Electron counting

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Electron counting in the inorganic chemistry and organometallic chemistry of transition metals, is a formalism used for characterizing a compound and for understanding its electronic structure and bonding. The valence shells of a transition metal are filled when they contain 18 electrons: 2 each in the 5 d orbitals, or 10 total; 2 each in the 3 p orbitals, or 6 total; and finally 2 in the single valence shell s orbital. The electrons contributed by the metal atom or ion are summed with the electrons contributed by each ligand (i.e. those valence electrons of each ligand participating in some way in a bonding interaction with the metal, and not otherwise occupied only in intraligand bonding or in lone pairs not interacting with the metal center). A compound or ion which satisfies this 18 electron rule is considered to be qualitatively more stable than other configurations or electronic states of the molecule. The "18 electron rule" applies mostly to organometallic complexes, compounds in which there are metal-carbon bonds, such as ferrocene, iron pentacarbonyl, chromium carbonyl and nickel carbonyl. Coordination compounds without metal-carbon bonds don't usually obey the "18 electron rule."

Other electron counting rules are the octet rule for carbon, oxygen and halogen compounds and the polyhedral skeletal electron pair theory or Wade's rule for polyhedral boron compounds such as boranes and carboranes.

The so called "32-electron rule", which would be the extension of the 18-electron rule comprising lanthanide and actinide elements and their molecules, has not explained many compounds of these groups, though it may be used for predicting which molecules are likely to be somewhat stabler. The "radiuses" of the participating elements in such compounds must be considered, as d- and f-orbitals are close each other in energy.

Counting rules for ligands

Add one for every halide or other anionic ligand which binds to the metal through a sigma bond.

Add two for every lone pair bonding to the metal (e.g. each phosphine ligand can bind with a lone pair)

Nitrosyl ligands can either donate one or three electrons to a metal centre.

For unsaturated ligands such as alkenes, count the number of carbon atoms binding to the metal. Each carbon atom provides one electron. Some examples:

Ligand	Electrons contributed
Ethylene	2
Allyl	3
Butadiene	4
Cyclopentadienyl	5
Benzene	6

Examples of the 18 VE rule

There are two different approaches one can use when counting electrons, each arriving at the same total. The constituents (i.e. metal and ligands) can be regarded as ions, or as neutral species.

Using ferrocene as an example, and using the neutral approach first, the iron atom has 8 valence electrons. Each of the two cyclopentadiene radicals contributes 5 electrons, totalling 10 electrons from the ligands.

10+8=18

Using the ionic approach, iron is taken in its common oxidation state Fe²⁺, contributing only 6 valence electrons. However, the cyclopentadiene moieties are counted as aromatic cyclopentadiene anions, contributing 6 electrons each as well.

6+6+6=18

The utility of electron counting 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 create 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. 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

Cp 5 + Fe 8 + CO 4 + Fe 1 = 18

Weaknesses of the 18 VE rule

Many examples of 16 valence electron compounds exist, for instance Vaska's compound which was first made by Lauri Vaska is [IrCl(CO)(PPh_{3)2] which has}

9+1+2+(2x2)=16 VE

Many square plannar d⁸ compounds of groups 8, 9 and 10 are 16 VE compounds.

The 18 VE rule applies best to complexes where the metal is in a low oxidation state, and the metal has ligands which have strong ligand fields (e.g. alkyls, hydrides and carbonyls).

Also for the early transition metals it is the sometimes the case that it is not possible to pack the required number of ligands around a metal centre to attain an 18 VE complex. For instance imagine Ti(CO)_{7 or ZrMe2(CO)6, such compounds are impossible because it not possible to pack the required number of ligands round the metal.}

Furthermore, for metals in high oxidation states with weaker field ligands, the rule breaks down. Here the crystal field (or more correctly ligand field) energy effects are more able to influence the structure of the complexes. For instance the hexaaqua cobalt(II) ion is an octahedral complex where the cobalt has

9+(6x2)-2=19 VE

While tetrachlorocobalt(II) [CoCl₄]^2- has

9+(4x1)+2=15 VE