Infrared Spectroscopy of Carbonyl Ligands

Time-resolved infrared spectroscopy, using CO or CN⁻ ligands as vibrational reporters, is now a routine tool for watching organometallic reaction intermediates form and decay on picosecond-to-microsecond timescales — following, for example, the loss of a CO ligand from a metal carbonyl photocatalyst and the subsequent formation of a solvento or substrate-bound intermediate, all tracked by the shift and disappearance of ν(CO) bands. In homogeneous catalysis, industrial process chemists screen new phosphine and phosphite ligands for hydroformylation, Suzuki coupling, and hydrogenation catalysts using Tolman electronic parameters measured (or estimated) from quick Ni(CO)₃L or Rh(CO)ClL₂ IR spectra before ever running a catalytic test, because ν(CO) tells them in minutes what a full catalytic screen would take days to reveal about a ligand's donor strength. Bioinorganic chemistry exploits the same physics in an unexpected place: [NiFe]- and [FeFe]-hydrogenase enzymes carry intrinsic CO and CN⁻ ligands on their catalytic iron centers, and the ν(CO)/ν(CN) bands in these metalloenzymes — invisible to almost every other spectroscopic handle because the rest of the protein is IR-silent in that window — are used to fingerprint different catalytic states of the enzyme active site during turnover, exactly the same logic used for simple synthetic carbonyls. Materials chemists building CO-releasing molecules (CORMs) for pharmaceutical and biomedical applications design the ancillary ligand set specifically to tune ν(CO), and hence the thermal or photochemical CO-release threshold, using the electronic trends worked out in this article. And every organometallic synthesis lab, from undergraduate teaching labs to industrial process R&D, still runs the same diagnostic first: dissolve the new carbonyl complex, record a quick solution IR spectrum, and read off oxidation state, ligand donor strength, and (via band count) local symmetry — the cheapest, fastest structural probe in the entire toolkit, setting up the richer analysis of bridging modes and cluster carbonyl bonding patterns that builds on it.

:::quiz[In the isoelectronic series [V(CO)₆]⁻, Cr(CO)₆, [Mn(CO)₆]⁺ (all d⁶, octahedral), how does ν(CO) change as charge increases from −1 to +1?]

• ν(CO) stays constant since all are isoelectronic
• ν(CO) rises steadily, because increasing positive charge weakens backbonding ✓
• ν(CO) falls steadily, because higher charge always favors backbonding
• ν(CO) shows no consistent trend across isoelectronic series

Ask the tutor: How do semi-bridging carbonyls (with intermediate M···C–O angles) show ν(CO) values that overlap the terminal and bridging ranges, and how do chemists resolve the ambiguity?

Free carbon monoxide absorbs at 2143 cm⁻¹, corresponding to a bond order of essentially 3 (a σ bond plus two orthogonal π bonds) and a force constant near 1902 N m⁻¹ (19.02 mdyn/Å). The molecule has a filled 5σ HOMO that is weakly antibonding (localized more on carbon, which is why it prefers to bond through carbon) and a pair of empty, degenerate 2π orbitals that are strongly antibonding with respect to the C–O bond. When CO coordinates to a metal, two donor–acceptor interactions turn on simultaneously, exactly as developed for the synergic bonding model: the filled CO 5σ orbital donates into an empty metal d/s/p hybrid (σ donation), and filled, symmetry-matched metal d orbitals donate back into the empty CO 2π orbitals (π backdonation, or backbonding). Both interactions push electron density onto carbon in ways that would, in isolation, be expected to have opposite effects on the C–O bond — σ donation depletes a weakly antibonding orbital (slightly strengthening C–O), while π backdonation populates a strongly antibonding orbital (substantially weakening C–O). In essentially every real system the π effect dominates numerically, so any perturbation that increases backbonding lowers ν(CO), and any perturbation that decreases backbonding (or increases σ donation's relative importance) raises ν(CO). This asymmetry is the entire basis of the spectroscopic method: ν(CO) is, to a very good first approximation, a monotonic proxy for backbonding. The consequence for the harmonic oscillator model is direct. A CO stretch is well described, near equilibrium, as a diatomic vibration with a reduced mass fixed by isotope composition and a force constant $k$ set by the electronic structure of the C–O bond. Backbonding lowers $k$; the diatomic formula converts that into a lower observed wavenumber. Because $k$ falls roughly linearly with the amount of electron density placed in π*, and because different ligands, charges, and metals perturb that population in well-understood, additive ways, the observed ν(CO) becomes a calibrated ruler for backbonding strength across the entire d-block. Symmetry adds a second, independent layer of information. A complex with $n$ chemically equivalent carbonyls does not, in general, show $n$ separate IR bands: the individual C–O stretches combine into symmetry-adapted normal modes, and only those normal modes that transform as $x$, $y$, or $z$ (i.e., carry a component of the molecular dipole moment) are IR-active. Group theory converts "how many carbonyls, in what geometric arrangement" into "how many IR bands, with what relative intensities," and running that logic backward — counting observed bands — lets a chemist assign fac vs. mer, cis vs. trans, and axial vs. equatorial substitution patterns from the fingerprint region alone.

