PM Piaggi and R Car, Mol. Phys. e1916634 (2021)
Ice Ih, the common form of ice in the biosphere, contains proton disorder. Its proton-ordered counterpart, ice XI, is thermodynamically stable below 72 K. However, even below this temperature the formation of ice XI is kinetically hindered and experimentally it is obtained by doping ice with KOH. Doping creates ionic defects that promote the migration of protons and the associated change in proton configuration. In this article, we mimic the effect of doping in molecular dynamics simulations using a bias potential that enhances the formation of ionic defects. The recombination of the ions thus formed proceeds through fast migration of the hydroxide and results in the jump of protons along a hydrogen bond loop. This provides a physical and expedite way to change the proton configuration, and to accelerate diffusion in proton configuration space. A key ingredient of this approach is a machine learning potential trained with density functional theory data and capable of modeling molecular dissociation. We exemplify the usefulness of this idea by studying the order-disorder transition using an appropriate order parameter to distinguish the proton environments in ice Ih and XI. We calculate the changes in free energy, enthalpy, and entropy associated with the transition. Our estimated entropy agrees with experiment within the error bars of our calculation.