Structure of a proton wire in the harmonic model with allowance for the interproton interaction for the first and second neighbors

Abstract

Differential equations based on the one-component harmonic model of a water chain are proposed for description of the proton wire structure with allowance for the interproton interaction of near and far neighbors. The solution to the Sturm-Liouville problem is considered for a fourth-order differential equation that takes into account interproton interactions with the first and second adjacent links of a one-dimensional chain. The function of proton displacements in such a wire is shown to describe a quasi-periodical structure, depending on the ratio of constants D1 and D2 for the interproton interaction of the first and second neighbors. According to calculations using the parameters characteristic of the water chain, the curve of the proton displacement is a plot of function y = cosk1x + sink2x and is similar to the curve of the hydrogen bond length distribution obtained earlier in the quantum-chemical calculations of the proton channel model.