Chemistry Reference
In-Depth Information
provided guiding principles for unifying these areas, and this review has
summarised these developments and extended the analysis to a wider range of
clusters. This will perhaps emphasise that the two areas have many common
features and may both be understood within a common framework which is based
on free electron models. This review has suggested that although closed spherical
shells derived from the free electron model provide important milestones, the
kinetic control of the cluster growth sequence and the stabilising effects of the
ligands can lead to a wide range of cluster compounds which have partially filled
shells. In the context of cluster chemistry these partially filled shells have important
geometric consequences. Specifically, smaller clusters adopt spherical structures
when they have closed S
σ
,P
σ
or D
σ
shells, but those which have partially filled
shells adopt prolate and oblate structures when the P
σ
shell is partially filled. Larger
clusters may be described by a “superatom” spherical model, but only if the cluster
has a high sphericity index. For condensed clusters a polyspherical free electron
model which models the effect of spherical clusters fusing together through vertex,
edge and face sharing is more appropriate. Figure
28
suggests that the cluster
condensation process for two clusters is akin to two drops progressively coming
together. Initially the two drops retain their initial characteristics, but as they touch
they progress through a series of stages where the diameter of the newly formed
double drop decreases. Initially it has some concave surfaces at the interface and
then forms an oblate spheroid before finally forming a new sphere. The quantum
mechanical analogue of this is the formation of diatomic molecule from two
separated atoms and the final molecule which has been described for more than
80 years as the
united atom model
[
125
]. Therefore, there are a series of clusters
with 13-25 metal atoms which may be described using the
united cluster model
illustrated in Fig.
28
. The molecular orbitals of the condensed clusters are
represented by linear combinations of the molecular orbitals of the isolated clusters
in the same way that linear combinations of atomic orbitals are taken together in
diatomic molecules [
125
]. As the two initial clusters are squeezed together, the
number of available bonding molecular orbitals decreases until a super cluster is
formed which is characterised by a sec of 8 corresponding to occupation of S
σ
and
P
σ
. The figure also provides specific examples of clusters, which span the spectrum
of electron counts from 16 to 8. The examples are drawn from phosphine and
organothiolato-cluster areas. The sphericity and in particular the distance between
the two interstitial gold atoms play a very important role in determining the specific
position of a cluster along the united atom coordinate. Small changes in the ligands
or metals may influence the observed electron count. For example, the central fused
cuboctahedral kernel in [Au]
2+18
{[Au
2
(SR)
3
]
4
(
2
-SR)
8
} has a sec electron count of
8 making it analogous to [Pt
19
(CO)
17
]
8
, which has a fused icosahedral structure.
However, [Au
17
Ag
2
(PR
3
)
10
(NO
3
)
9
][
126
], which has a fused icosahedral structure,
has a sec of 10, which suggests that D
z
2
σ
is occupied in the former cluster.
Comparing [Pt
19
(CO)
17
]
8
and [Pt
19
(CO)
22
]
4
[
127
], the sec count increases
from 8 to 14 as a result in the change of geometry of the central moiety from
pentagonal antiprismatic to pentagonal prismatic, which results in an increased
separation between the interstitial atoms and a more prolate geometry for the cluster
ʼ
