# Did O₄ turn out to explain why liquid oxygen appeared to defy Curie's law? If not, what does?

Wikipedia's Liquid Oxygen says:

The tetraoxygen molecule ($$\ce{O4}$$) was first predicted in 1924 by Gilbert N. Lewis, who proposed it to explain why liquid oxygen defied Curie's law. Modern computer simulations indicate that, although there are no stable $$\ce{O4}$$ molecules in liquid oxygen, $$\ce{O2}$$ molecules do tend to associate in pairs with antiparallel spins, forming transient $$\ce{O4}$$ units.

The paragraph is a bit ambiguous and doesn't rule out that the "transient $$\ce{O4}$$ units" do not explain why "liquid oxygen defied Curie's law", so I'd like to ask:

Question: Did $$\ce{O4}$$ turn out to explain why liquid oxygen appeared to defy Curie's law, at least in some way? If not, or not completely, what does?

• @andselisk I never used to for reasons mentioned in the answer there, but then one day a moderator reverted my title to MathJax which left me scratching my head. I'll try to keep track that Chemistry does it "the right way" ;-) – uhoh Jun 2 '20 at 5:11
• I found Lewis (1924): The Magnetism of Oxygen and the Molecule 0₄ – uhoh Jun 2 '20 at 5:19
• I guess there is no right or wrong way in a sense that one cannot always find a decent workaround (Unicode or re-phrasing) for the expression written with MathJax, especially complex formulas often required on Physics.SE and Math.SE. So, the rules might deviate from site to site. Since you are quite active across the SE network, it might be hard to keep the track of these preferences, so no biggie, considering how literate your questions always are, MathJax in title is the least problem and can usually easily be fixed. – andselisk Jun 2 '20 at 5:22
• It might be worth mentioning that Curie's Law is only an approximation - or, rather, it only works under certain conditions. One of the conditions is that the particles need to be magnetically isolated/independent from each other. As "in liquid oxygen, O2 molecules do tend to associate in pairs with antiparallel spins", this condition is not met. The English Wikipedia Curie's Law article is a bit of a sad affair; it only mentions that the law only applied to "many paramagnetic material" (not all!). The German one is better. Technically O4 does not violate the law, as the law does not apply. – Klaws Feb 26 at 7:43
• @Klaws thanks, I've changed it to "appeared to defy" – uhoh Feb 26 at 7:46

The observation that oxygen did not seem to strictly follow Curie's law (where $$1/\chi$$ is linear with temperature) has been known since Kammerlingh Onnes pointed it out in the 1910's. By the late 1920's, it was known that diluting the liquid with nitrogen preserved Curie's law, suggesting that it took oxygen in close proximity to other oxygen to be the issue.
Fast forward some 80 years, and the computational tools available to us provide some key insight. As one such paper, Ab Initio Molecular Dynamics Investigation of the Structure and the Noncollinear Magnetism in Liquid Oxygen: Occurrence of O$$_{4}$$ Molecular Units takes a look at structure and properties of liquid oxygen. Quoting from their conclusion:
In conclusion, we performed ab initio molecular dynamics to investigate the noncollinear magnetism of a system with an evolving atomic structure. Application to liquid oxygen provides us with a picture in which the large majority of colliding O$$_{2}$$ molecules assume structural and magnetic configurations which closely resemble those in the O$$_{4}$$ molecule. Formation of truly long-living molecular O4 units also occurs but involves a considerably smaller fraction of O$$_{2}$$ molecules.
So, it would seem that O$$_{4}$$ units, whether long lived 'molecules' or temporary short ranged order is the answer to the deviation from Curie's law in liquid oxygen.
Several comments on these O$$_{4}$$ units - first, as noted in the paper above, 'long lived' means under a picosecond (which doesn't really seem long-lived to me, but...). Further, the authors above point to The Infrared Spectrum of Bound State Oxygen Dimers in the Gas Phase to explain what they mean by O$$_{4}$$, which they call a "somewhat rigid (O$$_{2}$$)$$_{2}$$ molecule".