Do two hydrogens with same spin make H_2 ?

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To form molecular hydrogen (H2), hydrogen atoms must have opposite spins due to the principles of quantum mechanics and the Pauli exclusion principle. When two hydrogen atoms possess the same spin, they cannot couple to form H2. In a scenario where a gas of hydrogen atoms is polarized with all spins aligned in the same direction, the formation of H2 is not possible. The discussion specifically refers to electron spin as the critical factor in this coupling process.

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As I know from the laws of chemistry,to form H_2 the H atoms must have opposite spin.
What if they have the same spin?
I mean, can an H atom rotate to swap his spin (i'm not expert of the dynamics of spin), or there is no way to couple them?
In the case I have a gas of H with all of them polarized in the same direction is the formation of H_2 possible?
 
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What spin are you talking about? Electron spin?
 

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