Unit 9 Metal Clusters II

UNIT 9
METAL CLUSTERS II

Structure
9.1 Introduction 9.4 Electron Counting in Medium
Size Clusters and the Capping
Expected Learning Outcomes
Rule
9.2 Compounds with Metal-Metal
Limitations and Exceptions
Multiple Bonds
9.5 Summary
9.3 Metal Atom Cluster
Compounds and Metal 9.6 Terminal Questions
Carbonyl Type Clusters
9.7 Answers

9.1 INTRODUCTION
In the previous unit you have studied about the metal clusters, specially the
higher boranes, Wade’s rules, carboranes, metalloboranes and
metallocarboranes. In this unit you are going to learn about other aspects of
the metal clusters specially the compounds with metal-metal multiple bonds,
metal atom cluster compounds and metal carbonyl type clusters. Thereafter
you will also learn about electron counting in medium size clusters and the
capping rules along with their limitations and exceptions. This unit is the last unit
of the block on organometallic chemistry. In the next block you will be learning
about the electronic structure and bonding of d-metal complexes.

Expected Learning Outcomes

After studying this unit you should be able to:
 discuss compounds with metal-metal multiple bonds;
 describe metal atom cluster compounds and metal carbonyl type
clusters; and
 discuss electron counting in medium size clusters and the Capping Rule
along with their limitations and exceptions.

9.2 COMPOUNDS WITH METAL-METAL

MULTIPLE BONDS
Since the 1960s, compounds having direct M-M bonds, including multiple
ones, have been found and compounds containing such bonds are not
embraced by classical (Werner) coordination theory. 231
Block 2 Organometallic Chemistry

9.2.1 Metal-Metal Bonding in Metal Clusters

Now let us first understand what is a metal-metal bond. Specifically it is
Hg-Hg bond was between two transition metal atoms, where the bond is between two metal
identified in the Hg22  centres. The bond may be single, double or even quadruple bond. The
ion (Hg2Cl2), the first transition metals have (n + 1)s, (n + 1)p and nd orbitals as valence shell
d-block metal-metal electronic configuration which enables them to form metal-metal bond.
bonded species.
Metal clusters show three major types of bondings, such as covalent bonds,
dative bonds and weak metal-metal symmetry interactions as discussed
below:
The compounds (i) Covalent Bonding
containing a large
number of metal- This is the most common type of metal-metal bond. The bonds may range
metal bonds forming from single upto a quadruple metal-metal bond. Each M-M bond between the
triangular and larger two metal atoms have a single electron from each metal atom.
structures are called
cluster compounds. Examples of multiple bonds containing metal clusters are given in Fig. 9.1:
Even linear M-M PhH 2C
bonds are included in CH 2Ph
these. The metal PhH 2C
clusters may be Mo Mo Me Me
defined as any entity O O
CH 2Ph
that contains a metal-
PhH 2C CH 2Ph Cr
metal bond. Cr

H3C CH 3
Re
H3C CH 3
H 3C CH 3
Re
H3C CH 3
Fig. 9.1: Some metal clusters with multiple bonds.

Below in Table 9.1 is given the basis on which criteria for cluster formation is
determined. The number of bonds between the two metal atoms increases
with increasing number of electrons. When d8 or d10 electronic configurations
arise for the metal atoms, the antibonding orbitals gets filled and chance of
bond formation becomes much less.
Table 9.1: Criteria for cluster formation
Electron Count Resuting M-M Bond
d 1
 d 1 Single bond

d 2
 d2 Double bond

d3  d3 Triple bond

d4  d4 Quadruple bond  Optimum

d5  d5 Triple bond

d 6
 d 6 Double bond (M-L bonding usually dominates)

d7  d7 Single bond

d8  d8 No bond (symmetry interaction)

232
Unit 9 Metal Clusters II

(ii) Dative Bond:

This dative bond (represented by an arrow) arises due to donation of a lone

pair of electron by one of the metal having filled d-orbitals which coordinate to
another metal atom having empty d-orbitals. The bimetallic Ni complex shown
in Fig. 9.2 has one dative bond, where the donor Ni has a d10 electronic
configuration whereas the acceptor nickel atom is a d8 (Ni(II)).
t-Bu t-Bu

P
CO
OC Ni Ni
CO
P

t-Bu t-Bu
Ni - Ni = 2.41 A

Fig. 9.2: Bimetallic Ni complex.

(iii) Weak metal-metal symmetry interactions:

The symmetrical overlap of molecular orbitals give rise to weak metal-metal

symmetry interactions. This overlap is generally between filled and empty
metal-metal bonding and/or anti-bonding orbitals. Harry Gray was the scientist
who proposed such mechanism of these interactions. Some bi- or polymetallic
d8 complexes exhibit these interactions both in solution and in the solid state.

For example, the iridium tetrakis(isocyanide) complexes form oligomeric

chains as shown in Fig. 9.3 through M-M interacted stacks in solution and in
the solid state without showing any evidence of a metal-metal covalent bond.

Fig. 9.3: Iridium tetrakis(isocyanide) complex.

