Quantum Monte Carlo studies of 13-atom simple metallic clusters

We have performed diffusion quantum Monte Carlo calculations for nine isomers of 13-atom clusters of the sp-bonded elements Li, Na, Be, Mg, and Al and compared the energies with density functional theory (DFT) results. Taking the diffusion Monte Carlo (DMC) data as the benchmark, we find that the local spin-density approximation (LSDA) and Perdew-Burke-Ernzerhof (PBE) semilocal generalized gradient approximation functionals give good descriptions of the energy differences between the clusters for each of the elements and their cations. The errors in the energy differences between clusters are a little larger for the PBE functional, but on average the errors for both functionals are smaller than 10 meV per atom, except for Be₁₃ clusters, which yield errors of 17 and 22 meV per atom from LSDA and PBE, respectively. We have, in addition, investigated using an inhomogeneous backflow transformation to improve the nodal surface of the trial wave functions used in the DMC calculations. We find that backflow lowers the DMC energies but does not affect the relative stabilities of the clusters.