Free energy sampling is performed using one or two collective variables (CVs). For a simple OOH* dissociation step (step (ii) in Fig. ), the CV is straightforwardly defined as the intermolecular O-O distance. Similarly, for OOH* desorption (step (iv) in Fig. ), we can simply use the height of the molecule's center of mass above the Au surface. For the protonation steps (steps (i) & (iii) in Fig. ), however, we use two variants ξ ± of the coordination number CV: 36 ξ -counts the difference in covalently bonded H atoms between the two O atoms and is therefore used for studying protonation of the outer O leading to H 2 O. On the other hand, ξ + counts the total number of H atoms that form covalent bonds to the two O atoms and is an appropriate CV for the protonation step producing H 2 O 2 . More information on how these CVs are defined is provided in the SI, Section S4.1.