---
title: "Organometallic Chemistry: Bonding and Ligands"
book: "University Chemistry — Year 3"
subject: chemistry
language: en
chapter: 20
exercises: 12
source: https://one-course.com/books/chemistry/4/en/chapter/20-organometallic-chemistry-bonding-and-ligands
license: CC-BY-NC-SA-4.0
credit: "One Chemistry Book, One Course (one-course.com)"
---

# Chapter 20 — Organometallic Chemistry: Bonding and Ligands

In 1951 two research groups, independently, obtained an orange, air-stable powder of formula $\ce{FeC10H10}$ that made no sense: iron does not usually form stable bonds to carbon, and certainly not to two cyclopentadienyl rings at once. Within a year its structure was established: the iron sits between two parallel rings, bonded equally to all ten carbon atoms, a sandwich. Ferrocene opened modern organometallic chemistry, whose catalysts now make most of the world’s polymers, drugs and fine chemicals ([Chapter 21](https://one-course.com/books/chemistry/4/en/chapter/21-homogeneous-catalysis-in-industry#ch-b3-homogeneous-catalysis)). This chapter explains how metals bond to carbon monoxide, phosphines, alkenes, rings, [carbenes](#def-b3-organometallic-bonding-carbene) and to each other, and how the [isolobal analogy](#def-b3-organometallic-bonding-isolobal) connects organometallic fragments to the organic chemistry of carbon.

**You already know.**

The Year 1 volume defined organometallic compounds and used Grignard reagents. The Year 2 volume introduced the 18-electron rule and valence electron counts, hapticity, $\pi$-acceptor and $\pi$-donor ligands with back-donation, the elementary steps of organometallic reactions (oxidative addition, reductive elimination, insertion) and fragment orbitals. [Chapter 5](https://one-course.com/books/chemistry/4/en/chapter/5-group-theory-applied#ch-b3-group-theory-applied) counted the IR-active CO stretches of carbonyls and built symmetry-adapted combinations; [Chapter 18](https://one-course.com/books/chemistry/4/en/chapter/18-electronic-spectra-and-magnetism-of-complexes#ch-b3-complex-spectra-magnetism) related magnetic moments to unpaired electrons.

![Crystals of ferrocene, Fe(C5H5)2: an orange organometallic compound stable in air, that sublimes on gentle warming.](https://one-course.com/images/onecourse/chapters/chemistry-4/b3-organometallic-bonding/img-4529b6b9c2ec.jpg)

*Crystals of ferrocene, $\ce{Fe(C5H5)2}$: an orange organometallic compound stable in air, that sublimes on gentle warming.*

## 20.1 Electron counting and oxidation states

**Method 20.1 (Counting electrons, two ways).**

1. Neutral-ligand (covalent) method: the metal brings its group number of electrons; each ligand, taken neutral, brings 1 (H, $\ce{CH3}$ , Cl, the $\eta^1$ -allyl) or 2 (CO, $\ce{PR3}$ , alkene) or more ( $\eta^5$ - $\ce{C5H5}$ 5, $\eta^6$ - $\ce{C6H6}$ 6); add one per metal–metal bond and correct for the overall charge.
2. Ionic method: ligands such as H, $\ce{CH3}$ , Cl, $\ce{C5H5}$ are counted as anions (2, 2, 2 and 6 electrons), and the metal as the cation $d^n$ that results; neutral ligands as before.
3. Both give the same total; the ionic method also gives the oxidation state and the $d^n$ count.

**Example 20.2 (Counting).**

$\ce{Fe(CO)5}$: $8 + 5 \times 2 = 18$, iron(0), $d^8$. Ferrocene: neutral method $8 + 2 \times 5 = 18$; ionic method $\ce{Fe^{2+}}$ ($d^6$, 6) $+ 2 \times 6$ ($\ce{C5H5-}$) $= 18$, iron(II). $\ce{Mn2(CO)10}$: each Mn $7 + 5 \times 2 + 1$ (the Mn–Mn bond) $= 18$. Square-planar $d^8$ complexes such as $\ce{[PtCl4]^{2-}}$ or Wilkinson’s catalyst $\ce{RhCl(PPh3)3}$ have 16 electrons: their empty $p_z$-like orbital is too high to fill, and 16-electron square-planar complexes are as stable as 18-electron ones.

## 20.2 Carbonyls and phosphines

**Definition 20.3 (Metal carbonyls).**

A *metal carbonyl* is a complex with carbon monoxide ligands. A *terminal carbonyl* is bonded to one metal through carbon; a *bridging carbonyl* spans two (or three) metals.

Ludwig Mond found in 1890 that nickel reacts with carbon monoxide at ordinary temperature to give the volatile liquid $\ce{Ni(CO)4}$, which decomposes back to pure nickel on heating: the basis of a refining process. Carbon monoxide binds transition metals through its highest occupied orbital, a $\sigma$ lone pair mostly on carbon, and accepts electrons into its empty $\pi^*$ orbitals, also larger on carbon.

