Electron counting
Encyclopedia
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:
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.
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 rewards the user with a knowledge of oxidation state
s, which can be valuable. One can check one's calculation by employing both approaches, though it is important to be aware that most chemical species exist between the purely covalent and ionic extremes.
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!), 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!
Chemical bond
A chemical bond is an attraction between atoms that allows the formation of chemical substances that contain two or more atoms. The bond is caused by the electromagnetic force attraction between opposite charges, either between electrons and nuclei, or as the result of a dipole attraction...
. Many rules in chemistry rely on electron-counting:
- Octet ruleOctet ruleThe octet rule is a chemical rule of thumb that states that atoms of low The octet rule is a chemical rule of thumb that states that atoms of low The octet rule is a chemical rule of thumb that states that atoms of low (The octet rule is a chemical rule of thumb that states that atoms of low (...
is used with Lewis structureLewis structureLewis structures 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...
s for main group elements, especially the lighter ones such as carbonCarbonCarbon is the chemical element with symbol C and atomic number 6. As a member of group 14 on the periodic table, it is nonmetallic and tetravalent—making four electrons available to form covalent chemical bonds...
, nitrogenNitrogenNitrogen is a chemical element that has the symbol N, atomic number of 7 and atomic mass 14.00674 u. Elemental nitrogen is a colorless, odorless, tasteless, and mostly inert diatomic gas at standard conditions, constituting 78.08% by volume of Earth's atmosphere...
, and oxygenOxygenOxygen is the element with atomic number 8 and represented by the symbol O. Its name derives from the Greek roots ὀξύς and -γενής , because at the time of naming, it was mistakenly thought that all acids required oxygen in their composition...
, - Eighteen electron rule18-Electron ruleThe 18-electron rule is a rule of thumb used primarily for predicting formulas for stable metal complexes. The rule rests on the fact that valence shells of a transition metal consists of nine valence orbitals, which collectively can accommodate 18 electrons either as nonbinding electron pairs or...
in inorganic chemistryInorganic chemistryInorganic chemistry is the branch of chemistry concerned with the properties and behavior of inorganic compounds. This field covers all chemical compounds except the myriad organic compounds , which are the subjects of organic chemistry...
and organometallic chemistryOrganometallic chemistryOrganometallic chemistry is the study of chemical compounds containing bonds between carbon and a metal. Since many compounds without such bonds are chemically similar, an alternative may be compounds containing metal-element bonds of a largely covalent character...
of transition metalTransition metalThe term transition metal has two possible meanings:*The IUPAC definition states that a transition metal is "an element whose atom has an incomplete d sub-shell, or which can give rise to cations with an incomplete d sub-shell." Group 12 elements are not transition metals in this definition.*Some...
s, - Polyhedral skeletal electron pair theoryPolyhedral skeletal electron pair theoryIn chemistry the polyhedral skeletal electron pair theory 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 Kenneth Wade and were further developed by D. M. P. Mingos and...
for cluster compounds, including transition metals and main group elements such as boronBoronBoron is the chemical element with atomic number 5 and the chemical symbol B. Boron is a metalloid. Because boron is not produced by stellar nucleosynthesis, it is a low-abundance element in both the solar system and the Earth's crust. However, boron is concentrated on Earth by the...
including Wade's rules for polyhedralPolyhedronIn elementary geometry a polyhedron is a geometric solid in three dimensions with flat faces and straight edges...
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
Noble gas
The noble gases are a group of chemical elements with very similar properties: under standard conditions, they are all odorless, colorless, monatomic gases, with very low chemical reactivity...
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.
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 was popularized by M.L.H. GreenMalcolm Green (chemist)
Malcolm Green also known as M. L. H. Green is a British Emeritus Professor of Inorganic Chemistry.Born in Eastleigh, Hampshire, he received his BSc degree from Acton Technical College in 1956 and his PhD from Imperial College of Science and Technology in 1959 under the supervision of Professor...
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 rewards the user with a knowledge of oxidation state
Oxidation state
In chemistry, the oxidation state is an indicator of the degree of oxidation of an atom in a chemical compound. The formal oxidation state is the hypothetical charge that an atom would have if all bonds to atoms of different elements were 100% ionic. Oxidation states are typically represented by...
s, which can be valuable. One can check one's calculation by 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 halideHalideA halide is a binary compound, 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, or astatide compound. Many salts are halides...
or other anionic ligand which binds to the central atom 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.
- Add one for every halide
Ionic counting
- Calculate the number of electrons of the element, assuming an oxidation state
- e.g. for a Fe2+ has 6 electrons
- S2- has 8 electrons
- Add two for every halideHalideA halide is a binary compound, 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, or astatide compound. Many salts are halides...
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.
