Editing Electron counting

{{Short description|Formalism used for classifying compounds}}
In [[chemistry]], '''electron counting''' is a formalism for assigning a number of [[valence electrons]] to individual atoms in a molecule.  It is used for classifying compounds and for explaining or predicting their electronic structure and [[chemical bond|bonding]].<ref>{{Cite journal
| issn = 0021-9584
| volume = 83
| pages = 791
| last = Parkin
| first = Gerard
| title = Valence, Oxidation Number, and Formal Charge: Three Related but Fundamentally Different Concepts
| journal = Journal of Chemical Education
| access-date = 2009-11-10
| year = 2006
| issue = 5
| url = http://jchemed.chem.wisc.edu/Journal/Issues/2006/May/abs791.html
|bibcode = 2006JChEd..83..791P |doi = 10.1021/ed083p791 | url-access = subscription
}}</ref>  Many rules in chemistry rely on electron-counting:

*[[Octet rule]] is used with [[Lewis structure]]s for [[main group element]]s, especially the lighter ones such as [[carbon]], [[nitrogen]], and [[oxygen]],
*[[18-electron rule]]<ref>{{Cite journal |last=Rasmussen |first=Seth C. |date=March 2015 |title=The 18-electron rule and electron counting in transition metal compounds: theory and application |url=http://link.springer.com/10.1007/s40828-015-0010-4 |journal=ChemTexts |language=en |volume=1 |issue=1 |doi=10.1007/s40828-015-0010-4 |issn=2199-3793|url-access=subscription }}</ref> in [[inorganic chemistry]] and [[organometallic chemistry]] of [[transition metal]]s,
*[[Hückel's rule]] for the [[pi electron|π-electron]]s of [[aromaticity|aromatic compounds]],
*[[Polyhedral skeletal electron pair theory]] for [[Polyhedron|polyhedral]] [[cluster compound]]s, including transition metals and main group elements and mixtures thereof, such as [[boranes]].

Atoms are called "[[electron deficiency|electron-deficient]]" when they have too few electrons as compared to their respective rules, or "[[hypervalent molecule|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.  While the counting formalism considers each atom separately, these individual atoms (with their hypothetical assigned charge) do not generally exist as free [[chemical species|species]].

==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 bond]]s. It was popularized by [[Malcolm Green (chemist)|Malcolm Green]] along with the L and X [[ligand]] notation.<ref>{{Cite journal
| doi = 10.1016/0022-328X(95)00508-N
| issn = 0022-328X
| volume = 500
| issue = 1–2
| pages = 127–148
| last = Green
| first = M. L. H.
| title = A new approach to the formal classification of covalent compounds of the elements
| journal = [[Journal of Organometallic Chemistry]]
| date = 1995-09-20
}}</ref> It is usually considered easier especially for low-valent transition metals.<ref>{{Cite journal |last=Green |first=M. L. H. |date=1995-09-20 |title=A new approach to the formal classification of covalent compounds of the elements |url=https://dx.doi.org/10.1016/0022-328X%2895%2900508-N |journal=Journal of Organometallic Chemistry |volume=500 |issue=1 |pages=127–148 |doi=10.1016/0022-328X(95)00508-N |issn=0022-328X|url-access=subscription }}</ref>

*The "ionic counting" approach assumes purely [[Ionic bonding|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 base]]s. Similarly [[Lewis acids and bases|Lewis]] and [[Bronsted acid]]s (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===

* Ionic counting 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 Fe<sup>2+</sup> has 6 electrons
:S<sup>2−</sup> 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==
{| class="wikitable"
|-
! Ligand !! Electrons contributed<br/>(neutral counting) !! Electrons contributed<br/>(ionic counting) !! Ionic equivalent
|-
| [[Halide|X]] || 1 || 2 ||X<sup>−</sup>; X = F, Cl, Br, I
|-
| [[Hydride|H]] || 1 || 2 ||H<sup>−</sup>
|-
| [[Hydrogen|H]] || 1 || 0 ||H<sup>+</sup>
|-
| [[Oxide|O]] || 2 || 4 ||O<sup>2−</sup>
|-
| [[Nitride|N]] || 3 || 6 ||N<sup>3−</sup>
|-
|[[Carbonyl ligand|CO]]
|2
|2
|CO
|-
| [[Amine|NR<sub>3</sub>]] || 2 || 2 ||NR<sub>3</sub>; R = H, alkyl, aryl
|-
| [[Alkylidene|CR<sub>2</sub>]] || 2 || 4 ||{{chem2|CR2(2−)}}
|-
| [[Ethylene]] || 2 || 2 ||C<sub>2</sub>H<sub>4</sub>
|-
| [[Cyclopentadienyl complex|cyclopentadienyl]] || 5 || 6 ||{{chem2|C5H5-}}
|-
| [[benzene]] || 6 || 6 ||C<sub>6</sub>H<sub>6</sub>
|}

==="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–[[Nitrosyl|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''<sup>3</sup> versus the ''η''<sup>1</sup> allyl.  Another unusual ligand from the electron counting perspective is [[sulfur dioxide]]. 
<!-- -SCN vs. -NCS? -->

