Quantifying electron-correlation effects in small coinage-metal clusters calculations.

We investigate many-electron correlation effects in neutral and charged coinage-metal clusters Cun, Agn, and Aun (n = 1-4) via ab initio calculations using fixed-node diffusion Monte Carlo (FN-DMC) simulations, density functional theory (DFT), and the Hartree-Fock (HF) method. From very accurate FN-DMC total energies of the clusters and the HF results in the infinity large complete-basis-set limit, we obtain correlation energies in these strongly correlated many-electron clusters involving d orbitals. The obtained bond lengths of the clusters, atomic binding and dissociation energies, ionization potentials, and electron affinities are in satisfactory agreement with the available experiments. In the analysis, the electron correlation effects on these observable physical quantities are quantified by relative correlation contributions determined by the difference between the calculated FN-DMC and HF results. We show that the correlation contribution is not only significant for the quantities related to electronic structures of the coinage-metal clusters, such as electron affinity, but it is also essential for the stability of the atomic structures of these clusters. For example, the electron correlation contribution is responsible for more than 90% of the atomic binding energies of the small neutral copper clusters. We also demonstrate the orbital-occupation dependence of the correlation energy and electron pairing of the valence electrons in these coinage-metal clusters from the electron correlation-energy gain and spin-multiplicity change in the electron addition processes, which are reflected in their ionization potentials and electron affinities.