Electron counting

Last updated

Electron counting is a formalism used for classifying compounds and for explaining or predicting electronic structure and bonding. [1] Many rules in chemistry rely on electron-counting:

Chemical bond lasting attraction between atoms that enables the formation of chemical compounds

A chemical bond is a lasting attraction between atoms, ions or molecules that enables the formation of chemical compounds. The bond may result from the electrostatic force of attraction between oppositely charged ions as in ionic bonds or through the sharing of electrons as in covalent bonds. The strength of chemical bonds varies considerably; there are "strong bonds" or "primary bonds" such as covalent, ionic and metallic bonds, and "weak bonds" or "secondary bonds" such as dipole–dipole interactions, the London dispersion force and hydrogen bonding.


Octet rule Chemical rule of thumblets

The octet rule is a chemical rule of thumb that reflects observation that 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 rule is especially applicable to carbon, nitrogen, oxygen, and the halogens, but also to metals such as sodium or magnesium.

Lewis structures, also known as Lewis dot diagrams, 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 and the lone pairs of electrons that may exist in the molecule. A Lewis structure can be drawn for any covalently bonded molecule, as well as coordination compounds. The Lewis structure was named after Gilbert N. Lewis, who introduced it in his 1916 article The Atom and the Molecule. Lewis structures extend the concept of the electron dot diagram by adding lines between atoms to represent shared pairs in a chemical bond.

Carbon Chemical element with atomic number 6

Carbon is a chemical element with the symbol C and atomic number 6. It is nonmetallic and tetravalent—making four electrons available to form covalent chemical bonds. It belongs to group 14 of the periodic table. Three isotopes occur naturally, 12C and 13C being stable, while 14C is a radionuclide, decaying with a half-life of about 5,730 years. Carbon is one of the few elements known since antiquity.

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.

Counting rules

Two methods of electron counting are popular and both give the same result.

Malcolm Leslie Hodder Green is Emeritus Professor of inorganic chemistry at the University of Oxford. He has made many contributions to organometallic chemistry.

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

Neutral counting

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.

A halide is a binary phase, of which one part is a halogen atom and the other part is an element or radical that is less electronegative than the halogen, to make a fluoride, chloride, bromide, iodide, astatide, or theoretically tennesside compound. The alkali metals combine directly with halogens under appropriate conditions forming halides of the general formula, MX. Many salts are halides; the hal- syllable in halide and halite reflects this correlation. All Group 1 metals form halides that are white solids at room temperature.

Ionic counting

E.g. for a Fe2+ has 6 electrons
S2− has 8 electrons

Electrons donated by common fragments

LigandElectrons contributed
(neutral counting)
Electrons contributed
(ionic counting)
Ionic equivalent
X 12X; X = F, Cl, Br, I
H 12H
H 10H+
O 24O2−
N 36N3−
NR3 22NR3; R = H, alkyl, aryl
CR2 24CR2−
Ethylene 22C2H4
cyclopentadienyl 56C
benzene 66C6H6

"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 η3 versus the η1 allyl. Another unusual ligand from the electron counting perspective is sulfur dioxide.


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)
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 pseudotetrahedral if one considers the two lone pairs.
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.
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.
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.
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.
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 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), 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!

See also

Related Research Articles

Covalent bond chemical bond that involves the sharing of electron pairs between atoms

A covalent bond, also called a molecular bond, is a chemical bond that involves the sharing of electron pairs between atoms. These electron pairs are known as shared pairs or bonding pairs, and the stable balance of attractive and repulsive forces between atoms, when they share electrons, is known as covalent bonding. For many molecules, the sharing of electrons allows each atom to attain the equivalent of a full outer shell, corresponding to a stable electronic configuration. In organic chemistry covalent bonds are much more common than ionic bonds.

Coordination complex molecule or ion containing ligands covalently bonded to a central atom

In chemistry, a coordination complex consists of a central atom or ion, which is usually metallic and is called the coordination centre, and a surrounding array of bound molecules or ions, that are in turn known as ligands or complexing agents. Many metal-containing compounds, especially those of transition metals, are coordination complexes. A coordination complex whose centre is a metal atom is called a metal complex.

