Structure of Water and Hydrophobic Bonding in Proteins. IV. The Thermodynamic Properties of Liquid Deuterium Oxide

A model, proposed earlier for the theoretical derivation of the thermodynamic parameters of liquid water, is shown to be applicable to liquid deuterium oxide as well. The model, based on the ``flickering cluster'' concept proposed by Frank and Wen, and the partition function were described in a previous publication. In the application to D2O, the intermolecular vibrational frequencies are changed in accord with the theoretical ratios for isotopic substitution. The energy of the hydrogen bond is the only adjustable parameter; its value is 0.24 kcal/mole higher than for H2O. The calculated structural parameters indicate that more structural order exists in D2O than in H2O at a given temperature. The calculated values of the free energy, enthalpy, and entropy of the liquid have an over-all average error of 6%, as compared with experimental data, over the range 0° to 65°C. The deviation of cv is of the same magnitude as for H2O. The temperature dependence of the molar volume is reproduced with an error of less than 0.4%, and the temperature of maximum density is obtained within one degree of the experimental value. Excellent agreement is also obtained between the calculated and observed compressibility. The calculation of the PVT data involved no new assumptions. Calculated first peak areas for the radial distribution functions of H2O and D2O are shown to be almost identical.