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A carbonyl ligand is coordinated carbon monoxide, usually attached through carbon. Sigma donation and pi backbonding cooperate in the metal–carbon bond. Terminal and bridging forms have different electron-counting descriptions.

For a series of comparable metal carbonyls, greater metal-to-CO pi backbonding populates CO antibonding orbitals, weakens its internal bond and lowers its infrared stretching frequency. Coupled normal modes and changing geometry must be considered when comparing observed bands.

The Dewar-Chatt-Duncanson model describes an alkene–metal bond through donation from the filled alkene $\pi$ orbital to the metal and pi backbonding from the metal into alkene ${\pi }^{\ast }$. Backbonding weakens and lengthens the alkene double bond. A $d^0$ early-metal ion has little conventional $d$-electron backbonding.

An intact ${\mathrm{N}}_2$ group coordinated to a metal. End-on neutral dinitrogen normally counts as a two-electron L-type donor; metal-to-ligand pi backbonding can weaken its N–N bond without making it a fully cleaved nitride.

A ligand field describes how ligands split and mix the central metal orbitals. Sigma donation, pi donation and pi backbonding explain trends that a purely electrostatic picture misses.

Each cyanide contributes charge $-1$, so the formal nickel oxidation state is $+2$ and the metal has $d^8$. The requested diagram retains only the five principally metal-$3d$ molecular orbitals; the mainly ligand bonding molecular orbitals lie below them and are omitted.

In the square, $d_{x^2-y^2}$ points directly towards all four ligand donors and gives the highest, strongly antibonding molecular orbital, $B_{1g}$. The $d_{z^2}$ function also has an allowed $A_{1g}$ interaction, but its in-plane overlap is smaller. Including the allowed nickel $4s$ mixing gives a principally $d$ $A_{1g}$ level with relatively weak antibonding character. The $B_{2g}$ and $E_g$ metal functions have no ligand partner in the sigma bond donor basis and are nonbonding in this minimal model. The useful qualitative ordering is thereforeThe three nonbonding functions are shown together because the sigma-only model does not determine their finer splitting. Additional electrostatic and pi backbonding interactions can change the ordering of the lower $d$ levels; molecular symmetry alone does not fix these energy gaps.^[ref]

In the tetrahedron, the ligand $T_2$ combinations interact with the metal $T_2$ functions, producing higher $d$-derived antibonding molecular orbitals. The metal $E$ pair has no sigma donor partner and remains nonbonding:The diagram fills both arrangements with eight metal electrons; the square is shown in its fully paired state.

Take the M–C–O direction as $z$. carbon monoxide binds through carbon because its occupied $5\sigma$ donor orbital has a substantial carbon-end lobe. End-on overlap with an empty metal orbital of sigma symmetry gives CO-to-metal sigma donation. At the same time, occupied metal $d_{xz}$ and $d_{yz}$ orbitals overlap sideways with the two corresponding empty CO $2{\pi }^{\ast }$ orbitals, giving metal-to-CO pi backbonding. Both channels strengthen the metal–carbon bond, while backbonding lowers the internal C–O bond order. The processes are synergic: sigma donation helps supply metal electron density for backbonding, while backbonding relieves electron accumulation at the metal.

The original orbital sketch shows one of the two perpendicular pi channels. It is the occupied metal orbital, rather than an empty metal orbital, that supplies electrons to CO antibonding orbitals.

The methoxy substituent donates electron density into the coordinated arene by chemical resonance. This increases the electron density available at chromium for pi backbonding to CO, weakening C–O and lowering its stretching frequencies. The ester substituent withdraws electron density from the arene, reducing pi backbonding and raising the carbonyl stretching frequencies. For both observed bands, the methoxy-substituted compound has the lowest carbonyl frequency, the unsubstituted compound is intermediate, and the ester-substituted compound has the highest.

In the harmonic oscillator approximation,so the trend reflects an increasing effective C–O bond force constant rather than a change in the CO reduced mass. For example, comparison of the higher-frequency bands gives $k_{\mathrm{ester}}/k_{\mathrm{methoxy}}\approx (1992/1983{)}^2=1.0091$. This is only an approximate local-bond interpretation because the observed normal modes couple the three CO oscillators. In the idealized local $C_{3v}$ geometry they span $A_1+E$, giving two infrared-active frequencies. A substituted arene can lower the exact molecular symmetry and split the $E$ pair, even if that splitting is unresolved experimentally.

triphenylphosphine is a good sigma donor and a substantially poorer pi acceptor than CO. Replacing CO by this phosphine ligand increases electron density at chromium and reduces competition among carbonyl ligands for pi backbonding. Backbonding into each remaining CO therefore strengthens, their internal bond force constants fall, and both remaining carbonyl stretching frequencies are expected to shift downward relative to the parent tricarbonyl.

