Coupled protons, hydrogen bonds, tunneling

Besides the peaks of the local proton modes typical for hydrogen bond, a sharp peak at 28 meV was observed in KDP [34] and attracted much attention [34,38,39]. This peak exists in DKDP at somewhat higher frequency its intensity decreases in both crystals and its width decreases upon the transition from the FE to the PE phase, without any softening of its frequency [38]. Hence, it is concluded that this mode is connected with the phase transition dynamics, i.e., coupled to the polarization fluctuations. This mode is not the tunneling mode or any local mode of proton or deuteron, but rather some collective optical mode of the lattice that involves substantial proton or deuteron displacement. It has been suggested [38] that this mode corresponds to the mode that has a peak at about 200 cm (25 meV) in Raman scattering and infrared reflectivity spectra, and that it is coupled to the soft mode and usually... 

Thus, the proton-phonon coupling being inserted into the initial Hamiltonian is able to suppress or enlarge the coherent tunnel repolarization of the chain. The realization of this or that option depends not only on the spin-phonon interaction, but also on the form of the two-well potential of the hydrogen bond. 

The benzoic acid dimer is stabilized by two hydrogen bonds, with the two monomers being coplanar in the electronic ground state [21]. The proton transfer is shown to strongly couple to the heavy nuclei, implying that the whole benzoic acid frame rearranges itself slightly as the protons tunnel. 

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