9.2.2 Principal Types of Compounds Having Multiple

Metal-Metal Bonds
Quadruple bonds are
Next, we are going to learn about the four principal types of compounds based on d orbital
having multiple metal-metal bonds which constitute a bulk of transition metal overlaps and they are
chemistry. to be expected only
among the transition
i) Edge-sharing Bioctahedra. elements.

In Fig. 9.5 are shown the three d-d overlaps for edge-sharing bioctahedral
structure. In Fig. 9.4a and Fig. 9.4b are given examples of molecules
which show single (2) and double (22) bonds. When two d4 metal 233
Block 2 Organometallic Chemistry

atoms interact, both the  type of orbitals will be filled. So instead of a

probable triple bond, actually double bond exists. In similar lines, for a d3-
d3 system the bond order may be 1 and not 3. As the energies of the 
orbitals are very close, sometimes spin state equilibria (singlet-triplet) are
observed also.

Fig. 9.4: a) Molecule showing single (2) bond. b) Molecule showing double
2 2
(  ) bonds.

9.5: (a) Possible d-d overlaps in an edge-sharing bioctahedral structure.

(b) Energy levels for direct overlaps.

ii) Face-Sharing Bioctahedra

The W=W bond in the [W 2Cl9]3- ion as shown in Fig. 9.6 is the first
example of a M-M triple bond. Fig. 9.7 shows the structure of the general
type of compounds of NbIII and TaIII complexes having M-M double bonds.

3-
Fig. 9.6: Structure of [W2Cl9] ion.

234 Fig. 9.7: General structure of complexes having M-M double bonds.
Unit 9 Metal Clusters II

iii) Tetragonal Prismatic Structures

These group of compounds have M-M bonds up to quadruple and have

been studied in detail. [Re2Cl8]2- and [Mo2Cl8]4- ions, are some examples
and they have idealized structure as shown in Fig. 9.9. In Fig. 9.8 is
shown the five possible overlaps of the d orbitals on adjacent two metal
atoms. Namely they are the , , and  overlaps. In this way the possible
M-M bonds within this structure can be predicted. Look at Fig. 9.8, you
can see that the relative values of , , and  overlaps decrease in that
order.

Fig. 9.8: The five possible overlaps of the d orbitals on two metal atoms.

With the help of molecular orbital theory, the overlap of various orbitals to form
three types of bonds namely the -bond, -bond and -bond (quadruple bond)
may be studied now as given in Fig. 9.8. You have to see that d-orbitals
overlap on adjacent metal atoms so that the following cases arise:

 Each atom of the two metal atoms gives its d orbital for overlap and
z2

form a -bond.
 The dzx and dyz orbitals overlap to form two -bonds.
 Two -bonds can arise from the two face-to-face overlap of dxy and
d 2 2 orbitals. The d 2 2 orbital is also utilized for bonding with ligands.
x y x y

Fig. 9.9: Idealised Tetragonal Prismatic Structures. 235

Block 2 Organometallic Chemistry

The electron configuration of a metal-metal quadruple bond has been found to

be 222 from MO theory. (dxy – dxy) overlap gives rise to strong  bond and it
becomes maximum when the two ML4 halves are in eclipsed position. But this
conformation makes the L-L nonbonded repulsions maximum too. This
Quadruple bond situation makes this conformation a bit twisted from the exactly eclipsed one.
(recognized in 1964) This sort of rotation can be up to 20, but generally eclipsed structure of
was first identified in quadruple bonds are observed.
the [ Re2 Cl8 ]2  ion
iv) Trigonal Antiprismatic Structure.
and also found in
compounds formed In (Fig. 9.10) is shown this type of major structural pattern. The six ligands
by the elements Cr, approach in the manner shown in (Fig. 9.10) (an ethane like pattern) which
Mo, W, Tc, and Re. favours formation of triple bonds with 22 configurations. Molybdenum(III) and
tungsten(III) generally form such compounds.

Cotton’s MO scheme
was qualitative in the
real sense, and
combination of AOs
was involved in it.
The  2 4 2 bonding
model is supported by
Fig. 9.10: Trigonal Antiprismatic Structure.
many theoretical
studies. Quadruple Bonds in metal clusters

The  orbital involved in the quadruple bond is only weakly bonding and the 
orbital only weakly antibonding. So their separation is very small. The
characteristic absorption band for quadruply bonded clusters is in the visible
region which results from the excitation of an electron from a singlet
 2 4 2 ground state to the singlet on  2 4  excited state. These sort of
weak transitions are capable of giving the clusters a characteristic intense
colour, for example, royal blue of [ Re 2 Cl8 ]2 , intense red of [ Mo 2Cl8 ] 4  , and
yellow of Mo 2 (O 2CCH3 )4 are due to  transitions at 7000, 5250, and 4350
Å, respectively.

Because of the weakness of the  bond, the gain or loss of electrons from  or
 orbitals has only a slight effect on the strength of the M–M bond. But the
M–M bond length may change when the electron is removed from  or 
orbital as there is a drastic change in the effective nuclear charge as a
consequence. For example for the following series of structures:

Metal-metal bond

Re 2 Cl 4 (PMe 2Ph )4  2 4 2 2 2.241Å

[Re 2 Cl 4 (PMe 2Ph)4 ]   2 4 2 1 2.218Å

[Re 2 Cl 4 (PMe 2Ph) 4 ]2  2 4 2 0 2.215Å

236
Unit 9 Metal Clusters II

The formal bond order changes from 3.0 through 3.5 to 4.0 when the 
electrons are removed, but there is only a small change in the Re–Re
distance. This happens as the d orbitals contract making poorer overlap in the
 bonds as there is the simultaneous increase in the oxidation state of the
metal atoms. So even though the antibonding electrons are lost, the bonds do
not become stronger.

