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18-Electron rule

The 18-electron rule is a rule of thumb used primarily in transition metal chemistry for characterizing and predicting the stability of metal complexes. Valence shells of a transition metal can accommodate 18 electrons: 2 in each of the five d orbitals (10 in total); 2 in each of the three p orbitals (6 in total); and 2 in the s orbital (see Electron counting). In practice, of course, these orbitals cannot directly accept electrons, otherwise one would encounter ions such as Fe¹⁰⁻ and Pt⁸⁻. However, combination of these atomic orbitals with ligand orbitals gives rise to nine molecular orbitals which are either metal-ligand bonding or non-bonding. (There are also some higher energy anti-bonding orbitals). The complete filling of these nine lowest energy orbitals with electrons, whether those electrons originate from the metal or from any ligands, is the basis of the 18-electron rule. When the metal has 18 electrons, it has then achieved the same electron configuration as the noble gas at the end of the period.

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Application of the 18-electron rule

The majority of metal complexes do not satisfy the 18-electron rule. It is, however, especially useful for organometallic complexes of the Cr, Mn, Fe, and Co triads, and applies to compounds such as ferrocene, iron pentacarbonyl, chromium carbonyl and nickel carbonyl. In compounds such as these, the nine bonding molecular orbitals are all low in energy. Because putting electrons into them is a favourable process, and as each orbital can take two electrons, the greatest stability is achieved when there are a total of 18 electrons in these orbitals - this includes both the electrons that come from the metal, and those donated to it from the ligands. This is the basis of the 18-electron rule. This stability is such that much chemistry is guided by a metal's need to retain or get 18 electrons.

The ligands in a complex play an important role in determining whether or not it obeys the 18-electron rule. Generally, complexes that do obey the rule have ligands that are π-acids. This kind of ligand typically exerts a very strong ligand field, which causes the resultant molecular orbitals to be very low in energy and thus makes it good to fill them. Typical ligands include olefins, phosphines and carbonyls. Metals form the best complexes with π-acids when the metal is in a low-oxidation state (because then you get good overlap of metal and ligand orbitals, and the metal can donate electrons back to the ligand in a synergic fashion), so complexes that obey the 18-electron rule generally have the metal in a low-oxidation state too.

This is not to say that all complexes with a low oxidation-state metal and π-acidic ligands have 18 electrons - see below for counterexamples. It is also not to say that if a metal is in a high oxidation state or does not have π-acidic ligands it cannot have 18 electrons.

Compounds that obey the 18 VE rule are typically "exchange inert," such as [Co(NH₃)₅Cl]²⁺ and [Fe(CN)₆]^4-.

As the rule is essentially the result of filling the valence orbitals of the metal by covalent bonding between metal and ligands, metals that display largely ionic chemistry don't obey it. This includes the s-block metals, the lanthanides and the actinides. It can, however, be compared to the octet rule for carbon, which equally makes enough covalent bonds to fill its valence orbitals.

Using the 18-electron rule

The usefulness of the 18-electron rule becomes more apparent when one considers what chemical transformations or derivatives might be readily accessible. For example, what piano stool compound might one be able to prepare by formally removing one of the cyclopentadienyl ligands from ferrocene and replacing it with some number of carbon monoxide ligands?

Using the ionic approach, removing one cyclopentadienyl anion yields a cationic fragment containing one cyclopentadienyl (Cp) fragment and 12 valence shell electrons. Since each carbon monoxide ligand contributes 2 electrons (3 CO ligands give the requisite 6 electrons), it should be possible to create an iron-containing complex cation containing one cyclopentadienyl group, one iron atom, and 3 carbon monoxide ligands:

CpFe(CO)₃⁺

What one finds is that the iron complex satisfies the 18 electron count another way, by forming a dimer with an Fe-Fe bond (see Cyclopentadienyliron dicarbonyl dimer). Counting electrons for just one iron center can be done by considering the other iron as contributing 1 electron to the count:

[CpFe(CO)₂]₂

neutral counting: Cp 5 + Fe 8 + 2 CO 4 + Fe 1 = 18

Another stable compound is obtained, when one small monoanionic ligand is used:

CpFe(CH₃)(CO)₂

Neutral counting: Cp 5 + Fe 8 + CH₃ 1 + 2 CO 4 = 18

Deviations from the 18-electron rule

The 18-electron rule is just that - a rule, not a law. Many transition metal complexes do not follow this rule, and, furthermore, compounds which have fewer than 18 valence electrons tend to show enhanced reactivity. In fact, 18 electrons is often a recipe for non-reactivity in either a stoichiometric or catalytic sense. The fact that the rule is broken often and is mainly a guide to unreactive species does not detract from its usefulness - it remains an invaluable guide for the classification of compounds and as a predictor of structures and mechanism. For example, 18-electron compounds almost invariably react with donor ligands via pathways that are dissociative, whereas most catalytic processes rely on agents that react via associative steps. On the other hand, 18-electron compounds can be highly reactive toward electrophiles such as protons, and such reactions are associative in mechanism, being acid-base like processes.

