Solitons in hydrogen-bonded chains: A microscopic model

A Su-Schrieffer-Heeger-type Hamiltonian is presented, which reproduces the features of phenomenologically motivated ${\mathrm{\phi }}^4$ models of hydrogen-bonded chains. The primary application is a chain composed of poly(hydrogen fluoride), which is considered an idealization of Bernal-Fowler filaments consisting of water molecules. C-number solutions are derived in the continuum limit, and the fractional charges and the energy of the kink solutions are computed. It is shown that certain approximations usually made in such calculations have to be reexamined in this extreme case of a diatomic polymer. However, the application of the continuum model is justified, since a comparison of the results with numerical calculations indicates that the essential features of the spectra are reproduced by our simple model. Quantum-chemical calculations were made to obtain parameters necessary to estimate the characteristics of the amplitude kink, such as its width and energy. We found an energy of ∼0.35 eV and a half-width of ∼1.5 lattice sites, which fairly well confirms the continuum limit necessary to obtain analytical solutions.