Editing Oxidation state (section)

=== Ambiguous oxidation states ===
[[Lewis formula]]e are rule-based approximations of chemical reality, as are [[Electronegativity#Allen electronegativity|Allen electronegativities]]. Still, oxidation states may seem ambiguous when their determination is not straightforward. If only an experiment can determine the oxidation state, the rule-based determination is ambiguous (insufficient). There are also truly [[dichotomy|dichotomous]] values that are decided arbitrarily.

==== Oxidation-state determination from resonance formulas ====
Seemingly ambiguous oxidation states are derived from a set of [[resonance]] formulas of equal weights for a molecule having heteronuclear bonds where the atom connectivity does not correspond to the number of two-electron bonds dictated by the 8&nbsp;−&nbsp;''N'' rule.<ref name="10.1515/pac-2013-0505" />{{rp|1027}} An example is [[Disulfur dinitride|S<sub>2</sub>N<sub>2</sub>]] where four resonance formulas featuring one S=N double bond have oxidation states +2 and +4 for the two sulfur atoms, which average to +3 because the two sulfur atoms are equivalent in this square-shaped molecule.

==== A physical measurement is needed to determine oxidation state ====
* when a [[non-innocent ligand|non-innocent]] [[ligand]] is present, of hidden or unexpected redox properties that could otherwise be assigned to the central atom. An example is the [[nickel]] [[metal dithiolene complex|dithiolate]] complex, {{chem|Ni(S|2|C|2|H|2|)|2|2−}}.<ref name="10.1515/pac-2013-0505" />{{rp|1056–1057}}
* when the redox ambiguity of a central atom and ligand yields dichotomous oxidation states of close stability, thermally induced [[tautomerism]] may result, as exemplified by [[manganese]] [[catecholate]], {{chem2|Mn(C6H4O2)3}}.<ref name="10.1515/pac-2013-0505" />{{rp|1057–1058}} Assignment of such oxidation states requires spectroscopic,<ref>{{cite book|first=C. K.|last=Jørgensen|contribution=Electric Polarizability, Innocent Ligands and Spectroscopic Oxidation States|title=Structure and Bonding|volume=1|pages=234–248|publisher=Springer-Verlag|location=Berlin|date=1966}}</ref> magnetic or structural data.
* when the bond order has to be ascertained along with an isolated tandem of a heteronuclear and a homonuclear bond. An example is [[thiosulfate]] {{chem|S|2|O|3|2−}} having two possible oxidation states (bond orders are in blue and formal charges in green):

::[[File:21oxstate.svg|frameless|500px]]

:The S–S distance measurement in [[thiosulfate]] is needed to reveal that this bond order is very close to 1, as in the formula on the left.

==== Ambiguous/arbitrary oxidation states ====
* when the electronegativity difference between two bonded atoms is very small (as in [[phosphorous acid|H<sub>3</sub>PO<sub>3</sub>]]). Two almost equivalent pairs of oxidation states, arbitrarily chosen, are obtained for these atoms.
* when an electronegative [[p-block]] atom forms solely homonuclear bonds, the number of which differs from the number of two-electron bonds suggested by [[Octet rule|rules]]. Examples are homonuclear finite chains like [[azide|{{chem|N|3|−}}]] (the central nitrogen connects two atoms with four two-electron bonds while only three two-electron bonds<ref>{{Cite web|url=https://chem.libretexts.org/Bookshelves/General_Chemistry/Book%3A_General_Chemistry_Supplement_(Eames)/Lewis_Bonding_Theory/The_Two-Electron_Bond|title=The Two-Electron Bond|date=June 25, 2016|website=Chemistry LibreTexts|access-date=September 1, 2020|archive-date=February 9, 2021|archive-url=https://web.archive.org/web/20210209034153/https://chem.libretexts.org/Bookshelves/General_Chemistry/Book:_General_Chemistry_Supplement_(Eames)/Lewis_Bonding_Theory/The_Two-Electron_Bond|url-status=live}}</ref> are required by the 8&nbsp;−&nbsp;''N'' rule<ref name="10.1515/pac-2013-0505" />{{rp|1027}}) or [[triiodide|{{chem|I|3|−}}]] (the central iodine connects two atoms with two two-electron bonds while only one two-electron bond fulfills the 8&nbsp;−&nbsp;''N'' rule). A sensible approach is to distribute the ionic charge over the two outer atoms.<ref name="10.1515/pac-2013-0505" /> Such a placement of charges in a [[polysulfide]] {{chem|S|''n''|2−}} (where all inner sulfurs form two bonds, fulfilling the 8&nbsp;−&nbsp;''N'' rule) follows already from its Lewis structure.<ref name="10.1515/pac-2013-0505" />
* when the isolated tandem of a heteronuclear and a homonuclear bond leads to a bonding compromise in between two Lewis structures of limiting bond orders. An example is [[nitrous oxide|N<sub>2</sub>O]]:

::[[File:18oxstate.svg|frameless|420px]]

:The typical oxidation state of nitrogen in N<sub>2</sub>O is +1, which also obtains for both nitrogens by a molecular orbital approach.<ref name="10.1002/anie.201407561" /> The formal charges on the right comply with electronegativities, which implies an added ionic bonding contribution. Indeed, the estimated N−N and N−O bond orders are 2.76 and 1.9, respectively,<ref name="10.1515/pac-2013-0505" /> approaching the formula of integer bond orders that would include the ionic contribution explicitly as a bond (in green):

::[[File:19oxstate.svg|frameless|280px]]

:Conversely, formal charges against electronegativities in a Lewis structure decrease the bond order of the corresponding bond. An example is [[carbon monoxide]] with a bond-order estimate of 2.6.<ref>{{cite journal|first1=R. J.|last1=Martinie|first2=J. J.|last2=Bultema|first3=M. N. V.|last3=Wal|first4=B. J.|last4=Burkhart|first5=D. A. V.|last5=Griend|first6=R. L.|last6=DeCock|title=Bond order and chemical properties of BF, CO, and N<sub>2</sub>|journal=J. Chem. Educ.|volume=88|date=2011|issue=8|pages=1094–1097|doi=10.1021/ed100758t|bibcode=2011JChEd..88.1094M}}</ref>