagram:

        σ* eg
        σ* t1u
        π* (from CO) ← π-backbonding ← t2g (Cr 3d)
        Nonbonding t2g (partially filled)
        σ eg (bonding)
        σ t1u (bonding)
        σ a1g (bonding)

• Bonding MOs: a₁g, t₁u, eg
• Non-bonding/weakly bonding: t₂g (π-backbonding region)
• Antibonding: t₁u*, eg*