SCF Calculation for proton-phonon coupling in a linear model of ice

The effective protonic potential for the ionic defect H3O+ has been calculated in an ice-like system as a function of the displacement of neighboring lattice sites. The symmetry and shift of the double minimum potential are related to the proton-phonon coupling. The coupling is found to be strong. This indicates that low order perturbation theory can not be applied to the study of protonic motion in hydrogen bonded systems.