Challenges in molecular simulation of homogeneous ice nucleation

Abstract

We address the problem of recognition and growth of ice nuclei in simulation of supercooledbulk water. Bond orientation order parameters based on the spherical harmonics analysisare shown to be ineffective when applied to ice nucleation. Here we present an alternativemethod which robustly differentiates between hexagonal and cubic ice forms. The methodis based on accumulation of the maximum projection of bond orientations onto a set ofpredetermined vectors, where different terms can contribute with opposite signs with theresult that the irrelevant or incompatible molecular arrangements are damped out. We alsointroduce an effective cluster size by assigning a quality weight to each moleculein an ice-like cluster. We employ our cluster analysis in Monte Carlo simulationof homogeneous ice formation. Replica-exchange umbrella sampling is used forbiasing the growth of the largest cluster and calculating the associated free energybarrier. Our results suggest that the ice formation can be seen as a two-stageprocess. Initially, short tetrahedrally arranged threads and rings are present; thesebecome correlated and form a diffuse ice-genic network. Later, hydrogen bondarrangements within the amorphous ice-like structure gradually settle down andsimultaneously ‘tune-up’ nearby water molecules. As a result, a well-shaped icecore emerges and spreads throughout the system. The process is very slow anddiverse owing to the rough energetic landscape and sluggish molecular motion insupercooled water, while large configurational fluctuations are needed for crystallizationto occur. In the small systems studied so far the highly cooperative molecularrearrangements eventually lead to a relatively fast percolation of the forming ice structurethrough the periodic boundaries, which inevitably affects the simulation results.