Unknown magnetic moment of orthohydrogen Conforming to present atomic physics, the two elementary particles in hydrogen atoms can have either parallel or antiparallel magnetic moments, and the energy differences between these two kinds of hydrogen atom are the cause of the hyperfine splitting of all S terms and all P, D, F fine subterms in the line spectrum assigned to atomic hydrogen.
Conforming to present molecular physics, the two electrons in all hydrogen molecules can only have antiparallel spins and magnetic moments, while their two protons can have spins and magnetic moments either antiparallel, as in diamagnetic parahydrogen, or parallel, as in orthohydrogen with nuclear magnetism.
Still the electronic spectrum of molecular hydrogen exhibits two distinct scales, one made of singlet terms, the other of triplets, and this fact can be explained only by admitting a diamagnetic orthohydrogen with a total spin number S = 0 of its electrons, but also a paramagnetic orthohydrogen with parallel magnetic moments of its electrons S = 1, at least in the excited states of molecular hydrogen. If this paramagnetism of orthohydrogen exits also in its fundamental state, even despite the Pauli’s principle of exclusion, it should have had to be cleared up for a long time by measuring experimentally the magnetic moment of orthohydrogen.
Unfortunately, even now we have no measured magnetic moment of orthohydrogen. In the 1930’s the proton magnetic moment was measured accurately enough in a Ster-Gerlach apparatus with adequate gradients of the non-uniform magnetic field, but in the case of orthohydrogen similar attempts failed for reasons never clearly explained, although the proton and orthohydrogen molecule with nuclear magnetism have the same ratio mass/magnetic moment, therefore the same trajectory in a non-uniform magnetic field. And after discovering magnetic resonance, many magnetic moments of particles with nuclear magnetism have been exactly measured through this method, but not that of orthohydrogen. Or, if that old failure in Stern-Gerlach installation could be explained now by a possible paramagnetism of orthohydrogen, which requires magnetic gradients much smaller than those used for particles with nuclear magnetism, this absence of an orthohydrogen magnetic moment measured by magnetic resonance remains a mystery.
Moreover, such a measured magnetic moment of orthohydrogen is necessary because paramagnetic orthohydrogen is supported also by other arguments. For example, a logical one: if two kinds of hydrogen atom really exist, one of smaller energy, the other of higher energy, then we ought to have three isomers of orthohydrogen: (1) made of two atoms of smaller energy, (2) made of two atoms of higher energy, and (3) made of different atoms. Still only two isomers of molecular hydrogen exist, and this is possible only if all hydrogen molecules are made of identical atoms, but whose electrons can have magnetic moments either parallel or antiparallel.
In these circumstances, I ask two questions:


*

*Can someone give me a measured magnetic moment of orthohydrogen molecule?

*If not, what could be the possible cause of this strange omission?
 A: I think your assumption that orthohydrogen and parahydrogen should have different bulk magnetic properties is dubious.
Magnetic behavior is strongly dominated by electronic properties, because the Bohr magneton,
$$
\mu_\text{Bohr} = \frac{e\hbar}{2m_\text{electron}}
$$
is larger than the nuclear magneton
$$
\mu_\text{nuclear} = \frac{e\hbar}{2m_\text{proton}}
$$
by about three orders of magnitude. 
The difference between ortho- and para-hydrogen is the orientation of the nuclear spins; the electron spins, while the molecule is held together by a sigma bond, must be antisymmetric.
Liquid hydrogen likes to be in the $L=0,S=0$ rotational ground state of the molecule. The rotational energy is approximately given by 
$$
E_\mathrm{H_2} \approx \frac{\rm 15\,meV}{2} \cdot L\,(L+1)
$$
where $L$ is the orbital angular momentum quantum number for the two nuclei.
The odd-$L$ states are all orthohydrogen, and the even-$L$ states are all parahydrogen. This means that liquid orthohydrogen is not stable, but spontaneously converts to para; furthermore the ortho-to-para downconversion releases enough heat to boil away a substantial fraction of the liquid hydrogen. Liquid orthohydrogen isn't stable.
If liquid hydrogen, with zero angular momentum avaiable to orient nuclear magnetism, is diamagnetic, then the diamagnetism is entirely due to the electron orientation. (That seems to be consistent with discussions about magnetism in other diatomic gases, which typically discuss Hund's rules.)  Nuclear magnetism due to nuclear spins should be a tiny correction, and nuclear magnetism due to molecular orbital angular momentum should affect warm parahydrogen and warm orthohydrogen in the same way.
In your question you make a claim about a split electronic excitation spectrum for molecular hydrogen. I don't quite understand this claim.  If that confusion invalidates my answer, please reply with a reference and I'll follow up after a few days.
A: Obviously, first question above is only rhetorical, it is just an incentive for those interested to check themselves the absence in literature of a measured value of orthohydrogen magnetic moment.
As for the second one, there is no logical explanation of this strange absence, maybe excepting an unfair will to avoid the unpleasant consequences of a proved paramagnetism of orthohydrogen (see in this regard my answer to the question in my post entitled Orbital magnetic moment versus Biot-Savart law).
