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Counting rules

Two methods of electron counting are "neutral counting" and "ionic counting". Both approaches give the same result (and can therefore be used to verify one's calculation).

• 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.

E.g. in period 2: B, C, N, O, and F have 3, 4, 5, 6, and 7 valence electrons, respectively.

E.g. in period 4: K, Ca, Sc, Ti, V, Cr, Fe, Ni have 1, 2, 3, 4, 5, 6, 8, 10 valence electrons respectively.

• 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 (e.g. each Lewis base binds with a lone pair). Unsaturated hydrocarbons such as alkenes and alkynes are considered Lewis bases. Similarly Lewis and Bronsted acids (protons) 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

• It 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

E.g. for a Fe²⁺ has 6 electrons

S²⁻ has 8 electrons

• 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 (e.g. each phosphine ligand can bind with a lone pair). Similarly Lewis and Bronsted acids (protons) contribute nothing.
• For unsaturated ligands such as alkenes, one electron is added for each carbon atom binding to the metal.

Example

H₂O

For a water molecule (H₂O), using both neutral counting and ionic counting result in a total of 8 electrons.

This figure of the water molecule shows how the electrons are distributed with the covalent counting method. The red ones are the oxygen electrons, and the blue ones are electrons from hydrogen.

Neutral counting

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

The neutral counting method assumes each OH bond is split equally (each atom gets one electron from the bond). 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.

This figure of the water molecule shows how the electrons are distributed with the ionic counting method. The red ones are the oxygen electrons, and the blue ones are electrons from hydrogen. All electrons in the OH bonds belong to the more electronegative oxygen.

Ionic counting

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

Wtih the ionic counting method, the more electronegative oxygen will gain electrons donated by the two hydrogen atoms in the two OH bonds to become O^2-. It now has 8 total valence electrons, which obeys the octet rule.

RuCl₂(bpy)₂

The geometry of cis-Dichlorobis(bipyridine)­ruthenium(II).

RuCl₂(bpy)₂ is an octahedral metal complex with two bidentate 2,2′-Bipyridine (bpy) ligands and two chloride ligands.

Neutral counting

Metal/ligand	Electrons contributed	Electron count
Ru(0)	d8 (8 d electrons)	8 electrons
bpy	4 electrons x 2	8 electrons
Cl .	1 electron x 2	2 electrons
		Total = 18 electrons

In the neutral counting method, the Ruthenium of the complex is treated as Ru(0). 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 hallides and thus 1 electron donors, donating 1 electron each to the electron count. The total electron count of RuCl₂(bpy)₂ is 18.

Ionic counting

metal/ligand	electrons contributed	number of electrons
Ru(II)	d6 (6 d electrons)	6 electrons
bpy	4 electrons x 2	8 electrons
Cl-	2 electrons x 2	4 electrons
		Total = 18 electrons

In the ionic counting method, the Ruthenium of the complex is treated as Ru(II). 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 RuCl₂(bpy)₂ is 18, agreeing with the result of neural counting.