**Definition 20.4 (Synergic bonding).**

*Synergic bonding* is the mutual reinforcement of $\sigma$ donation from a ligand to a metal and $\pi$ back-donation from the metal to the ligand: donation makes the metal richer in electrons and readier to give them back, back-donation relieves the charge built up by donation.

![Synergic bonding of carbon monoxide. Left: the carbon lone pair ( orbital) donates into an empty -type metal orbital. Right: a filled metal d orbital (d_xz, with its two axes) overlaps the empty π* orbital of CO, larger on carbon, whose lobes match its phases: electrons flow back into an orbital that is antibonding between C and O.](https://one-course.com/images/onecourse/chapters/chemistry-4/b3-organometallic-bonding/fig-7d947c8c81f3.svg)

*[Synergic bonding](#def-b3-organometallic-bonding-synergic) of carbon monoxide. Left: the carbon lone pair ($\sigma$ orbital) donates into an empty $\sigma$-type metal orbital. Right: a filled metal $d$ orbital ($d_{xz}$, with its two axes) overlaps the empty $\pi^*$ orbital of CO, larger on carbon, whose lobes match its phases: electrons flow back into an orbital that is antibonding between C and O.*

**Proposition 20.5 (CO stretching frequencies).**

The more a metal back-donates into the $\pi^*$ orbitals of a CO ligand, the lower the C–O stretching wavenumber.

**Argued.** The $\pi^*$ orbitals of CO are antibonding between C and O: populating them weakens the C–O bond, lowers its [force constant](https://one-course.com/books/chemistry/4/en/chapter/1-quantum-mechanics-for-chemists-model-systems#def-b3-quantum-model-systems-oscillator), and hence the stretching wavenumber, which varies as the square root of the [force constant](https://one-course.com/books/chemistry/4/en/chapter/1-quantum-mechanics-for-chemists-model-systems#def-b3-quantum-model-systems-oscillator) ([Chapter 6](https://one-course.com/books/chemistry/4/en/chapter/6-rotational-and-vibrational-spectroscopy#ch-b3-rovibrational-spectroscopy)). $\sigma$ donation removes electrons from an orbital nearly non-bonding (slightly antibonding) for C–O, which by itself would raise the wavenumber a little: the observed decrease shows that back-donation dominates. ∎

Free carbon monoxide has its fundamental at $\omega_e - 2\omega_ex_e = 2143\,\mathrm{cm}^{-1}$; [terminal carbonyls](#def-b3-organometallic-bonding-carbonyl) of neutral complexes absorb roughly between 1900 and $2100\,\mathrm{cm}^{-1}$, [bridging carbonyls](#def-b3-organometallic-bonding-carbonyl) lower still. Along an isoelectronic series, an anionic carbonyl absorbs at lower wavenumber than the neutral one, a cationic one at higher: the more electron-rich the metal, the more it back-donates. The number of bands, from symmetry ([Chapter 5](https://one-course.com/books/chemistry/4/en/chapter/5-group-theory-applied#ch-b3-group-theory-applied)), gives the geometry.

**Proposition 20.6 (π\piπ interactions and the ligand-field splitting).**

In an octahedral complex, $\pi$-acceptor ligands increase $\Delta_{\mathrm o}$ and $\pi$-donor ligands decrease it.

**Proof.** The $e_g$ orbitals have $\sigma$ symmetry only. The $t_{2g}$ orbitals ($d_{xy}$, $d_{xz}$, $d_{yz}$) match a $t_{2g}$ combination of ligand $\pi$ orbitals: for $d_{xy}$, the four ligands in the $xy$ plane each offer a $\pi$ orbital perpendicular to their M–L axis in that plane, and the combination with alternating signs has the symmetry of $d_{xy}$ (the remaining combinations transform as $t_{1g}$, $t_{1u}$ and $t_{2u}$ and find no $d$ partner). Two orbitals of the same symmetry mix and repel: the lower is pushed down, the upper up. A $\pi$ acceptor offers empty orbitals above the $t_{2g}$ set, which is pushed down: $\Delta_{\mathrm o}$ increases. A $\pi$ donor offers filled orbitals below it, which push it up: $\Delta_{\mathrm o}$ decreases. The $e_g$ level is unaffected in both cases. ∎

This is why CO and $\ce{CN-}$ sit at the strong end of the spectrochemical series, and halides and hydroxide at the weak end, as the Year 2 volume stated.

**Definition 20.7 (Tolman parameters).**

The *Tolman cone angle* of a phosphine is the apex angle of the cone, centred on the metal at a standard distance, that just encloses the van der Waals surfaces of its substituents: a measure of its size. The *Tolman electronic parameter* is the wavenumber of the symmetric CO stretch of $\ce{Ni(CO)3L}$: the more strongly the phosphine L donates, the lower it is.

Phosphines are tuned independently in size and electron donation by their substituents: trialkylphosphines are stronger donors than triarylphosphines, phosphites the weakest; $\ce{P(tBu)3}$ is far bulkier than $\ce{PMe3}$. Bulky phosphines favour low coordination numbers and fast ligand dissociation, which is why they appear in so many catalysts.

## 20.3 $\pi$ ligands

**Definition 20.8 (Dewar–Chatt–Duncanson model).**

The *Dewar–Chatt–Duncanson model* of the bonding of an alkene to a metal combines $\sigma$ donation from the C=C $\pi$ orbital to an empty metal orbital with back-donation from a filled metal $d$ orbital into the C=C $\pi^*$ orbital. Its limit of strong back-donation is a *metallacyclopropane*, a three-membered ring with two M–C $\sigma$ bonds and a C–C single bond.

**Proposition 20.9 (Consequences of back-donation to an alkene).**

Coordination lengthens the C=C bond and bends the substituents back, away from the metal, more so as back-donation increases.

**Argued.** Removing electrons from the $\pi$ (bonding) orbital and adding them to the $\pi^*$ (antibonding) orbital both lower the C–C bond order. Mixing $\pi^*$ character rehybridises the carbons towards $sp^3$, whose bonds to the substituents point away from the metal, towards the [metallacyclopropane](#def-b3-organometallic-bonding-dcd) geometry. ∎

![The Dewar–Chatt–Duncanson model of an alkene bound side-on (C=C vertical, the metal on the left). Left: the filled π orbital (two p orbitals in phase) donates into an empty metal orbital. Right: a filled metal d orbital of matching phases donates into the empty π* orbital (the two p orbitals out of phase).](https://one-course.com/images/onecourse/chapters/chemistry-4/b3-organometallic-bonding/fig-358d3732d854.svg)

*The [Dewar–Chatt–Duncanson model](#def-b3-organometallic-bonding-dcd) of an alkene bound side-on (C=C vertical, the metal on the left). Left: the filled $\pi$ orbital (two $p$ orbitals in phase) donates into an empty metal orbital. Right: a filled metal $d$ orbital of matching phases donates into the empty $\pi^*$ orbital (the two $p$ orbitals out of phase).*

Zeise’s salt, $\ce{K[PtCl3(C2H4)]}$, made in 1827, was the first organometallic compound of a transition metal; its ethene lies perpendicular to the $\ce{PtCl3}$ plane, as the model predicts. Allyl ($\eta^3$), dienes ($\eta^4$), arenes ($\eta^6$) and the cyclopentadienyl ring ($\eta^5$) bind in the same way through several carbons at once.

**Definition 20.10 (Metallocenes).**

A *sandwich compound* has a metal between two parallel planar ring ligands bonded through all their carbons; a *metallocene* is a sandwich compound with two $\eta^5$-cyclopentadienyl rings, $\ce{M(C5H5)2}$.

**Proposition 20.11 (The frontier orbitals of ferrocene).**

In a [metallocene](#def-b3-organometallic-bonding-metallocene) with parallel rings ($D_{5d}$), the metal $d$ orbitals split into $e_{2g}$ ($d_{xy}$, $d_{x^2-y^2}$) and $a_{1g}$ ($d_{z^2}$), nearly non-bonding and close together, and $e_{1g}^\ast$ ($d_{xz}$, $d_{yz}$), strongly antibonding; ferrocene, with six $d$ electrons in $e_{2g}^4a_{1g}^2$, has 18 electrons and no unpaired electron.

**Argued.** The $\pi$ orbitals of the two rings combine into symmetry-adapted pairs $a_{1g}$, $a_{2u}$, $e_{1g}$, $e_{1u}$, $e_{2g}$, $e_{2u}$ (from the five $\pi$ orbitals of each ring, with zero, one and two nodal planes through the axis). The filled ring $e_{1g}$ combination overlaps strongly with $d_{xz}$, $d_{yz}$ (one nodal plane through the axis each): they form bonding orbitals, mostly ring, and antibonding $e_{1g}^\ast$, mostly metal, pushed high. $d_{xy}$, $d_{x^2-y^2}$ (two nodal planes) meet only the empty ring $e_{2g}$ orbitals and are slightly stabilised by back-donation; $d_{z^2}$ points at the hole in the middle of each ring and hardly overlaps. Six electrons fill $e_{2g}$ and $a_{1g}$; with the twelve electrons of the bonding ring combinations, the count is 18. ∎