In Fig. 9.11 shows how one can delete or add either one or two electrons to
the  2 4 2 configuration taking into consideration the nonbonding character

of both  and  orbitals.

 
+e

 
-e -e +e

 

 

Bond Orders 3.0 3.5 4.0 3.5 3.0

(a) (b) (c) (d) (e)

Fig. 9.11: Qualitative MO diagram for dinuclear rhenium and molybdenum

complexes.
[Source: Cotton, F.A. Chem. Soc. Rev. 1983, 12, 35.]

Examples are:

For (a) [Mo 2 (HPO 4 )]2  , (b) [Mo 2 (SO 4 )]3  , (c) [Re2 Cl8 ]2  ,
(d) [Re 2 Cl4 (PMe2Ph)4 ]4 , (e) Re2 Cl4 (PMe 2Ph )4 .

When  level gets an electron, the bond orders reduce as in the situation (d)
and (e). In (a) and (b) the electrons are removed from  bond which also leads
to lower bond order.

So, this sort of tetragonal prismatic framework may have bond orders ranging
from 3 and 3.5. Examples range from those with V24  , Nb 24  and Mo 62  cores
that have triple bonds ( 2 4 ) which is electron-poor to those with
Tc 24 ,Re 24 and Os 66  cores that also have triple bonds ( 2 4 2 2 ) that are

electron-rich. If you add more electrons, then the  will be filled up and and

finally the  orbitals, which would decrease the formal bond orders
proportionately. For example for many dirhodium compounds there is a Rh 24 
core, which has a single bond based on the  2 4 2 2 4 configuration. Also,
in Table 9.2 are given examples of diplatinum compounds which have bond
order 1 to 0. 237
Block 2 Organometallic Chemistry

Table 9.2: Compounds with different Pt–Pt bond orders

n+

H
Ar C Ar
N N
4

X Pt Pt X

Bond order X n Pt-Pt, Å Configuration

1 Cl 0 2.517  2 4 2 * *4
½ --- 1 2.530  2 4 2 *2 *4 *
0 --- 0 2.649 *
 2 4 2 *2 *2
[Source: F.A. Cotton et al., Inorganic Chemistry Acta 1997, 264, 61].

SAQ 1
Explain why the metal-metal bond length change is very small for the metal
clusters of rhenium even though the bond order changes.

Re 2 Cl4 (PMe 2Ph)4 , [Re 2 Cl 4 (PMe 2Ph)4 ]  , [Re 2 Cl 4 (PMe 2Ph) 4 ]2

9.3 METAL ATOM CLUSTER COMPOUNDS AND

METAL CARBONYL TYPE CLUSTERS
Types of metal-metal clusters

i) Dinuclear clusters:

In Fig. 9.12 is given [Re2X8]2, the first dinuclear cluster which was studied in
detail by Prof. F. A. Cotton. The Re-Re bond distance in this compound was
found to be 224 pm which did not match with the average Re-Re distance
which is 275 pm. Also, the distance between the chlorine atoms is nearly 330
pm whereas the sum of their van der Waals radii (340-360 pm) is much
greater.

Cl Cl 2
Cl Cl

Re Re

Cl Cl
Cl Cl

Fig. 9.12: [Re2X8]2 dinuclear cluster.

The concept of quadruple bond between the two rhenium centres was
proposed by Cotton. The chlorine atoms are connected to the rhenium ion in a
square planar array. A staggered configuration results which forms a square
anti-prism structure. Metal-metal multiple bonded cluster are also found in the
hexa-alkoxo dinuclear tungsten and molybdenum complexes of the formula
238 [M2(OR)6] where M = Mo, W.
Unit 9 Metal Clusters II

ii) Trinuclear cluster:

Among all, the best studied examples of trinuclear clusters are those of Re
such as rhenium trihalides [(ReCl3)3] and their derivatives. Each rhenium atom
is bonded to two other rhenium atoms directly by metal-metal bonds as shown
in Fig. 9.13.

Fig. 9.13: Re3Cl9 structure.

The rhenium atoms form a triangle. Above and below Re triangular planes two
chloride ions also bond with each rhenium ion. The Re(III) ions have a d4
configuration. A paramagnetic complex would result with only Re-Re single
bonds in the complex. Double bonding of Re ions is thus suggested as the
complex is diamagnetic.

iii) Tetranuclear cluster:

Many tetranuclear carbonyl clusters are found. Many other tetranuclear

clusters are found where most of them exist as halides and oxides of tungsten
and molybdenum metals as given in Fig. 9.14.

W2(OR)6 dimerizes to form W 4(OR)12, a tetranuclear cluster. W 4(OR)16, a

tetramer has also been prepared similarly.

