Phonon Frequency and Segmental Stiffness

The Raman or the spectroscopy is one of the powerful techniques that could resolve the vibrations of the intermolecular 0 H non-covalent bond and the intramolecular H-O bond according to their stiffness based on Fourier transformation. Any permrbation even sunlight irradiation can change the spectra feature of liquid water [63]. 

From the dimensional point of view, the second-order derivative of the u (r) at equilibrium is proportional to the bind energy E divided by the square of bond length in the form of The e]/ /d = VYA with Yc Ej /d is right the square root of the stiffness being the product of the Young s modulus and the bond length [14, 64]. In practice, polarization effect on the elasticity needs to be included. 

It is universally true that if one segment becomes shorter, it will be stiffer on expansion, it becomes softer [5]. Therefore, the phonon frequency shift tells directly the variation in length, strength, and stiffness of the respective segment under applied stimulus. Because of the Coulomb repulsion mediation, the col coh shift in such a way that if one becomes stiffer, the other becomes softer, and vice versa. 

Therefore, all detectable quantities (q) of the specimen depend functionally on the order, length, and energy of the representative segment of the H-bond. The relaxation of the 0 H bond contributes to the volume expansion, polarization, and molecular dissociation energy. The stiffening of the H-0 bond increases the 01s core-level shift, elevates the critical temperature Tq for phase transition 

Ex is the cohesive energy of the respective bond. Theoretical reproduction of the critical temperature Tq for ice VII-VIII phase transition under compression confirmed that the H-O bond energy determines the Tq [14]. 

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