Ab initio simulation of the first-order proton-ordering transition in water ice

Abstract

Proton ordering in water ice is a paradigmatic order-disorder transition in a locally constrained system. The ice rules require exactly two hydrogens close to each oxygen, restricting the disorder to an exponentially large yet strongly correlated manifold of hydrogen-bond configurations. Within this constrained space, meV-scale energy differences drive the transition from disordered ice Ih to ordered ice XI, while distinct configurations are separated by eV-scale barriers. These barriers hinder equilibration in experiments, and efficient sampling of this space with the required energy accuracy has remained a long-standing challenge in simulation. We address this by combining a machine learning interatomic potential with loop updates that preserve the ice rules and continuous updates of atomic coordinates, enabling equilibrium sampling with ab initio accuracy and capturing configurational entropic effects. In systems of up to 360 water molecules, with over 10^6 samples retained per temperature point, the simulations reveal clear first-order transition signatures at 83 K: a negative Binder cumulant, a bimodal potential energy distribution, and a sharp step in the lattice aspect ratio. Nuclear quantum effects are estimated to lower the transition temperature by approximately 20 K, bringing the prediction closer to the experimental value of 72 K.