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How does $\ce{H2}$ triplet state exist if there are electrons in both bonding and antibonding ($1\sigma$ and $1\sigma^*$) orbitals?

Or am I being taught the hypothetical triplet states of the hydrogen molecule?

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    $\begingroup$ Are you sure you are talking about the electronic and not nuclear spin states? $\endgroup$ – Ivan Neretin Mar 30 '16 at 7:54
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Assuming that you're talking about electronically excited states and not spin isomers of the $\ce{H2}$ molecule (as anticipated by Ivan Neretin), note first that there are many triplet states, of which the lowest lying one corresponds to $1 \sigma 1 \sigma^∗$ configuration. Under ordinary conditions this particular triplet state is indeed unstable towards the dissociation to the hydrogen atoms. But it is not hypothetical, as you said, it is just unstable. Besides, in some extraordinary conditions, say, in an ultrahigh magnetic field, the triplet state of the hydrogen molecule is the ground state.

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