Symmetry Properties of non-Hunds Case a Basis Functions

2 Symmetry Properties of non-Hund s Case (a) Basis Functions 

The preceding discussion is focussed on the parity and e/f symmetry of case (a) basis states (Eq. 3.2.4a). Since it is often useful to construct basis sets of the form (ion-core) (Rydberg electron)) where the ion-core can be in cases a+, b+, or c+ and the Rydberg electron can be in cases a, b, c, d, or e (Watson 1999), the effects of cxv(xz) on each of these basis states are summarized here (Field, unpublished)  

All of the ion-core quantum numbers appear with a right superscript +. The orbital reflection symmetry index is s+ = 1 for A+ = 0 or = 0 0 states 

The spin of a single electron is always s = 1/2. No orbital reflection symmetry index is needed for a Rydberg orbital because all A = 0 states have E+ symmetry and the reflection symmetry of u = 0 states is (—1)J.  

Note that the parity of the Rydberg electron case (d) or (e) part of the basis state is determined by l alone, that the values of the rotation axis r projection quantum numbers Sr, Ir, sr, and jR do not enter into the specification of parity, and the signs of the rotation axis projection quantum numbers are not reversed upon application of crv(xz). 

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