Isotope effects in condensed phases, the benzene example. Influence of anharmonicity; harmonic and anharmonic potential surfaces and their isotope independence. Molar volume effects in isotopic benzenes

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Abstract
Application of the harmonic oscillator cell model (HOCM) for condensed phase isotope effects to the benzene/deuterobenzene system using temperature dependent force fields, which yield good calculated values for vapor pressure isotope effects (VPIE) and reasonable agreement with spectroscopically observed frequency shifts on condensation, gives calculated values of isotope effect on energies of vaporization which are not in agreement with experiment. Pseudoharmonic corrections are inadequate to restore agreement with experiment. The VPIE in benzene is dominated by the contributions of the CH/CD stretching vibrations and consistency is achieved by expanding the model to include anharmonic corrections for these frequencies. In this fashion a combination of thermodynamic measurements of free energies (by vapor pressure) and energies (from the temperature coefficient of the vapor pressure or from calorimetry) can be employed to yield shifts in anharmonic vibrational constants on condensation. In the second part of the paper the molar volume isotope effect (MVIE) and the effects of volume, pressure, and temperature on the internal energy and its isotope effects (as monitored by the expansivity, compressibility, heat capacity, and their derivatives) are interpreted. The low-lying lattice modes make important contributions to these properties.