Fig. 4: Free energy surfaces and kinetics of SO₂ hydrolysis in the bulk and at the interface.

a, b Free energy surfaces (FESs) for SO₂ hydrolysis as functions of the S-O coordination number (S-O CN) and the Voronoi-based collective variable (s_a) for the surface (a) and bulk phase (b). The minimum free energy pathways (R → P → P1) are highlighted in red (surface) and blue (bulk). The dashed lines indicate energy levels of −5, 5, 15, 17, 20, and 22 kJ mol⁻¹. Representative snapshots of key species are shown as insets: R (SO₂), R’ (prereactive state), TS (transition state), P (HSO₃⁻), P1 (SO₃²⁻), and P2 (H₂SO₃). c Free energy profiles along the MFEPs at the surface (red) and in the bulk (blue). Shaded regions indicate statistical uncertainty from block averaging. d Cumulative probability distributions of hydrolysis times (black lines) that are fitted by first-order Poisson models (colored lines). The blue line corresponds to bulk hydrolysis (k_b =1.7 × 10⁷ s⁻¹), and the red line corresponds to interfacial hydrolysis (k_s = 9.7 × 10⁵ s⁻¹). The Kolmogorov–Smirnov tests yielded p values of 0.67 (surface) and 0.93 (bulk), thus supporting first-order kinetics. Source data are provided as a Source Data file.