Fig. 9.14: Tetranuclear clusters. 239

Block 2 Organometallic Chemistry

iv) Hexanuclear Cluster:

Such metal clusters mostly consist of molybdenum, niobium and tantalum

atoms. First type of hexanuclear clusters out of the metal chlorides is the
octahedron of six metal atoms surrounded by eight chloride ions one on each
face of the octahedron. So, the chloride ions form a cube around the metal
octahedron like that found in ‘molybdenum dichloride’ Mo6Cl12 or [Mo6Cl8]Cl4,
structure of Mo 6Cl82  is shown in Fig. 9.15. Four single bonds of one Mo(II) ion
is shared with four other Mo(II) ions and four dative bonds from four chloride
ions are also received by it.

In the second type, twelve halide ions are surrounding the metal octahedron
and placed along the edges. Such types of clusters are formed by niobium and
tantalum as shown in Fig. 9.15b. A very different case arises here where each
metal ion is surrounded by a distorted square prism of four metals and four
chloride ions. This results in electron deficient compounds similar to boranes
and so fractional bond orders exist.

2
Fig. 9.15: Structure of (a) Mo6Cl28 - (b) M6 X12 (M(red balls) = Nb, Ta; (Green balls)
Cl, Br).

Metal Atom cluster Compounds

Before X-ray crystallography came into the picture, the study of compounds
containing metal atom clusters were not much understood. Compounds like
W2Cl39  and Mo 6 Cl 84  with few metal-metal bonds were discovered around
1930s and 1940s. But the studies were actually organized around the early
1960s. The discovery of the [Re 3 Cl12 ]3 ion created lot of interest, for this
class of compounds. Also, structural elucidation of metal carbonyl cluster
Many copper sulfide,
compounds such as the tetrahedral M4 (CO)12 (M  Co,Rh,Ir ) molecules
selenide, and telluride
aggregates exist helped in the growth of this field.
which are termed as
“clusters”, even Metal atom cluster should be restricted to cases where two or more metal
though they have little atoms form a group in which there are direct bonds between metal atoms.
or no direct metal- Classical polynuclear complexes in which the metal atoms are held together
metal bonding. solely by M–X–M bridge bonds are not metal clusters. Fe 4 S 4 aggregates in
So by definition they
ferredoxins, where there are some direct M–M bonding are borderline cases.
are not metal atom
clusters. The two main classes of metal atom cluster compounds which are generally
240 found are:
Unit 9 Metal Clusters II

(1) Those with the metal atoms in very low formal oxidation states and are
mostly with the later transition elements, groups 7-10. Mostly the CO
groups act as ligands here.

(2) Those in which the metal atoms are in somewhat higher oxidation states
(+2 to +4) early transition elements, groups 5-7. halide, sulfide, or oxide
ions earily elements, groups 5-7.

It is because these two classes do not have any related chemistry convenient
to discuss them separately.

Metal Carbonyl Type Clusters

You will find that starting from dinuclear (Mn2 (CO)10 , Co 2 (CO)8 ) to some of
very high nuclearity, with twenty or more metal atoms many metal carbonyl
clusters exist. Some mixed metal clusters, such as H2FeRu2Os(CO)13 are
there too. Non-metal atoms, such as C, O, N, S may often be present as
bound or encapsulated atom. Hydrogen atoms may serve as bridges and are
sometimes even encapsulated.

Generally the trinuclear clusters are triangular. They are often heteronuclear
and many of them exist. Typical cluster chemistry can be understood from the
extensive studies of M3 (CO)12 clusters of Fe, Ru, and Os. Look at Fig. 9.16 a,
where the structure (CO groups are denoted simply by lines) of Os3 (CO)12
cluster is given. Closed shell configuration where each metal atom has an 18-
electron is there in it. So total of 48 electrons exist and each M–M bond has
bond order as 1. It is found that the unsaturated H2Os3 (CO)10 cluster can be
derived from Os 3 (CO)12 . There are only 46 electrons in it and the structure is
given in Fig. 9.16 b. This has unequal lengths of the edges of the triangle
formed by osmium atoms and is bridged by hydrogen atoms. The formal
18-electron configurations of the Os atoms can be attained if there is one
Os=Os double bond.

Os Os

H
Os Os Os Os
H

(a) (b)

Fig. 9.16: Trinuclear clusters of osmium (CO groups are denoted by lines).

More reactive derivatives can be obtained from the Ru3(CO)12 and Os3(CO)12
clusters and thereby interesting chemistry can be generated. Three important
points of departure are the following:

1. If you replace one or two CO ligands with CH3CN, then more reactive
species are generated. Some of the chemistry for the osmium system is
summarized in Scheme 9.1. Ru3(CO)12 also behave similarly. 241
Block 2 Organometallic Chemistry

Os Os
Me
C
N
Os Os Os Os

N N
C C
Me Me

C2H4 r.t. C2H4 r.t.

Os Os
o
125 C
H
Os Os Os Os
H
CH 2 C
H2C CH 2

o
125 C

H Os
H C H H H
C C C
Os Os Os
Os
H
H H
Os

Scheme 9.1: Reactions of Os3(CO)11(MeCN) and Os3(CO)10(MeCN)2. (CO groups

are denoted by lines)

2. In Eq. (9.1) is given the reaction of Os3(CO)12 with H2 at 125C, whereby

displacing two CO groups, unsaturated and reactive H 2Os(CO)10 is
formed.