![Left: the sandwich structure of ferrocene (eclipsed rings). Right: the d-based frontier orbitals of metallocenes, e_2g and a_1g nearly non-bonding, e_1g antibonding, filled for the ferrocenium cation (17 electrons), ferrocene (18), cobaltocene (19) and nickelocene (20, one electron in each e_1g orbital, spins parallel by Hund’s rule).](https://one-course.com/images/onecourse/chapters/chemistry-4/b3-organometallic-bonding/fig-7017e9d894ea.svg)

*Left: the sandwich structure of ferrocene (eclipsed rings). Right: the $d$-based frontier orbitals of [metallocenes](#def-b3-organometallic-bonding-metallocene), $e_{2g}$ and $a_{1g}$ nearly non-bonding, $e_{1g}^\ast$ antibonding, filled for the ferrocenium cation (17 electrons), ferrocene (18), cobaltocene (19) and nickelocene (20, one electron in each $e_{1g}^\ast$ orbital, spins parallel by Hund’s rule).*

## 20.4 Carbenes, carbynes and metal–metal bonds

**Definition 20.12 (Carbenes and carbene complexes).**

A *carbene* is a neutral species $\ce{R2C}$ with a divalent carbon carrying two non-bonding electrons. A *carbene complex* has a $\ce{CR2}$ ligand bonded to a metal by a double bond, $\ce{M=CR2}$. A *Fischer carbene* complex has a heteroatom substituent on the carbene carbon and a low-valent metal with $\pi$-acceptor ligands; its carbene carbon is electrophilic. A *Schrock carbene* (alkylidene) complex has only C or H substituents and a high-valent early metal; its carbon is nucleophilic. An *N-heterocyclic carbene* is a cyclic carbene flanked by two nitrogen atoms, stable as a free compound and a strong $\sigma$-donor ligand.

The two kinds of [carbene complexes](#def-b3-organometallic-bonding-carbene) differ in the way the M=C bond is shared. In a [Fischer carbene](#def-b3-organometallic-bonding-carbene) a singlet [carbene](#def-b3-organometallic-bonding-carbene) donates its lone pair to the metal and receives back-donation into its empty $p$ orbital, which the heteroatom lone pair also stabilises: the carbon stays electron-poor, attacked by nucleophiles. In a [Schrock carbene](#def-b3-organometallic-bonding-carbene) two triplet fragments, metal and [carbene](#def-b3-organometallic-bonding-carbene), form a covalent $\sigma +
\pi$ bond, polarised towards carbon: the alkylidene behaves like a Wittig ylide.

**Definition 20.13 (Carbyne complex).**

A *carbyne complex* has a triple bond between a metal and a carbon carrying one substituent, $\ce{M#CR}$.

**Definition 20.14 (δ\deltaδ bond, quadruple bond).**

A *$\delta$ bond* is a bond whose orbital has two nodal planes containing the internuclear axis, formed by the face-to-face overlap of two $d$ orbitals such as $d_{xy}$ and $d_{xy}$. A *quadruple bond* combines one $\sigma$, two $\pi$ and one $\delta$ bond between two metal atoms.

**Proposition 20.15 (The quadruple bond of [Re2Cl8]2−[\mathrm{Re_2Cl_8}]^{2-}[Re2​Cl8​]2−).**

In $\ce{[Re2Cl8]^{2-}}$ (two $\ce{Re^{III}}$, $d^4$ each), the eight $d$ electrons occupy $\sigma^2\pi^4\delta^2$: a bond order of 4, which requires the eclipsed arrangement of the two $\ce{ReCl4}$ units.

**Proof.** With $z$ along the Re–Re axis and the Cl atoms along $\pm x$ and $\pm y$ on each Re, $d_{x^2-y^2}$ points at the chlorides and is used in Re–Cl bonding. The other four $d$ orbitals of each metal overlap pairwise: $d_{z^2}$ with $d_{z^2}$ along the axis ($\sigma$), $d_{xz}$ with $d_{xz}$ and $d_{yz}$ with $d_{yz}$ side by side ($\pi$, twice), $d_{xy}$ with $d_{xy}$ face to face ($\delta$, the weakest). Eight electrons fill the four bonding combinations. Rotating one unit by $45^\circ$ about $z$ turns its $d_{xy}$ into $d_{x^2-y^2}$, which has zero overlap with the other $d_{xy}$ by symmetry: the $\delta$ bond, and with it the eclipsed preference, is lost. The other three overlaps are cylindrically symmetric or unchanged in magnitude. ∎

The Re–Re distance of $2.24\,\text{Å}$ in the potassium salt is very short for two metal atoms, and the chlorides of the two halves are indeed eclipsed, against their steric repulsion: the $\delta$ bond, weak as it is, holds them there.

