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I wondered if this was a typo in the notes given to me. I haven’t come across notation like this before:

Branching — steps in which number of radicals increases (can lead to explosion)

$$\ce{H^. + O2 -> OH^. + O^{..}}$$

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    $\begingroup$ Alone, the oxygen atom has always two separated uncoupled electrons. It never lasts a long time like this, but It has two doublets and two independent electrons in the outer shell. This makes a total of $6$ electrons. On the other hand, the molecule $\ce{O2}$ is a double radical, with one free electron on either Oxygen atoms.. $\endgroup$
    – Maurice
    Apr 27 at 16:16
  • $\begingroup$ Ahh, that makes sense. Thank you so much for this $\endgroup$ Apr 27 at 16:42
  • $\begingroup$ It's call diradical or biradical, just saying ;) $\endgroup$
    – Mithoron
    Apr 27 at 20:51
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TL;DR: The double dot notation is reserved for lone pairs. Diradicals are depicted either with the appropriately placed superscripted dots within a structural formula (e.g. $\ce{^.O-O^.}),$ or superscripted multiplier–dot pair (e.g. $\ce{O2^{2.}}).$ The recommended notation for monooxygen 1,1-diradical is $\ce{O^{2.}}.$


First, let's sort out terminology. The recommended name for “double radical” is diradical [1, p. 1333]:

diradicals:
Molecular species having two unpaired electrons, in which at least two different electronic states with different multiplicities [electron-paired (singlet state) or electron-unpaired (triplet state)] can be identified.
E.g. $\ce{H2C^.-CH2C^.H2}$ propane-1,3-diyl (trimethylene). See biradicals.

The term biradical, although being synonymous, is less preferable [1, p. 1322]:

biradicals:
Although this term has been recommended in the past for diradicals, specialists working in the field prefer the latter term.

So, we are dealing with a diradical. You are probably familiar with a low-energy oxygen 1,2-diradical commonly depicted as $\ce{^.O-O^.}.$ What if we are dealing with a 1,1-diradical? Note that two dots next to each other signify a lone pair (remember water $(\ce{H-\overset{\Large .\!\!.}{\underset{\Large .\!\!.}{O}}-H})$ or ammonia $(\ce{:\!\!NH3})?)$ and when being used for the depiction of diradicals will inevitably cause confusion.

This seeming contradiction is resolved if you follow guidelines provided in section IR-4.6.2 Formulae of radical from Nomenclature of Inorganic Chemistry – IUPAC Recommendations 2005 (Red Book) (emphasis mine) [2, p. 66]:

A radical is an atom or molecule with one or more unpaired electrons. It may have positive, negative or zero charge. An unpaired electron may be indicated in a formula by a superscript dot. The dot is placed as a right upper index to the chemical symbol, so as not to interfere with indications of mass number, atomic number or composition. In the case of diradicals, etc., the superscript dot is preceded by the appropriate superscript multiplier. The radical dot with its multiplier, if any, precedes any charge. To avoid confusion, the multiplier and the radical dot can be placed within parentheses.

[…]

Examples:

[…]

  1. $\ce{O2^{2.}}$

[…]

  1. $\ce{NO^{(2.)-}}$
  2. $\ce{N2^{(2.)2+}}$

Here you can also find nomenclature for this species [2, p. 319]:

$\ce{O^{2.}},$ oxidanylidene, monooxygen(2•)

Following these recommendations, I would suggest to rewrite your scheme as follows:

$$\ce{H^. + O2 -> HO^. + O^{2.}}$$

References

  1. Moss, G. P.; Smith, P. A. S.; Tavernier, D. Glossary of Class Names of Organic Compounds and Reactivity Intermediates Based on Structure (IUPAC Recommendations 1995). Pure and Applied Chemistry 1995, 67 (8–9), 1307–1375. DOI: 10.1351/pac199567081307.
  2. IUPAC. Nomenclature of Inorganic Chemistry, IUPAC Recommendations 2005 (the “Red Book”), 1st ed.; Connelly, N. G., Damhus, T., Hartshorn, R. M., Hutton, A. T., Eds.; RSC Publishing: Cambridge, UK, 2005. ISBN 978-0-85404-438-2.
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  • $\begingroup$ Molecular oxygen still has unpaired electrons in its molecular orbitals. $\endgroup$
    – Miss Mulan
    Jul 9 at 12:15

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