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I think that I understand most of the parts of the symbol shown for ground state oxygen $\ce{{}^{16}O2}$, which is ${}^{3}\Sigma^{-}_{g}$.

However, I was hoping that someone could tell me what exactly the negative superscript sign means? And how do you identify between a positive and negative state? I think it has something to do with a mirror plane.

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  • $\begingroup$ The ground state term symbol doesn't depend on the isotope - it is also $^3\Sigma_g^-$ for $\ce{^{17}O ^{16}O}$, $\ce{^{18}O2}$ etc. However, the resulting nuclear spin statistics for rotational states will of course be different for different isotopomers. $\endgroup$
    – user1915639
    Jan 30 '14 at 17:53
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You're right that it has to do with a mirror plane. The negative sign means that the overall electronic wavefunction changes sign when reflected in a mirror plane that includes the internuclear axis.

For ground-state oxygen, reflecting in a mirror plane will change the sign of one unpaired $\pi$ electron (the one that sticks out of the mirror plane) but not the other, resulting in an overall change in sign. (This is slightly simplified, a more rigorous explanation would take into account the complex-valued orbitals rather than their real-valued linear combinations.)

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  • $\begingroup$ If you look at the point group $D_{\infty h} $ you will see how the symmetry works $\endgroup$
    – porphyrin
    Jul 9 '16 at 8:42

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