Relations Between Vibrational Spectroscopy and the Isotope Effect on Vapor Pressures

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Abstract
The vapor-pressure difference between isotopes of diatomic molecules is calculated for systems in which the rotational and translational molecular motion show small quantum deviations from classical behavior. Four different terms contribute significantly to the isotope effect on vapor pressures. (1) The mean-squared force on a molecule in the condensed phase; (2) The mean-squared torque about the center of mass of a molecule; (3) The change in mean-squared torque when the position of the center of mass is changed by isotopic substitution; (4) The mean change in intermolecular potential due to isotopic substitution. The last three of these four terms are shown to be observable separately in the infrared or vibrational Raman spectrum of the system. Therefore by combining the thermodynamic and spectroscopic data, it is possible to derive experimental values of the mean-squared force on a molecule and the mean-squared torque as a function of the point on the molecular axis about which the torque is measured. Thus, the ``center of force,'' the point about which the mean-squared torque is a minimum, may be experimentally determined. The analysis is applied to liquid and solid carbon monoxide.