Determining Potentials of Zero Charge of Metal Electrodes versus the Standard Hydrogen Electrode from Density-Functional-Theory-Based Molecular Dynamics

We develop a computationally efficient scheme to determine the potentials of zero charge (PZC) of metal-water interfaces with respect to the standard hydrogen electrode. We calculate the PZC of Pt(111), Au(111), Pd(111) and Ag(111) at a good accuracy using this scheme. Moreover, we find that the interface dipole potentials are almost entirely caused by charge transfer from water to the surfaces, the magnitude of which depends on the bonding strength between water and the metals, while water orientation hardly contributes at the PZC conditions.

Figure 1

(a) The upper panel sketches the process of computing the reference deprotonation free energies of a solvated hydronium ion in interface and pure water models under the PBC (${\mathrm{\Delta }}_{\mathrm{DP}}{A}_{{\mathrm{H}}_3{\mathrm{O}}^{+}}^{(i)}$ and ${\mathrm{\Delta }}_{\mathrm{DP}}{A}_{{\mathrm{H}}_3{\mathrm{O}}^{+}}^{(w)}$, respectively). The lower panel indicates how the potential “zero” is aligned to the SHE scale. $C$ is a constant, equal to $-{\mu }_{{\mathrm{H}}^{+}}^{g,\circ }-\mathrm{\Delta }{E}_{\mathrm{ZP}}$ in Eqs. (1) and (2). $\mathrm{\Delta }V$ stands for the HPS difference between the periodic interface and pure water models. (b) Schematic representation of the alignment of electrostatic potentials of bulk water in periodic interface and pure water models (${\varphi }_{\text{wat}}^{(i)}$ and ${\varphi }_{\text{wat}}^{(w)}$, respectively).

Figure 2

The profiles of water density (a), dipole orientation (b), and electron redistribution (c) along the surface normal $z$ at the Pt(111) and Au(111) water interfaces. They are obtained by averaging over the two symmetric interfaces in our models. The zero in $z$ coordinates indicates the position of the metal surface.

Figure 3

(a) A snapshot of the Pt(111)-water interface model. Pt, O, and H atoms are in silver, red, and white, respectively. Depending on the positions, watA, watB, and watC are distinguished and represented by balls, bonds, and lines, respectively. (b) Projected DOS plots of Pt and water at the interface computed by the PBE functional. They are averaged over a DFTMD trajectory.