FROM CLUSTERS TO BULK - A RELATIVISTIC DENSITY-FUNCTIONAL INVESTIGATION ON A SERIES OF GOLD CLUSTERS AU-N, N=6,...,147

A series of gold clusters spanning the size range from Au-6 through Au -147 (with diameters from 0.7 to 1.7 nm) in icosahedral, octahedral, a nd cuboctahedral structure has been theoretically investigated by mean s of a scalar relativistic all-electron density functional method. One of the main objectives of this work was to analyze the convergence of cluster properties toward the corresponding bulk metal values and to compare the results obtained for the local density approximation (LDA) to those for a generalized gradient approximation (GGA) to the exchan ge-correlation functional. The average gold-gold distance in the clust ers increases with their nuclearity and correlates essentially linearl y with the average coordination number in the clusters. An extrapolati on to the bulk coordination of 12 yields a gold-gold distance of 289 p m in LDA, very close to the experimental bulk value of 288 pm, while t he extrapolated GGA gold-gold distance is 297 pm. The cluster cohesive energy varies linearly with the inverse of the calculated cluster rad ius? indicating that the surface-to-volume ratio is the primary determ inant of the convergence of this quantity toward bulk. The extrapolate d LDA binding energy per atom, 4.7 eV, overestimates the experimental bulk value of 3.8 eV, while the GGA value, 3.2 eV, underestimates the experiment by almost the same amount. The calculated ionization potent ials and electron affinities of the clusters may be related to the met allic droplet model, although deviations due to the electronic shell s tructure are noticeable. The GGA extrapolation to bulk values yields 4 .8 and 4.9 eV for the ionization potential and the electron affinity, respectively, remarkably close to the experimental polycrystalline wor k function of bulk gold, 5.1 eV. Gold 4f core level binding energies w ere calculated for sites with bulk coordination and for different surf ace sites. The core level shifts for the surface sites are all positiv e and distinguish among the corner, edge, and face-centered sites; sit es in the first subsurface layer show still small positive shifts. (C) 1997 American Institute of Physics.