Wave function symmetry under interchange

This situation is depicted in Figure 4.18. In addition to the local-mode notation, (va, vb, vc), Figure 4.18 also shows the normal notation, (V, v2, v3), corresponding to the modes of Figure 4.19, and the A, B (Herzberg, 1950) notation characterizing the symmetry of the wave function under interchange of bonds 1 < - > 2,... 

This is the correct expression for the rotational partition function of a heteronuclear diatomic molecule. For a homonuclear diatomic molecule, however, it must be taken into account that the total wave function must be either symmetric or antisymmetric under the interchange of the two identical nuclei symmetric if the nuclei have integral spins or antisymmetric if they have half-integral spins. The effect on Qrot is that it should be replaced by Qrot/u, where a is a symmetry number that represents the number of indistinguishable orientations that the molecule can have (i.e., the number of ways the molecule can be rotated into itself ). Thus, Qrot in Eq. (A.19) should be replaced by Qrot/u, where a = 1 for a heteronuclear diatomic molecule and a = 2... 

---