Coordination Compounds · TOPIC LESSON
Count charges and local electrons while connecting carbonyl bonding to structure, spectra and reactivity.
BY THE END, YOU CAN
BEFORE YOU START
Original educational lesson. Work through the examples before revealing the practice answers. Check the current official syllabus separately; historical question frequency does not establish eligibility or predict future questions.
CONNECT THE CONCEPT TO THE EXAM
These selected examples are separate from the original practice below. Each identifies its exam, year and wording. They do not represent every paper or every selected year.
No source-verified exam questions have been published for this lesson yet. The worked examples and practice below are original teaching material, not past-exam questions.
01 / UNDERSTAND & APPLY
A metal carbonyl contains carbon monoxide coordinated to a metal, usually through carbon. A terminal CO is attached to one metal; a bridging CO connects two or more metals. The formula alone may not specify which arrangement occurs. Electron counting is a bookkeeping test of a proposed structure, not a measurement of charge sitting on an atom.
Keep three numbers separate. Oxidation state comes from a formal ionic assignment of ligands. The d count is the metal group number minus that oxidation state. The valence electron count adds electrons formally donated by ligands and metal–metal bonds to the metal contribution. Confusing these quantities produces answers such as calling an 18-electron metal d¹⁸, which is impossible for a d subshell.
CO is neutral in the usual ligand classification and contributes two electrons when terminal. Thus a neutral homoleptic carbonyl has metal oxidation state zero even though electron density moves in both directions within its bonds. Neutral oxidation state does not imply that the metal–ligand bonds are nonpolar or that CO cannot change the metal electron distribution.
This lesson uses the ionic method for mononuclear species and explicitly stated local conventions for dimers. Count one centre at a time before adding anything across a cluster. Every problem below is original practice, rather than an attributed past-examination question.
02 / UNDERSTAND & APPLY
The carbon end of CO has a filled donor orbital with suitable symmetry to overlap along the M–C axis with a metal acceptor orbital. This is σ donation from CO toward M. In addition, a filled metal d orbital of appropriate orientation can overlap sideways with an empty CO π* orbital. This is π back-donation from M toward CO.
The two interactions cooperate: donation supplies electron density to the metal, and back-donation allows some metal density to enter ligand acceptor orbitals. The term synergic describes this mutual reinforcement, not two independent ionic transfers that assign integral opposite charges. The M–C bond is strengthened by the additional π interaction.
A π* orbital is antibonding with respect to C–O. Greater occupation therefore reduces the effective C–O bond order and usually lengthens and weakens that bond. In an otherwise comparable series, stronger back-donation gives a lower C–O stretching wavenumber. The metal–carbon and carbon–oxygen bonds need not strengthen together.
The terminal M–C–O linkage is approximately linear because this permits favourable σ and π overlap. CO is a strong-field ligand, and many common homoleptic metal carbonyls have paired electrons. Neither the word carbonyl nor a neutral formula alone guarantees diamagnetism: odd electron counts and cluster structures require separate analysis.
Full-size scientific diagram. Swipe or scroll horizontally; keyboard users can focus the diagram and use arrow keys.
ORIGINAL PRACTICE · 1
M–C generally strengthens; C–O weakens; its stretching wavenumber falls.
The donated density occupies a ligand orbital that is antibonding for C–O but participates in metal–ligand bonding. Do not assign the same bond-order trend to both links.
03 / UNDERSTAND & APPLY
First solve the charge equation: metal oxidation state plus all ligand charges equals the charge written outside the coordination sphere. Then calculate dⁿ from the group number. Finally add the electron donation from each ligand. Terminal CO, NH₃ and phosphines are neutral two-electron donors in this method. A coordinated halide or hydride is formally negative and also contributes two electrons in the ionic method.
A negative complex charge is not added a second time after the oxidation state has already incorporated it. For [Co(CO)₄]⁻, the oxidation state is −1, so the group-9 metal contributes d¹⁰; four CO ligands then contribute eight. For [Mn(CO)₆]⁺, Mn is +1 and d⁶; six CO ligands supply twelve. Both totals are eighteen.
The neutral method is an alternative consistent convention: use the metal group number, count neutral CO as two, neutral-radical X fragments such as Cl as one, and add electrons for negative overall charge or subtract for positive charge. It agrees with the ionic method if applied consistently. Mixing a d count already corrected for oxidation state with neutral-method charge adjustments does not.
d count = group number − oxidation state
A formal d-electron count for the common transition-metal centres considered here.
VEC = d count + Σ(ligand donations) + metal–metal contributions
VEC is a local valence-electron count, not the metal oxidation state.
ORIGINAL WORKED EXAMPLE
Determine oxidation state, d count and VEC for [Co(CO)₄]⁻.
