Tuesday, March 20, 2018

quantum chemistry - Letter codes in molecular term symbols


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


X3Σg


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



Answer



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 in order of increasing energy. States with multiplicity different from that of the ground state are labelled a,b,c in order of increasing energy.



As such, for the oxygen molecule, where the lowest three states are 3Σg, 1Δ and 1Σ+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 IX2, where the ground state is a singlet)



The transition B3Σ0+uX1Σ+g involves the Ω=0 component of the B state [...] The labelling of the B3Σ0+u state follows general usage rather than convention, which would label it b3Σ0+u.



Wikipedia also adds, although without a citation:




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



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