Acoustic vibrations, hydrogen bonds

Thus, for the motion of the next state along the chain it is necessary to repolarize the chain into its initial state, which can be achieved by Bjerrum-fault transfer. The semiphenomenological theory of proton transfer along the hydrogen-bonded chain of the ice-like structure, developed in Ref. 161, includes the influence of longitudinal acoustic vibrations of the chain sites on the proton subsystem. Reference 162, in which the dynamics of the ionic state formation in the hydrogen-bonded chains is considered, resembles roughly Ref. 161. 

Apart from the bilinear connection between acoustic and optical vibrations, the usual phonon anharmonicity takes place in the chain. The acoustic vibrations modulate the distances between A atoms and thus influence the frequency of proton vibrations on hydrogen bonds. The proton vibration frequency can be presented as... 

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