Hydrogen dissociation on Mg(0001) studied via quantum Monte Carlo calculations

We have used diffusion Monte Carlo (DMC) simulations to calculate the energy barrier for ${\text{H}}_2$ dissociation on the Mg(0001) surface. The calculations employ pseudopotentials and systematically improvable $B$-spline basis sets to expand the single-particle orbitals used to construct the trial wave functions. Extensive tests on system size, time step, and other sources of errors, performed on periodically repeated systems of up to 550 atoms, show that all these errors together can be reduced to $\sim 0.03\text{eV}$. The DMC dissociation barrier is calculated to be $1.18\pm 0.03\text{eV}$ and is compared to those obtained with density-functional theory using various exchange-correlation functionals, with values ranging between 0.44 and 1.07 eV.

Figure 1

(Color online) Initial-state (left), transition state (center), and final-state (right) geometries for the ${\text{H}}_2$ dissociation reaction on the Mg(0001) surface. Top and bottom panels show side and top views, respectively.

Figure 2

(Color online) Minimum-energy profiles for the ${\text{H}}_2$ dissociation reaction on the Mg(0001) surface calculated with various DFT functionals: LDA (black stars), PW91 (blue triangles), PBE (green diamonds), and RPBE (red circles). Also shown are the DMC energies (maroon squares) at the TS and the FS. Lines are guides for the eyes.

Figure 3

(Color online) Diffusion Monte Carlo energies for the initial state (black circles), the transition state (red squares), and the final state (green triangles) for the ${\text{H}}_2$ dissociation reaction on the Mg(0001) surface as a function of $N^{-5/4}$, with $N$ as the number of atoms in the simulation cell.

Figure 4

(Color online) Diffusion Monte Carlo energy differences between the transition state and the initial state (red squares) and between the final state and the initial state (green triangles) for the ${\text{H}}_2$ dissociation reaction on the Mg(0001) surface as a function of $N^{-5/4}$, with $N$ as the number of atoms in the simulation cell.