Diatomic molecules nuclear statistical weights

In summary, for a homonuclear diatomic molecule there are generally (2/ + 1) (7+1) symmetric and (27+1)7 antisymmetric nuclear spin functions. For example, from Eqs. (50) and (51), the statistical weights of the symmetric and antisymmetric nuclear spin functions of Li2 will be and respectively. This is also true when one considers Li2 Li and Li2 Li. For the former, the statistical weights of the symmetric and antisymmetiic nuclear spin functions are and, respectively for the latter, they are and in the same order. 

Figure 5.18 Nuclear spin statistical weights (ns stat wts) of rotational states of various diatomic molecules a, antisymmetric s, symmetric o, ortho p, para and rotational, nuclear spin...

All other homonuclear diatomic molecules with / = for each nucleus, such as F2, also have ortho and para forms with odd and even J and nuclear spin statistical weights of 3 and 1, respectively, as shown in Figure 5.18. 

For a homonuclear diatomic molecule composed of even(odd) mass-ntmber nuclei, the total wave function, which we assume to be a product of electronic, vibrational, rotational, and nuclear-spin functions, must be symmetric (antisymmetric). If the electronic wave function is symmetric, and if the nuclear spin is zero, as in the ground state of 0a, only even values of J, the rotational quantum number, are allowed. If the nuclear spin is not zero, both even and odd values of J (l.e., symmetric and antisymmetric rotational wave functions) are allowed, but with different statistical weights. These may be determined from the nuclear-spin part of the wave function. 

In any homonuclear diatomic molecule, with nuclear spin s, the statistical weight of the ortho states is s + 1) 2s + 1) that of the para states is s(2s -b 1). The rotational partition function will thus in general be... 

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