Os
… (9.1)
H
H2Os 3(CO) 10 L
Os Os
H
L
3. Scheme 9.2 shows how first the Os3(CO)12 with KOH in MeOH gives the
[HOs3(CO)11] ion, which again can be further converted via reactions into
a methyl derivative, Os3(CO)10(H)CH3 which is electronically unsaturated
(46 electrons). It thus develops a strong interaction between one C–H
bond and an adjacent osmium atom (refer to “agostic” hydrogen atoms).
The term agostic (from Greek, drawing towards) is used to describe
C–H … M interactions. This type of interaction is not the same as that of
hydrogen bond as here the C–H bond gives electrons to the metal atom
242 resulting in 3c–2e bonds.
Unit 9 Metal Clusters II

M M

M M KOH
M M
C MeOH
O

MeSO 3F

Os
M LiBEt 3H
M = Os H
H Os Os
M M C
C H
OMe
O
Me CF 3COOH

H
C
Os
Os
Os H
Os
H LiBEt 3H

Os Os
C H + -
H [HOs 3(CO) 10(CH 2)]
H
H

Os
Os
H
H H C H
Os Os -CO H
Os Os
C
H2 H

Scheme 9.2: Reactions of Os3(CO)12 and, in part, of its Fe and Ru analogues.

(CO groups are denoted by lines).

The methyl compound remains in equilibrium with the methylene bridged

isomer (which is a 48 electron species) and the latter has been isolated from
solution and crystallographically characterized. It loses CO to form a stable
CH- capped cluster.

Four-atom clusters are found in large numbers and most of them are
heteronuclear. Their structures are generally tetrahedral and M4(CO)12
(M=Co, Rh, and Ir) are the best known homonuclear molecules. Here each
metal atom forms six M–M single bonds and satisfies the 18-electron rule as
the total electron count is 60. 60 electron systems are also found in the
representative heteronuclear analogues shown as Fig. 9.17 a and 9.17 b.

Fe Co
OC CO

H
Os Os Ru Ru

H H H
Ru H
Ru

(a) (b)
Fig. 9.17: Heteronuclear four-atom clusters. 243
Block 2 Organometallic Chemistry

Only 56 electrons are there in the compound H4Re4(CO)12, but it does have a
regular tetrahedral Re4 core. So you see, this structure rules out existence of
discrete, localized Re=Re double bonds [comparable to the Os=Os bond in
H2Os3(CO)10]. Thus both resonating double bonds and the formation of three-
centre (face) bonding may be present in it.

Four-atom clusters also exist in butterfly (Fig. 9.18 a) and planar (Fig. 9.18 b)
structures.

M M
M M M

M M M

(a) (b)
Fig. 9.18: Four-atom clusters with (a) butterfly structure and (b) planar structure.

Anionic and Hydrido Clusters

These are found in large numbers. If you count the total electrons in them you
will see that one CO can be replaced by:

 two hydrogen atoms

 one H and one negative charge
 or two negative charges.

Easily the protonation or deprotonation reactions takes place and there is no

change in the cluster structure as a result. Exceptions do happen as shown in
the example given in Eq. 9.1 and the change in structure is shown in Fig. 9.19.

… (9.1)

O
O O
Os6 octahedra O O
O
O O O
O
O O

Fig. 9.19: Osmium cluster.

Large clusters are relatively strong polyacids in many cases. So it is difficult to

isolate and characterize them as different species may be formed together as
different stages of ionization occur. The locations of the hydrogen atoms in the
hydrido clusters (and in some cases even the total number present) are often
difficult to ascertain. Neutron diffraction has given clear cut results. Also X-ray
diffraction coupled with steric considerations indirectly indicated about this.
Neutron diffraction studies have given the following results:

 [FeRu3(CO)13H] has one Ru–R edge of the metal atom tetrahedron

symmetrically bridged by the hydrogen
 Os4H4(CO)11P(OMe)3 has four edges bridged (Fig. 9.20).
 H atoms may occupy a position within an octahedral cluster, e.g.,
244 [Co6(CO)15H], [Ru6(CO)18H], [Ni12(CO)12H2]2.
Unit 9 Metal Clusters II

H H

H H The first six-atom

cluster, Rh6(CO)16,
Fig. 9.20: Structure of Os4H4(CO)11P(OMe)3. was structurally
elucidated by Corey,
The existence of larger carbonyl clusters makes one ponder that how large Dahl, and Beck in
does a particle of metal have to be before bulk metal properties begin to 1963.
appear?

The four major types of structure found are:

1. Closed polyhedra:

(i) Octahedron: it is very common, e.g. [Os6(CO)18]2, Rh6(CO)16 and

Ru6(CO)18H2. Sometimes hetero atom such as C, N, or H may be
encapsulated, e.g. [Co6(CO)15 H],

(ii) trigonal bipyramid: also very common, e.g. (Ni5(CO12)2,

Ni3Mo2(CO)13 and Os5(CO)16,

(iii) trigonally distorted octahedron (a trigonal antiprism): e.g.

