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Lesson 11 · 35 min

Metal carbonyls and the 18-electron rule

Why does a neutral nickel atom hold exactly four neutral CO molecules? Count valence electrons, see how σ donation and π back-donation leave a fingerprint in the infrared, and tell isomers apart by counting bands.

In this lesson

  • Count the valence electrons of an organometallic compound by the neutral-ligand method and judge from the 18-electron rule whether it is saturated
  • Explain the metal–carbonyl bond by σ donation and π back-donation, and use ν(CO) to compare how electron-rich metals are
  • Predict the number of infrared ν(CO) bands of a carbonyl complex from its symmetry, and use it to tell isomers apart

In 1890 Ludwig Mond and his co-workers found that carbon monoxide flowing over finely divided nickel carried the metal away: nickel and carbon monoxide combine into a volatile liquid, Ni(CO)X4\ce{Ni(CO)4}, boiling at only 43 °C. Mond saw the use at once: crude nickel reacts with CO at 50–60 °C and leaves as a gas, impurities stay behind, and heating the Ni(CO)X4\ce{Ni(CO)4} to 220–250 °C returns pure nickel. The Mond process still refines nickel today. But nickel is a neutral atom and CO a neutral molecule — what holds them together, and why exactly four?

Predict first

Iron (group 8) also forms a stable binary carbonyl, Fe(CO)x\mathrm{Fe(CO)}_{x}. If the metal’s valence electrons plus 2 from each CO make exactly 18, what is x?

Pick an answer and lock it in before you look. A wrong guess teaches more than no guess.

The 18-electron rule

The valence shell of a main-group element is one s and three p orbitals, at most 8 electrons — the octet rule. A transition metal adds five d orbitals: nine valence orbitals, at most 18 electrons. Most stable organometallic compounds fill exactly these 18: the 18-electron rule.

The easiest way to count is the neutral-ligand method: take the metal as a neutral atom giving its group number of valence electrons; give each ligand the electrons it offers as a neutral fragment (2 each for CO and phosphines; 1 each for H, Cl and CH₃; 5 for η⁵-cyclopentadienyl; 6 for η⁶-benzene); add 1 for every metal–metal bond; and subtract the overall charge of the complex.

NVE=G+∑LnL+nM–M−qN_\text{VE} = G + \sum_L n_L + n_{\text{M–M}} - q
N_VE = 18 means a full valence shell. Ionic counting (ligands as charged ions, the metal in its oxidation state) gives the same total.
NVEN_\text{VE}
valence electrons around the metal
GG
group number of the metal
nLn_L
electrons from each ligand as a neutral fragment
nM–Mn_{\text{M–M}}
number of metal–metal bonds
qq
charge on the complex

Worked example

Ferrocene and dimanganese decacarbonyl

Count the valence electrons around each metal in ferrocene, Fe(CX5HX5)X2\ce{Fe(C5H5)2}, and in MnX2(CO)X10\ce{Mn2(CO)10}.

Neutral-ligand counting

The 18-electron counter

Build your own
CO\ce{CO} × 6
PRX3\ce{PR3} × 0
H\ce{H} × 0
Cl\ce{Cl} × 0
CHX3\ce{CH3} × 0
η2-CX2HX4\eta^2\text{-}\ce{C2H4} × 0
η5-CX5HX5\eta^5\text{-}\ce{C5H5} × 0
η6-CX6HX6\eta^6\text{-}\ce{C6H6} × 0
Charge 0

V(CO)X6\ce{V(CO)6} Hexacarbonylvanadium

spppddddd
Nine valence orbitals (one s, three p, five d) hold at most 18 electrons; the colours show where each electron comes from.
  • metal (group 5) 5
  • 6 × CO 12

17 valence electrons in all = 5 + 12

Fewer than 18: the shell is not full, and such species tend to gain electrons — by reduction, a metal–metal bond or another ligand.

Paramagnetic with one unpaired electron, and easily reduced to [V(CO)₆]⁻.

