I'm trying to find an explanation for the letter codes (X, A, B, C, etc) when you get a term symbol like this


Can anyone point me to some literature that explains these letter codes?

  • 1
    $\begingroup$ en.wikipedia.org/wiki/… In this case it is referring to the ground state (I guess probably $\ce{O2}$). $\endgroup$
    – orthocresol
    Sep 17 '16 at 11:40
  • 1
    $\begingroup$ have a look also in the tables at the end of any of the Herzberg books 'Molecular Spectra & Molecular Structure' $\endgroup$
    – porphyrin
    Sep 17 '16 at 12:49

Quoting from Hollas, Modern Spectroscopy, 4th ed. (p 236):

There is a convention, which is commonly but not always used, for labelling electronic states. The ground state is labelled $X$ and higher states of the same multiplicity are labelled $A, B, C\ldots$ in order of increasing energy. States with multiplicity different from that of the ground state are labelled $a, b, c \ldots$ in order of increasing energy.

As such, for the oxygen molecule, where the lowest three states are ${}^3{\Sigma}_g^-$, ${}^1{\Delta}$ and ${}^1{\Sigma}^+_g$ (in increasing order of energy), the triplet ground state would be labelled $X$ and the next two states $a$ and $b$ respectively.

A word of caution: it seems that this convention is not always obeyed. On the next page, Hollas writes (for $\ce{I2}$, where the ground state is a singlet)

The transition $B\,{}^3{\Sigma}_{0_u^+} - X\,{}^1{\Sigma}_g^+$ involves the $\Omega = 0$ component of the $B$ state [...] The labelling of the $B\,{}^3{\Sigma}_{0_u^+}$ state follows general usage rather than convention, which would label it $b\,{}^3{\Sigma}_{0_u^+}$.

Wikipedia also adds, although without a citation:

In polyatomic molecules (but not in diatomics) it is customary to add a tilde (e.g. $\tilde{X}$, $\tilde{a}$) to these empirical labels to prevent possible confusion with symmetry labels based on group representations.

  • $\begingroup$ I don't think you explained what ${}^3{\Sigma}^{-}_g$ means. $\endgroup$
    – DHMO
    Sep 17 '16 at 12:24
  • 1
    $\begingroup$ That explanation is here. $\endgroup$ Sep 17 '16 at 14:11
  • 1
    $\begingroup$ The $\ce{^3\Sigma ^-_g}$ is a term symbol for the not-fully filled orbitals of a homo-nuclear diatomic molecule and comes from the $\ce{D_{\infty h}}$ point group. The 3 indicates a triplet spin state, $\ce{\Sigma}$ zero orbital angular momentum, g (gerade) means orbitals have a centre of inversion, otherwise u (ungerade). The superscript - indicates -1 to reflection in plane containing nuclei, i.e. no plane of reflection. A superscript + would indicate a +1 reflection, i.e. has plane. The $\ce{O2}$ ground state is $\ce{^3\Sigma ^-_g}$ . $\endgroup$
    – porphyrin
    Sep 17 '16 at 16:00
  • $\begingroup$ Thanks for mentioning your source. I totally missed the footnote on that page. It's been a while since I last had to use a lot of quantum mechanics thanks for the quick refresher. $\endgroup$ Sep 17 '16 at 17:25
  • 2
    $\begingroup$ The question didn't ask for an explanation of the term symbol anyway, but I appreciate the links/explanations in the comments. :) Just want to point out that the superscript minus indicates that the wavefunction is antisymmetric with respect to reflection in a plane containing the nuclei, not that such a plane does not exist. $\endgroup$
    – orthocresol
    Sep 18 '16 at 18:14

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.