Is there an example of a closed shell molecule with a permanent ground state magnetic dipole?

It seems that molecules of point group C$\_{n}$ and C$\_{nh}$ can in principle support a permanent magnetic dipole moment (Barron, 2004). However, I cannot think of any closed shell molecules that physically have a magnetic dipole in the ground state.


Is this ever observed, and can you give an example of such a case?


Citation: Barron, Laurence D. Molecular light scattering and optical activity. Cambridge University Press, 2004.




**Updated 4/6/2017:** It turns out that singlet ($^1\Delta\_g$) molecular oxygen is [paramagnetic due to orbital angular momentum only](https://en.wikipedia.org/wiki/Singlet_oxygen#Paramagnetism_due_to_orbital_angular_momentum), as all electrons are paired. It has a magnetic dipole moment of $1\hbar$ and can be determined experimentally. (This makes sense from a computational perspective, given that the lowest restricted Hartree Fock solution of [singlet oxygen is always complex](http://aip.scitation.org/doi/10.1063/1.4905120), and only complex wave functions yield non-zero expectation values of orbital angular momentum.) 




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For closed shell (even number of electrons) molecules the answer is no.


After a little more reading, I found the answer. The reason is that the magnetic dipole is odd under time reversal (Table 4.1, p. 218 in Barron, 2004).


Apparently, (Barron, p. 221) "the expectation value of a time-odd operator [e.g. magnetic dipole] vanishes for states invariant under time reversal, which can always be constructed for an even electron system and hence any nondegenerate state".


I do not believe this applies to transition properties, however, as we can see magnetic dipole allowed transitions.


Citation: Barron, Laurence D. Molecular light scattering and optical activity. Cambridge University Press, 2004.


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