Goldschmidt-Pauling contraction of the H-O polar-covalent bond elongates and polarizes the other noncovalent part of the hydrogen bond (O:H-O), that is, the O:H van der Waals bond, significantly, through the Coulomb repulsion between the electron pairs of adjacent oxygen (O-O). This process enlarges and stiffens those H2O molecules having fewer than four neighbors such as molecular clusters, hydration shells, and the surface skins of water and ice. The shortening of the H-O bond raises the local density of bonding electrons, which in turn polarizes the lone pairs of electrons on oxygen. The stiffening of the shortened H-O bond increases the magnitude of the O1s binding energy shift, causes the blue shift of the H-O phonon frequencies, and elevates the melting point of molecular clusters and ultrathin films of water, which gives rise to their elastic, hydrophobic, highly-polarized, ice-like, and low-density behavior at room temperature.

Hydrogen-bond relaxation dynamics: Resolving mysteries of water iceCoordination Chemistry Reviews: CCR-D-14-00064R4 (42 words, 412 Refs, 65 figures, 10 tables, 45 equations)  An extended tetrahedron unifies the length scale, geometry, and density of water ice  O:H-O bond cooperative relaxation stems anomalies of water and ice  Water prefers 4-coordinated mono-phase with a supersolid skin unless at nanoscale  An elastic, hydrophobic and less dense skin slipperizes ice and toughens water skin  H-bond memory and skin supersolidity resolve Mpemba effecthot water freezes faster

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.

Compression shortens the O:H nonbond and lengthens the H-O bond simultaneously via O-O Coulomb repulsion. The H-O elongation and its energy loss lower the melting point.

Consistency in experimental observations, numerical calculations, and theoretical predictions have revealed that the skins of water and ice share the same attribute of supersolidity characterized by an identical H-O vibration frequency of 3450 cm(-1). Molecular undercoordination and inter-electron-pair repulsion shortens the H-O bond and lengthens the O:H nonbond, leading to a dual process of nonbonding electron polarization. This relaxation-polarization process enhances the dipole moment, elasticity, viscosity, and thermal stability of these skins with a 25% density loss, which is responsible for the hydrophobicity and toughness of the water skin and results in the slippery behavior of ice.

The Mpemba paradox, that is, hotter water freezes faster than colder water, has baffled thinkers like Francis Bacon, René Descartes, and Aristotle since B.C. 350. However, a commonly accepted understanding or theoretical reproduction of this effect remains challenging. Numerical reproduction of observations, shown herewith, confirms that water skin supersolidity [Zhang et al., Phys. Chem. Chem. Phys., DOI: ] enhances the local thermal diffusivity favoring heat flowing outwardly in the liquid path. Analysis of experimental database reveals that the hydrogen bond (O:H-O) possesses memory to emit energy at a rate depending on its initial storage. Unlike other usual materials that lengthen and soften all bonds when they absorb thermal energy, water performs abnormally under heating to lengthen the O:H nonbond and shorten the H-O covalent bond through inter-oxygen Coulomb coupling [Sun et al., J. Phys. Chem. Lett., 2013, 4, 3238]. Cooling does the opposite to release energy, like releasing a coupled pair of bungees, at a rate of history dependence. Being sensitive to the source volume, skin radiation, and the drain temperature, the Mpemba effect proceeds only in the strictly non-adiabatic 'source-path-drain' cycling system for the heat "emission-conduction-dissipation" dynamics with a relaxation time that drops exponentially with the rise of the initial temperature of the liquid source.

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