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In my book there's a question:

Does $\ce{H2}$ show allotropy ? Describe its allotropes and their applications.

Wikipedia doesn't list any allotropes of $\ce{H2}$. However, when searching on the Internet, I found a few resources which call the nuclear spin isomers of dihydrogen (ortho- and para-$\ce{H2}$) "allotropes".

Can nuclear spin isomers of a compound be considered as allotropes (if there is only one element present, as is the case in $\ce{H2}$? If so, then how does the nuclear spin isomer affect their physical form/structure?

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Some peer review journal articles and an India high school textbook and various study guides do refer to the spin isomers as allotropes.

There are physical differences such as different heat capacities. See Orthohydrogen, Parahydrogen and Heavy Hydrogen for comprehensive information.

However, aside from the spin isomers, there are genuine allotropes of hydrogen. Solid hydrogen has two normal pressure allotropes, a face centered cubic and a hexagonal closest packed allotrope.

Also, at high pressure, there is metallic hydrogen.

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  • $\begingroup$ So is this a general consensus among chemistry community to consider NSI to be allotrope? Are physical difference other than structural composition sufficient to define an element as "Allotrope"(The definition of allotrope i've heard is based only on structure and rest of the physical properties as a consequences of it)? As a follow-up question:Is there any example of element in which NSIs have different physical structures/effect on structure? $\endgroup$
    – Xasel
    Jan 26, 2017 at 15:40
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    $\begingroup$ @Xasel The IUPAC definition of "allotropes" is "Different structural modifications of an element" goldbook.iupac.org/A00243.html so I would say, no, it is not a consensus. $\endgroup$
    – DavePhD
    Jan 26, 2017 at 15:45
  • $\begingroup$ @Xasel one article says "In H2, the crystal structure as a function of temperature and pressure depends upon the ortho-para (o-p) concentration. At low pressure, single molecules are in almost free-rotor states. Parahydrogen molecules are in the spherically symmetric state with rotational quantum number J=0 and cannot orientationally order, whereas o-H2 molecules are in the J=1 states and the molecules can order along crystallographic directions. Orthohydrogen has an hcp (hexagonal-closepacked) to fcc (face-centered-cubic) transition at zero pressure and 2.8 K..." $\endgroup$
    – DavePhD
    Jan 26, 2017 at 15:53
  • $\begingroup$ @Xasel journals.aps.org/prl/abstract/10.1103/PhysRevLett.63.2080 $\endgroup$
    – DavePhD
    Jan 26, 2017 at 15:53
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Apart from the sources that DavePhD listed, there is also the 1932 Nobel Prize in Physics, awarded to Werner Heisenberg:

"for the creation of quantum mechanics, the application of which has, inter alia, led to the discovery of the allotropic forms of hydrogen."

The "allotropic forms" of hydrogen mentioned here refer to the nuclear spin isomers ortho-$\ce{H2}$ and para-$\ce{H2}$. So, there is some sort of precedent for it; although I'm not sure where it originated. Heisenberg's original paper (in German) can be found at Z. Physik 1927, 43 (3-4), 172–198. Sadly, I don't know German, so I can't verify whether he used the term "allotrope" or anything similar there.

To the best of my knowledge, this usage of "allotrope" is not in common use any more. Most textbooks just use "nuclear spin isomers".

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    $\begingroup$ I wonder if eventual acceptation of NSI as allotropes would open gates for similar acceptance of different molecular states as allotropes. E.g. would be singlet O2 an oxygen allotrope if o-and p-H2 were allotropes ? $\endgroup$
    – Poutnik
    May 31, 2021 at 8:09
  • $\begingroup$ Hmmm I totally missed your comment @Poutnik. It's a slippery slope—those are just different electronic states and after that soon we might be accepting different vibrational states, or perhaps even different conformers, as allotropes... In any case, the current trend is in the opposite direction, i.e. once upon a time we called NSI allotropes and nowadays we don't, so I think we're safe. $\endgroup$ Jun 21, 2021 at 22:33

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