# Is it possible for one specific atom in a molecule to have a non-integer oxidation state?

I am wondering if fractional oxidation states of an atom are possible. I'm not referring to cases such as $\ce{Fe3O4}$ or $\ce{Mn3O4}$ where the average oxidation state is fractional, since these actually comprise a mixture of atoms which are individually in the +2 and +3 oxidation states. What I mean is, is it possible for an individual atom in some compound to have an oxidation state of (for example) 2.5?

To me it doesn't seem possible just because of the way oxidation states are defined. However I have seen some sources which state that fractional oxidation states are possible. I would be interested in knowing if there is some weird compound that has fractional oxidation states?

Note: This is not a duplicate of Are fractional oxidation states possible? I want to know if it is possible for an individual atom in some compound to have a fractional oxidation state, not its average fractional oxidation states.

• en.wikipedia.org/wiki/… An example with true fractional oxidation states for equivalent atoms is potassium superoxide, KO2. The diatomic superoxide ion has an overall charge of −1, so each of its two oxygen atoms is assigned an oxidation state of −1⁄2, This ion can be described as a resonance hybrid of two Lewis structures, where each oxygen has oxidation state 0 in one structure and −1 in the other. – Rodriguez May 31 '16 at 8:40

It depends. Consider various radicals such as the superoxide anion $\ce{O2^{.-}}$ or $\ce{NO2^{.}}$. For both of these, we can draw simple Lewis representations:

In these structures, the oxygen atoms would have different oxidation states ($\mathrm{-I}$ and $\pm 0$ for superoxide, $\mathrm{-II}$ and $\mathrm{-I}$ for $\ce{NO2}$). That is the strict, theoretical IUPAC answer to the question.

However, we also see that the oxygens are symmetry-equivalent (homotopic) and should thus be identical. Different oxidation states violate the identity rule. For each compound, we can imagine an additional resonance structure that puts the radical on the other oxygen. (For $\ce{NO2}$, we can also draw resonance structures that locate a radical on both oxygens and another one that expands nitrogen’s octet and localises the radical there.) To better explain this physical reality theoretically, we can calculate a ‘resonance-derived average oxidation state’ which would be $-\frac{1}{2}$ for superoxide and $-\frac{3}{2}$ for $\ce{NO2}$. This is not in agreement with IUPAC’s formal definition but closer to the physical reality.

• In other words, oxidation states are just a useful model that works quite well with a few tweaks, but they are not "reality". For the superoxide "bound" electrons, the question "which of the two possible electrons is participating in the binding" doesn't make any sense, and in fact, they are in a superposition that observably changes the binding energy according to QM predictions. The simplified oxidation states work reasonably well when you pretend that the superoxide anion is one "unit" with a definite "oxidation state" of -1, considering each atom separately doesn't work quite as well. – Luaan May 31 '16 at 12:21

IUPAC recognizes that there are fractional oxidation states, but asks that you avoid writing them.

IR 4.6.1 says not to write an oxidation state "where it is not feasible or reasonable to define" because:

This avoids the use of fractional oxidation states.

Examples:

1. $\ce{O2-}$

2. $\ce{Fe4S4^3+}$

See also IR-5.4.2.2 which says "oxidation numbers are no longer recommended when naming homopolyatomic ions" because "ions such as pentabismuth(4+) (see Section IR-5.3.2.3) and dioxide(1—) (see Section IR-5.3.3.3), with fractional formal oxidation numbers, could not be named at all"

According to the IUPAC Gold Book[1], oxidation state is defined as:

A measure of the degree of oxidation of an atom in a substance. It is defined as the charge an atom might be imagined to have when electrons are counted according to an agreed-upon set of rules ...

Since the definition explicitly involves counting electrons, it is not possible for an individual atom to have a fractional oxidation state since it cannot have a non-integer number of electrons.

• Thanks for the answer. From Rodriquez comment on the superoxide ion, am I correct in saying that atoms involved in resonance structures will technically have a fractional oxidation state? – Nanoputian May 31 '16 at 8:52
• @Nanoputian I hadn't considered resonance here. I think the IUPAC definition still doesn't allow fractional oxidation states but Jan's point about them being more realistic is very true. – bon May 31 '16 at 10:27