Fig. 3: Water-mediated proton transfer at the air-water interface.

a Variation of COM z-positions for HCHO (red line) and \({{{{\rm{HOSO}}}}}_{2}^{-}\) (purple line) as a function of the simulation time with average density along z-axis (grey region). Two black dash lines represent the outmost (z = 13.0 Å) and the subsurface (z = 10.4 Å). b Variation of the angle between the C=O direction vector and the z-axis (at θ₁, 0–180°, red line) and the dihedral angle between C=O direction vector and the S−OH direction vector (at θ₂, 0–180°, blue line) as a function of the simulation time. Shaded areas are the corresponding angles of every frame. Bold lines are the smoothed value (2000 points) to clarify the trend. c Variation of C···O (red line) and S···OH (purple dash line) distances as a function of the simulation time. Shaded areas are the corresponding distances of every frame. Bold lines are the smoothed value (500 points) to clarify the trend. d (Top) Relevant O···H distance differences (D₁–D₇) variation as a function of the simulation time. The symbols indicate the corresponding D value at the events (i to vii). (Middle) Definition of the distance differences (D₁–D₇). (Bottom) Schematic representation of the water-mediated proton transfer at the air-water interface. Red and blue marks represent the O and H atoms participating the proton transfer. Relevant pathway is represented as dash lines. e Snapshots of the events (i to vii) of the water-mediated proton transfer process extracted from the metadynamics-biased AIMD simulations of the heterogeneous reaction of HCHO + \({{{{\rm{HOSO}}}}}_{2}^{-}\).