Fig. 4: Effect of solvation and interfacial electric field on HCHO + HOSO₂⁻ reaction.

a Comparison of Gibbs free-energy for the HCHO + \({{{{\rm{HOSO}}}}}_{2}^{-}\) + H₂O (red lines, stationary structures labeled as R’, TS’, and P’) and the HCHO + \({{{{\rm{HOSO}}}}}_{2}^{-}\) + 4H₂O reaction in the gas phase (purple dash lines, stationary structures labeled as R”, TS”, and P”). The calculation level is same as Fig. 2b. b Calculated electrophilicity index for the carbonyl carbon for HCHO−H₂O complex and HCHO molecule. c (Top) CDA analysis for TS (black lines) and TS’ (red lines), relative orbital energies (eV), and the isovalue surfaces of their frontier orbitals (isovalue = ±0.005) of the fragments. (Bottom) Variation of orbital energy with (red) and without (black) a water molecule as proton transfer participant. d Relative free-energy contribution of TS and P for HCHO + \({{{{\rm{HOSO}}}}}_{2}^{-}\) reaction by RxDFT calculations, blue: polarization, red: solvation. e Comparison of Gibbs free-energy for HCHO + \({{{{\rm{HOSO}}}}}_{2}^{-}\) reaction with (blue dash lines, stationary structures labeled as R_E, TS_E, and P_E) and without (black lines) an external electric field of 0.1 V/Å in gas phase. The calculation level is same as Fig. 2b. f Electrostatic potential surface of TS (Top) and TS_E (Bottom). Red denotes regions of positive electrostatic potential and blue represents regions of negative potential. g (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.