Inorganic chemistry deals with the synthesis and behavior of inorganic and organometallic compounds. This field covers all chemical compounds except the myriad organic compounds, which are the subjects of organic chemistry. The distinction between the two disciplines is far from absolute, as there is much overlap in the subdiscipline of organometallic chemistry. It has applications in every aspect of the chemical industry, including catalysis, materials science, pigments, surfactants, coatings, medications, fuels, and agriculture.

Metallocene class of chemical compounds

A metallocene is a compound typically consisting of two cyclopentadienyl anions (C
, abbreviated Cp) bound to a metal center (M) in the oxidation state II, with the resulting general formula (C5H5)2M. Closely related to the metallocenes are the metallocene derivatives, e.g. titanocene dichloride, vanadocene dichloride. Certain metallocenes and their derivatives exhibit catalytic properties, although metallocenes are rarely used industrially. Cationic group 4 metallocene derivatives related to [Cp2ZrCH3]+ catalyze olefin polymerization.

The oxidation state, sometimes referred to as oxidation number, describes the degree of oxidation of an atom in a chemical compound. Conceptually, the oxidation state, which may be positive, negative or zero, is the hypothetical charge that an atom would have if all bonds to atoms of different elements were 100% ionic, with no covalent component. This is never exactly true for real bonds.

A coordinate covalent bond, also known as a dative bond or coordinate bond is a kind of 2-center, 2-electron covalent bond in which the two electrons derive from the same atom. The bonding of metal ions to ligands involves this kind of interaction. This type of interaction is central to Lewis acid-base theory.

Valence electron outer shell electron that is associated with an atom, and that can participate in the formation of a chemical bond if the outer shell is not closed

In chemistry, a valence electron is an outer shell electron that is associated with an atom, and that can participate in the formation of a chemical bond if the outer shell is not closed; in a single covalent bond, both atoms in the bond contribute one valence electron in order to form a shared pair. The presence of valence electrons can determine the element's chemical properties, such as its valence—whether it may bond with other elements and, if so, how readily and with how many. For a main group element, a valence electron can exist only in the outermost electron shell; in a transition metal, a valence electron can also be in an inner shell.

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 pentachloride (PCl5), sulfur hexafluoride (SF6), chlorine trifluoride (ClF3), the chlorite (ClO2) ion, and the triiodide (I3) ion are examples of hypervalent molecules.

VSEPR theory theoretical model used in chemistry

Valence shell electron pair repulsion theory, or 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 theory after its two main developers, Ronald Gillespie and Ronald Nyholm. The premise of VSEPR is that the valence electron pairs surrounding an atom tend to repel each other and will, therefore, adopt an arrangement that minimizes this repulsion, thus determining the molecule's geometry. Gillespie has emphasized that the electron-electron repulsion due to the Pauli exclusion principle is more important in determining molecular geometry than the electrostatic repulsion.

In chemistry, orbital hybridisation is the concept of mixing atomic orbitals into new hybrid orbitals suitable for the pairing of electrons to form chemical bonds in valence bond theory. Hybrid orbitals are very useful in the explanation of molecular geometry and atomic bonding properties and are symmetrically disposed in space. Although sometimes taught together with the valence shell electron-pair repulsion (VSEPR) theory, valence bond and hybridisation are in fact not related to the VSEPR model.

Isolobal principle

The isolobal principle is a strategy used in organometallic chemistry to relate the structure of organic and inorganic molecular fragments in order to predict bonding properties of organometallic compounds. Roald Hoffmann described molecular fragments as isolobal "if the number, symmetry properties, approximate energy and shape of the frontier orbitals and the number of electrons in them are similar – not identical, but similar." One can predict the bonding and reactivity of a lesser-known species from that of a better-known species if the two molecular fragments have similar frontier orbitals, the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO). Isolobal compounds are analogues to isoelectronic compounds that share the same number of valence electrons and structure. A graphic representation of isolobal structures, with the isolobal pairs connected through a double-headed arrow with half an orbital below, is found in Figure 1.

