Since the total wavefunction must be odd, the even " J " levels can only use the antisymmetric functions ( only one for"
2.
For D2, " I = 1 " and thus there are six symmetric functions, which go with the even " J " levels to produce an overall symmetric wavefunction, and three antisymmetric functions that must go with odd " J " rotational levels to produce an overall even function.
3.
For the case of a symmetric diatomic with nuclear spin quantum number " I " for each nucleus, there are ( I + 1 ) ( 2I + 1 ) symmetric spin functions and I ( 2I + 1 ) are antisymmetric functions for a total number of nuclear functions g ^ { ns } = ( 2 I + 1 ) ^ 2.
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