Neutral-ligand (covalent) counting: the metal gives its group number of valence electrons as a neutral atom; CO, PR₃ and η²-ethene give 2 each, H, Cl and CH₃ 1 each, η⁵-C₅H₅ 5 and η⁶-C₆H₆ 6; each M–M bond adds 1, and the overall charge is subtracted. Ionic counting, which treats ligands as charged ions, gives the same totals. The 18-electron rule is empirical: it works best for organometallics with strong-field, π-accepting ligands such as CO, phosphines and cyclopentadienyl, and does not apply to Werner-type complexes such as aqua ions.
V(CO)X6\ce{V(CO)6} has only 17 electrons: try giving it a negative charge. Then pick a metal and build your own 18-electron compound — for manganese, HMn(CO)X5\ce{HMn(CO)5} and [Mn(CO)X6]X+\ce{[Mn(CO)6]+} both exist. Cobaltocene has 19 electrons, which is why it is a strong reducing agent.

σ donation and π back-donation

CO donates the lone pair on its carbon into an empty metal orbital (σ donation); at the same time the metal pushes electrons from its filled d orbitals back into the empty π* orbitals of CO (π back-donation). The two flows reinforce each other and make the metal–carbon bond strong — back-bonding. The price is a weaker C–O bond: π* is antibonding, and the more electrons it receives, the lower the C–O stretching frequency ν(CO).

So ν(CO) is a fingerprint of how electron-rich the metal is. Free CO absorbs at 2143 cm⁻¹ (the band origin of the rotation–vibration band in the spectroscopy unit); across the isoelectronic hexacarbonyls, the more negative the complex, the stronger the back-donation and the lower ν(CO).

Measured infrared data

The fingerprint of back-bonding: ν(CO)

Free CO (gas) 2143 [Ti(CO)₆]²⁻[V(CO)₆]⁻Cr(CO)₆[Mn(CO)₆]⁺[Fe(CO)₆]²⁺−2−1012Charge on the complex170018001900200021002200ν(CO) / cm⁻¹

Cr(CO)₆: ν(CO) = 2000 cm⁻¹, 143 cm⁻¹ below free CO; the C–O force constant is about 0.87 of free CO’s (k ∝ ν̃²).

Free CO: 2143 cm⁻¹ — the C–O bond on its own, with no metal involved.

The hexacarbonyl ν(CO) values are the IR-active T₁u bands, as compiled in the Wikipedia article “Metal carbonyl” (sources include Ellis and Chi 1990 and Finze et al. 2005); they vary by a few cm⁻¹ between media. Tolman parameters are from C. A. Tolman, Chem. Rev. 77, 313 (1977): the A₁ band of [Ni(CO)₃L] in CH₂Cl₂. Force-constant ratios assume one C–O oscillator with k ∝ ν̃², ignoring coupling to other vibrations.
From [Ti(CO)X6]X2−\ce{[Ti(CO)6]^2-} to [Fe(CO)X6]X2+\ce{[Fe(CO)6]^2+}, each extra positive charge raises ν(CO) by 100–140 cm⁻¹. Even the cation [Mn(CO)X6]X+\ce{[Mn(CO)6]+} stays below free CO; only the dication [Fe(CO)X6]X2+\ce{[Fe(CO)6]^2+} rises above it — there is almost no back-donation left, and σ donation slightly strengthens the C–O bond. Switch to the phosphines to see how ligands tune the metal.

Try the calculation

Cr(CO)X6\ce{Cr(CO)6} absorbs at ν(CO) = 2000 cm⁻¹ and free CO at 2143 cm⁻¹. Treating C–O as the same oscillator (k ∝ ν̃²), what fraction of free CO’s force constant does the C–O bond keep in the complex?

Ligands change the metal’s electron density as well. Tolman put a range of phosphines L into [Ni(CO)X3L]\ce{[Ni(CO)3L]} and measured ν(CO): the strongly donating P(tBu)X3\ce{P(\mathit{t}Bu)3} makes the metal electron-rich and ν(CO) falls to 2056.1 cm⁻¹, while PFX3\ce{PF3}, itself a π acceptor, competes with CO for the metal’s electrons and ν(CO) rises to 2110.8 cm⁻¹. This “Tolman electronic parameter” is still a yardstick for choosing ligands in catalysis.

Counting bands to find a structure

Each C≡O stretch can be treated as one oscillator. Just as for molecular vibrations, the character of an operation is the number of C≡O groups it leaves in place, and reducing it tells how many infrared ν(CO) bands to expect. Cr(CO)X6\ce{Cr(CO)6} has six carbonyls yet a single infrared ν(CO) band; Fe(CO)X5\ce{Fe(CO)5} has two (2022 and 2000 cm⁻¹). Substitution lowers the symmetry and adds bands, and cis and trans, fac and mer isomers give different counts — which is how chemists often tell which isomer they have just made.