![The component of the quadruple bond of (Re2Cl8)2-: the d_xy orbitals of the two rhenium atoms (four lobes each, signs blue and orange) face each other across the Re–Re axis, lobe over lobe of the same sign. The chlorides (green), eclipsed, lie along x and y, between the lobes.](https://one-course.com/images/onecourse/chapters/chemistry-4/b3-organometallic-bonding/fig-3846e006a6f0.svg)

*The $\delta$ component of the [quadruple bond](#def-b3-organometallic-bonding-delta) of $\ce{[Re2Cl8]^{2-}}$: the $d_{xy}$ orbitals of the two rhenium atoms (four lobes each, signs blue and orange) face each other across the Re–Re axis, lobe over lobe of the same sign. The chlorides (green), eclipsed, lie along $x$ and $y$, between the lobes.*

## 20.5 The isolobal analogy

**Definition 20.16 (Isolobal fragments).**

Two molecular fragments are *isolobal* when the number, symmetry, approximate energy and shape of their frontier orbitals, and the number of electrons in them, are similar. The *isolobal analogy* predicts that isolobal fragments can replace one another in molecules.

**Proposition 20.17 (Isolobal series).**

$\ce{CH3}$, $\ce{Mn(CO)5}$ and $\ce{CpFe(CO)2}$ are [isolobal](#def-b3-organometallic-bonding-isolobal) (one frontier orbital, one electron); $\ce{CH2}$ and $\ce{Fe(CO)4}$ (two orbitals, two electrons); $\ce{CH}$ and $\ce{Co(CO)3}$ (three orbitals, three electrons).

**Argued.** $\ce{CH3}$ is a tetrahedral fragment missing one bond: one $sp^3$-like orbital with one electron, one short of an octet. $\ce{Mn(CO)5}$ is an octahedron missing one ligand: the empty site holds one hybrid orbital pointing out; with $7 + 10 = 17$ electrons it is one short of 18, and its single electron sits in that hybrid. Removing two or three ligands (or bonds) gives two or three such orbitals and electrons, with the same counting on both sides: $\ce{Fe(CO)4}$ has 16 electrons ($8 + 8$), two short of 18; $\ce{Co(CO)3}$ has 15 ($9 + 6$), three short. ∎

**Method 20.18 (Predicting a structure by isolobal replacement).**

1. Break the compound into fragments and count each one’s frontier orbitals and electrons.
2. Replace each fragment by its organic [isolobal](#def-b3-organometallic-bonding-isolobal) partner.
3. The organic analogue, if it exists, suggests the bonding and the shape: $\ce{Mn2(CO)10}$ is “ethane”, $\ce{Co3(CO)9CH}$ is “tetrahedrane” $\ce{(CH)4}$ with three CH replaced by $\ce{Co(CO)3}$ .

![The isolobal series (frontier hybrids drawn schematically): each organic fragment and the metal carbonyl fragment opposite it have the same number of outward-pointing frontier orbitals and of electrons in them, and combine in analogous ways.](https://one-course.com/images/onecourse/chapters/chemistry-4/b3-organometallic-bonding/fig-4409e1f37f86.svg)

*The [isolobal](#def-b3-organometallic-bonding-isolobal) series (frontier hybrids drawn schematically): each organic fragment and the [metal carbonyl](#def-b3-organometallic-bonding-carbonyl) fragment opposite it have the same number of outward-pointing frontier orbitals and of electrons in them, and combine in analogous ways.*

**Definition 20.19 (Agostic interaction).**

An *agostic interaction* is a three-centre, two-electron bond between a metal and a C–H bond of one of its own ligands, in which the C–H bonding pair donates into an empty metal orbital.

Agostic hydrogens show up as short metal–hydrogen distances in diffraction structures, as unusually low C–H stretching wavenumbers, and in NMR as a high-field shift and a reduced $^1J_{\mathrm{CH}}$ coupling. They are frozen snapshots of C–H activation, the first step of many catalytic reactions.

**In the lab — Working with metal carbonyls.**

[Metal carbonyls](#def-b3-organometallic-bonding-carbonyl) are handled in a fume hood with a working extraction, under nitrogen or argon, with no open flame: many release carbon monoxide on warming. Volatile carbonyls are transferred by cannula or on a vacuum line, never poured; residues are destroyed by slow oxidation (bleach or bromine water) in the hood. Nickel tetracarbonyl, the most dangerous, is not used in teaching laboratories at all.

**Safety.**

![](https://one-course.com/images/onecourse/chapters/chemistry-4/b3-organometallic-bonding/fig-16b2e9efd290.svg)

![](https://one-course.com/images/onecourse/chapters/chemistry-4/b3-organometallic-bonding/fig-8f09793f6441.svg)

![](https://one-course.com/images/onecourse/chapters/chemistry-4/b3-organometallic-bonding/fig-68fedba7b87e.svg)

![](https://one-course.com/images/onecourse/chapters/chemistry-4/b3-organometallic-bonding/fig-ce8aa75a0f1b.svg)

![](https://one-course.com/images/onecourse/chapters/chemistry-4/b3-organometallic-bonding/fig-584c0be6faf1.svg)

Nickel tetracarbonyl: highly flammable, fatal if inhaled, suspected carcinogen, may damage the unborn child. Ferrocene: a flammable solid, harmful if swallowed; handled as a fine chemical with gloves and dust precautions.