The two remaining carbonyl ligands have coupled approximately symmetric and antisymmetric stretches; both are generally infrared active in this geometry. One should not treat the spectral change as simply deleting one of the original two bands. The substituted complex still has $6+6+2(2)+2=18$ valence electrons. No numerical frequency shift follows from electron counting alone.

Choose $z$ along M–N–N. The occupied dinitrogen $3{\sigma }_g$ orbital, with amplitude on the terminal N atoms, overlaps an empty metal orbital of sigma symmetry to give N${}_2$-to-metal sigma donation. Filled metal $d_{xz}$ and $d_{yz}$ orbitals separately overlap the two empty N${}_2$ ${\pi }_g^{\ast }$ orbitals, giving metal-to-N${}_2$ pi backbonding. The lower-energy combination of each interacting pair is bonding and the higher is antibonding; each donation channel starts with two electrons in the occupied fragment orbital. The lower panel of the original orbital diagram shows these three channels.

As for a terminal carbonyl ligand, the donor and acceptor interactions reinforce one another: sigma donation helps make electron density available at the metal, while pi backbonding strengthens M–N and weakens N–N. For conventional electron counting an intact end-on neutral N${}_2$ ligand is an L-type two-electron donor; counting the backbonded electrons a second time as extra donated ligand electrons would double count them.

The carbon end of a carbonyl ligand has a filled $5\sigma$ molecular orbital with an outward-facing lobe. Its overlap with a vacant metal orbital of the same axial symmetry gives CO-to-metal sigma donation. Occupied metal $d_{\pi }$ orbitals can simultaneously overlap with the empty CO $2{\pi }^{\ast }$ antibonding molecular orbitals, giving metal-to-CO pi backbonding. Two perpendicular pi channels are possible; the schematic represents one. Orbital signs indicate phase, not electric charge.

The two interactions reinforce one another: sigma donation transfers density toward the metal, and pi backbonding distributes it into the ligand acceptor orbitals. Both strengthen M–C attachment, while backbonding weakens C–O. Occupation of CO ${\pi }^{\ast }$ decreases the internal C–O bond order, generally increasing its bond length and lowering its stretching spectroscopic wavenumber. This is why a strongly backbonded carbonyl ligand can have a strong metal–carbon bond and a weakened internal carbon–oxygen bond at the same time.

The principal electronic variable is the net population of metal–metal bonding molecular orbitals relative to antibonding molecular orbitals. For otherwise comparable complexes, a larger bond order generally gives a shorter metal-metal bond; removing an antibonding electron can shorten a bond even though the total electron count falls. Different orbital symmetries also matter: sigma, pi and delta overlaps respond differently to distance and rotation of the metal fragments.

metal size, oxidation state and radial orbital extent set the underlying distance scale. Comparing a first-row metal with a larger heavier congener does not isolate bond order. Increasing positive charge often contracts the metal orbitals, but can also change electron occupancy, ligand binding and electrostatic interactions. The ligand field and donor/acceptor properties of the surrounding ligands in coordination chemistry determine which metal orbitals remain available for direct bonding and how much density instead participates in pi backbonding.

Finally, the geometry can enforce or oppose the preferred separation. Bridging ligands impose bond-angle and bond-length constraints; bulky substituents produce steric hindrance; crystal packing can perturb the observed distance. A bond length is evidence for bonding only in its electronic and structural context. In particular, two bridges can hold metals close without proving a high direct bond order, while a sterically congested formal single bond can be unusually long.

For an octahedral complex, strong axial sigma donation raises the metal–ligand antibonding $e_g$-derived orbitals. A hydride is a very strong sigma donor: its occupied $1s$ orbital overlaps effectively along a metal–ligand axis and has no filled perpendicular p orbitals to act as a conventional pi donor. It can therefore produce a large octahedral splitting by raising $e_g$ relative to $t_{2g}$.

