# Multiplicity letter codes for large amount of states

Well, let's say we have a large amount of states computed (e.g. over 50), all with the same multiplicity.

So, our ground state can be $$X^2\Sigma^+_g$$ and we can continue with $$B^2, C^2$$ etc. as described in Molecular orbitals symmetry - states notation and Letter codes in molecular term symbols.

But what is the convention of the number of states is larger, than the number of letters? Does any convention like $$B^2_2$$ exist?

• My guess is that this system of letter codes loses its convenience if you are interested in more than ~10 states. It would likely be more intuitive to switch to a numerical system like $S_0$ for ground, $S_1$ for first excited singlet, etc. One issue I have hear of with this letter code is that the labels often go unchanged if a state is latter discovered to be in the wrong order. citeseerx.ist.psu.edu/viewdoc/… – Tyberius May 22 at 18:25
• @Tyberius Thank you for the answer! The new notation seems quite nice, but, unfortunately, it omits the information about symmetry which I consider to be really important. Have you ever seen some sort of "joined usage" like $D_0\Sigma^+_g, D_1\Sigma^+_u...$? – Eenoku May 22 at 18:48
• I haven't seen it before, but I think it would be understood correctly. – Tyberius May 22 at 18:57