Quantum Monte Carlo for Activated Reactions at Solid Surfaces: Time Well Spent on Stretched Bonds

摘要

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 N2 dissociation. The molecule is strongly bound and stretched geometries are chosen. Heterogeneous catalysis by copper is simulated. It was investigated in our previous work as it is in many ways a prototype metal presenting a close-packed surface here. These nitrogen molecules are adsorbed on copper and fixed geometries on the dissociation reaction pathway for stretched N2 are given using density functional theory (DFT) calculations in a plane-wave basis. This dissociating molecule appears to be underbound using the ab initio Perdew, Burke, Ernzerhof (PBE) DFT functional but while this phenomenon accounts for a few percent at 5 ?, at 6 ?, PBE gives less than 30% of the binding energy. This indicates the onset of dissociation. The PBE wave-functions at these bondlengths 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. The geometries from this bond-stretching study mimic the transition state (TS). This procedure requires no search for the actual TS geometry. 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. Unfolding the cell to simulate a 9 k-point grid (rather than a single k-point) reduces the remainder by at least a factor 130 but relations for calibrating the remaining (2 mHa) error on converged grids are also used. The pseudopotential 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 pseudopotential. VC 2014 Wiley Periodicals, Inc.