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atom of the [Au(SR)
2
] and [Au
2
(SR)
3
] staple ligands. The higher curvature of
the core surface in the lower nuclearity clusters results in a preference for
[Au
2
(SR)
3
] staples and [Au(SR)
2
] staples in higher nuclearity clusters. Theoret-
ical calculations have also indicated that the [Au
3
(SR)
4
] and [Au
4
(SR)
5
] ligands
may also act as staples.
3. Bridging SR ligands have only been observed to date in lower nuclearity
clusters.
Knowledge of these structural generalisations combined with DFT calculations
have led Pei and Zeng [
106
-
111
] to propose a more general “inherent structural
rule”, which highlights principles based on the constraints which accompany
the general formula of the subset of clusters, which do not have SR ligands,
i.e. [Au]
a
+
a
0
[Au(SR)
2
]
b
[Au
2
(SR)
3
]
c
, where
a
,
a
0
,
b
,
c
,
are integers. This analysis
provides a more efficient starting point for DFT calculations by limiting the number
of initial structures which have to be considered. H¨kkinen has proposed an
alternative “superatom model” for these gold clusters which draws heavily on the
jellium model described above and to a lesser extent on earlier theoretical studies on
gold phosphine clusters [
97
,
99
-
105
]. This superatom model which is based on the
Aufbau filling of the electronic shells 1s
...
<
1p
1d
<
2s
<
1f
<
2p
<
1g
<
2d
<
. The superatom approach partitions the cluster so that the total
number of free valence electrons in a cluster [Au
m
(SR)
n
]
q
is
m
-
n
-
q
where
m
is
the number of gold atoms. This corresponds to sec defined above. It follows that
[Au
25
(SCH
2
CH
2
Ph)
18
]
and [Au
102
(p-MBA)
44
] have 8 and 58 free valence
electrons which correspond to the following shell closings in the jellium model:
1s
2
1p
6
and 1s
2
1p
6
1d
10
2s
2
1f
14
2p
6
1g
18
.H¨kkinen has promoted the extension of
the jellium model to these “superatom” clusters with closed shells for 2, 8, 20, 34,
40, 58, 92, 138 and 198 electrons. H
¨
kkinen has also developed his model to
understand the reactivities of gold cluster in catalysis. Both approaches described
above have provided valuable insights into the bonding in organothiolato-gold
clusters, although they have not fully united the phosphine and organothiolato-
subdisciplines. The following section provides an analysis which encourages the
attainment of this goal.
3s
<
1h
...
3.7 Construction of Organothiolato-Clusters from Phosphine
Cluster Building Blocks
The bonding paradigm for phosphine clusters summarised in Fig.
21
may be used as
a convenient starting point for understanding the structures and stoichiometries of
organothiolate clusters and also serves a useful role in reducing the number of
options required for more detailed DFT calculations [
106
]. Initially one may
imagine that for [Au
m
(SR)
n
]
q
the DFT calculations may be used to minimise the
energy until a global minimum is identified, but the process is complicated by the
“divide and protect” principle which has the gold atoms alternating between ligand
