Figure 3

The minimum energy path (MEP) of the Tafel (A) and Heyrovský (B) reactions (top) as derived from density functional theory (DFT) calculations using the climbing image nudged elastic band (NEB) method on a Mg(0001) surface. Each NEB computation consists of 24 images; the MEP is presented by a force-based cubic spline. Initial and final states are illustrated along with their according energy barriers \(E_{\mathrm{c}}\) and \(E_{\mathrm{d}}\). Tafel: (a) Two adsorbed \(\hbox {H}^{-}\) atoms (b) Passing bridging site (c) Adsorption at adjacent hcp and fcc sites (d) Decreasing distance at bridging site (transition state) (e) adsorbed \(\hbox {H}_2\) (f) \(\hbox {H}_2\) desorbs. Heyrovský: (a) Relaxed water bilayer with adsorbed \(\hbox {H}^-\) (b) Rotation of \(\hbox {H}_2\hbox {O}\) and surface interaction (c) Dissociation (transition state) (d) \(\hbox {H}_2\) formation, integration of \(\hbox {OH}^{-}\) into water bilayer (e) breaking H bond (f) OH adsorption. (bottom) Top view of the images (a-f). Atoms are colored according to their respective Bader charge. For the sake of clarity, the representation of the charges was limited to a range between − 1 and 1 as the charges of atoms involved in the reactions do not exceed these values.