Triphenylphosphine also gives sigma donation, but its useful acceptor orbitals additionally receive metal pi backbonding. This lowers the metal $t_{2g}$-derived levels and enlarges their separation from $e_g$. The acceptors have substantial P–C antibonding character; invoking a dominant phosphorus $3d$ acceptor is unnecessary. Thus hydride is strong-field principally through sigma bonding, while PPh${}_3$ combines sigma donation with pi acceptance. The spectrochemical series describes the resulting splitting, not just a ranking of ligand basicity.

The all-carbonyl hydride, HCo(CO)${}_4$, is more acidic. Loss of ${\mathrm{H}}^{+}$ gives $[\mathrm{Co}(\mathrm{CO}{)}_4{]}^{-}$, whose negative charge is stabilized by pi backbonding into four carbonyl ligands. Replacing one CO by triphenyl phosphite reduces the net electron-withdrawing character of the ligand set relative to four carbonyls. The substituted hydride is more electron rich and its conjugate-base anion is less stabilized against protonation.Both conjugate bases have a conventional 18-electron count, so the difference is not a missing-electron argument. It is the relative stabilization of acid and base by the ligands in coordination chemistry. This concerns heterolytic deprotonation, not the homolytic Co–H bond-dissociation energy.

The filled alkene $\pi$ molecular orbital donates into a vacant metal acceptor orbital directed toward the center of the C=C bond. In the reverse direction, a filled metal $d$ orbital can overlap with the alkene ${\pi }^{\ast }$ antibonding molecular orbital. These are the donation and pi backbonding components of the Dewar-Chatt-Duncanson model, illustrated in the lower part of the bonding schematic. The alkene is an ${\eta }^2$ alkene ligand, attached through both carbons. Increasing backbonding weakens and lengthens C=C and can push the bonding toward a metallacyclopropane description.

Zr(IV) is $d^0$, so alkene-to-metal donation predominates. It has suitable empty orbitals but no occupied metal $d$ set to provide substantial conventional backbonding. An electron-deficient cationic zirconocene can consequently bind and activate an alkene largely through its Lewis acidity; it should not be drawn as a strongly backbonded late-metal alkene merely because its formal coordination mode is ${\eta }^2$.

In the chromium complex, Cr(0) is $d^6$ and receives substantial donation from four carbonyl ligands. Its occupied orbitals can give pi backbonding into the boron-rich acceptor orbitals of the B${}_2$N${}_2$ ring, while the nitrogen-rich occupied ring orbitals donate to the metal. This favors binding across the ring face, approximately ${\eta }^4$, with all four ring atoms participating. A nearly planar ring maintains the p-orbital alignment needed for that interaction and accounts for comparable Cr–B and Cr–N distances. A four-electron ring donor also gives the useful count $6_d+8_{\mathrm{CO}}+4_{\mathrm{ring}}=18$.

Ti(IV) in TiCl${}_4$ is $d^0$ and strongly electron deficient. It is a good acceptor for the two nitrogen lone pairs, but has no filled $d$ set for comparable backbonding into the boron acceptors. chromium therefore favors a face-bound pi complex, while titanium favors N,N sigma coordination. Donation makes the nitrogen environments more nearly tetrahedral and permits the 2,4-Diazadiboretidine ring to pucker. The borons are not directly bound in the same way, explaining $d(\mathrm{Ti}\cdots \mathrm{B})>d(\mathrm{Ti}-\mathrm{N})$. The distinction follows from electron availability, rather than simply calling every short metal–ring contact a separate ordinary sigma bond.

The nitrite ion is an ambidentate ligand: its Lewis structures leave donor lone pairs on both nitrogen and oxygen. In the N-bound mode, $\mathrm{M}-\mathrm{N}(\mathrm{O}{)}_2$, the nitrogen lone pair makes a sigma bond to the metal, while a suitable unoccupied nitrite molecular orbital can accept metal $d$ electron density by pi backbonding. Thus N-bound nitro is a sigma donor and pi acceptor. The nitrite group remains bent at nitrogen; N coordination does not make it a linear nitrosyl.

In the O-bound mode, $\mathrm{M}-\mathrm{O}-\mathrm{N}=\mathrm{O}$, an oxygen lone pair makes the metal–oxygen sigma bond. A second occupied oxygen orbital can donate sideways into an available metal orbital: O-bound nitrito is a sigma and pi donor, rather than the strong pi acceptor of the N-bound description. oxygen's greater electronegativity lowers its donor orbital energies, but the occupied oxygen orbitals still explain its pi-donor classification. Actual mixing depends on metal oxidation state and geometry.

