Au ₂₀ : A Tetrahedral Cluster

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Relativistic density functional calculations on Au 20 and its anion were performed at the level of a generalized gradient approach using a Perdew-Wang exchange-correlation functional (30). The zero-order regular approximation Hamiltonian was used to account for the scalar (mass velocity and Darwin) and spin-orbit relativistic effects (31). The standard Slater-type orbital basis sets with quality of triple-zeta plus p - and f -polarization functions (TZ2P) were used for the valence orbitals of the Au atoms with frozen core approximation to the [1 s 2 -4 f 14 ] core. The vertical detachment energies of the anions were calculated via the self-consistent field energy difference between the neutral and anion ground states and the excitation energies of the neutral state calculated by the time-dependent density functional theory method (32). All the calculations were accomplished with the Amsterdam Density Functional (ADF 2002) program (33). We found that these theoretical methods are suitable for smaller gold clusters as well as for gold clusters doped with an impurity atom (28).

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The calculations show that the A B and C peaks in the PES spectra (Fig. 1) correspond to the triplet and singlet states formed by electron detachment from the HOMO (16e) and HOMO-1 (29t 2 ) wheras the D and E peaks are due to transitions from HOMO-2 (18t 1 ). See the supporting online material (fig. S1) for the molecular orbital energy-level diagram of T d Au 20 .

Preliminary calculations on four CO molecules absorbed on the apex and face-center sites reveal a HOMO-LUMO gap of 1.43 and 1.50 eV for the Au 20 (CO) 4 clusters and a binding energy of 0.84 and 0.15 eV per CO molecule respectively. The large HOMO-LUMO gaps in the naked and CO-adsorbed clusters indicate that the T d Au 20 is highly chemically inert and will maintain its structural integrity during catalysis.

We thank B. Kiran for helpful discussion. This work was supported by NSF (grant CHE-9817811) and performed at the Environmental Molecular Sciences Laboratory (EMSL) a national scientific user facility sponsored by the U.S. Department of Energy's (DOE's) Office of Biological and Environmental Research and located at Pacific Northwest National Laboratory operated for DOE by Battelle. All the calculations were performed with supercomputers at the EMSL Molecular Science Computing Facility.