Mobility and conductivity of the proton transfer in hydrogen-bonded molecular systems

We calculate the mobility and conductivity of the proton transfer in hydrogen-bonded systems by quantum mechanics. We first give the equation of change of velocity of the kink–antikink pair resulting from proton transfer, from the Hamiltonian in our model. Utilizing the values of the physical parameters we finally find out the mobility of kink–antikink pairs and the electrical conductivity due to the proton transfer in an externally applied electric-field in the systems. These are about (6.5–6.9)×10−6 m2/V s and (7.6–8.1)×10−3/(Ω m) for ice, respectively, which are basically consistent with experimental data.