Fig. 7: Coherent quantitative mechanism of the HMS formation in atmospheric aerosol.

a The reaction pathways of HMS formation in acidic aerosols. Although \({{{{\rm{HSO}}}}}_{3}^{-}\) predominates in the equilibrium with \({{{{\rm{HOSO}}}}}_{2}^{-}\) under moderate acidic conditions, the reaction between \({{{{\rm{HOSO}}}}}_{2}^{-}\) and surface-accumulated HCHO at the gas-liquid interface proceeds with a relatively low energy barrier (\(\Delta {G}_{{{{\rm{inter}}}}}^{{{\ddagger}} }\) = ~7.6 kcal/mol) compared to the HMS isomer formation (\(\Delta {G}_{{{{\rm{sul}}}}}^{{{\ddagger}} }\) = ~18.1 kcal/mol), leading to the cascade formation of HMS. This process depletes the concentration of \({{{{\rm{HOSO}}}}}_{2}^{-}\), driving the ongoing conversion of \({{{{\rm{HSO}}}}}_{3}^{-}\) to \({{{{\rm{HOSO}}}}}_{2}^{-}\). As a result, \({{{{\rm{HOSO}}}}}_{2}^{-}\) continuously reacts with HCHO to generate HMS. b (Left) The nucleophilic addition with intramolecular proton-transfer mechanism and the corresponding free-energy profile of gaseous HMS formation. (Middle) Free-energy profile for the homogeneous HMS formation with full solvated and solvent polarized HCHO and \({{{{\rm{HOSO}}}}}_{2}^{-}\) via water-mediated proton transfer process. (Right) Free-energy profile for the heterogeneous HMS formation. The HCHO is partial solvated and the \({{{{\rm{HOSO}}}}}_{2}^{-}\) is located at subsurface with interfacial electric field and interfacial stabilization.