Bjerrum Defects as Quantum Nonlinear Excitations of Hydrogen-Bonded Systems

Abstract

It is well established that conductivity, dielectric and elastic relaxation, optical spectra etc in ice and other hydrogen-bonded (HB) systems (one- two and three dimensional)¹ is connected with structural imperfections (ionic and Bjerrum D and L) violating the Bernai-Fowler rules^{2, 3}. Here we will study the protonic structure of a D or L defect and consider the dominant effect which is the intrasite and intersite tunneling of the protons but taking properly into account the polarisation state of the environment in the sense discussed below. We will consider a zig-zag HB molecular chain model (see Fig.1) of a Bernai-Fowler filament². As a Bjerrum-like defect we will consider a situation when there are two protons (or lack of it) on the line between two adjacent heavy atoms which we will suppose to be immobile, and the protons are quantum particles. The ground state wavefunction and energy of the HB chain with one D (L) defect is calculated and it is shown that the appearence of D (L) defect is accompanied by the creation of ionic defect bounded to the D (L) defect.