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specific examples of spherical and toroidal clusters and their associated polyhedral
and skeletal electron counts (pec and sec).
The strong radial interactions in such clusters result in a soft potential energy
surface for skeletal rearrangements and consequently the broader classification
based on topology is more appropriate than the designation of specific polyhedra.
This difference distinguishes gold clusters from the carbonyl clusters of the earlier
transition metals, which conform to the PSEPT. The presence of these soft potential
energy surfaces also results in the observation of alternative skeletal geometries
depending on the precise nature of the ligands, the counterions and the mode of
crystallisation. Indeed for one cluster this has resulted in the structural character-
isation of skeletal isomers [
45
,
46
]. It also is manifested in geometry changes which
are induced by high pressures. The bonding analysis developed above has been
widely used to account for the structures of a wide range of homonuclear and
heteronuclear cluster compounds of gold [
49
].
The soft potential energy surface separating alternative skeletal geometries has
consequences also for understanding the geometries and bonding characteristics of
higher nuclearity clusters. For example, if one compares the energies of icosahedral
and cuboctahedral clusters, the energies are not greatly different. For both polyhe-
dra there are 12 strong radial interactions, but the icosahedron has marginally
stronger tangential interactions because it has exclusively triangular faces. The
surface interactions for both polyhedra are weaker than the radial interactions, and
the icosahedron has five (rather than four) nearest neighbour surface interactions
leading to this small energy difference. The relevant skeletal molecular orbitals for
a cuboctahedron are shown in Fig.
14
.
3.4 Bonding in Condensed and Fused Clusters
3.4.1 Linking of Polyhedra
The structures of capped clusters of gold have been introduced and the bonding
implications have been discussed above. Capping is just a specific example of a
more general mechanism of cluster growth based on the condensation of polyhedra
through sharing of vertices, edges or faces. It is noteworthy that higher-nuclearity
ligand-stabilised clusters do not necessarily adopt the close-packed arrangements
characteristic of the parent bulk metal, but frequently adopt less symmetrical
structures based on the condensation of symmetric polyhedra [
71
-
73
]. This sug-
gests that cluster growth is a kinetically controlled process where the activation
energies for the condensation processes are smaller than those which are required
for the rearrangement of the polyhedra into close-packed arrangements.
The closed shell requirements of these condensed clusters of the earlier transi-
tion metals, especially with carbonyl ligands, have been brought within the frame-
work of the PSEPT [
77
]. These principles are not directly applicable to cluster
