Standard molar internal energy of the molecule

The internal partition function is a sum of Boltzmann factors, multiplied by their degeneracies, Pj, over the vibrational and rotational states of the molecule. In the summation over the rotational states it is necessary to consider symmetry selection rules. This leads to a factor S in and + RlnS 

AE electronic is identically zero under the Born-Oppenheimer approximation. The only contribution to AEj comes from the molecular vibrations. 

Thus once the spectroscopic rotational and vibrational constants are known for a pair of isotopic molecules it is possible to calculate the partition function ratio of a pair of isotopic molecules 

ACS Symposium Series American Chemical Society Washington, DC, 1975. 

The experiments of Rlttenberg and Urey (20) confirmed their calculations on this exchange reaction within the uncertainty of their calculations. Their calculation of the enharmonic correction to Eo, like many subsequent ones, is Incomplete. In the exchange reaction of protlum and deuterium between hydrogen gas and water vapor the deuterium favors the water molecule. 

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