The18-electron rule is a chemical rule of thumb used primarily for predicting and rationalizing formulas for stabletransition metal complexes, especiallyorganometallic compounds.[1] The rule is based on the fact that thevalence orbitals in theelectron configuration of transition metals consist of five (n−1)d orbitals, onens orbital, and threenp orbitals, wheren is theprincipal quantum number. These orbitals can collectively accommodate 18electrons as either bonding or non-bonding electron pairs. This means that the combination of these nineatomic orbitals withligand orbitals creates ninemolecular 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 thenoble gas in theperiod, 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 chemistIrving Langmuir in 1921.[1][2]
The rule usefully predicts the formulas forlow-spin complexes of the Cr, Mn, Fe, and Co triads. Well-known examples includeferrocene,iron pentacarbonyl,chromium carbonyl, andnickel 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 ofπ-acceptor ligands (also known as π-acids). This kind of ligand exerts a very strongligand field, which lowers the energies of the resultant molecular orbitals so that they are favorably occupied. Typical ligands includeolefins,phosphines, andCO. 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 ofπ 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 viadissociative 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 astoichiometric or acatalytic sense.
Computational findings suggest valence p-orbitals on the metal participate in metal-ligand bonding, albeit weakly.[3] However, Weinhold and Landis within the context ofnatural bond orbitals do not count the metal p-orbitals in metal-ligand bonding,[4] although these orbitals are still included aspolarization 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.[5][6] 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.[7][8]
π-donor or σ-donor ligands with small interactions with the metal orbitals lead to a weakligand field which increases the energies of t2g orbitals. Thesemolecular orbitals becomenon-bonding or weakly anti-bonding orbitals (small Δoct). 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 (>18 e−) and π-donor ligands can make t2g antibonding (<18 e−). These types of ligand are located in the low-to-medium part of thespectrochemical 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−).
In terms of metal ions, Δoct increases down a group as well as with increasingoxidation number. Strong ligand fields lead tolow-spin complexes which cause some exceptions to the 18-electron rule.
An important class of complexes that violate the 18e rule are the 16-electron complexes with metal d8 configurations. Allhigh-spin d8 metal ions areoctahedral (ortetrahedral), but thelow-spin d8 metal ions are all square planar. Important examples of square-planar low-spin d8 metal Ions are Rh(I), Ir(I), Ni(II), Pd(II), and Pt(II). At picture below is shown the splitting of the d subshell in low-spin square-planar complexes. Examples are especially prevalent for derivatives of the cobalt and nickel triads. Such compounds are typicallysquare-planar. The most famous example isVaska's complex (IrCl(CO)(PPh3)2), [PtCl4]2−, andZeise's salt [PtCl3(η2-C2H4)]−. In such complexes, the dz2 orbital is doubly occupied and nonbonding.
Manycatalytic cycles operate via complexes that alternate between 18-electron and square-planar 16-electron configurations. Examples includeMonsanto 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 can preclude the approach of the full complement of ligands that would allow the metal to achieve the 18 electron configuration.Examples:
Sometimes such complexes engage inagostic interactions with the hydrocarbon framework of the bulky ligand. For example:
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 astrong field ligand can cause electron-pairing, thus creating a vacant orbital that it can donate into.Examples:
Complexes containing strongly π-donating ligands often violate the 18-electron rule. These ligands includefluoride (F−),oxide (O2−),nitride (N3−),alkoxides (RO−), andimides (RN2−). Examples:
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 e− 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:
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.
Ligands where the coordinating atoms bearing nonbonding lone pairs often stabilize unsaturated complexes. Metal amides and alkoxides often violate the 18e rule.
The above factors can sometimes combine. Examples include
Some complexes have more than 18 electrons. Examples:
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, thechelating nature of the cyclopentadienyl ligand stabilizes its bonding to the metal. Somewhat satisfying are the two following observations: cobaltocene is a strong electron donor, readily forming the 18-electron cobaltocenium cation; and nickelocene tends to react with substrates to give 18-electron complexes, e.g. CpNiCl(PR3) and free CpH.
In the case of nickelocene, the extra two electrons are in orbitals which are weakly metal-carbon antibonding; this is why it often participates in reactions where the M–C bonds are broken and the electron count of the metal changes to 18.[9]
The 20-electron systems TM(CO)8− (TM = Sc, Y) have a cubic (Oh) equilibrium geometry and a singlet (1A1g) electronic ground state. There is one occupied valence MO with a2u symmetry, which is formed only by ligand orbitals without a contribution from the metal AOs. But the adducts TM(CO)8− (TM=Sc, Y) fulfill the 18-electron rule when one considers only those valence electrons, which occupy metal–ligand bonding orbitals.[10]