The harmonic diatomic oscillator gives the master relationship between frequency and bonding:

where:

• $\tilde\nu$ is the observed wavenumber (cm⁻¹),
• $c$ is the speed of light,
• $k$ is the C–O stretching force constant (N m⁻¹, often quoted in mdyn/Å, 1 mdyn/Å = 100 N/m),
• $\mu = \dfrac{m_C m_O}{m_C+m_O}$ is the reduced mass of the C–O oscillator.

Reading: a stiffer bond (larger $k$) or lighter atoms (smaller $\mu$) both raise the frequency; since $\mu$ is essentially fixed by isotopic composition across the whole periodic table of metal carbonyls, essentially all the chemical information rides on $k$. The Cotton–Kraihanzel (CK) energy-factored force field extends this to polycarbonyl complexes, treating each C–O oscillator as coupled only weakly to its neighbors through the metal:

where:

• $k_{CO}$ is the "local" stretching force constant of a given carbonyl,
• $k_{ij}$ are small interaction (coupling) constants between carbonyls that share metal d-orbitals,
• the sum runs over all other CO ligands on the same metal.

Reading: because the interaction constants are small compared to $k_{CO}$, each observed IR band can be fit to recover a set of force constants that behave, ligand by ligand, in an almost additive way — this is what makes empirical scales like the Tolman electronic parameter possible. The additive ligand-electronic scale is built from a reference complex, usually Ni(CO)₃L:

where:

• $2056.1$ cm⁻¹ is the A₁ CO stretch of Ni(CO)₄ (all four ligands are CO, $\chi=0$ by definition),
• $\chi_L$ is the Tolman electronic parameter of ligand L, obtained by replacing three CO ligands with L in Ni(CO)L₃ and measuring the remaining A₁ band,
• more negative $\chi_L$ means L is a better net electron donor than CO (pushes more density onto Ni, more backbonding into the remaining CO, lower ν(CO)); more positive $\chi_L$ means L is a weaker donor / better π-acceptor than CO.

Reading: this equation turns a single infrared measurement into a numeric, transferable "electron-richness" rating for any phosphine, phosphite, or other two-electron donor ligand, usable to predict ν(CO) in a different complex entirely.

Example 1 — Foundational: comparing two simple carbonyls by force constant. Ni(CO)₄ absorbs at 2057 cm⁻¹ (its lone IR-active $T_2$ mode in $T_d$ symmetry); free CO absorbs at 2143 cm⁻¹. Using the same harmonic conversion as above,

With $2\pi c(2057) = 2\pi(2.998\times10^{10})(2057) = 3.874\times10^{14}\ \text{s}^{-1}$,

Compare to free CO's $k_0 = 1855\ \text{N m}^{-1}$ from the derivation above:

This modest drop (about 8% of $k_0$) is exactly what is expected for a neutral, moderately electron-rich d¹⁰ metal center: Ni(0) is a good backbonder, but Ni(CO)₄ is neutral (no extra anionic charge boosting backdonation further), so the frequency drop is real but far smaller than what anionic carbonyls show. This sets the "neutral, four-CO, d¹⁰, tetrahedral" baseline against which every other carbonyl complex in this article is implicitly compared.

