Electron counting

In chemistry, electron counting is a formalism for assigning a number of valence electrons to individual atoms in a molecule. It is used for classifying compounds and for explaining or predicting their electronic structure and bonding. Many rules in chemistry rely on electron-counting:

Octet rule is used with Lewis structures for main group elements, especially the lighter ones such as carbon, nitrogen, and oxygen,
18-electron rule in inorganic chemistry and organometallic chemistry of transition metals,
Hückel's rule for the π-electrons of aromatic compounds,
Polyhedral skeletal electron pair theory for polyhedral cluster compounds, including transition metals and main group elements and mixtures thereof, such as boranes.

Atoms are called "electron-deficient" when they have too few electrons as compared to their respective rules, or "hypervalent" when they have too many electrons. Since these compounds tend to be more reactive than compounds that obey their rule, electron counting is an important tool for identifying the reactivity of molecules. While the counting formalism considers each atom separately, these individual atoms do not generally exist as free species.

Counting rules

Two methods of electron counting are "neutral counting" and "ionic counting". Both approaches give the same result.

The neutral counting approach assumes the molecule or fragment being studied consists of purely covalent bonds. It was popularized by Malcolm Green along with the L and X ligand notation. It is usually considered easier especially for low-valent transition metals.
The "ionic counting" approach assumes purely ionic bonds between atoms.

It is important, though, to be aware that most chemical species exist between the purely covalent and ionic extremes.

Neutral counting

Neutral counting assumes each bond is equally split between two atoms.
This method begins with locating the central atom on the periodic table and determining the number of its valence electrons. One counts valence electrons for main group elements differently from transition metals, which use d electron count.
One is added for every halide or other anionic ligand which binds to the central atom through a sigma bond.
Two is added for every lone pair bonding to the metal. Unsaturated hydrocarbons such as alkenes and alkynes are considered Lewis bases. Similarly Lewis [acids and bases|Lewis] and Bronsted acids contribute nothing.
One is added for each homoelement bond.
One is added for each negative charge, and one is subtracted for each positive charge.

Ionic counting

Ionic counting assumes unequal sharing of electrons in the bond. The more electronegative atom in the bond gains electron lost from the less electronegative atom.
This method begins by calculating the number of electrons of the element, assuming an oxidation state.
Two is added for every halide or other anionic ligand which binds to the metal through a sigma bond.
Two is added for every lone pair bonding to the metal. Similarly Lewis and Bronsted acids contribute nothing.
For unsaturated ligands such as alkenes, one electron is added for each carbon atom binding to the metal.

Electrons donated by common fragments

"Special cases"

The numbers of electrons "donated" by some ligands depends on the geometry of the metal-ligand ensemble. An example of this complication is the M–NO entity. When this grouping is linear, the NO ligand is considered to be a three-electron ligand. When the M–NO subunit is strongly bent at N, the NO is treated as a pseudohalide and is thus a one electron. The situation is not very different from the η³ versus the η¹ allyl. Another unusual ligand from the electron counting perspective is sulfur dioxide.

Examples

H₂O

For a water molecule, using both neutral counting and ionic counting result in a total of 8 electrons.

Atom	Electrons contributed	Electron count
H^.	1 electron × 2	2 electrons
O	6 electrons	6 electrons
		Total = 8 electrons

The neutral counting method assumes each OH bond is split equally. Thus both hydrogen atoms have an electron count of one. The oxygen atom has 6 valence electrons. The total electron count is 8, which agrees with the octet rule.

Atom	Electrons contributed	Electron count
H⁺	none	0 electron
O²⁻	8 electrons	8 electrons
		Total = 8 electrons

With the ionic counting method, the more electronegative oxygen will gain electrons donated by the two hydrogen atoms in the two OH bonds to become O²⁻. It now has 8 total valence electrons, which obeys the octet rule.

CH₄, for the central C
H₂S, for the central S
SCl₂, for the central S
SF₆, for the central S
RuCl₂(bpy)₂

RuCl₂₂ is an octahedral metal complex with two bidentate 2,2′-bipyridine ligands and two chloride ligands.

Metal/ligand	Electrons contributed	Electron count
Ru	d⁸	8 electrons
bpy	4 electrons × 2	8 electrons
Cl·	1 electron × 2	2 electrons
		Total = 18 electrons

In the neutral counting method, the Ruthenium of the complex is treated as Ru. It has 8 d electrons to contribute to the electron count. The two bpy ligands are L-type ligand neutral ligands, thus contributing two electrons each. The two chloride ligands halides and thus 1 electron donors, donating 1 electron each to the electron count. The total electron count of RuCl₂₂ is 18.

Metal/ligand	Electrons contributed	Number of electrons
Ru	d⁶	6 electrons
bpy	4 electrons × 2	8 electrons
Cl⁻	2 electrons × 2	4 electrons
		Total = 18 electrons

In the ionic counting method, the Ruthenium of the complex is treated as Ru. It has 6 d electrons to contribute to the electron count. The two bpy ligands are L-type ligand neutral ligands, thus contributing two electrons each. The two chloride ligands are anionic ligands, thus donating 2 electrons each to the electron count. The total electron count of RuCl₂₂ is 18, agreeing with the result of neural counting.

TiCl₄, for the central Ti
Fe(CO)₅
Ferrocene, (C₅H₅)₂Fe, for the central Fe: