On the role of intermolecular vibrational motions for ice polymorphs. III. Mode characteristics associated with negative thermal expansion.

Low-pressure ice forms, such as hexagonal and cubic ice, expand on cooling below temperature 60 K. This negative thermal expansivity has been explored in terms of phonon frequency modulation with varying volume and attributed to the negative Grüneisen parameters unique mostly to tetrahedrally coordinated substances. However, an underlying mechanism for the negative Grüneisen parameters has not been known except some schematic analyses. We investigate in this study the characteristics of the intermolecular vibrational modes whose Grüneisen parameters are negative by examining the individual vibrational modes rigorously. It is found that the low frequency modes below 100 cm, which we explicitly show are mostly bending motions of three hydrogen-bonded molecules, necessarily accompany elongation of the hydrogen bond length at peak amplitudes compared with that at the equilibrium position in executing the vibrational motions. The elongation gives rise to a decrease in the repulsive interaction while an increase in the Coulombic one. The decrease in the repulsive interaction is relaxed substantially by expansion due to its steep slope against molecular separation compared with the sluggish increase in the Coulombic one, and therefore, the negative Grüneisen parameters are obtainable. This scenario is tested against some variants of cubic ice with various water potential models. It is demonstrated that four interaction-site models are suitable to describe the intermolecular vibrations and the thermal expansivity because of the moderate tendency to favor the tetrahedral coordination.