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Theoretically it is said that the compound can show oxidation states in the interval $[n,n-8]$ where $n$ is the number of valence electrons.

Is there any compound in which oxygen shows +1/2 oxidation state. If so, then please provide an example.

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    $\begingroup$ $\ce{O2+[PtF6]-}$ is an example. $\endgroup$ – Ivan Neretin Jul 10 '16 at 15:54
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    $\begingroup$ And a famous one at that. Its synthesis heralded the similar synthesis with $\ce{Xe}$ in place of molecular oxygen, and thus the coming of noble-gas chemistry. $\endgroup$ – Oscar Lanzi Jul 16 '16 at 0:18
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    $\begingroup$ The rule doesn't work with d-elements that good. FYI, Mn shows oxidation states -3 ... +7 afaik except -2 and for Iridium it's -3..+8 .... $\endgroup$ – permeakra Aug 9 '16 at 18:56
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Yes. The dioxygenyl ion, $\ce{O_{2}^+}$, is a rarely-encountered oxycation in which both oxygen atoms have a formal oxidation state of +1/2. It is formally derived from oxygen by the removal of an electron:

$$\ce{O_{2} → O_{2}^+ + e^{-}}$$

Source

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