Chemistry Reference
In-Depth Information
Fig. 6 The skeletal
molecular orbitals of a
tetrahedral gold cluster. The
molecular orbitals are
illustrated in terms of 6s
orbitals on the gold atoms,
but calculations indicate
significant 6s/5d
z
2
hybridisation
t
2
P
s
P
z
s
P
x
,
y
s
a
1
S
s
A
u
4
L
4
2+
which hybridise to some extent with the 5d
z
2
. The relative energies of the 5d, 6s and
6p valence orbitals are greatly affected by relativistic effects [
36
-
38
,
77
] which
place the 6s and 5d orbitals at similar energies and thereby encourage effective
hybridisation. The relativistic effects create a large energy gap between these
orbitals and the 6p orbitals. Consequently the 6p orbitals do not participate greatly
in the metal-metal bonds in cluster compounds. This simplifications lead to the
following generalisations [
77
]:
1. The energies of the bonding skeletal molecular orbitals in single shell gold
clusters are dominated primarily by radial bonding interactions and the number
of nearest gold neighbours.
2. Low nuclearity [Au
n
L
n
](
n
¼ 2-4) are characterised by a single bonding molec-
ular orbital resulting from the in-phase overlap of 6s orbitals on the individual
gold atoms. This in-phase combination has no angular nodes and therefore
resembles an s atomic orbital and is designated the symbol S
σ
(see Fig.
6
).
3. For larger clusters [Au
n
L
n
](
n
4) additional P
σ
skeletal molecular orbitals,
which are singly noded, become available and contribute significantly to the
skeletal bonding.
4. The partial filling of these P
σ
molecular orbital shell leads to prolate- and oblate-
shaped clusters which maximise the occupation of the components of the P
σ
shell which are bonding.
5. If the P
σ
shell is completely filled, then a spherical cluster geometry which
maximises the number of nearest neighbours is preferred.
>
Figure
6
uses the point group symmetry labels for the skeletal molecular orbitals,
and the pseudo-spherical symmetry labels which emphasises the number of nodes
associated with each orbital are also given. The number of nodes determines the
relative energies of the molecular orbitals, viz. S
σ
which has no nodes along the
