Manning-type potential induced by kink scatterings with phonons in molecular chains with hyperbolic double-well substrates

Abstract

A rescaled Manning potential is obtained in the analysis of scatterings of small-amplitude excitations with a kink defect. The generic model is a nonlinear Klein–Gordon Hamiltonian describing a one-dimensional chain of identical molecules subjected to a hyperbolic single-particle substrate potential. To account for isotope effects that are likely to affect characteristic equilibrium parameters of the molecular chain, including the lattice spacing (i.e., the characteristic intermolecular distance) and/or the barrier height, the hyperbolic substrate potential is endowed with a real parameter whose variation makes it suitable for the description of molecular excitations in a broad range of systems with inversion symmetry. These include hydrogen-bonded molecular crystals, α-helix proteins, long polymer chains, and two-state quantum-tunneling systems in general. Double-well models with deformable profiles are relevant in physical contexts where the equilibrium configurations are sensitive to atomic or molecular substitutions, dilution, solvation, and so on.