- Add two for every halide
Electrons donated by common fragments
| Ligand | Electrons contributed (neutral counting) | Electrons contributed (ionic counting) |
|---|---|---|
| X Halide A halide is a binary compound, 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, or astatide compound. Many salts are halides... |
1 | 2 (X-; X = F, Cl, Br, I) |
| H Hydride In chemistry, a hydride is the anion of hydrogen, H−, or, more commonly, a compound in which one or more hydrogen centres have nucleophilic, reducing, or basic properties. In compounds that are regarded as hydrides, hydrogen is bonded to a more electropositive element or group... |
1 | 2 (H-) |
| H Hydrogen Hydrogen is the chemical element with atomic number 1. It is represented by the symbol H. With an average atomic weight of , hydrogen is the lightest and most abundant chemical element, constituting roughly 75% of the Universe's chemical elemental mass. Stars in the main sequence are mainly... |
1 | 0 (H+) |
| O Oxide An oxide is a chemical compound that contains at least one oxygen atom in its chemical formula. Metal oxides typically contain an anion of oxygen in the oxidation state of −2.... |
2 | 4(O2-) |
| N Nitride In chemistry, a nitride is a compound of nitrogen where nitrogen has a formal oxidation state of −3. Nitrides are a large class of compounds with a wide range of properties and applications.... |
3 | 6 (N3-) |
| NR3 Amine Amines are organic compounds and functional groups that contain a basic nitrogen atom with a lone pair. Amines are derivatives of ammonia, wherein one or more hydrogen atoms have been replaced by a substituent such as an alkyl or aryl group. Important amines include amino acids, biogenic amines,... |
2 | 2 (NR3; R = H, alkyl, aryl) |
| CR2 | 2 | 4 (CR22-) |
| Ethylene Ethylene Ethylene is a gaseous organic compound with the formula . It is the simplest alkene . Because it contains a carbon-carbon double bond, ethylene is classified as an unsaturated hydrocarbon. Ethylene is widely used in industry and is also a plant hormone... |
2 | 2 (C2H4) |
| cyclopentadienyl Cyclopentadienyl complex A cyclopentadienyl complex is a metal complex with one or more cyclopentadienyl groups . Based on the type of bonding between the metals and the cyclopentadienyl]] moieties, cyclopentadienyl complexes are classified into the following three categories: a) π-complexes, b) σ-complexes, and c) ionic... |
5 | 6(C5H5-) |
| benzene Benzene Benzene is an organic chemical compound. It is composed of 6 carbon atoms in a ring, with 1 hydrogen atom attached to each carbon atom, with the molecular formula C6H6.... |
6 | 6 (C6H6) |
"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
- CH4MethaneMethane is a chemical compound with the chemical formula . It is the simplest alkane, the principal component of natural gas, and probably the most abundant organic compound on earth. The relative abundance of methane makes it an attractive fuel...
, 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)
- H2SHydrogen sulfideHydrogen sulfide is the chemical compound with the formula . It is a colorless, very poisonous, flammable gas with the characteristic foul odor of expired eggs perceptible at concentrations as low as 0.00047 parts per million...
, 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 pseudotetrahedral if one considers the two lone pairs.
- SCl2Sulfur dichlorideSulfur dichloride is the chemical compound with the formula SCl2. This cherry-red liquid is the simplest sulfur chloride and one of the most common. It is used as a precursor to organosulfur compounds.-Chlorination of sulfur:...
, 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.
- SF6Sulfur hexafluorideSulfur hexafluoride is an inorganic, colorless, odorless, and non-flammable greenhouse gas. has an octahedral geometry, consisting of six fluorine atoms attached to a central sulfur atom. It is a hypervalent molecule. Typical for a nonpolar gas, it is poorly soluble in water but soluble in...
, 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.
- TiCl4Titanium tetrachlorideTitanium tetrachloride is the inorganic compound with the formula TiCl4. It is an important intermediate in the production of titanium metal and the pigment titanium dioxide. TiCl4 is an unusual example of a metal halide that is highly volatile...
, 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)5Iron pentacarbonylIron pentacarbonyl, also known as iron carbonyl, is the compound with formula 5. Under standard conditions Fe5 is a free-flowing, straw-colored liquid with a pungent odour. This compound is a common precursor to diverse iron compounds, including many that are useful in organic synthesis. Fe5 is...
- 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)2FeFerroceneFerrocene is an organometallic compound with the formula Fe2. It is the prototypical metallocene, a type of organometallic chemical compound consisting of two cyclopentadienyl rings bound on opposite sides of a central metal atom. Such organometallic compounds are also known as sandwich compounds...
, for the central Fe:
- neutral counting: Fe contributes 8 electrons, the 2 cyclopentadienyl-ringsCyclopentadienyl complexA cyclopentadienyl complex is a metal complex with one or more cyclopentadienyl groups . Based on the type of bonding between the metals and the cyclopentadienyl]] moieties, cyclopentadienyl complexes are classified into the following three categories: a) π-complexes, b) σ-complexes, and c) ionic...
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!), 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!