Editing Oxidation state (section)

=== Algorithm of assigning bonds ===
This algorithm is performed on a [[Lewis structure]] (a diagram that shows all [[valence electron]]s). Oxidation state equals the charge of an atom after each of its [[heteronuclear]] bonds has been assigned to the more [[Electronegativity#Methods of calculation|electronegative]] partner of the bond ([[#The algorithm's caveat|except when that partner is a reversibly bonded Lewis-acid ligand]]) and [[homonuclear]] bonds have been divided equally:

:[[File:1oxstate.svg|frameless|240px]]

where each "—" represents an electron pair (either shared between two atoms or solely on one atom), and "OS" is the oxidation state as a numerical variable.

After the electrons have been assigned according to the vertical red lines on the formula, the total number of valence electrons that now "belong" to each atom is subtracted from the number {{mvar|N}} of valence electrons of the neutral atom (such as 5 for nitrogen in [[Pnictogen|group 15]]) to yield that atom's oxidation state.

This example shows the importance of describing the bonding. Its summary formula, {{chem2|HNO3}}, corresponds to two [[structural isomer]]s; the [[peroxynitrous acid]] in the above figure and the more stable [[nitric acid]]. With the formula {{chem2|HNO3}}, the [[#Simple approach without bonding considerations|simple approach without bonding considerations]] yields −2 for all three oxygens and +5 for nitrogen, which is correct for nitric acid. For the peroxynitrous acid, however, both oxygens in the O–O bond have OS = −1, and the nitrogen has OS = +3, which requires a structure to understand.

[[Organic compound]]s are treated in a similar manner; exemplified here on [[functional group]]s occurring in between [[methane]] ({{chem2|CH4}}) and [[carbon dioxide]] ({{chem2|CO2}}):

:[[File:3oxstate.svg|frameless|500px]]

Analogously for [[transition-metal]] compounds; {{chem2|CrO(O2)2}} on the left has a total of 36 valence electrons (18 pairs to be distributed), and [[hexacarbonylchromium]] ({{chem2|Cr(CO)6}}) on the right has 66 valence electrons (33 pairs):

:[[File:2oxstate.svg|frameless|380px]]

A key step is drawing the Lewis structure of the molecule (neutral, cationic, anionic): Atom symbols are arranged so that pairs of atoms can be joined by single two-electron bonds as in the molecule (a sort of "skeletal" structure), and the remaining valence electrons are distributed such that sp atoms obtain an [[octet rule|octet]] (duet for hydrogen) with a priority that increases in proportion with electronegativity. In some cases, this leads to alternative formulae that differ in bond orders (the full set of which is called the [[Resonance (chemistry)|resonance formulas]]). Consider the [[sulfate]] anion ({{chem2|SO4(2-)}}) with 32 valence electrons; 24 from oxygens, 6 from sulfur, 2 of the anion charge obtained from the implied cation. The [[bond order]]s to the terminal oxygens do not affect the oxidation state so long as the oxygens have octets. Already the skeletal structure, top left, yields the correct oxidation states, as does the Lewis structure, top right (one of the resonance formulas):

:[[File:7oxstate.svg|frameless|450px]]

The bond-order formula at the bottom is closest to the reality of four equivalent oxygens each having a total bond order of 2. That total includes the bond of order {{sfrac|1|2}} to the implied cation and follows the 8&nbsp;−&nbsp;''N'' rule<ref name="10.1515/pac-2013-0505" /> requiring that the main-group atom's bond-order total equals 8&nbsp;−&nbsp;''N'' valence electrons of the neutral atom, enforced with a priority that proportionately increases with electronegativity.

This algorithm works equally for molecular cations composed of several atoms. An example is the [[ammonium]] cation of 8 valence electrons (5 from nitrogen, 4 from hydrogens, minus 1 electron for the cation's positive charge):

:[[File:5oxstate.svg|frameless|240px]]

Drawing Lewis structures with electron pairs as dashes emphasizes the essential equivalence of bond pairs and lone pairs when counting electrons and moving bonds onto atoms. Structures drawn with electron dot pairs are of course identical in every way:

:[[File:4oxstate.svg|frameless|200px]]

==== The algorithm's caveat ====
The algorithm contains a caveat, which concerns rare cases of [[transition-metal]] [[coordination complex|complexes]] with a type of [[ligand]] that is reversibly bonded as a [[Lewis acid]] (as an acceptor of the electron pair from the transition metal); termed a "Z-type" ligand in Green's [[covalent bond classification method]]. The caveat originates from the simplifying use of electronegativity instead of the [[molecular orbital|MO]]-based electron allegiance to decide the ionic sign.<ref name="10.1515/pac-2015-1204" /> One early example is the {{chem2|O2S\sRhCl(CO)([[triphenylphosphine|PPh3]])2}} complex<ref>{{cite journal|first1=K. W.|last1=Muir|first2=J. A.|last2=Ibers|title=The structure of chlorocarbonyl(sulfur dioxide)bis(triphenylphosphine)rhodium, (RhCl(CO)(SO2)(P(C6H5)3 2)|journal=Inorg. Chem.|volume=8|date=1969|issue=9|pages=1921–1928|doi=10.1021/ic50079a024}}</ref> with [[sulfur dioxide]] ({{chem2|SO2}}) as the reversibly-bonded acceptor ligand (released upon heating). The Rh−S bond is therefore extrapolated ionic against Allen electronegativities of [[rhodium]] and sulfur, yielding oxidation state +1 for rhodium:

:[[File:8oxstate.svg|frameless|450px]]