Chemistry Reference
In-Depth Information
therefore Eq. (
4
) is no longer valid. These clusters resemble those phosphine
clusters which do not conform to the simple formula [Au
n
(PR
3
)
n
]
x
+
(see Fig.
7
).
Accepting this caveat it follows that
b n
/2 and
c n
/3 and that [Au(SR)
2
] and
[Au
2
(SR)
3
] will only coexist when
n
is divisible by 3 and 4, i.e.
n
¼ 12, 24, 36,
48
, and if it is only divisible by 3, then only [Au
2
(SR)
3
] will be present with
c
¼
n
/3 and
b
¼
0. [Au(SR)
2
] will be exclusively present when
n
is even and not
divisible by 2, i.e. when
n
¼
10, 14, 16, 20, 22, 26, 28, 32
...
, and will equal to
n
/2.
Since the total number of SR groups must equal those in the two ligand classes in
the ratio 2:3,
b
max
¼
a
0
max
/2 and
c
max
¼
a
0
max
/3. The number of solutions to
Eqs. (
2
)-(
4
)is{(
b
max
b
min
)/3 + 1} and {(
c
max
c
min
)/2 + 1} (see Fig.
23
). Pei
and Zeng [
109
] have confirmed that for [Au
38
(SR)
24
] the equations lead to the
following 5 possibilities:
...
2
þ
24
Au
SR
2
12
Au
3
þ
22
Au
SR
2
9
Au
2
SR
3
2
½
Au
½
4
þ
20
Au
SR
2
6
Au
2
SR
3
4
Au
5
þ
18
Au
SR
2
3
Au
2
SR
3
6
g
½
Au
½
6
þ
16
Au
SR
2
0
Au
2
SR
3
8
½
Au
Pei and Zeng [
109
] explored these alternative possibilities using DFT calcula-
tions and concluded that [Au]
5+18
{[Au(SR)
2
]
3
[Au
2
(SR)
3
]
6
} (in bold above) was the
most stable by a large margin. The structure which is based on a bi-icosahedral
structure with two icosahedra fused subunits forming the core and the staples
distributed evenly over this core has been described above and illustrated in
Fig.
26
. Their recent review [
109
] has expanded on the consequences of “the
inherent structural rule” and DFT calculations to other gold thiolato-clusters.
The above solutions form a series which may be understood by recognising that
addition of an interstitial atom to the core (
a ! a
+ 1) removes a pair of donor S
sites from
b
and
c
and therefore
a
0
must be reduced by 2. Furthermore, the loss of a
gold atom from the staples must be compensated by replacing [Au(SR)
2
] ligands by
[Au
2
(SR)
3
] in the ratio of 2:3, i.e.
a !
(
a
+ 1) leads
b !
(
b
2) and
c !
(
c
+ 2),
thereby satisfying the following equation:
Au
þ b
Au S
ð
2
þ c
Au
2
S
ð
3
! b
3
ð
Þ
Au S
ð
2
þ c þ
2
ð
Þ
Au
2
S
ð
3
:
The limited restraints on
a
,
a
0
and
a
+
a
0
makes it impossible to reduce the
number of possibilities further unless additional constraints are introduced.
The five solutions enumerated above have been based exclusively on the for-
mulae of the compounds and the valency requirements of sulphur and gold(I).
Additional relationships may be derived if the conclusions of the molecular orbital
analysis and electron counting rules discussed in the previous section are incorpo-
rated. Specifically the sec count of cluster
s
is equal to
m n
, because the total
number of gold atoms contributes
m
6s valence electrons, but
n
gold atoms bare a
charge of +1 because of coordination to SR ligands to make up the staple ligands.