**History — Mond’s carbonyl and the sandwich.**

Ludwig Mond and his co-workers discovered nickel tetracarbonyl in 1890 while studying the corrosion of nickel valves by carbon monoxide, and built on it a process for refining nickel. Ferrocene was made in 1951 by Thomas Kealy and Peter Pauson, and independently by Samuel Miller, John Tebboth and John Tremaine; in 1952 Geoffrey Wilkinson and Robert Woodward, and Ernst Otto Fischer, proposed the sandwich structure. Fischer and Wilkinson shared the 1973 Nobel Prize in Chemistry for their work on [sandwich compounds](#def-b3-organometallic-bonding-metallocene).

## 20.6 Exercises

**Exercise 20.1 ★.**

Count the valence electrons of $\ce{Fe(CO)5}$, $\ce{Mn2(CO)10}$ (per Mn), $\ce{CpMo(CO)3H}$, Zeise’s anion $\ce{[PtCl3(C2H4)]-}$, $\ce{Cr($\eta^6$-C6H6)(CO)3}$ and $\ce{Cp2ZrCl2}$.

**Solution of Exercise 20.1.**

$\ce{Fe(CO)5}$: $8 + 10 = 18$. $\ce{Mn2(CO)10}$: $7 + 10 + 1 = 18$ per Mn. $\ce{CpMo(CO)3H}$: $6 + 5 + 6 + 1 =
18$. $\ce{[PtCl3(C2H4)]-}$: $10 + 3 + 2 + 1 = 16$. $\ce{Cr($\eta^6$-C6H6)(CO)3}$: $6 + 6 + 6 = 18$. $\ce{Cp2ZrCl2}$: $4 + 10 + 2 = 16$.

**Exercise 20.2 ★.**

Give the oxidation state and $d^n$ count of the metal in each compound of the previous exercise.

**Solution of Exercise 20.2.**

Fe(0) $d^8$; Mn(0) $d^7$; Mo(II) $d^4$; Pt(II) $d^8$; Cr(0) $d^6$; Zr(IV) $d^0$.

**Exercise 20.3 ★.**

Rank the CO stretching wavenumbers of $\ce{[V(CO)6]-}$, $\ce{Cr(CO)6}$ and $\ce{[Mn(CO)6]+}$, and justify.

**Solution of Exercise 20.3.**

$\ce{[Mn(CO)6]+} > \ce{Cr(CO)6} > \ce{[V(CO)6]-}$: the more electron-rich the metal, the more it back-donates into $\pi^*$ and the weaker the C–O bonds.

**Exercise 20.4 ★.**

Give the organic [isolobal](#def-b3-organometallic-bonding-isolobal) analogues of $\ce{Mn2(CO)10}$, $\ce{[CpFe(CO)2]2}$ and $\ce{Co3(CO)9CH}$.

**Solution of Exercise 20.4.**

Ethane ($\ce{Mn(CO)5}$ and $\ce{CpFe(CO)2}$ are [isolobal](#def-b3-organometallic-bonding-isolobal) with $\ce{CH3}$); ethane again; tetrahedrane $\ce{(CH)4}$ with three CH replaced by $\ce{Co(CO)3}$.

**Exercise 20.5 ★★.**

How many CO stretching bands do $fac$- and $mer$-$\ce{M(CO)3L3}$ show in the IR?

**Solution of Exercise 20.5.**

$fac$ ($C_{3v}$): two (A$_1$ + E). $mer$ ($C_{2v}$): three (2A$_1$ + B$_1$).

**Exercise 20.6 ★★.**

Explain why replacing $\ce{PMe3}$ by $\ce{P(tBu)3}$ in a catalyst can speed up a step that needs a ligand to leave the metal.

**Solution of Exercise 20.6.**

The bulky phosphine crowds the metal: dissociation relieves the strain, so it is faster, and low-coordinate intermediates are favoured.

**Exercise 20.7 ★★.**

Classify $\ce{(CO)5Cr=C(OMe)Ph}$ and $\ce{Ta(=CHCMe3)(CH2CMe3)3}$ as Fischer or Schrock [carbene complexes](#def-b3-organometallic-bonding-carbene), and predict their reactions with an amine and with a ketone.

