Resolving next the kinetic competition between the peroxide path (iii) and desorption path (iv) requires a similar analysis to that of Fig. above. Here the challenge lies in isolating spontaneous protonation that forms a surface-bound peroxide (HOOH*) species from direct OOH* desorption. In this situation, our two-dimensional umbrella sampling uses the O-H coordination number ξ + for H + transfer towards HOOH* (x-axes in Fig. ) and the height of the molecule's center of mass above Au(111) to describe desorption (y-axes in Fig. ). In a similar style as previously, the results of this analysis are presented in Fig.