Chemistry Reference
In-Depth Information
Au
79
SR
21
Au
79
Au
SR
2
21
Au
79
Au
2
SR
3
21
21
þ
½
Au
79
L
42
Au
79
Au S
ð
2
19
Au
2
SR
3
3
:
The latter is the structurally determined structure with the Au
2
(SR)
3
ligands and
the Au(SR)
2
capping opposite vertices of square faces.
3.8
Inherent Structure Rule and the Superatom Model
[
97
,
99
-
112
]
In the initial stages of characterisation when the formula of [Au
m
(SR)
n
] has been
established, but the single crystal analysis has not defined the structure, it is helpful
to reduce the number of structural possibilities. The previous section has suggested
a method for reducing the possibilities based on phosphine analogies. Tsukuda
[
112
] and Pei and Zeng [
106
-
111
] have proposed an alternative algorithm for a
subset of gold clusters with the general formula [Au]
a
+
a
0
[Au(SR)
2
]
b
[Au
2
(SR)
3
]
c
.
They have set up a set of equations which limit the number of structural possibil-
ities, and the following section amplifies their analyses and relates it to the bonding
analyses described in the previous section. The problem is mathematically
underdetermined and consequently multiple integer solutions result. The relation-
ships between the integer variables combine mathematically and chemically based
information in order to limit the number of structural possibilities. Taking as a
specific example [Au
25
(SR)
18
]
, which may be represented as [Au]
a
+
a
0
¼ [Au]
1+12
,
where
a
¼ 1 (representing the interstitial atom) and
a
0
¼ 12 (the surface atoms of
the core which bond to SR), and
c
¼ 6; [Au
102
(SR)
44
] is represented as [Au]
39+40
[Au(SR)
2
]
19
[Au
2
(SR)
3
]
2
, with
b
¼ 19 and
c
¼ 4. More generally for [Au]
a
+
a
0
[Au(SR)
2
]
b
[Au
2
(SR)
3
]
c
the following mathematical relationships follow directly
from the general formula by connecting the variables which contain the number of
SR ligands,
n
, the number of metal atoms,
m,
and the number of metal sites which
form metal-sulphur bonds to the bidentate gold organothiolato-ligands:
n
¼ 2
b þ
3
c
:
ð
2
Þ
m
¼
a þ a
0
þ b þ
2
c
:
ð
3
Þ
a
0
¼ 2
b þ
2
c
:
ð
4
Þ
Equation (
3
) follows from the recognition that each of the
a
0
outer surface gold
atoms are coordinated to one sulphur atom and both [Au(SR)
2
] and [Au
2
(SR)
3
]
have two sulphur donors. This limits
a
0
to an even integer. This conclusion agrees
with that proposed in the previous section, namely SR, Au(SR)
2
or Au
2
(SR)
3
replace two phosphine ligands in [A
a
+
a
0
(PR
3
)
a
0
]
x
+
clusters. Some of the clusters
with SR ligands have two SR ligands coordinated to a single gold atom, and