**Solution of Exercise 20.7.**

The chromium complex is a [Fischer carbene](#def-b3-organometallic-bonding-carbene) (OMe substituent, Cr(0), CO ligands): an amine attacks the electrophilic [carbene](#def-b3-organometallic-bonding-carbene) carbon and replaces OMe. The tantalum alkylidene is a [Schrock carbene](#def-b3-organometallic-bonding-carbene): its nucleophilic carbon attacks the carbonyl of a ketone, giving an alkene and a Ta=O unit, as in a Wittig reaction.

**Exercise 20.8 ★★.**

What bond order would a staggered $\ce{[Re2Cl8]^{2-}}$ have? What is the bond order of $\ce{[Re2Cl8]^{4-}}$, with two more electrons?

**Solution of Exercise 20.8.**

Staggered: no $\delta$ overlap, the two $\delta$ electrons are non-bonding: bond order 3. $\ce{[Re2Cl8]^{4-}}$: $\sigma^2\pi^4\delta^2\delta^{\ast2}$, bond order 3.

**Exercise 20.9 ★★.**

List three kinds of evidence for an agostic C–H interaction.

**Solution of Exercise 20.9.**

A short M$\cdots$H distance (diffraction, best neutron); a low C–H stretching wavenumber; an NMR signal at high field with a reduced one-bond C–H coupling.

**Exercise 20.10 ★★★.**

Give examples of stable complexes with 16, 17 and 19 valence electrons, and explain each exception to the 18-electron rule.

**Solution of Exercise 20.10.**

16: square-planar $d^8$ ($\ce{[PtCl4]^{2-}}$, Wilkinson’s catalyst), whose 18th-electron orbital is too high; early-metal [metallocenes](#def-b3-organometallic-bonding-metallocene) such as $\ce{Cp2ZrCl2}$, too crowded for more ligands. 17: $\ce{V(CO)6}$, which cannot dimerise for steric reasons. 19: cobaltocene, whose extra electron sits in an antibonding orbital (and is easily lost).

**Exercise 20.11 ★★★.**

$\ce{Cr(CO)6}$ is colourless and diamagnetic. Explain, using the $\pi$-acceptor effect on $\Delta_{\mathrm o}$, why it is low spin and why its $d$–$d$ bands lie in the ultraviolet.

**Solution of Exercise 20.11.**

CO is a strong $\pi$ acceptor: it lowers the $t_{2g}$ level and makes $\Delta_{\mathrm o}$ large, far above the pairing energy: $t_{2g}^6$, diamagnetic. The $d$–$d$ transitions, at $\Delta_{\mathrm o}$, fall in the ultraviolet, and no visible light is absorbed.

**Exercise 20.12 ★★★.**

The C–C bond of ethene lengthens from $1.34\,\text{Å}$ to $1.37\,\text{Å}$ in Zeise’s salt and to about $1.43\,\text{Å}$ in a complex of a low-valent metal with strong back-donation (data of the exercise). Interpret with the [Dewar–Chatt–Duncanson model](#def-b3-organometallic-bonding-dcd).

**Solution of Exercise 20.12.**

Donation from $\pi$ and back-donation into $\pi^*$ both lower the C–C bond order. In Zeise’s salt (Pt(II), moderate back-donation) the bond lengthens a little; a low-valent, electron-rich metal back-donates strongly and the complex approaches the [metallacyclopropane](#def-b3-organometallic-bonding-dcd) limit, with a C–C bond close to a single bond.

## 20.7 Problem: Sandwiches

**Problem 20.1.**

Weekend problem — sandwiches: electron counts of four metallocenes, their frontier orbitals and unpaired electrons, their redox chemistry, and two isolobal and spectroscopic questions

[Metallocenes](#def-b3-organometallic-bonding-metallocene) $\ce{MCp2}$ ($\ce{Cp} = \eta^5$-$\ce{C5H5}$) are known for M = Fe, Co, Ni and for the ferrocenium cation.

**Part I — Counting.**

1. Count the electrons of ferrocene by the ionic method.
2. Count them by the neutral method.
3. Count cobaltocene.
4. Count nickelocene.
5. Count the ferrocenium cation.
6. Give the oxidation state and $d^n$ count of each metal.

**Part II — Orbitals and magnetism.**

7. Classify the five $d$ orbitals in $D_{5d}$ .
8. Which of them overlap strongly with the ring $\pi$ orbitals, and with what consequence?
9. Give the order of the $d$ -based levels.
10. Fill them for ferrocene: unpaired electrons?
11. Fill them for cobaltocene: unpaired electrons and [spin-only moment](https://one-course.com/books/chemistry/4/en/chapter/18-electronic-spectra-and-magnetism-of-complexes#def-b3-complex-spectra-magnetism-moment) ?
12. Fill them for nickelocene: unpaired electrons and [spin-only moment](https://one-course.com/books/chemistry/4/en/chapter/18-electronic-spectra-and-magnetism-of-complexes#def-b3-complex-spectra-magnetism-moment) ?
13. Fill them for ferrocenium: unpaired electrons? Why is its measured moment above the spin-only value?

