Fig. 4: Activation free energy results with respect to electrochemical potentials.

Activation free energy results of Volmer and Heyrovsky mechanisms with respect to electrochemical potentials under classical and quantum situations at T = 300 K. Blue (Red) hollow circles and solid squares represent the Volmer (Heyrovsky) reaction for the classical and quantum cases, respectively. Solid and dashed lines derived from a linear fitting simply perform as guidelines illustrating the trend. The black dashed line represents the activation energy result (0.54 eV) of the Tafel reaction, which does not change with respect to voltage variation, and has almost identical values under classical and quantum conditions. Source data are provided as a Source Data file.