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number of surface atoms and
ʔ
i
reflects the closed shell requirements of the
interstitial group of atoms, i.e. 34 for M
2
, 48 for M
3
, 60 for a tetrahedron, 86 for
octahedron and 162 for a centred icosahedron or cuboctahedron.
The model has important implications for the insulator to conductor transition
for metal clusters and nano-particles. The recognition that even high nuclearity
clusters conform to electron counting rules suggests that they are attaining well-
defined closed shells. This behaviour is different from that which is characteristic of
the bulk metal, which has partially filled bands. As the nuclearity of the cluster
increases, the HOMO-LUMO gaps which define the closed shells decreases and the
electron counting rules will become less valid.
3.6 Bonding Interrelationships Between Organothiolato-
and Gold Phosphine Clusters
Following the development of flexible and convenient syntheses of organothiolato-
gold cluster in the 1990s, a wide range of cluster compounds with radii less than
2 nm have been isolated and studied. The synthesis, separation and crystallisation of
these new cluster compounds and their detailed structural analysis by single crystal
X-ray crystallographic techniques presented a tremendous challenge to experimen-
talists, but their efforts have been rewarded by the determination of some key
clusters structures, which have provided a profound insight into the structures of
gold clusters, nanoparticles and colloids [
32
,
33
,
91
-
96
].
Until 2007 [Au
39
(PPh
3
)
14
Cl
6
]
2+
, which has a close-packed core of gold atoms
stabilised by phosphine and chloro-ligands, represented the highest nuclearity gold
cluster compound [
21
]. It was initially assumed that organothiolato-gold cluster,
which were isolated from the reductive routes developed initially for making gold
colloids, also had structures based on a central close-packed core of gold atoms
stabilised by SR ligands. It was appreciated, however, that SR ligands are more
flexible than phosphines because they are able to bridge edges and faces of a close-
packed gold polyhedron of metal atoms in a way which is not accessible to a simple
Lewis base such as PR
3
. The structural determinations of [Au
102
(p-MBA)
44
] and
[Au
25
(SCH
2
CH
2
Ph)
18
]
represented major breakthroughs [
91
-
94
], because they
demonstrated that these clusters have several interesting features which differenti-
ated them from the previously studied gold phosphine clusters. The structures
revealed that in addition to an approximately spherical close-packed core of gold
atoms, some of the gold atoms had separated from the core and combined with the
SR ligands to form novel bidentate ligands, which are bound to the central metal
core by dative S-Au bonds. Figure
22
illustrates the [Au(SR)
2
] and [Au
2
(SR)
3
]
metallothiolato-ligands, which have been revealed by recent crystallographic stud-
ies, and shows how these ligands bond to the central cluster core. The adoption of
two distinct roles by the gold atoms in these gold cluster molecules has been
described as the “divide and protect” principle. The oligomeric ligands [Au(SR)
2
]
