Quantum Monte Carlo activation barrier for hydrogen dissociation on copper to unprecedented accuracy

Abstract: Many chemical reactions involve bond-dissociation. This is also true for reactions at solid surfaces, in which the dissociation step is often limiting but facilitated in comparison to gas phase reaction channels. This work considers hydrogen dissociation. Reliable molecular beam results are available for this reaction at some copper surfaces. Heterogeneous catalysis by copper is simulated. It was investigated in our previous work since it is in many ways a prototype metal presenting a close-packed surface here. These hydrogen molecules are adsorbed at Cu(111) and fixed geometries on the dissociation reaction pathway for stretched and distant equilibrium H$_2$ are given by using Density Functional Theory (DFT) calculations in a plane wave basis. The PBE wave-functions at these bond-lengths serve as trial input for Quantum Monte Carlo (QMC) simulations of the ground states to obtain highly accurate correlated results for the associated activation barriers indicating the catalytic effect on this dissociation. This correlation varies as bonds dissociate, requiring its accurate evaluation. Finite size effects and fixed-node error are possible limitations to accuracy of this type of QMC study. We are able to limit fixed node error, using certain trial wave-functions. The finite size effect is considerable, although comparing two adsorbed geometries cancels about 90% with respect to clean surfaces. The pseudo-potential used to represent the atomic core of copper must also be determined carefully: we leave 11 active electrons but include the 3d shell in the pseudo-potential.