Interfacial topological selection links structural motifs to the free-energy barrier in methane hydrate nucleation

Methane hydrate nucleation is a stochastic process critical to energy and flow-assurance technologies, yet the structural changes associated with crossing its free-energy barrier remain poorly resolved. We hypothesize that transient topological motifs in the interface hydrogen-bonded network provide information about barrier crossing beyond bulk nucleus growth alone.

To test this hypothesis, we integrate molecular dynamics (MD) simulations with machine learning (ML). We perform 20 independent, long-timescale MD simulations of methane hydrate nucleation and identify transient structural motifs using the Hierarchical Topological Ring algorithm, including polyhedral cages and ternary water-ring aggregations (TWRAs). Time-lagged independent component analysis (tICA) is applied to construct a free-energy landscape, while extreme gradient boosting (XGBoost) with Local Interpretable Model-Agnostic Explanations (LIME) interpretation quantifies associations between structural descriptors and the resulting free-energy coordinate. Trajectory-level data partitioning is used for model evaluation.

Across the nucleation trajectories, barrier ascent is accompanied by depletion of topologically incompatible 2-1-0 TWRAs and enrichment of compatible 0-3-0 and 0-2-1 motifs at the hydrate-water interface. The XGBoost/LIME analysis identifies these TWRA proportions as informative structural descriptors of free-energy coordinate. In trajectory-level leave-one-out cross-validation, adding the three key TWRA proportions to the instantaneous free energy improves prediction of subsequent free-energy evolution at 50-100 ns relative to using instantaneous free energy alone. These results support interfacial topological selection as a structural signature of barrier crossing and connect local hydrogen-bonded network reorganization with the free-energy evolution of methane hydrate nucleation.