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 The octet rule is a chemical rule of thumb that reflects the theory that main-group elements tend to bond in such a way that each atom has eight electrons in its valence shell, giving it the same electronic configuration as a noble gas. The rul ...

is used with

Lewis structure Lewis structures, also known as Lewis dot formulas, Lewis dot structures, electron dot structures, or Lewis electron dot structures (LEDS), are diagrams that show the bonding between atoms of a molecule, as well as the lone pairs of electrons t ...

s for main group elements, especially the lighter ones such as

carbon Carbon () is a chemical element with the symbol C and atomic number 6. It is nonmetallic and tetravalent—its atom making four electrons available to form covalent chemical bonds. It belongs to group 14 of the periodic table. Carbon mak ...

nitrogen Nitrogen is the chemical element with the symbol N and atomic number 7. Nitrogen is a nonmetal and the lightest member of group 15 of the periodic table, often called the pnictogens. It is a common element in the universe, estimated at se ...

, and

oxygen Oxygen is the chemical element with the symbol O and atomic number 8. It is a member of the chalcogen group in the periodic table, a highly reactive nonmetal, and an oxidizing agent that readily forms oxides with most elements as ...

, * 18-electron rule in inorganic chemistry and organometallic chemistry of

transition metal In chemistry, a transition metal (or transition element) is a chemical element in the d-block of the periodic table (groups 3 to 12), though the elements of group 12 (and less often group 3) are sometimes excluded. They are the elements that ca ...

s, *

Hückel's rule In organic chemistry, Hückel's rule predicts that a planar ring molecule will have aromatic properties if it has 4''n'' + 2 π electrons, where ''n'' is a non-negative integer. The quantum mechanical basis for its formulation was ...

for the π-electrons of

aromatic compounds Aromatic compounds, also known as "mono- and polycyclic aromatic hydrocarbons", are organic compounds containing one or more aromatic rings. The parent member of aromatic compounds is benzene. The word "aromatic" originates from the past groupin ...

, *

Polyhedral skeletal electron pair theory In chemistry the polyhedral skeletal electron pair theory (PSEPT) provides electron counting rules useful for predicting the structures of clusters such as borane and carborane clusters. The electron counting rules were originally formulated by ...

for polyhedral

cluster compound In chemistry, an atom cluster (or simply cluster) is an ensemble of bound atoms or molecules that is intermediate in size between a simple molecule and a nanoparticle; that is, up to a few nanometers (nm) in diameter. The term ''microcluster' ...

s, including transition metals and main group elements and mixtures thereof, such as

boranes Boranes is the name given to compounds with the formula BxHy and related anions. Many such boranes are known. Most common are those with 1 to 12 boron atoms. Although they have few practical applications, the boranes exhibit structures and bond ...

. Atoms are called " electron-deficient" when they have too few electrons as compared to their respective rules, or "

hypervalent In chemistry, a hypervalent molecule (the phenomenon is sometimes colloquially known as expanded octet) is a molecule that contains one or more main group elements apparently bearing more than eight electrons in their valence shells. Phosphorus pe ...

" 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.

Counting rules

Two methods 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 was popularized by Malcolm Green along with the L and X

ligand In coordination chemistry, a ligand is an ion or molecule ( functional group) that binds to a central metal atom to form a coordination complex. The bonding with the metal generally involves formal donation of one or more of the ligand's elec ...

notation. It is usually considered easier especially for low-valent transition metals. *The "ionic counting" approach assumes purely ionic bonds between atoms. One can check one's calculation by employing both approaches. It is important, though, to be aware that most chemical species exist between the purely covalent and ionic extremes.

Neutral counting

* 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. :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 Lewis may refer to: Names * Lewis (given name), including a list of people with the given name * Lewis (surname), including a list of people with the surname Music * Lewis (musician), Canadian singer * "Lewis (Mistreated)", a song by Radiohead ...

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

* 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.

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 (in the neutral counting approach). The situation is not very different from the ''η''³ versus the ''η''¹ allyl. Another unusual ligand from the electron counting perspective is sulfur dioxide.

Examples

* 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: C⁴⁻ 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⁺), C⁴⁻ 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: S²⁻ 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 pseudo-tetrahedral 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. 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 Valence shell electron pair repulsion (VSEPR) theory ( , ), is a model used in chemistry to predict the geometry of individual molecules from the number of electron pairs surrounding their central atoms. It is also named the Gillespie-Nyholm the ...

. 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 each: 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. 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 tetra-anionic C, the neutral Ti, and the tetra-cationic 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), C⁴⁻ 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!

References

{{DEFAULTSORT:Electron Counting Inorganic chemistry Chemical bonding