Answer Co(−I), d¹⁰, 18 electrons.
ORIGINAL PRACTICE · 1
18 electrons by either method.
Ionic: Mn(I) is d⁶ and 6×2 gives 18. Neutral: group 7+12−1 gives 18. The positive charge removes one electron only in the neutral-method sum.
04 / UNDERSTAND & APPLY
A transition-metal valence set includes one s, three p and five d orbitals: nine orbitals can accommodate eighteen electrons. In favourable metal–ligand molecular-orbital patterns, filling bonding and suitable nonbonding levels while leaving higher antibonding levels empty produces an 18-electron configuration. This helps rationalize many low-oxidation-state carbonyls.
The atomic-orbital count is a motivation rather than a proof that every complex must have eighteen electrons. Orbital energies, ligand symmetry, steric crowding and the metal identity determine which orbitals are accessible and whether extra electrons are stabilizing. Stable 16-electron square-planar d⁸ complexes are an important counterexample. Electron-deficient intermediates can also be essential to catalysis.
In the simplest all-terminal mononuclear carbonyl model, group-6 Cr needs six CO, group-8 Fe needs five, and group-10 Ni needs four to reach eighteen. The resulting known structures are octahedral Cr(CO)₆, trigonal-bipyramidal Fe(CO)₅ and tetrahedral Ni(CO)₄. The electron count rationalizes the formulas but does not on its own derive those geometries.
Effective atomic number adds the formally donated electrons to the metal atomic number corrected for oxidation state. For these first-row 18-electron examples, EAN is 36. EAN and valence count use different baselines: one includes core electrons, the other does not.
ORIGINAL WORKED EXAMPLE
Under an all-terminal neutral mononuclear 18-electron assumption, how many CO ligands are needed for Cr and Ni?
Answer Cr(CO)₆ and Ni(CO)₄; the counting model alone does not establish geometry.
ORIGINAL PRACTICE · 1
The 18-electron rule is a stability guideline, not a universal existence rule.
The high-energy orbital directed strongly at four square-planar ligands can remain empty. Its occupation need not stabilize the complex.
05 / UNDERSTAND & APPLY
For a single ordinary M–M bond, each bonded centre receives one electron in a local count. Mn₂(CO)₁₀ has five terminal CO ligands at each Mn and an Mn–Mn bond: each centre counts 7+10+1=18. Counting two electrons from the same M–M bond at each metal would double its contribution.
For a symmetric conventional μ₂-CO bridge, a useful neutral local convention assigns one electron to each of the two linked metal centres. The same ligand contributes two electrons to the combined metal framework, not four as if it were two separate terminal CO ligands. Cluster counting can require more careful orbital models for other binding modes; never generalize this rule to every possible bridge.
The familiar bridged description of Co₂(CO)₈ has three terminal CO ligands at each Co, two shared bridging CO ligands, and a Co–Co bond. Each Co therefore counts 9+6+2+1=18. An unbridged isomer with four terminal CO ligands on each metal also gives 9+8+1=18. Electron count alone cannot distinguish these structural alternatives.
Always sketch connectivity before counting. A molecular formula states the total ligands, but the local count depends on which metal each ligand contacts and which M–M bonds exist. Carbonyl bridges often have lower stretching wavenumbers than terminal CO groups, but real spectra require symmetry and structural evidence rather than one absolute threshold.
Full-size scientific diagram. Swipe or scroll horizontally; keyboard users can focus the diagram and use arrow keys.
ORIGINAL WORKED EXAMPLE
For Mn₂(CO)₁₀ with ten terminal CO groups, explain why the Mn–Mn bond is consistent with eighteen electrons at each Mn.
Answer Each Mn is 18-electron: 7+10+1. The molecule has one Mn–Mn bond.
ORIGINAL PRACTICE · 1
Each shared μ₂-CO contributes one, not two, electrons to a given metal in this stated neutral local convention.
The corrected count is 9+6+2+1=18. The mistake treats each bridge as a complete terminal donor to both metals.
06 / UNDERSTAND & APPLY
An approximate diatomic oscillator relates vibrational frequency to bond force constant and reduced mass. For the same C and O isotopes, reduced mass is fixed; a lower force constant produces a lower stretching frequency. Back-donation provides a chemical reason why the C–O force constant commonly decreases upon coordination.
Wavenumber is frequency divided by the speed of light and is commonly reported in cm⁻¹. It is not wavelength in centimetres. A shift to lower wavenumber corresponds to a lower-energy vibration, while the wavelength becomes longer. Compare closely related complexes before attributing a shift entirely to electron density.
