We have used diffusion Monte Carlo (DMC) simulations to calculate the energy barrier for 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 wavefunctions. 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 $sim 0.03$ eV. The DMC dissociation barrier is calculated to be $1.18 pm 0.03$ 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.
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