Curvature-Corrected Surface Tension Governs Nucleation in Molecular Systems

Nucleation governs processes from cloud formation to crystallization and material assembly, yet classical nucleation theory (CNT) consistently mispredicts barriers by neglecting curvature-dependent surface tension. Here, we introduce a simulation-based framework that combines aggregation-volume-bias Monte Carlo (AVBMC) simulations with finite-difference free energy analyses (Δ²G and Δ³G) to extract both planar surface tension and the Tolman length from cluster-size-dependent nucleation free energies. Applied to four widely used water models (SPC, SPC/E, TIP4P, and TIP4P/2005), the method reveals a consistently negative Tolman length (≈ -0.48 Å), which increases nucleation barriers by 5-6 k_BT, relative to CNT predictions, in excellent agreement with experimental measurements. These findings resolve a long-standing discrepancy between theory and experiment and establish a general, predictive, and quantitative framework for understanding nucleation in molecular systems, with implications for atmospheric processes, biomolecular assembly, and materials design.