Within a comparable isoelectronic series, a more electron-rich metal tends to back-donate more strongly. Replacing a ligand with a stronger σ donor can also increase metal density and lower ν̃(CO). Oxidation, competing π-acceptor ligands, geometry, coupling between vibrations and solvent can change the spectrum. The number of observed infrared bands is governed by symmetry and selection rules as well as the number of CO ligands.
ν̃ ≈ (1/2πc)√(k/μ)
Harmonic local-bond approximation; use consistent units, with c in cm s⁻¹ for ν̃ in cm⁻¹ when the rest of the expression supplies s⁻¹.
ORIGINAL WORKED EXAMPLE
Two comparable terminal-CO complexes using the same isotopes have C–O force constants k and 0.81k. If the first local stretching wavenumber is 2000 cm⁻¹, estimate the second.
Answer 1800 cm⁻¹, consistent with a weaker C–O bond.
ORIGINAL PRACTICE · 1
Raise it.
Reduced back-donation leaves the C–O bond stronger. This is a trend under comparable conditions, not a universal identification rule.
07 / UNDERSTAND & APPLY
Replacing one terminal CO with one neutral two-electron phosphine leaves the final electron count unchanged. Yet the path can involve an intermediate with a different count. Loss of CO from an 18-electron complex yields a formal 16-electron fragment; binding a two-electron donor restores eighteen. The sequence helps explain how a saturated precursor can gain an available coordination site.
Do not infer a complete reaction mechanism merely from counts. Associative, dissociative and interchange pathways depend on the metal and ligands, and photochemical excitation may open pathways unavailable thermally. Similarly, an 18-electron product is not guaranteed to be formed in high yield or to be kinetically inert.
Carbon monoxide and several volatile metal carbonyls are highly toxic. Their discussion here is structural and quantitative chemistry, not a preparation or handling protocol. Industrial carbonyl chemistry requires engineered containment and specialist procedures.
ORIGINAL WORKED EXAMPLE
A neutral Cr(CO)₆ complex loses one CO, then binds one PR₃ ligand. Give the formal count at each stage.
Answer 18 → 16 → 18 electrons.
ORIGINAL PRACTICE · 1
No; it remains zero.
Both ligands are formally neutral. Electron-donation strength can change without a change in formal oxidation state.
08 / UNDERSTAND & APPLY
The ionic method becomes especially valuable when a formula contains both neutral and anionic ligands. In Mn(CO)₅Br, bromide is −1, so neutral overall charge requires Mn(I). A group-7 Mn(I) centre is d⁶; five CO ligands give ten and bromide gives two, for eighteen. Calling the metal Mn(0) because the molecule is neutral ignores ligand charge.
An answer should include the assumptions used. State terminal versus bridging ligands, the number of M–M bonds at the centre, and the counting convention. If a proposed formula has an odd total under the all-terminal model, flag the discrepancy rather than adding a fictitious ligand or bond. A dimer, radical or alternative structure may be possible, but evidence is needed.
ORIGINAL PRACTICE · 1
18 electrons.
Mn(I) contributes six, five CO ligands ten, and Br⁻ two: 6+10+2=18.
ORIGINAL PRACTICE · 2
17 electrons; no.
Group-9 Co plus eight donated electrons gives seventeen. The count suggests an odd-electron species or a tendency toward further reaction; the 18-electron guideline is not a proof of nonexistence.
09 / UNDERSTAND & APPLY
Use the order charge → oxidation state → metal contribution → ligand contribution → metal–metal contribution. Confirm that the same convention is used throughout. For CO-only mononuclear ions, CO is neutral, so the written charge fixes the metal oxidation state directly.
For bonding questions, draw two arrows with different meanings: σ donation from the carbon-end donor orbital toward metal, and π back-donation from metal toward CO π*. Increased back-donation normally strengthens M–C but weakens C–O, lowering the latter stretching wavenumber.
For structural questions, eighteen electrons can support a proposed formula but cannot uniquely select geometry, bridging pattern, reaction mechanism, colour or kinetic stability. Identify which conclusion follows from counting and which requires spectroscopy or structural evidence.
KEEP THE BIG IDEAS
READ WITH CONTEXT
The teaching notes, worked explanations and original practice are written for this lesson. Separately labeled selected exam questions identify their exam, year, source and whether wording is paraphrased or an exact excerpt. Educational references do not certify current exam coverage.
Author-attributed educational HTML reference inspected for the bonding model and carbonyl connectivity.
Educational HTML reference inspected for the electron-counting model and its limitations.
Book reference for school-level metal-carbonyl scope. Narrative and practice are original.
Analytics use a separately reviewed, incomplete historical corpus. Opening a topic does not change its counts or denominator.