[Ni6(CO)12]2,

(iv) cube, e.g. Ni8Se6(PR3)6.

2. Close-packed arrays, where similar grouping occurs for the metal atoms
as in bulk metal, eg. rhodium and platinum.

3. Stacked triangular arrays, e.g. [Ni3 (CO)6 ]2n  (n = 2-5) species, and similar
platinum ones.

4. Rafts: they are like large, triangulated, planar nets, eg. some osmium
species.

The triangular faces in these are exposed and cluster size may be increased
by capping one or more of these faces by another metal atom [e.g., by an
M(CO)3 group]. This way a tetrahedron fused to the main or central unit is
generated, e.g., Os7(CO)21. An additional metal atom (plus some ligands) may
also attach to one of the edges of a polyhedral or close-packed central array.

Synthesis of Metal Clusters

Not much mechanism has been studied for these and generally reactive
fragments may combine to form clusters. These fragments can be produced
thermally, photolytically, or by reduction processes. A very efficient mode of
preparing these may be pyrolysis reactions. The modification in the pyrolysis is
usually done as in Eq. (9.2) where first one or two CO groups are replaced.
This is done by pyridine or CH3CN (much more labile ligands) in milder
conditions and then the pyrolysis reaction is carried out. Vacuum pyrolysis of
Os3(CO)12 gave the opportunity to prepare large osmium clusters. 245
Block 2 Organometallic Chemistry

250oC acetone + PPN+

Os 3(CO) 11py (PPN) 2[Os10(CO) 24C] … (9.2)
64 h extract

Eq. (9.2) also shows that in similar way carbido clusters may be prepared.

Milder pathways are found in thermal reactions where partially substituted

starting materials provides a means to enlarge medium size clusters. So from
Os6(CO)18n(MeCN)n species CH3CN ligands are displaced by Os3(CO)4H2
to form heptanuclear clusters, Os7(CO)nH2 (n = 20, 21 and 22).

Larger clusters may be synthesized in milder thermal pathways by ligands with

unshared electron pairs. Example is given in Scheme 9.3 where reaction takes
place between a cluster containing one or more labile ligands and a cluster
with a capping sulfur atom whose lone pair may participate.
-CO, 2MeCN
Os 3(CO) 10(MeCN) 2 + Os39(CO) 10S

- 2CO

S S

Scheme 9.3: Reactions to form larger cluster of osmium.

Reactive anionic intermediates may be generated by reduction. Then they

condense to form large clusters of the cobalt and nickel subgroups, eg.
Co4(CO)12 is converted by treatment with alkali metals in THF to the
[Co6(CO)15]2 ion. Similarly, depending on the reaction conditions, the action of
strong, basic reductants (Na/THF, NaBH4/THF) on Ni(CO)4 leads to cluster
anions such as [Ni5(CO)12]2, [Ni6(CO)12]2, [Ni9(CO)18]2or [Ni12(CO)21]4.

Atoms may be introduced by addition of CCI4 for C, C2Cl6 for C2, H2S for S or
Ph3As for As to make clusters that encapsulate hetero atoms with the help of
these reductive reactions.

Heteronuclear products as shown in Eq. 9.3 and 9.4 can be prepared with the
help of the reaction between carbonyl metallates and neutral carbonyls having
a different metal.
2 3CO 2
[Rh 6(CO) 15] + Ni(CO) 4 [Rh 6Ni(CO) 16] …(9.3)
2 6CO 2
[Pt3(CO) 6] + 3Fe(CO) 5 [Fe3Pt3(CO) 15] …(9.4)

Also, simple metal halides may react with carbonyl anions, eg. Eq. (9.5) and
(9.6).
2 4
[Ni 6(CO) 12] + PtCl2 [Ni 38Pt 6(CO) 48H2]
…(9.5)
2 2
[Ni 6 (CO) 12] + Ph3PAuCl [Au6Ni 12(CO) 24] …(9.6)

The structure of the gold/nickel cluster has tetrahedral symmetry with the
metal core, for example the 18-vertex polyhedron is actually a face-to-face
condensation of four octahedral Au3Ni3 fragments at alternate faces of a
246 central Au6 octahedron (Fig. 9.21).
Unit 9 Metal Clusters II

The structure of the gold/nickel cluster has tetrahedral symmetry with the
metal core shown in Fig. 9.21. This 18-vertex polyhedron of cubic Td (43m)
symmetry may be viewed as a face-to-face condensation of four octahedral
Au3Ni3 fragments at alternate faces of a central Au6 octahedron.

Fig. 9.21: Au6Ni12 core of the 236-electron [Au6Ni12(CO)24]2 dianion.

Superlarge clusters as that of the anion, [Pd33Ni9(CO)41(PPh3)6]4 which

contains five central layers of metal atoms, stacked in the same manner as
that found in a hexagonally close-packed metal has also been found. The
outer metal atoms have the 41 CO groups and 6 Ph3P ligands attached.
Pd23(CO)22(PEt3)10 and Pd34(CO)24(PEt3)12 are more such clusters.

