From clusters to bulk: A relativistic density functional investigation on a series of gold clusters Aun, n=6,…,147

Abstract

A series of gold clusters spanning the size range from Au6 through Au147 (with diameters from 0.7 to 1.7 nm) in icosahedral, octahedral, and cuboctahedral structure has been theoretically investigated by means 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 exchange-correlation functional. The average gold–gold distance in the clusters increases with their nuclearity and correlates essentially linearly with the average coordination number in the clusters. An extrapolation to the bulk coordination of 12 yields a gold–gold distance of 289 pm in LDA, very close to the experimental bulk value of 288 pm, while the extrapolated GGA gold–gold distance is 297 pm. The cluster cohesive energy varies linearly with the inverse of the calculated cluster radius, indicating that the surface-to-volume ratio is the primary determinant of the convergence of this quantity toward bulk. The extrapolated 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 potentials and electron affinities of the clusters may be related to the metallic droplet model, although deviations due to the electronic shell structure 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 work function of bulk gold, 5.1 eV. Gold 4f core level binding energies were calculated for sites with bulk coordination and for different surface sites. The core level shifts for the surface sites are all positive and distinguish among the corner, edge, and face-centered sites; sites in the first subsurface layer show still small positive shifts.

Global minima of AlN, AuNand PtN,N⩽ 80, clusters described by the Voter–Chen version of embedded-atom potentials

“…Experiments suggest that gold nanoclusters with diameters of 1-2 nm, corresponding to aggregates with N=20-200 atoms, are amorphous [62,63]. The theoretical studies on gold nanoclusters change from empirical MD or MC simulations using EAM [67], Gupta [68], Sutton-Chen [14] and Murrell-Mottram [69] potentials to some first-principle calculations using DFT [70,71], generalized gradient approximation [72], spin-polarized Becke-Lee-Yang-Parr functional [73], and Hartree-Fock and post Hartree-Fock levels [74].…”

Density-functional study ofAun(n=2–20)clusters: Lowest-energy structures and electronic properties

“…From our calculations, the cuboctahedron is more stable than icosahedron, which has been predicted by Häberlen. 15 We have also examined the bond lengths distributions of different isomers for Au 13 . The disordered isomer shows broader bond length distributions than those for the high symmetric structures.…”

“…Bravo-Pérez et al investigated small gold clusters up to 6 atoms at ab initio Hartree-Fock (HF) and post-HF 24 level. For the large clusters with up to 147 atoms, Häberlen et al performed a scalar relativistic all-electron density functional calculations on several magic-sized clusters with icosahedral, octahedral and cuboctahedral structures 15 . By combining pseudopotential DFT calculations with an empirical genetic algorithm, Garzón found amorphous structures in Au n (n = 38, 55, 75) clusters.…”

“…Most previous ab initio calculations on gold clusters are limited by the presumed symmetric constraints. 5,15 A unconstrained global search on the cluster potential energy surface is needed. 13 In this work, we generate a number of structural isomers from empirical genetic algorithm simulations.…”

“…[1][2][3][4] During the past two decades, the structures of gold clusters have been studied both experimentally [5][6][7][8][9][10] and theoretically. [11][12][13][14][15][16][17][18][19][20][21][22] Experiments suggest that gold nanoclusters with diameters of 1 − 2 nm are amorphous. 5,6 Theoretical results from empirical molecular dynamics simulations or first-principles calculations also support this argument.…”