Fig. 6: HMS formation at weak acidic or neutral conditions.

a (Top) Schematic representation of the CV. (Bottom) Gibbs free-energy profiles for the HCHO + \({{{{\rm{SO}}}}}_{3}^{2-}\) reaction in bulk water (blue dash line) and at the air-water interface (red line) compared with the experimental result (\(\Delta {G}_{\exp }^{{{\ddagger}} }\)) by Boyce et al.³⁵. Shaded areas represent the error bands for each three simulations. Calculation of error band is as same as the HCHO + \({{{{\rm{HOSO}}}}}_{2}^{-}\) reaction simulation. b Snapshot structures obtained from the metadynamics-biased AIMD simulations for the aqueous (Top: R_bulk, TS_bulk, and P_bulk) and the heterogeneous reaction (Bottom: R_inter, TS_inter, and P_inter). c Gibbs free-energy profiles for HCHO + \({{{{\rm{SO}}}}}_{3}^{2-}\) reaction with (blue dash lines) and without (black lines) an external electric field of 0.1 V/Å in gas phase and their corresponding structures of the stationary points. The calculation level is same as Fig. 4e. d Electrostatic potential surface of TS (Top) and TS_E (Bottom). Red denotes regions of positive electrostatic potential and blue represents regions of negative potential. e (Top) The isodensity surface (isodensity = ±0.0015) of the electron density difference between TS and TS_E. Green denotes regions of positive value and blue represents regions of negative value. (Bottom) Contour representation of the electron density difference in the x-y plane. Green lines denote positive value and blue lines denote negative value.