Example 2 — Applied: predicting ν(CO) shifts across an isoelectronic series and rationalizing them with charge. The classic d⁶ octahedral hexacarbonyl series is:

All three are d⁶, all octahedral, all six CO's chemically equivalent — every one of them shows the single $T_{1u}$ IR band predicted in Step 4 of the second derivation. The trend, going from −1 to 0 to +1:

The physical story: adding one unit of positive charge pulls the metal 3d orbitals down in energy (increased effective nuclear charge), reducing their energetic match and spatial overlap with the CO 2π orbitals, so backbonding weakens and ν(CO) rises. Removing an electron (going from Cr(CO)₆ to [Mn(CO)₆]⁺, same d⁶ count but different metal/charge) still costs backbonding because Mn⁺ is more electronegative than neutral Cr and holds its d electrons more tightly. Conversely, adding negative charge (V⁻) swells the d-orbital radial extent and raises their energy, both of which improve π-overlap and π-energy-matching with CO's empty 2π, dramatically strengthening backdonation and dropping ν(CO) by over 140 cm⁻¹ relative to the neutral reference. The asymmetry between the two steps (141 cm⁻¹ vs. 90 cm⁻¹) itself is chemically meaningful: anionic charge is disproportionately effective at driving backbonding because it directly raises d-orbital energies into better resonance with the ligand's low-lying π* level, an effect that saturates somewhat as more CO's compete for the same electron density in the cationic direction.

Example 3 — Exam/competition level: using CK force constants and a bridging-carbonyl comparison to assign structure from an unlabeled IR spectrum. A student is given an unknown dinuclear iron carbonyl, Fe₂(CO)₉, and told its IR spectrum (hydrocarbon solution) shows bands at approximately 2082, 2019, 1829, and no bands above 2100 cm⁻¹. Using only ν(CO) values and the chemical trend that bridging (μ₂) carbonyls absorb roughly 150–250 cm⁻¹ lower than terminal ones on the same metal framework, assign the spectrum to a specific bonding pattern and justify the electron count. Reasoning. Terminal M–CO bands for a neutral, moderately backbonding Fe(0) center typically fall in the 2000–2100 cm⁻¹ window (consistent with the 2082 and 2019 cm⁻¹ bands observed — assign these to terminal carbonyls). The 1829 cm⁻¹ band lies far below this window, in the diagnostic zone for bridging carbonyls, because a μ₂-CO donates its π density into two metal centers simultaneously rather than one: each metal need only contribute part of the backbonding density that a terminal CO's single metal partner would supply, but crucially the CO π system is now stabilized by simultaneous overlap with d-orbitals on both metals, and the C–O σ/π mixing in the bridging geometry substantially lowers the effective force constant relative to a terminal carbonyl on the same metal fragment. Structurally, this matches the known solid-state structure of Fe₂(CO)₉: two Fe(CO)₃ units connected by an Fe–Fe bond and bridged by three μ₂-CO ligands, giving formula Fe₂(CO)₆(terminal) + (CO)₃(bridging) = Fe₂(CO)₉ overall. Applying the harmonic conversion to the bridging band,

versus a terminal-band estimate at 2019 cm⁻¹:

This ~18% reduction in force constant for the bridging mode, on the same molecule, is exactly the signature that lets a chemist assign bridging geometry without any diffraction data at all — a preview of the fuller bridging-carbonyl analysis (including the μ₂ vs. μ₃ distinction and semi-bridging intermediate cases) that follows separately.

Carbonyl IR spectroscopy as a diagnostic tool owes its systematic, quantitative form largely to F. Albert Cotton, who — with Charles Kraihanzel in 1962 — built the energy-factored force field that converts a set of observed ν(CO) bands into individual force constants for cis and trans carbonyls, making possible quantitative comparisons across entire families of substituted metal carbonyls. Cotton's broader career reshaped inorganic chemistry's engagement with symmetry and bonding theory: his textbook treatments of group theory, multiple metal–metal bonding (the first unambiguous quadruple bond, in [Re₂Cl₈]²⁻), and the electronic structure of organometallic complexes made rigorous symmetry analysis a working tool for every synthetic inorganic chemist, not merely a spectroscopist's specialty. Parallel and complementary to this, Chadwick Tolman, working at DuPont in the 1970s on catalytic phosphine complexes, built the empirical electronic (χ) and steric (cone angle, θ) parameter scheme from Ni(CO)₃L complexes, giving industrial and academic chemists alike a two-number "passport" for any phosphine or phosphite ligand — a scheme still cited in essentially every paper reporting a new phosphine-ligated catalyst.