Chemistry Reference
In-Depth Information
Therefore the number of electrons which remain for skeletal bonding in the gold
core is (
m n
):
s ¼
m n
:
ð
5
Þ
It follows from this that
s
is a constant for the series of isomers which are
consistent with the equations. Therefore
m
,
n
and
s
are constant for [Au
m
(SR)
n
] and
the equations may be used to define
a
,
a
0
,
b
,
c
and the charges on the central core
and the surface ligands.
H
¨
kkinen [
97
,
98
,
102
-
112
] has used this relationship to develop his superatom
model which has been discussed above. This analysis if used in conjunction with
the jellium model does not provide a specific geometric description of the cluster or
the number and type of staple ligands since it can only conclude that the cluster has
a spherical close-packed structure with a closed shell electronic shell with 8, 18,
20,
...
valence electrons.
The charge on the core gold cluster (
x
) and the staple ligands are equal and of
opposite sign. In a neutral [Au
m
(SR)
n
] and it follows that:
m
¼ s
þ x
:
ð
6
Þ
x
¼
b þ c
:
ð
7
Þ
x
¼
a þ a
0
s
:
ð
8
Þ
The total number of valence electrons for sulphur (3
n
) and gold (
m
) leads to the
following equalities:
3
n þ m
¼ 2
a
0
þ
4
b þ
8
c þ
s
:
ð
9
Þ
x
¼
n b
2
c
:
ð
10
Þ
The maximum value of
x
¼
b
max
and the minimum value ¼
c
max
¼ 8, whereas
s
is independent of
b
and
c
and
a
and
a
0
and is equal to 14 for all possible structures
in the series.
[Au
38
(SR)
24
]
a
a
0
b
c
x
s
[Au]
2+24
{[Au(SR)
2
]
12
}
2
24
12
0
12
14
[Au]
3+22
{[Au(SR)
2
]
9
[Au
2
(SR)
3
]
2
}
3
22
9
2
11
14
[Au]
4+20
{[Au(SR)
2
]
6
[Au
2
(SR)
3
]
4
}4
4
20
6
4
10
14
[Au]
5+18
{[Au(SR)
2
]
3
[Au
2
(SR)
3
]
6
} observed
5
18
3
6
9
14
[Au]
6+16
{[Au(SR)
2
]
0
] [Au
2
(SR)
3
]
8
6
16
0
8
8
14
s
carries the information regarding the relationship between the number of the
electrons in skeletal molecular orbitals and the polyhedral geometry of the core.
This links this approach to the polyhedral electron counting paradigm for gold
phosphine clusters summarised in Fig.
22
. Although
s
is constant within the series,
the other variables vary as shown above. Chemical considerations may be used to