In chemistry, the valence or valency of an element is a measure of its combining power with other atoms when it forms chemical compounds or molecules. The concept of valence was developed in the second half of the 19th century and helped successfully explain the molecular structure of inorganic and organic compounds. The quest for the underlying causes of valence led to the modern theories of chemical bonding, including the cubical atom (1902), Lewis structures (1916), valence bond theory (1927), molecular orbitals (1928), valence shell electron pair repulsion theory (1958), and all of the advanced methods of quantum chemistry.

In chemistry, a cluster is an ensemble of bound atoms or molecules that is intermediate in size between a molecule and a bulk solid. Clusters exist of diverse stoichiometries and nuclearities. For example, carbon and boron atoms form fullerene and borane clusters, respectively. Transition metals and main group elements form especially robust clusters. Clusters can also consist solely of a certain kind of molecules, such as water clusters.

Hapticity coordination of a ligand to a metal center via an uninterrupted and contiguous series of atoms.

Hapticity is the coordination of a ligand to a metal center via an uninterrupted and contiguous series of atoms. The hapticity of a ligand is described with the Greek letter η ('eta'). For example, η2 describes a ligand that coordinates through 2 contiguous atoms. In general the η-notation only applies when multiple atoms are coordinated. In addition, if the ligand coordinates through multiple atoms that are not contiguous then this is considered denticity, and the κ-notation is used once again. When naming complexes care should be taken not to confuse η with μ ('mu'), which relates to bridging ligands.

The 18-electron rule is a rule used primarily for predicting and rationalizing formulas for stable metal complexes, especially organometallic compounds. The rule is based on the fact that the valence shells of transition metals consist of nine valence orbitals, which collectively can accommodate 18 electrons as either bonding or nonbonding electron pairs. This means that, the combination of these nine atomic orbitals with ligand orbitals creates nine molecular orbitals that are either metal-ligand bonding or non-bonding. When a metal complex has 18 valence electrons, it is said to have achieved the same electron configuration as the noble gas in the period. The rule and its exceptions are similar to the application of the octet rule to main group elements. The rule is not helpful for complexes of metals that are not transition metals, and interesting or useful transition metal complexes will violate the rule because of the consequences deviating from the rule bears on reactivity. The rule was first proposed by American chemist Irving Langmuir in 1921.

In chemistry, crystallography, and materials science, the coordination number, also called ligancy, of a central atom in a molecule or crystal is the number of atoms, molecules or ions bonded to it. The ion/molecule/atom surrounding the central ion/molecule/atom is called a ligand. This number is determined somewhat differently for molecules than for crystals.

The covalent bond classification (CBC) method is also referred to as the LXZ notation. It was published by M. L. H. Green in the mid-1990s as a solution for the need to describe covalent compounds such as organometallic complexes in a way that is not prone to limitations resulting from the definition of oxidation state. Instead of simply assigning a charge to an atom in the molecule, the covalent bond classification method analyzes the nature of the ligands surrounding the atom of interest, which is often a transition metal. According to this method, there are three basic types of interactions that allow for coordination of the ligand. The three types of interaction are classified according to whether the ligating group donates two, one, or zero electrons. These three classes of ligands are respectively given the symbols L, X and Z.

In covalent bond classification, a Z-type ligand refers to a ligand that accepts two electrons from the metal center. This is in contrast to X-type ligands, which form a bond with the ligand and metal center each donating one electron, and L-type ligands, which form a bond with the ligand donating two electrons. Typically, these Z-type ligands are Lewis acids, or electron acceptors. They are also known as zero-electron reagents.


  1. Parkin, Gerard (2006). "Valence, Oxidation Number, and Formal Charge: Three Related but Fundamentally Different Concepts". Journal of Chemical Education. 83: 791. Bibcode:2006JChEd..83..791P. doi:10.1021/ed083p791. ISSN   0021-9584 . Retrieved 2009-11-10.
  2. Green, M. L. H. (1995-09-20). "A new approach to the formal classification of covalent compounds of the elements". Journal of Organometallic Chemistry . 500 (1–2): 127–148. doi:10.1016/0022-328X(95)00508-N. ISSN   0022-328X.
  3. "MLXZ". www.columbia.edu.