# What does the negative superscript in the term symbol for ground state Oxygen stand for?

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.

• 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. – user1915639 Jan 30 '14 at 17:53

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