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The 18-electron rule is a rule used primarily for predicting formulae for stable metal complexes. ^[1] The rule is based on the fact that the valence shells of transition metals consist of nine valence orbitals, which collectively can accommodate 18 electrons as either bonding or nonbonding electron pairs. This means that, the combination of these nine atomic orbitals with ligand orbitals creates nine molecular orbitals that are either metal-ligand bonding or non-bonding. When a metal complex has 18 valence electrons, it is said to have achieved the same electron configuration as the noble gas in the period. The rule and its exceptions are similar to the application of the octet rule to main group elements. The rule is not helpful for complexes of metals that are not transition metals, and in fact the majority of transition metal complexes violate the rule. The rule was first proposed by American chemist Irving Langmuir in 1921. ^[2] ^[3]

Applicability of the 18-electron rule

Although the majority of metal complexes do not satisfy the 18-electron rule, the rule usefully predicts the formulae for low-spin complexes of the Cr, Mn, Fe, and Co triads. Well-known examples include ferrocene, iron pentacarbonyl, chromium carbonyl, and nickel carbonyl.

Ligands in a complex determine the applicability of the 18-electron rule. In general, complexes that obey the rule are composed at least partly of π-acid ligands. This kind of ligand exerts a very strong ligand field, which lowers the energies of the resultant molecular orbitals and thus favorably occupied. Typical ligands include olefins, phosphines, and CO. Complexes of π-acids typically feature metal in a low-oxidation state. The relationship between oxidation state and the nature of the ligands is rationalized within the framework of π backbonding.

Consequences for reactivity

Compounds that obey the 18 VE rule are typically "exchange inert." Examples include [Co(NH₃)₅Cl]²⁺, Mo(CO)₆, and [Fe(CN)₆]^4-. In such cases, in general ligand exchange occurs via dissociative substitution mechanisms, wherein the rate of reaction is determined by the rate of dissociation of a ligand. 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 reactions.

Complexes with fewer than 18 valence electrons tend to show enhanced reactivity. Thus, the 18-electron rule is often a recipe for non-reactivity in either a stoichiometric or a catalytic sense.

Alternative analysis

In the prevalent LF analysis, the valence p orbitals on the metal participate in metal-ligand bonding, albeit weakly. Some new theoretical treatments do not count the metal p-orbitals in metal-ligand bonding,^[4] although these orbitals are still included as polarization functions. This results in a 12-electron rule which accommodates all low-spin complexes including linear 14e complexes such as Tollen's reagent and square planar 16e complexes as well as implies that such transition metal complexes are hypervalent, but has yet to be adopted by the general chemistry community.

Exceptions to the 18-electron rule

π-donor or σ-donor ligands with small intractions with the metal orbitals lead to a weak ligand field which increases the energies of t_2g orbitals. These molecular orbitals become non-bonding or weakly anti-bonding orbitals (small Δ_oct). Therefore, addition or removal of electron has little effect on complex stability. In this case, there is no restriction on the number of d-electrons and complexes with 12 -22 electrons are possible. Small Δoct makes filling eg* possible ( > 18e-) and π-donor ligands can make t_2g antibonding ( < 18 e-). These types of ligand are located in low to medium of the spectrochemical series. For example: [TiF₆]^2- (Ti⁴⁺, d⁰, 12 e), [Co(NH3)₆]³⁺ (Co³⁺, d⁶, 18 e), [Cu(OH2)₆]²⁺ (Cu²⁺, d⁹, 21 e) In tems of metal ions, Δoct increases down a group as well as increasing oxidation number. Strong ligand fields lead to low-spin complexes which cause some exceptions to 18-electron rule.

16e complexes

A popular class of complexes that violate the 18e rule are the 16e complexes with d⁸ configurations. Examples are especially prevalent for derivatives of the cobalt and nickel triads. Such compounds are typically square-planar. The most famous example is Vaska's complex (IrCl(CO)(PPh₃)₂), [PtCl₄]²⁻, and Zeise's salt [PtCl₃(η²-C₂H₄)]⁻. In such complexes, the d_z2 orbital is doubly occupied and nonbonding.

Many catalytic cycles operate via complexes that alternate between 18e and square-planar 16 configurations. Examples include Monsanto acetic acid synthesis, hydrogenations, hydroformylations, olefin isomerizations, and some alkene polymerizations.

Other violations can be classified according to the kinds of ligands on the metal center.

Bulky ligands

Bulky ligands can preclude the approach of the full complement of ligands that would allow the metal to achieve the 18 electron configuration. 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 (13 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 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 into which ligands could donate electron density. In general, 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 (O²⁻), nitride (N³⁻), alkoxide (RO⁻), and imide (oxide (RN²⁻). 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)₂ (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.

Pi-donating ligands

Ligands where the coordinating atom bear nonbonding lone pairs often stabilize unsaturated complexes. Metal amides and alkoxides often violate the 18e rule.

Combinations of effects

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 to 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. (1921). "Types of Valence". Science. 54 (1386): 59–67. Bibcode:1921Sci....54...59L. doi:10.1126/science.54.1386.59.
^ The Origin of the 18-Electron Rule William B. Jensen Journal of Chemical Education 2005 82 (1), 28 doi:10.1021/ed082p28
^ Langmuir, I. (1921). "Types of Valence". Science. 54 (1386): 59–67. Bibcode:1921Sci....54...59L. doi:10.1126/science.54.1386.59.
^ Weinhold, Frank; Landis, Clark R. (2005). Valency and bonding: A Natural Bond Orbital Donor-Acceptor Perspective. Cambridge: Cambridge University Press. pp. 447–49. ISBN 0-521-83128-8.{{cite book}}: CS1 maint: multiple names: authors list (link)

v t e Organometallic chemistry
Principles	Crystal field theory Ligand field theory 18-electron rule d electron count Polyhedral skeletal electron pair theory Isolobal principle π backbonding Dewar–Chatt–Duncanson model Hapticity spin states Agostic interaction Metal–ligand multiple bond
Reactions	Oxidative addition / reductive elimination Migratory insertion β-hydride elimination Transmetalation Carbometalation
Types of compounds	Gilman reagents Grignard reagents Cyclopentadienyl complexes Transition metal indenyl complexes Transition metal fullerene complexes Metallocenes Metal tetranorbornyls Sandwich compounds Half sandwich compounds Transition metal acyl complexes Transition metal carbene complexes Transition metal carbyne complexes Transition metal alkene complexes Transition metal alkyne complexes Transition-metal allyl complexes Transition metal carbides Arene complexes of univalent gallium, indium, and thallium
Applications	Carbonylation Cativa process Grignard reaction Monsanto process Olefin metathesis Shell higher olefin process Ziegler–Natta process
Related branches of chemistry	Organic chemistry Inorganic chemistry Bioinorganic chemistry