Locating the rate-limiting step for the interaction of hydrogen with $\mathrm{Mg}\left(0001\right)$ using density-functional theory calculations and rate theory

The dissociation of molecular hydrogen on a $\mathrm{Mg}\left(0001\right)$ surface and the subsequent diffusion of atomic hydrogen into the magnesium substrate is investigated using Density Functional Theory (DFT) calculations and rate theory. The minimum energy path and corresponding transition states are located using the nudged elastic band method, and rates of the activated processes are calculated within the harmonic approximation to transition state rate theory, using both classical and quantum partition functions based atomic vibrational frequencies calculated by DFT. The dissociation/recombination of ${\mathrm{H}}_2$ is found to be rate-limiting for the ab- and desorption of hydrogen, respectively. Zero-point energy contributions are found to be substantial for the diffusion of atomic hydrogen, but classical rates are still found to be within an order of magnitude at room temperature.

Figure 1

(Color) The transition state for the dissociation of a hydrogen molecule (white) on a $\mathrm{Mg}\left(0001\right)$ surface (green). The $2\times 2$ supercell (red) consists of 5 closed packed (0001) layers. The adsorption sites “$\mathrm{A}$” (octahedral) and “$\mathrm{B}$” (tetrahedral) are termed fcc- and hcp-sites, respectively.

Figure 2

(Color) The dissociation pathway for a hydrogen molecule on a $\mathrm{Mg}\left(0001\right)$ surface. The corresponding activation energy as a function of the reaction coordinate is found in Fig. 3.

Figure 3

The barrier for dissociation of a ${\mathrm{H}}_2$ molecule on a $\mathrm{Mg}\left(0001\right)$ surface as a function of the reaction coordinate $\left(\mathrm{\AA }\right)$. The NEB simulation consists of 21 images, and the spline-fit includes the forces to determine the gradients at each point.

Figure 4

The barrier for hydrogen diffusion from the hcp to the fcc site, and onward down the “fcc-channel,” as a function of the reaction coordinate $\left(\mathrm{\AA }\right)$. The NEB-simulation consist of 25 images located between ${\mathrm{IS}}_0^{\prime }$ and ${\mathrm{FS}}^{\prime }$, passing three transition states (${\mathrm{TS}}_1^{\prime }$, ${\mathrm{TS}}_2^{\prime }$, and ${\mathrm{TS}}_3^{\prime }$).