Qrot, partition function

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... 

Here qrot,s and qvib,s are the microscopic partition functions for rotation and vibration of M in the solution while Hm.s and Am, indicate the related numeral densities and the momentum partition functions, respectively. The functional (G ) has now the meaning of the free energy of the entire solute-solvent system, at the temperature T, with respect to a reference state given by non-interaction nuclei and electron, supplemented by the imperturbed pure liquid S, at the same temperature. Then, the fundamental energetic quantity connected with the insertion of the solute in the solvent, i.e. the free energy of solvation can be obtained as... 

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