A further possibility is bidentate coordination, $\mathrm{M}({\kappa }^2\text{-}O,O\text{-}\mathrm{N}{\mathrm{O}}_2)$, with both oxygen atoms attached to one metal. Each attachment has oxygen-to-metal sigma donation; additional pi donation depends on orbital alignment. nitrite can also be a bridging ligand between metals. Neither alternative should be confused with linkage isomerism, which specifically compares attachment through different atoms at the same binding site.

For the same pair of atoms, the harmonic approximation gives $\tilde{\nu }=(2\pi c{)}^{-1}\sqrt{k/\mu }$, where $k$ is the bond force constant and $\mu$ the reduced mass. The large shifts mainly reflect changes in $k$ from CO pi backbonding; the complexes are not distinguished simply by their total number of valence electrons.

$\mathrm{W}(\mathrm{CO}{)}_6$ has stronger net backbonding than $\mathrm{Cr}(\mathrm{CO}{)}_6$. Both are group-6 M(0), $d^6$, 18-electron complexes. The more spatially extended tungsten $5d$ orbitals provide effective overlap with CO ${\pi }^{\ast }$, consistent with the lower stretching frequency. As a simple same-mode force-constant comparison, $(1977/2000{)}^2=0.977$, about a 2.3% reduction.

$\mathrm{Ni}(\mathrm{CO}{)}_3(\mathrm{PM}{\mathrm{e}}_3)$ has appreciable but less C–O weakening than those hexacarbonyls. Ni(0) is $d^{10}$ and the complex is also 18-electron. The more contracted, lower-energy late-3d occupied orbitals give less effective donation into CO ${\pi }^{\ast }$ than the group-6 carbonyls in this comparison. Trimethylphosphine donates electron density and increases backbonding relative to an otherwise comparable less-donating nickel complex; that effect does not force its frequency below chromium's. Comparing different metals requires both orbital energies and overlap.

$[\mathrm{Cu}(\mathrm{CO}{)}_4{]}^{+}$ has very weak backbonding and a frequency above free CO. Cu(I) is $d^{10}$ and 18-electron here, but positive charge lowers its occupied orbital energies and suppresses backdonation. Sigma donation and the cation's electrostatic polarization can strengthen the internal C–O bond. Consequently the usual free-CO reference, about $2143\mathrm{c}{\mathrm{m}}^{-1}$, lies below this cation's band. A blue shift is compatible with carbon coordination; it does not imply absence of a metal–CO bond. Coupled normal modes and measurement conditions limit literal extraction of a local bond force constant from one band.

A carbonyl ligand binds through carbon, whose occupied $5\sigma$ molecular orbital has a substantial outward-facing carbon lobe. Overlap with an empty metal orbital along the M–C axis gives ligand-to-metal sigma donation. Conversely, an occupied metal $d_{\pi }$ orbital overlaps sideways with an empty CO $2{\pi }^{\ast }$ antibonding molecular orbital, giving metal-to-ligand pi backbonding. There are two mutually perpendicular pi channels. The original orbital schematic below shows one of them; $+$ and $-$ denote orbital phase, not electric charge.

The interactions are synergic: donation makes electron density available at the metal, and backbonding helps accommodate it while strengthening the metal–carbon interaction. Occupying CO ${\pi }^{\ast }$ reduces the C–O bond order, lengthens that bond and lowers its bond force constant. Therefore stronger pi backbonding generally lowers the carbonyl stretching spectroscopic wavenumber even while strengthening the M–C attachment.

A dissociative substitution begins with slow CO loss,followed by capture of the incoming ligand in coordination chemistry. A more electron-releasing $L$ increases metal-to-CO pi backbonding in the six-coordinate reactant, stabilizing it and strengthening its M–CO attachments. Removing CO sacrifices a useful pi acceptor from that electron-rich center. Thus the activation free energy for CO dissociation often rises and the substitution slows. Within an otherwise matched series, $k_d\propto \exp [-\Delta G^{‡}/(RT)]$ captures this sensitivity. The rate depends on the relative energies of reactant and dissociation transition state, so the trend is conditional: large changes in steric hindrance, geometry or mechanism can override the electronic effect.