Does the $H_2$ in cosmic clouds virtually not radiate? I am reading the lecture notes of a friend. He has written about the cold (3-20 K) molecular $H_2$ cosmic gas, that "practically doesn't radiate, due to symmetry". Can someone confirm that $H_2$ has this feature of radiating much less electromagnetic radiation than other molecules? And how can this be explained with the symmetry of the molecule? Excuse me, for making you interpret vague statements. Nevertheless, I am very curious
 A: Yes, it is correct that cold $H_2$ radiates much less electromagnetic radiation than other molecules (for example, carbon monoxide).
Here's one way to think about this intuitively.  On macroscopic scales, electromagnetic radiation is produced when charged objects accelerate.  The atoms in a hydrogen molecule consist of charged particles (protons and electrons).  These particles are certainly capable of accelerating.  However, since momentum is conserved and the two hydrogen atoms are identical, if one of the atoms accelerates, the other atom must accelerate by exactly the same amount in the opposite direction.  Therefore, the radiation from the two atoms cancels out.  (This assumes that the molecule does not interact with other molecules, which is very reasonable in the interstellar medium.)
At molecular scale, the relative acceleration of the two atoms in a diatomic molecule becomes quantized as rotational and vibrational transitions.  But the same intuition applies: if the molecule rotates or vibrates, conservation of momentum implies that there is no net radiation.
Of course, the protons and electrons in the two atoms can still accelerate relative to each other.  Since protons and electrons have very different mass-to-charge ratios, this does produce radiation.  However, the proton-electron interaction is much stronger than the atom-atom interaction.  Using quantum mechanics, that means that the available energy levels (the electronic levels) are much more widely separated than the rotational and vibrational levels.  At the very low temperatures of the interstellar medium,  there simply isn't enough energy available to jump between different electronic levels at any significant rate.  As such, interstellar hydrogen can't produce much radiation through this process either.