C≡O stretches · reduction of characters

Counting carbonyl stretching bands

Loading 3D view…

Drag to rotate · scroll or pinch to zoom · arrow keys rotate too

Example: fac-Mo(CO)X3(PMeX3)X3\textit{fac}\text{-}\ce{Mo(CO)3(PMe3)3}

Point group C3vC_{3v}

Characters of the C≡O stretches in C3v
OperationEE2C32C_{3}3σv3\sigma_{v}
C≡O left in place301

Γ(CO)=A1+E\Gamma(\mathrm{CO}) = A_{1} + E

2IR bands
2Raman bands

fac-M(CO)₃L₃: 3 C≡O groups, 2 infrared ν(CO) band(s) and 2 Raman band(s).

Each C≡O stretch is treated as one oscillator: the character under an operation R is the number of C≡O groups R leaves in place. The point group is computed from the atomic coordinates (phosphines drawn as their P atom) and the representation reduced; species transforming like x, y or z are infrared active, those like quadratic functions Raman active. Only the number of bands is predicted, not their positions or intensities — weak bands can be hard to see in practice.
Compare fac with mer and cis with trans: point group, characters and band counts are all computed from the 3D structure. trans-M(CO)X4LX2\ce{M(CO)4L2} has a centre of inversion, so its infrared and Raman bands never coincide.
Numbers of ν(CO) bands in carbonyl complexes
ComplexPoint groupInfraredRaman
M(CO)X6\ce{M(CO)6}OhO_h12
M(CO)X5L\ce{M(CO)5L}C4vC_{4v}34
cis-M(CO)X4LX2\textit{cis}\text{-}\ce{M(CO)4L2}C2vC_{2v}44
trans-M(CO)X4LX2\textit{trans}\text{-}\ce{M(CO)4L2}D4hD_{4h}12
fac-M(CO)X3LX3\textit{fac}\text{-}\ce{M(CO)3L3}C3vC_{3v}22
mer-M(CO)X3LX3\textit{mer}\text{-}\ce{M(CO)3L3}C2vC_{2v}33
M(CO)X4\ce{M(CO)4}TdT_d12
M(CO)X5\ce{M(CO)5}D3hD_{3h}23

Concept check

A freshly made sample of Mo(CO)X3(PMeX3)X3\ce{Mo(CO)3(PMe3)3} shows 3 ν(CO) bands in the infrared. Is it fac or mer?

Key takeaways

  • Valence electrons N = group number + ligand electrons + M–M bonds − charge; 18 fill the nine valence orbitals, and most stable organometallics have 18.
  • 17-electron species tend to gain an electron or form M–M bonds, 19-electron species to lose one; square-planar d⁸ complexes often have 16.
  • σ donation and π back-donation strengthen M–C and weaken C–O; the more electron-rich the metal, the lower ν(CO) (free CO 2143, Cr(CO)₆ 2000 cm⁻¹).
  • The number of ν(CO) bands follows from symmetry: 1 for M(CO)₆, 2 for fac-M(CO)₃L₃, 3 for mer, 4 for cis-M(CO)₄L₂ and 1 for trans.
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Data and references

  1. L. Mond, C. Langer and F. Quincke, “Action of carbon monoxide on nickel”, J. Chem. Soc., Trans. 57, 749–753 (1890).
  2. C. A. Tolman, “Steric effects of phosphorus ligands in organometallic chemistry and homogeneous catalysis”, Chem. Rev. 77, 313–348 (1977).
  3. C. E. Housecroft and A. G. Sharpe, Inorganic Chemistry, 5th ed., Pearson, 2018, chapter 24 (organometallic compounds of the d-block).
  4. F. A. Cotton, Chemical Applications of Group Theory, 3rd ed., Wiley, 1990, chapter 10 (vibrations; carbonyl stretching bands).
  5. Wikipedia, “Metal carbonyl”, table of ν(CO) for the isoelectronic hexacarbonyls (accessed 2026-09-29; sources there include J. E. Ellis and K.-M. Chi, J. Am. Chem. Soc. 112, 6022 (1990), and M. Finze et al., Inorg. Chem. 44, 4206 (2005)).