Trends in the structure and bonding of noble metal clusters

Abstract

We present a systematic study of the electronic properties and the geometric structure of noble metal clusters X n (X = Cu, Ag, Au; =−1,0, +1; n ഛ 13 and n =20), obtained from first-principles generalized gradient approximation density functional calculations based on norm-conserving pseudopotentials and numerical atomic basis sets. We obtain planar structures for the ground state of anionic ͑ =−1͒, neutral ͑ =0͒, and cationic ͑ =1͒ species of gold clusters with up to 12, 11, and 7 atoms, respectively. In contrast, the maximum size of planar clusters with =−1,0, +1 are n = ͑5,6,5͒ for silver and (5,6,4) for copper. For X 20 we find a T d symmetry for gold and a compact C s structure for silver and copper. Our results for the cluster geometries agree partially with previous first-principles calculations, and they are in good agreement with recent experimental results for anionic and cationic gold clusters. The tendency to planarity of gold clusters, which is much larger than in copper and silver, is strongly favored by relativistic effects, which decrease the s-d promotion energy and lead to hybridization of the half-filled 6s orbital with the fully occupied 5d z 2 orbital. That picture is substantiated by analyzing our calculated density matrix for planar and three-dimensional clusters of gold and copper. The trends for the cohesive energy, ionization potentials, electron affinities, and highest accupied and lowest unoccupied molecular orbital gap, as the cluster size increases, are studied in detail for each noble metal and rationalized in terms of two-and three-dimensional electronic shell models. The most probable fragmentation channels for X n clusters are in very good agreement with available experiments.

A first principles density functional investigation of ligand-protected eight atom gold nanoclusters

“…The structures were then optimized and the binding energies E B 's were calculated and average bond lengths were obtained. In accordance with previously reported results 13,[15][16][17][18]37 we find the edge-bridged rhombus (star) structure (left most figure in the top panel of Fig. 1) to be the most stable of the 2D structures (E B = 2.78 eV/atom).…”

“…For vertical IPs and EAs, the total energies were obtained at the optimized coordinates of the neutral cluster with a difference in the number of electrons and for adiabatic IPs and EAs, the geometries were relaxed. We have calculated the hybridization between the s and d states according to Ref [15]:…”

“…Theoretical calculations for neutral clusters have predicted the transition to occur at six, 8 seven, 9, 10 eight 11,12 as well as in the range from 11-15 atom clusters. [13][14][15][16][17][18][19][20] It has been anticipated that the different methods and models adopted to determine the cluster size at which the 2D-3D transition takes place can possibly be one of the reasons for the large spread in the obtained results (from [6][7][8][9][10][11][12][13][14][15]. Gold clusters are reported to retain their planar structures to cluster sizes larger compared to Ag and Cu clusters which remain planar upto 7 atom cluster sizes only.…”

“…Several experimental and theoretical studies have predicted this number to fall in a range from 6 to 13. [8][9][10][11][12][13][14][15][16][17][18][19][20] For anionic and cationic gold clusters the 2D-3D transitions are observed to occur at N = 13 and N = 8, respectively. Theoretical calculations for neutral clusters have predicted the transition to occur at six, 8 seven, 9, 10 eight 11,12 as well as in the range from 11-15 atom clusters.…”

Phase Transitions in Metal Clusters and Cluster Catalysts

“…This process may be considered to be a result of structural transitions for a gold clusters when they bond with CO molecules. 34 One more example of this type relates to a fuel cell with a platinum catalyst in which the oxidation of hydrocarbons (and possibly hydrogen) creates an electric potential; that is, chemical energy is converted to electrical energy. Then, the addition of gold clusters to a platinum surface increases the lifetime of the catalyst without its becoming contaminated.…”