==Examples==

* [[Water|H<sub>2</sub>O]]

For a water molecule (H<sub>2</sub>O), using both neutral counting and ionic counting result in a total of 8 electrons.
[[File:Water_molecule_covalent_counting.jpg|thumb|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 the hydrogen atoms.]]
{| class="wikitable"
|+'''Neutral counting'''
!Atom
!Electrons contributed
!Electron count
|-
|H<sup>.</sup>
|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.
[[File:Water_molecule_ionic_countin.jpg|thumb|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.]]
{| class="wikitable"
|+Ionic counting
!Atom
!Electrons contributed
!Electron count
|-
|H<sup>+</sup>
|none
|0 electron
|-
|O<sup>2-</sup>
|8 electrons
|8 electrons
|-
|
|
|'''Total = 8 electrons'''
|}
With 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<sup>2-</sup>. It now has 8 total valence electrons, which obeys the octet rule.

*[[Methane|CH<sub>4</sub>]], 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<sup>4−</sup> 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<sup>+</sup>), C<sup>4−</sup> 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)

*[[Hydrogen sulfide|H<sub>2</sub>S]], 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<sup>2−</sup> 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 H<sub>2</sub>S would be pseudo-tetrahedral if one considers the two lone pairs.

*[[Sulfur dichloride|SCl<sub>2</sub>]], for the central S
:neutral counting: S contributes 6 electrons, each chlorine radical contributes one each: 6 + 2 × 1 = 8 valence electrons
:ionic counting: S<sup>2+</sup> contributes 4 electrons, each chloride anion contributes 2: 4 + 2 × 2 = 8 valence electrons
:conclusion: see discussion for H<sub>2</sub>S above. Both SCl<sub>2</sub> and H<sub>2</sub>S follow the octet rule - the behavior of these molecules is however quite different.

*[[Sulfur hexafluoride|SF<sub>6</sub>]], for the central S
:neutral counting: S contributes 6 electrons, each fluorine radical contributes one each: 6 + 6 × 1 = 12 valence electrons
:ionic counting: S<sup>6+</sup> 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: SF<sub>6</sub> is inert, and it is widely used in industry because of this property.

* [[Cis-Dichlorobis(bipyridine)ruthenium(II)|RuCl<sub>2</sub>(bpy)<sub>2</sub>]]

[[File:RuCl2(bpy)2.jpg|thumb|The geometry of ''cis''-Dichlorobis(bipyridine)ruthenium(II).]]
RuCl<sub>2</sub>(bpy)<sub>2</sub> is an octahedral metal complex with two [[bidentate]] [[2,2′-Bipyridine]] (bpy) ligands and two chloride ligands.
{| class="wikitable"
|+'''Neutral counting'''
|'''Metal/ligand'''
|'''Electrons contributed'''
|'''Electron count'''
|-
|Ru(0)
|d<sup>8</sup> (8 d electrons)
|8 electrons
|-
|bpy
|4 electrons x 2
|8 electrons
|-
|Cl <sup>.</sup>
|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 RuCl<sub>2</sub>(bpy)<sub>2</sub> is 18.
{| class="wikitable"
|+'''Ionic counting'''
|'''metal/ligand'''
|'''electrons contributed'''
|'''number of electrons'''
|-
|Ru(II)
|d<sup>6</sup> (6 d electrons)
|6 electrons
|-
|bpy
|4 electrons x 2
|8 electrons
|-
|Cl<sup>−</sup>
|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 RuCl<sub>2</sub>(bpy)<sub>2</sub> is 18, agreeing with the result of neural counting.

* [[Titanium tetrachloride|TiCl<sub>4</sub>]], for the central Ti
:neutral counting: Ti contributes 4 electrons, each chlorine radical contributes one each: 4 + 4 × 1 = 8 valence electrons
:ionic counting: Ti<sup>4+</sup> contributes 0 electrons, each chloride anion contributes two each: 0 + 4 × 2 = 8 valence electrons
:conclusion: Having only 8e (vs. [[Eighteen electron rule|18]] possible), we can anticipate that TiCl<sub>4</sub> will be a good Lewis acid.  Indeed, it reacts (in some cases violently) with water, alcohols, ethers, amines.

* [[Iron pentacarbonyl|Fe(CO)<sub>5</sub>]]
: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|Ferrocene, (C<sub>5</sub>H<sub>5</sub>)<sub>2</sub>Fe]], for the central Fe:
:neutral counting: Fe contributes 8 electrons, the 2 [[Cyclopentadienyl complex|cyclopentadienyl-rings]] contribute 5 each: 8 + 2 × 5 = 18 electrons
:ionic counting: Fe<sup>2+</sup> 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.

<!-- A bimetallic species with sharing ligands -->
<!-- A bimetallic species with a metal-metal bond -->

==See also==

* [[d electron count]]
* [[Tolman's rule]]

==References==
{{Reflist}}

{{Electron configuration navbox}}
{{Chemical bonds}}

{{DEFAULTSORT:Electron Counting}}
[[Category:Inorganic chemistry]]
[[Category:Chemical bonding]]