18-electron rule

The 18-electron rule is a chemical rule of thumb used primarily for predicting and rationalizing formulas for stable transition metal complexes, especially organometallic compounds. The rule is based on the fact that the valence orbitals in the electron configuration of transition metals consist of five (n−1)d orbitals, one ns orbital, and three np orbitals, where n is the principal quantum number. These orbitals can collectively accommodate 18 electrons as either bonding or non-bonding 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, lending stability to the complex. Transition metal complexes that deviate from the rule are often interesting or useful because they tend to be more reactive. The rule is not helpful for complexes of metals that are not transition metals. The rule was first proposed by American chemist Irving Langmuir in 1921.

The rule usefully predicts the formulas 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-acceptor ligands (also known as π-acids). This kind of ligand exerts a very strong ligand field, which lowers the energies of the resultant molecular orbitals so that they are 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.

Compounds that obey the 18-electron rule are typically "exchange inert". Examples include [Co(NH₃)₆]Cl₃, 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.

Computational findings suggest valence p-orbitals on the metal participate in metal-ligand bonding, albeit weakly. However, Weinhold and Landis within the context of natural bond orbitals do not count the metal p-orbitals in metal-ligand bonding, although these orbitals are still included as polarization functions. This results in a duodectet (12-electron) rule for five d-orbitals and one s-orbital only.

The current consensus in the general chemistry community is that unlike the singular octet rule for main group elements, transition metals do not strictly obey either the 12-electron or 18-electron rule, but that the rules describe the lower bound and upper bound of valence electron count respectively. Thus, while transition metal d-orbital and s-orbital bonding readily occur, the involvement of the higher energy and more spatially diffuse p-orbitals in bonding depends on the central atom and coordination environment.

π-donor or σ-donor ligands with small interactions 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 Δ_oct makes filling e_g* possible (>18 e⁻) and π-donor ligands can make t_2g antibonding (<18 e⁻). These types of ligand are located in the low-to-medium part of the spectrochemical series. For example: [TiF₆]²⁻ (Ti(IV), d⁰, 12 e⁻), [Co(NH₃)₆]³⁺ (Co(III), d⁶, 18 e⁻), [Cu(OH₂)₆]²⁺ (Cu(II), d⁹, 21 e⁻).