The coordination geometry around the manganese in decacarbonyldimanganese(0) is:

🧠 Decacarbonyldimanganese = $\mathrm{Mn_2(CO)_{10}}$

Each Mn in $\mathrm{Mn_2(CO)_{10}}$ is bonded to:

• 5 terminal CO ligands.
• 1 Mn–Mn metal–metal bond.

Total: 6 connections around each Mn → octahedral geometry.

🗺️ 18-Electron Count

Mn is +0 here (CO is neutral; complex is neutral). Mn(0) is d⁷.

Per Mn: $7 + 5(2)_{\mathrm{CO}} + 1_{\mathrm{Mn–Mn}} = 18$ ✓.

Both Mn atoms achieve the 18-electron noble-gas configuration via the metal–metal bond + 5 terminal carbonyls.

⚡ The Common Carbonyl Geometries

| Carbonyl | Geometry around metal | Coordination # | |---|---|---| | $\mathrm{Ni(CO)_4}$ | Tetrahedral | 4 | | $\mathrm{Fe(CO)_5}$ | Trigonal bipyramidal | 5 | | $\mathrm{Cr(CO)_6}$, $\mathrm{Mo(CO)_6}$, $\mathrm{W(CO)_6}$ | Octahedral | 6 | | $\mathrm{Mn_2(CO)_{10}}$ | Octahedral (5 CO + Mn–Mn) | 6 | | $\mathrm{Co_2(CO)_8}$ | Distorted octahedral (3 t-CO + 2 b-CO + Co–Co) | 6 |

⚠️ Count the M–M Bond as a Coordination

When determining geometry around a metal in a polynuclear carbonyl, always include the M–M bond as one of the coordinations. In Mn₂(CO)₁₀: 5 CO + 1 Mn–Mn = 6 = octahedral.

$\boxed{\text{Answer: (1) Octahedral}}$