Second-order correction to the Bigeleisen-Mayer equation due to the nuclear field shift

The nuclear field shift affects the electronic, rotational, and vibrational energies of polyatomic molecules. The theory of the shifts in molecular spectra has been studied by Schlembach and Tiemann [Schlembach, J. & Tiemann, E. (1982) Chem. Phys. 68, 21]; measurements of the electronic and rotational shifts of the diatomic halides of Pb and Tl have been made by Tiemann et al. [Tiemann, E., Knöckel, H. & Schlembach, J. (1982) Ber. Bunsenges. Phys. Chem. 86, 821]. These authors have estimated the relative shifts in the harmonic frequencies of these compounds due to the nuclear field shift to be of the order of 10(-6). I have used this estimate of the relative shift in vibrational frequency to calculate the correction to the harmonic oscillator approximation to the isotopic reduced partition-function ratio (208)Pb(32)S/(207)Pb(32)S. The correction is 0.3% of the harmonic oscillator value at 300 K. In the absence of compelling evidence to the contrary, it suffices to calculate the nuclear field effect on the total isotopic partition-function ratio from its shift of the electronic zero point energy and the unperturbed molecular vibration.