  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.