The presence of heteroatoms (i.e., nonmetal atoms) within or intimately

associated with metal atom clusters has already been briefly mentioned. Apart
from H and C atoms, N, P, As, and S are fairly common. Nitrogen-containing
clusters are often formed with NO, N3 or NCO as the nitrogen source, as in
the reactions.
 +
[H3 Ru 4(CO) 12] + NO HRu 4N(CO) 12 + H3Ru 4 N(CO) 11
…(9.7)
 
[2Ru 3(CO) 12 + N3 [Ru 6 N(CO) 16]  8CO + N2
…(9.8)

SAQ 2
Give the classification of metal atom cluster compounds.

9.4 ELECTRON COUNTING IN MEDIUM SIZE

CLUSTERS AND THE CAPPING RULE
Until now, it has not been possible to study these clusters with traditional
molecular quantum mechanical methods since they frequently contain heavier
metal atoms. Instead, a lot of time and energy has been put into figuring out
how their structures and the number of electrons available for cluster bonding 247
Block 2 Organometallic Chemistry

relate to one another. Since enough electrons are not available in each of
these large clusters, so each electron-pair link cannot be assigned to every
neighbouring pair of metal atoms. This leads to electron deficiency in them.

For polyhedral clusters (sometimes called deltahedral, because the faces are
all triangles resembling the Greek letter delta) the Wade’s rules are used.
Wade first drew attention to the similarity of a M(CO)3 unit and a BH (or CH)
unit, a relationship that we would now call isolobality. He then proposed:

 the 2n + 2 rule for closo boranes (refer to Unit 8) would also apply to closo
metal cluster species such as [Os6(CO)18]2

 2n + 4 and 2n + 6 electron counts would, similarly, may be applicable for

stable Mn clusters with nido and arachno structures.

 Hydrogen atoms are assumed to contribute one electron each, an

interstitial carbon atom contributes four electrons, and so on.

While the number of skeletal electron pairs, denoted S, is at the root of the
correlation procedures, discussions found in the literature are often couched in
terms of other, related parameters, particularly the total electron count (TEC).
The TEC is obtained from the formula by adding the following contributions:

1. The number of valence electrons for each metal atom. For example, in an
Os6 cluster, 6  8 = 48.

2. Two electrons for each CO group, regardless of its structural type

(terminal, 2, or 3).

3. One electron for each negative charge.

4. The number of valence electrons for each hetero and/or interstitial atom.
For example, 1 for H, 4 for C, 5 for P. Column 2 of Table 9.4 presents
some examples of total electron counts.

Table 9.3: Correlation of some structures with total electron count

Cluster Total electron count No. of skeletal Vertices of parent Structural

(TEC) electron pairs (S) polyhedron conclusion

Rh6(CO)16 (69) + (216) = 86 ½[86(612)] = 7 6 Closo

Os5(CO)16 (58) + (216) = 72 ½[86(612)] = 7 5 Closo

Os5(CO)15 (58) + (215)+4 = 74 ½[74(512)] = 7 6 Nido

2
[Fe4C(CO)12] (48) + (212)+4+2 = 62 ½[62(412)] = 7 6 Arachno

[H3Ru4(CO)12] (48) + (212)+3+1 = 60 ½[60(412)] = 6 5 Nido

Let us now predict the correct total electron count for a stable cluster of known
structure (i.e., closo, nido, or arachno). To do this for metal carbonyl clusters, it
is postulated that in addition to the electrons necessary for skeletal bonding
each metal atom will also have 12 nonskeletal electrons. This is assumed
because in the pyramidal M(CO)3 unit each M–CO bond has two formally
“carbon”  electrons that are donated to the metal atom and two formally
“metal”  electrons that backbond, at least partially, to the CO ligand. So, while
248 predicting the total electron count for:
Unit 9 Metal Clusters II

 a closo polyhedral cluster of n vertices, the result would be 12n + 2(n + 1)

 for nido clusters that are derived from an n-vertex polyhedron (their parent
polyhedron) by removal of one vertex, there will be 12 fewer total
electrons
 for arachno clusters that are derived from an n-vertex polyhedron (their
parent polyhedron) by removal of two vertices, there will be 24 fewer total
electrons.

The predictions for TEC can therefore be stated in the following equations
(where n is the number of vertices in the parent polyhedron for the nido and
arachno cases – not the actual number of metal atoms in the cluster itself):

closo 12n + 2(n +1)

nido 12(n  1) + 2(n +1)
arachno 12(n  2) + 2(n +1)

When we want to predict the structure, then we do the reverse, that is, from
the actual TEC we have to subtract 12e for each metal atom and get the
number of skeletal pairs (S). On the basis that (S + 1) pairs are required for a
polyhedron of S vertices, one may select the most likely structure or
structures. Let us understand this better with the following example:

For Rh6(CO)16 the TEC is (6  9) + (2  16) = 86. The number of skeletal pairs
(S) will be obtained by subtracting 6  12 from 86 and dividing by 2; the result
is 7. Since the number of vertices of the parent polyhedron is S  1, so the
structure may be predicted as a six-vertex polyhedron (e.g., an octahedron).
Since there are six metal atoms, we conclude that a closo structure, so an
octahedron is the correct prediction.

Look at Table 9.3., where Rh6(CO)16 (octahedral) and Os5(CO)16 (a trigonal

bipyramid) clusters are correctly predicted as closo structures.