Violations to the 18-electron rule can be classified according to four main classes of complexes:

Bulky ligands

Bulky ligands can preclude the approach of additional ligands that would allow the metal to achieve the 18 electron configuration. Similarly, it is often not possible to fit sufficient numbers of ligands around early metals to get to 18 electrons. Examples:

Ti(neopentyl)₄ (8 VE)
Cp*₂Ti(C₂H₄) (16 VE)
V(CO)₆ (17 VE)
Cp*Cr(CO)₃ (17 VE)
Pt(P^tBu₃)₂ (14 VE)
Co(norbornyl)₄ (11 VE)
[FeCp₂]⁺ (17 VE)

Sometimes such complexes engage in agostic interactions with the hydrocarbon framework of the bulky ligand. For example:

W(CO)₃[P(C₆H₁₁)₃]₂ has 16 VE but clearly has a short bonding contact between one C-H bond and the W center.
Cp(PMe₃)V(CHCMe₃) (14 VE, diamagnetic) has a short V-H bond with the 'alkylidene-H', so the description of the compound is somewhere between Cp(PMe₃)V(CHCMe₃) and Cp(PMe₃)V(H)(CCMe₃).

High spin complexes

High spin metal complexes have singly-occupied orbitals and may not have any empty orbitals which ligands could donate electron density into. Generally, there are few or no π-acidic ligands in the complex. These singly-occupied orbitals can combine with the singly-occupied orbitals of radical ligands (e.g. oxygen), or addition of a strong field ligand can cause electron-pairing, thus creating a vacant orbital that it can donate into. Examples:

CrCl₃(THF)₃ (15 VE)
[Mn(H₂O)₆]²⁺ (17 VE)
[Cu(H₂O)₆]²⁺ (21 VE, see comments below)

Complexes containing strongly pi-donating ligands often violate the 18-electron rule. These ligands include fluoride (F^-), oxide (O^2-), nitride (N^3-), alkoxide (RO^-), and imide (oxide (RN^2-). Examples:

[CrO₄]^2- (16 VE)
Mo(=NR)₂Cl₂ (12 VE)

In the latter case, there is substantial donation of the nitrogen lone pairs to the Mo (so the compound could also be described as a 16 VE compound). This can be seen from the short Mo-N bond length, and from the angle Mo - N - C(R), which is nearly 180°. Counter-examples:

trans-WO₂(Me₂PCH₂CH₂PMe₂) (18 VE)
Cp*ReO₃ (18 VE)

In these cases the M=O bonds are "pure" double bonds (i.e. no donation of the lone pairs of the oxygen to the metal), as reflected in the relatively long bond distances.

'Inaccessible' high energy orbitals

"Late" transition metals, located toward the right half of the periodic table, often violate the 18-electron rule. Here, one or more of the d-orbitals is of high energy, and does not accept electrons. Examples:

[PtCl₄]^2- (16 VE)
CuCl(CO) (14 VE)
Vaska's compound - [IrCl(CO)(PPh₃)₂] (16 VE)
Zeise's salt - [PtCl₃(η²-C₂H₄)]^- (16 VE)

Combinations

The above factors can sometimes combine. Examples include

Cp*VOCl₂ (14 VE)
TiCl₄ (8 VE)

Higher electron counts

Some complexes have more than 18 electrons. Examples:

Cobaltocene (19 VE)
Nickelocene (20 VE)
The hexaaqua copper(II) ion [Cu(H₂O)₆]²⁺ (21 VE)

Often cases where complexes have more than 18 valence electrons are attributed to electrostatic forces - the metal attracts ligands to itself to try and counterbalance its positive charge, and the number of electrons it ends up with is unimportant. In the case of the metallocenes, the chelating nature of the cyclopentadienyl ligand stabilizes its bonding to the metal. Somewhat satisfying are the two following observations: (i) cobaltocene is a strong electron donor, readily forming the 18-electron cobaltocenium cation and (ii) nickelocene tends to react with substrates to give 18-electron complexes, e.g. CpNiCl(PR₃) and free CpH.

References

Langmuir, I. Types of Valence. Science 1921, 54, 59–67.
Mitchell, P. R.; Parish, J. The Eighteen-Electron Rule. J. Chem. Educ. 1969, 46, 811–814.
Jensen, W. B. The origin of the 18-electron rule. J. Chem. Educ. 2005, 82, 28.