**Part III — Redox.**

14. Why is cobaltocene a strong reducing agent?
15. Why is the ferrocene/ferrocenium couple fast and reversible?
16. Why is it used as an internal reference in non-aqueous electrochemistry ( [Chapter 15](https://one-course.com/books/chemistry/4/en/chapter/15-electrode-kinetics-and-electroanalysis#ch-b3-electrode-kinetics) )?
17. What would you expect of nickelocene’s reactions with two-electron ligands?

**Part IV — Fragments and spectra.**

18. Show that $\ce{CpFe(CO)2}$ is [isolobal](#def-b3-organometallic-bonding-isolobal) with $\ce{CH3}$ , and predict the structure of $\ce{[CpFe(CO)2]2}$ .
19. What mixed dimer could it form with $\ce{Mn(CO)5}$ ?
20. How does replacing a CO of $\ce{CpMn(CO)3}$ by $\ce{PPh3}$ change the remaining CO stretches?
21. How many CO bands does $\ce{Cr($\eta^6$-C6H6)(CO)3}$ ( $C_{3v}$ ) show?
22. Why can a $\eta^5$ -Cp ring slip to $\eta^3$ during a substitution?
23. State the result: the spin-only magnetic moment of nickelocene.

**Solution of Problem 20.1.**

**1.** $\ce{Fe^{2+}}$ ($d^6$) $+ 2 \times 6 = 18$. **2.** $8 + 2 \times 5 = 18$. **3.** $9 + 10 = 19$. **4.** $10 + 10 = 20$. **5.** $18 - 1 = 17$. **6.** Fe(II) $d^6$; Co(II) $d^7$; Ni(II) $d^8$; Fe(III) $d^5$. **7.** $a_{1g}$ ($d_{z^2}$), $e_{1g}$ ($d_{xz}$, $d_{yz}$), $e_{2g}$ ($d_{xy}$, $d_{x^2-y^2}$). **8.** The $e_{1g}$ pair overlaps strongly with the filled ring $e_{1g}$ combination: bonding orbitals mostly on the rings, antibonding $e_{1g}^\ast$ mostly on the metal, high in energy. **9.** $e_{2g} \approx a_{1g} < e_{1g}^\ast$. **10.** $e_{2g}^4a_{1g}^2$: no unpaired electron. **11.** One electron in $e_{1g}^\ast$: one unpaired electron, $1.73\,\mu_B$. **12.** Two electrons in the two $e_{1g}^\ast$ orbitals, parallel: two unpaired, $\sqrt{8} =
2.83\,\mu_B$. **13.** $e_{2g}^3a_{1g}^2$: one unpaired electron. An $e_{2g}^3$ hole gives an orbitally degenerate (E) state with an [orbital contribution](https://one-course.com/books/chemistry/4/en/chapter/18-electronic-spectra-and-magnetism-of-complexes#def-b3-complex-spectra-magnetism-moment). **14.** Its 19th electron is in an antibonding orbital and is easily removed, giving the 18-electron cobaltocenium cation. **15.** The electron removed comes from a nearly non-bonding orbital: the structure hardly changes (small [reorganisation energy](https://one-course.com/books/chemistry/4/en/chapter/19-reaction-mechanisms-of-complexes#def-b3-complex-mechanisms-reorganisation), [Chapter 19](https://one-course.com/books/chemistry/4/en/chapter/19-reaction-mechanisms-of-complexes#ch-b3-complex-mechanisms)). **16.** The couple is fast and reversible in most solvents, the compound is soluble and stable, and its potential depends little on the solvent because the charge is spread over a large ion. **17.** With 20 electrons, two of them antibonding, it reacts by losing them: it adds ligands with slippage or loss of a ring, or is oxidised. **18.** $\ce{CpFe(CO)2}$: $8 + 5 + 4 = 17$ electrons, one short of 18, one frontier orbital: [isolobal](#def-b3-organometallic-bonding-isolobal) with $\ce{CH3}$. The dimer $\ce{[CpFe(CO)2]2}$ is “ethane”, with an Fe–Fe bond (in practice two CO ligands bridge it). **19.** $\ce{CpFe(CO)2-Mn(CO)5}$, with an Fe–Mn bond. **20.** $\ce{PPh3}$ is a better donor and a poorer $\pi$ acceptor than CO: the metal back-donates more to the remaining CO, whose stretches fall. **21.** Two (A$_1$ + E). **22.** Ring slippage to $\eta^3$ frees two electrons’ worth of coordination: an entering ligand can bind associatively without the metal exceeding 18 electrons. **23.** **$\mu_{\text{spin only}}(\text{nickelocene}) = \sqrt{2 \times 4} = 2.83\,\mu_B$.**