Model Catalysts Based on Au Clusters and Nanoparticles - Gold Clusters, Colloids and Nanoparticles - page 101

Fig. 8 Spin-averaged
LDOS and orbital shapes for
(a)anAumonomer,(b)a
dimer, and (c) a trimer on
alumina/NiAl(110), as
calculated with DFT. The
black line marks the total Au
LDOS; the blue and red
lines denote the s- and
p z -contributions,
respectively. The dashed
line depicts the alumina
states. (d, e)Experimental
dI/dV spectra and
topographic images of an Au
monomer and a dimer.
(f) Trimer spectrum with
dI/dV images taken at the
two peak positions. All
images are 4.5 4.5 nm 2 in

size; the set point for
spectroscopy was set to
3.0 V

orbitals to QWS formed in the 1D potential well [ 43 , 51 ]. There, the HOMO of the
Au monomer derives from the Au 6s orbital and is doubly occupied ( E bind ¼

1.3 eV, Fig. 8a ). This double occupancy reflects the negative charge on the
adatom, as gas-phase Au features an Au 6s 1 ground state. The LUMO is a p z -like
state that locates at +2.5 eV above E F , hence inside the alumina conduction band. In
Au dimers, the two 6s orbitals hybridize and form two new states at

0.3 and

1.5 eV. Both states are filled, which brings the total number of s-electrons in the
dimer to four. As two of these electrons are transfer electrons from the NiAl
substrate, the Au 2 is twofold negatively charged. The Au 2 LUMO shifts to
+1.9 eV due to the superposition of the two p z states of each monomer (Fig. 8b ).
In linear Au 3 , a third s-like state appears directly at the Fermi level, while the two
other QWS shift to 2.5 eV. Due to the half-filled nature of the HOMO,

five s-electrons occupy the Au 3 valence orbitals, three intrinsic Au 6s electrons and
two transfer electrons from the metal beneath. The lowest-unoccupied Au 3 states
are the symmetric and antisymmetric combination of the 6p z orbitals, giving rise to
two QWS at +1.9 and +2.8 eV, respectively.
In extension of this concept, the electronic structure of an m-atom Au chain
arises from the consecutive splitting of the 6s- and 6p-like states and results in the
development of m mainly occupied s-derived QWS and m empty states with
p z -character (Fig. 9 ). The s-like states display the characteristic properties of a
particle-in-a-box system with infinite walls [ 43 ]. The eigenfunctions are sinusoidals
(

1.8 and

sin k n x ), defined by a wave-number k n that is proportional to the inverse
box-length L and a quantum number n :( k n ¼

ˈ n ¼

n π / L ). The resulting electron