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Encyclopedia of Physical Science and Technology EN009M-428 July 18, 2001 1:6

Metal Particles and Cluster Compounds 535

has also been demonstrated. There are, however, many the atomic p level are classified as high-lying antibond-
clusters that defy rationalization from within the 18- ing orbitals (HLAOs) and those with an energy below the
electron rule constructs. The mononuclear cases for which atomic p level are classified as cluster valence molecu-
the 18-electron rule works so well represents the limit lar orbitals (CVMOs). The HLAOs are assumed to lie too
of metal dispersion. The other extreme is bulk metal for high in energy to be used for metal–metal or cluster–ligand
which the 18-electron rule has no significance. As a clus- bonding, whereas the energy levels of the CVMOs are
ter increases in nuclearity the nature of the metal core suitable for these functions. The number of CVMOs dic-
becomes more like bulk metal. In general, the usefulness tates how many electrons a metal skeleton can accept and
of the 18-electron rule decreases with the increasing nu- therefore the bonding capabilities of a particular cluster.
clearity of clusters. A linear combination of n atomic orbitals will always
It became necessary to develop new approaches for pre- generate n molecular orbitals. Therefore, an M 3 cluster
dicting electron closed-shell structures, and ideas came with nine atomic orbitals per metal will have 27 molec-
from Williams, Wade, Mingos, and Rudolph, which now ular orbitals. The calculation for an equilateral triangle
make up the polyhedral skeletal electron pair theory shows that three of these 27 are high enough in energy to
(PSEPT). The bonding in clusters can sometimes be be classified as HLAOs, leaving 24 CVMOs. With orbital
described in terms of edge-localized, two-center two- occupancy being limited to two electrons, 48 electrons
electron bonds. Thus, through the formation of element- are required to electronically saturate an M 3 equilateral
element bonds, the atoms of a polyhedron can acquire an triangle cluster. In fact, 48 electrons is the number of va-
effective inert gas configuration (8 valence electrons for a lence electrons found in a host of three-metal clusters.
main group element and 18 for a transition metal atom). Fe 3 (CO) 12 and Co 3 (C 5 H 5 ) 3 (CO) 3 , for example, both have
In addition to the valence electrons that a metal atom 48 valence electrons.
can donate, it is important to know how many electrons There are several reasonable geometries that the metal
attached ligands generally donate. Typical one-electron atoms of a four-atom cluster may adopt. The number of
donors are H, CH 3 , C 6 H 5 , and SiR 3 ; two-electron donors: CVMOs for a four-atom cluster depends on which geom-
CO, CS, CNR, CR 2 , SO 2 ; three-electron donors: PR 2 , SR, etry the metal skeleton possesses. A tetrahedron, derived
OR, NO, Br, I, P; four-electron donors: PR, S, O; and five- from a metal atom capping the face of an equilateral tri-
angle precursor, is the closest packed arrangement. It is,
electron donors: Cl, Br, I, OR (face bridging such as µ 3
or µ 4 ). therefore, not surprising that the tetrahedron is the most
Interstitial atoms can be very versatile electron donors. frequently observed arrangement of four-atom clusters.
For example, B is a three-electron donor; C, Si, Ge are Extended H¨uckel calculations indicate that a tetrahedral
four-electron donors; and P, As, Bi, Sb are five-electron core of metal atoms generates 30 CVMOs. M 4 (CO) 12
donors. Even nine-electron donors (Rh, Co), ten (Pt, (M = Co, Rh, Ir) and Ni 4 (CO) 6 (PR 3 ) 4 are clusters with
Pd), and eleven (Au, Ag) have been observed in cluster a tetrahedral core of metal atoms and are all electronically
structure. saturated with 60 cluster valence electrons. Note the struc-
Other similar approaches to understanding electron fill- tures of the Co and Ir clusters (Fig. 19). The cobalt cluster
ing have been developed by Lauher and Wade. has three bridging carbonyls whereas the 5d Ir cluster has
Lauher’s approach to analyzing cluster compounds is only terminally bound CO.
to determine how many valence electrons a cluster with When a tetrahedron is distorted by lengthening one of
a given nuclearity and geometry can accommodate. This its edges the symmetry is lowered to C 2v . This skeletal
method, like the 18-electron rule, seeks to electronically change is accompanied by an increase in the number of
−
saturate a metal center, but instead of this metal center be- CVMOs from 30 to 31. The metal core of [Fe 4 (CO) 13 H] ,
ing an isolated metal atom it is the entire cluster core. By described as having a butterfly structure, has this C 2 sym-
carrying out extended H¨uckel calculations on bare metal metry (Fig. 20). In this compound one CO ligand acts as a
cluster the number of electrons the cluster can accom- four-electron donor thereby bringing the number of clus-
modate is determined. Thus, the bonding capabilities of ter valence electrons to 62, exactly the number needed to
that cluster are also known. (For example, how many two- electronically saturate the Fe 4 core. If 62 electrons were
electron-donating CO ligands can the cluster accept.) placed into the orbitals of a tetrahedral core of metal atoms
The molecular orbital calculations provide the orbital one HLAO would be filled. If this HLAO were a metal–
energy levels of the cluster and typically an energy gap of metal antibonding orbital the cleavage or lengthening of
about 1 eV separates a group of low-lying energy levels a metal–metal bond would be expected. This is totally
from a group of high-lying levels. The division occurs near consistent with the preceding discussion.
the energy of the atomic p orbitals of the isolated metal The addition of a fifth skeletal atom which caps the face
atom. Those molecular orbitals whose energies lie above of a tetrahedron creates a cluster with a trigonal bipyramid