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

534 Metal Particles and Cluster Compounds

metals, which form multiply bonded dimers, have fewer d
electrons than the later transition metals. When the early
transition metals are in a high oxidation state, as in the
dimers, they find themselves quite short of achieving the
18-electron, closed-shell configuration. The formation of
multiple metal–metal bonds is required to electronically
saturate each metal center. It is for this reason that when
two such metals come together all valence electrons are
used for metal–metal bonding.

C. Bonding in Metal Clusters:
The 18-Electron Rule

When used to analyze metal clusters, the 18-electron rule
finds its greatest success when applied to metal carbonyl
clusters. The rule does, however, hold for some nonzero-
valent clusters as well. Take, for example, [Re 3 Cl 12 ] 3−
˚
(Fig. 16) in which the Re Re bond distance of 2.46 A is
indicative of strong metal–metal bonding. This distance
is between the length of the Re Re quadruple bond in
˚
2−
[Re 2 Cl 8 ] (2.24 A) and the length of the Re Re single FIGURE 17 Structure of M 3 (CO) 12 (M Fe, RU, Os). One Fe Fe
˚
bond in Re 2 (CO) 10 (3.04 A). Assigning a Re Re double bond is bridged by two carbonyl ligands whereas the Ru and Os
bond in the Re trimer is not only consistent with the ob- clusters have only terminal carbonyls.
served bond lengths but also satisfies the 18-electron rule
at each metal center. This can be taken as further support is a general phenomenon. In fact no µ 2 - or µ 3 -carbonyls
or evidence for Re Re double bonds. have been observed bridging a 5d–5d metal bond.
The stability of the M 3 (CO) 12 clusters (M Fe,Ru,Os) Fe 5 C(CO) 15 is a particularly interesting cluster, whose
is easily explained by the 18-electron rule. The M 3 clus- stability may also be rationalized by the 18-electron rule.
ter frame is held together by metal–metal single bonds. The Fe 5 skeleton forms a square-based pyramid (Fig. 18).
8
Each d metal atom needs ten more electrons to satisfy Each iron atom has three terminally bound CO ligands
˚
the18-electronrule.Twometal–metalsinglebondstoeach and the carbide resides 0.08 A below the base of the pyra-
metal atom supply two of the needed ten electrons. Four mid. The apical iron atom with four single metal–metal
CO ligands per metal atom is sufficient to electronically bonds and three carbonyls, satisfies the 18-electron rule.
saturate each metal center. In the Ru and Os clusters the The basal iron atoms with only three metal–metal single
four carbonyls per metal atom are all terminally bound. bonds, would only acquire 17 valence electrons if it were
In the Fe cluster one Fe Fe bond is bridged by two car- not for the presence of the carbide. If the carbon donates
bonyl ligands. As such, this Fe Fe bond is shorter than one of its four valence electrons to each basal iron atom
the other two and the Fe 3 triangle is best described as they become electronically saturated.
isosceles whereas the Os and Ru cluster have equilateral For mononuclear transition metal complexes the ad-
cores (Fig. 17). The tendency for carbonyls to bridge 3d– herence to the 18-electron rule is extraordinary. The
4d metal bonds more than 4d–4d and 5d–5d metal bonds widespread applicability speaks well for the concept. The
adherence to the 18-electron rule by cluster compounds

FIGURE 18 Structure of Fe 5 C(CO) 15 . The carbide slightly pro-
FIGURE 16 Structure of [Re 3 Cl 12 ] 3− , formally containing Re— trudes out of the square-based pyramid core. (Terminal carbonyls
Re double bonds. are not shown for clarity.)