Electron counting

Electron counting is a formalism used for classifying compounds and for explaining or predicting electronic structure and bonding. Many rules in chemistry rely on electron-counting:

• Octet rule for main group elements, especially the lighter ones such as carbon, nitrogen, and oxygen,
• Eighteen electron rule in inorganic chemistry and organometallic chemistry of transition metals,
• Polyhedral skeletal electron pair theory for cluster compounds, including transition metals and main group elements such as boron including Wade's rules for polyhedral cluster compounds, including transition metals and main group elements and mixtures thereof.

Atoms that do not obey their rule are called "electron-deficient" when they have too few electrons to achieve a noble gas configuration, 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.

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Counting rules

Two styles of electron counting are popular and both give the same result. The neutral counting approach assumes the molecule or fragment being studied consists of purely covalent bonds. It is usually considered easier especially for low-valent transition metals. The "ionic counting" approach assumes purely ionic bonds between atoms. It rewards the user with a knowledge of oxidation states, which can be valuable. One can check one's calculation by counting employing both approaches, though it is important to be aware that most chemical species exist between the purely covalent and ionic extremes.

Neutral counting

• Locate the central atom on the periodic table and determine the number of its valence electrons. One counts valence electrons for main group elements differently from transition metals.

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.

• Add one for every halide or other anionic ligand which binds to the central through a sigma bond.
• Add two 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.
• Add one for each homoelement bond.
• Add one for each negative charge, and subtract one for each positive charge.

Ionic counting

• Calculate the number of electrons of the element, assuming an oxidation state

e.g. for a Fe²⁺ has 6 electrons

S^2- has 8 electrons

• Add two 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). Similarly Lewis and Bronsted acids (protons) contribute nothing.
• For unsaturated ligands such as alkenes, count the number of carbon atoms binding to the metal. Each carbon atom provides one electron.

Electrons donated by common fragments

"Special cases"

The numbers of electrons "donated" by some ligands depends on the geometry of the metal-ligand ensemble. Perhaps the most famous 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 (in the neutral counting approach). The situation is not very different from the η-3 vs. η-1 allyl. Another unusual ligand from the electron counting perspective is sulfur dioxide.

Examples of electron counting

• CH₄, for the central C

neutral counting: C contributes 4 electrons, each H radical contributes one each: 4+4(1) = 8 valence electrons

ionic counting: C^4- contributes 8 electrons, each proton contributes 0 each: 8 + 4(0) = 8 electrons.

Similar for H:

neutral counting: H contributes 1 electron, the C contributes 1 electron (the other 3 electrons of C are for the other 3 hydrogens in the molecule): 1 + 1(1) = 2 valence electrons.

ionic counting: H contributes 0 electrons (H⁺), C^4- contributes 2 electrons (per H), 0 + 1(2) = 2 valence electrons

conclusion: Methane follows the octet-rule for carbon, and the duet rule for hydrogen, and hence is expected to be a stable molecule (as we see from daily life)

• H₂S, for the central S

neutral counting: S contributes 6 electrons, each hydrogen radical contributes one each: 6+2(1) = 8 valence electrons

ionic counting: S^2- contributes 8 electrons, each proton contributes 0: 8+2(0) = 8 valence electrons

conclusion: with an octet electron count (on sulfur), we can anticipate that H₂S would be pseudotetrahedral if one considers the two lone pairs.

• SCl₂, for the central S

neutral counting: S contributes 6 electrons, each chlorine radical contributes one each: 6+2(1) = 8 valence electrons

ionic counting: S²⁺ contributes 4 electrons, each chloride anion contributes 2: 4+2(2) = 8 valence electrons

conclusion: see discussion for H₂S above. Notice that both SCl₂ and H₂S follow the octet rule - the behavior of these molecules is however quite different.

• SF₆, for the central S

neutral counting: S contributes 6 electrons, each fluorine radical contributes one each: 6+6(1) = 12 valence electrons

ionic counting: S⁶⁺ contributes 0 electrons, each fluoride anion contributes 2: 0+6(2) = 12 valence electrons

conclusion: ionic counting indicates a molecule lacking lone pairs of electrons, therefore its structure will be octahedral, as predicted by VSEPR. One might conclude that this molecule would be highly reactive - but the opposite is true: SF₆ is inert, and it is widely used in industry because of this property.

• TiCl₄, for the central Ti

neutral counting: Ti contributes 4 electrons, each chlorine radical contributes one each: 4+4(1) = 8 valence electrons

ionic counting: Ti⁴⁺ contributes 0 electrons, each chloride anion contributes two each: 0+4(2) = 8 valence electrons

conclusion: Having only 8e (vs. 18 possible), we can anticipate that TiCl₄ will be a good Lewis acid. Indeed, it reacts (in some cases violently) with water, alcohols, ethers, amines.

• Fe(CO)₅

neutral counting: Fe contributes 8 electrons, each CO contributes 2 each: 8 + 2(5) = 18 valence electrons

ionic counting: Fe(0) contributes 8 electrons, each CO contributes 2 ech: 8 + 2(5) = 18 valence electrons

conclusions: this is a special case, where ionic counting is the same as neutral counting, all fragments being neutral. Since this is an 18-electron complex, it is expected to be isolable compound.

• Ferrocene, (C₅H₅)₂Fe, for the central Fe:

neutral counting: Fe contributes 8 electrons, the 2 cyclopentadienyl-rings contribute 5 each: 8 + 2(5) = 18 electrons

ionic counting: Fe²⁺ contributes 6 electrons, the two aromatic cyclopentadienyl rings contribute 6 each: 6 + 2(6) = 18 valence electrons on iron.

conclusion: Ferrocene is expected to be an isolable compound.

Please Note: These examples show the methods of electron counting, they are a formalism, and don't have anything to do with real life chemical transformations. Most of the 'fragments' mentioned above do not exist as such; they cannot be kept in a bottle: e.g. the neutral C, the tetraanionic C, the neutral Ti, and the tetracationic Ti are not free species, they are always bound to something, for neutral C, it is commonly found in graphite, charcoal, diamond (sharing electrons with the neighboring carbons), as for Ti which can be found as its metal (where it shares its electrons with neighboring Ti atoms!), C^4- and Ti⁴⁺ 'exist' only with appropriate counterions (with which they probably share electrons). So these formalisms are only used to predict stabilities or properties of compounds!

See also

• Octet rule
• 18-Electron rule
• Electrovalency