Density and Phonon-Stiffness Anomalies of Water and Ice in the Full Temperature Range

The specific-heat difference between the O:H van der Waals bond
and the H–O polar-covalent bond and the Coulomb repulsion between
electron pairs on adjacent oxygen atoms determine the angle–length–stiffness
relaxation dynamics of the hydrogen bond (O:H–O), which is
responsible for the density and phonon-stiffness oscillation of water
ice over the full temperature range. Cooling shortens and stiffens
the part of relatively lower specific-heat, and meanwhile lengthens
and softens the other part of the O:H–O bond via repulsion.
Length contraction/elongation of a specific part always stiffens/softens
its corresponding phonon. In the liquid and in the solid phase, the
O:H bond contracts more than the H–O elongates, hence, an O:H–O
cooling contraction and the seemingly “regular” process
of cooling densification take place. During freezing, the H–O
contracts less than the O:H elongates, leading to an O:H–O
elongation and volume expansion. At extremely low temperatures, the
O:H–O angle stretching lowers the density slightly as the O:H
and the H–O lengths change insignificantly. In ice, the O–O
distance is longer than it is in water, resulting in a lower density,
so that ice floats.