Thermodynamics of molecular binding and clustering in the atmosphere revealed through conventional and ML-enhanced umbrella sampling

Accurately modeling the binding free energies associated with molecular cluster formation is critical for understanding atmospheric new particle formation. Conventional quantum-chemistry methods, however, often struggle to describe thermodynamic contributions, particularly in systems exhibiting significant anharmonicity and configurational complexity. We employed umbrella sampling, an enhanced-sampling molecular dynamics technique, to compute Gibbs binding free energies for clusters formed from a diverse set of new particle formation precursors, including sulfuric acid, ammonia, dimethylamine, and water. By performing umbrella sampling along the evaporation coordinate, using forces computed at the semi-empirical GFN1-xTB level of theory, we effectively capture entropic effects such as vibrational anharmonicities and transitions between different configurational minima, while avoiding errors from symmetry overcounting. In addition, we explored machine-learning-enhanced umbrella sampling simulations using neural network potentials trained on higher-level quantum chemistry data, demonstrating the feasibility of this approach for improving accuracy while maintaining computational efficiency. Our results show improved agreement with experimental values compared to conventional methods. We also present examples of gas-to-particle uptake processes, providing insights into cluster and aerosol--surface chemistry using first-principles approaches rather than commonly used molecular-mechanics force fields. This study demonstrates the importance of accounting for dynamics in predicting molecular binding thermodynamics in complex environments and highlights the potential of combining physics-based simulations with machine learning for reliable and scalable predictions.