In Table 9.3, next are Os5C(CO)15 and [Fe4C(CO)12]2 which are predicted to
have nido and arachno structures respectively. The nido structure for the iron
analogue, Fe5C(CO)15, should be derived by removal of one vertex from the
parent polyhedron, which is an octahedron. The [Fe4C(CO)12]2 cluster which
is arachno should be isostructural with the Fe4C(CO)13 cluster. They are
derived from a parent octahedron by removal of two vertices.

The last compound given in Table 9.4 shows that a tetrahedron is treated as a
trigonal bipyramid that is missing one vertex, that is, as a nido structure. This
is done to comply with the general rules.

9.4.1 The Capping Rule

Many carbonyl-type clusters consist of a central polyhedron to which one or
more additional metal atoms are appended by placement over a triangular
face. Such metal atoms which are appended are called capping atoms. The
electron counting rules we have discussed can be extended to cover such
structures by the rule that the addition of a capping atom does not change the
skeletal electron requirement for the central cluster. Thus, the addition of a
capping atom simply increases the total electron count by 12 electrons. 249
Block 2 Organometallic Chemistry

For example, Os7(CO)21 cluster (Fig. 9.22):

 TEC =(7  8) + (21  2)= 98. Subtracting 7  12 = 84 and dividing by 2, we

obtain S = 7
 So the prediction is six-vertex central polyhedron, that is closo
octahedron, capped on one face-which is correct.
[Os8(CO)22]2 which is a bicapped octahedron is similarly predicted.

[Os10C(CO)24]2, which is a tetracapped octahedron:

TEC: (10  8) + 4 + (2  24) + 2 = 134

S: ½[134  (10  12)] = 7

Fig. 9.22: Structure of Os7(CO)21.

Table 9.4: TEC, number of electron pairs and predicted structures of

some high nuclearity carbonyl clusters
Compound TEC n# Number of electron pairs Predicted
structure
Rh6(CO)16 86 6 86 – (12 x 6) = 7e pair; (n + 1) Closo (Oct)
Ru6(CO)17C 86 6 86 – (12 x 6) = 7e pair; (n + 1) Closo (Oct)
Os5(CO)15C 74 5 74 – (12 x 5) = 7e pair; (n + 2) Nido-Oct (Sq Py)
2-
[Fe4 (CO)12C] 62 4 62 – (12 x 4) = 7e pair; (n + 3) Arachno (Oct)
butterfly)
62 5 62 – (12 x 4)-2 = 6e pair; (n + 1) Closo (TBP)**
Os5(CO)16 72 5 72 – (12 x 5) = 6e pair; (n + 1) Closo (TBP)
2-
[Oss(CO)15] 72 5 72 – (12 x 5) = 6e pair; (n + 1) Closo (TBP)
-
*[HOs5(CO)15] 72 5 72 – (12 x 5) = 6e pair; (n + 1) Closo (TBP)
*[H2Os5(CO)15] 72 5 72 – (12 x 5) = 6e pair; (n + 1) Closo (TBP)
Ru5C(CO)16 76 5 76 – (12 x 5) = 8e pair; (n + 3) Arachno
(pentagonal
bipyramid)

# Number of vertices in parent polyhedron, *Wades rule cannot predict the position of H,
**carbon is on the vertex.

In Table 9.4 are given the total electron count, number of electron pairs and
predicted structures of some high nuclearity carbonyl clusters.

9.4.2 Limitations and Exception

The transition metal clusters which have high nuclearity are formed by the
condensation of smaller clusters like the tetrahedron, octahedron and trigonal
250 prism. The sharing of vertex, edge or face takes place so that condensation
Unit 9 Metal Clusters II

can happen. We can apply the basis of a fragment molecular orbital analysis
of the condensation process to derive rules that account for polyhedral
electron for the condensed polyhedral. We have to look at the condensed
polyhedral as a complex between two individual polyhedral with one
polyhedron acting as ligand towards the other polyhedron. Basically the rules
are:

(i) The number of atoms and numbers of electrons in the individual

polyhedron should be known.

(ii) Once the condensation has occurred, it is necessary to know the

polyhedron electron count (PEC), note that the meaning of this term is
different from the term used in Wade’s rules. PEC in Mingo’s rule is the
same as TEC in Wade’s rules.

You can apply this procdure only to those metal carbonyl cluster compounds
that follow the inert gas formalism. In Table 9.5 is shown the electron count
for such cluster compounds.
Table 9.5: Electron count of the individual polyhedra used in the condensation
process

Metal atoms Structure of Cluster valence Edges*

framework electron count
1 18 0
2 34 1
3 Closed triangle 48 3
Open triangle 50 2
4 Tetrahedron 60 6
Butterfly 62 5
Square planar 64 4
5 TBP 72 9
Square pyramid 74 8
6 Octahedron 86 12
Trigonal prism 90 9

* Considering that all edges are 2c-2e bonds 251

Block 2 Organometallic Chemistry

(i) Now, we cannot predict which isomer will be formed with the help of
capping rules. Let us take the example of a bicapped octahedron whose
three possible isomers are shown in Fig. 9.23.

Fig. 9.23: The possible isomers of a bicapped octahedron.

(ii) Let us take the compounds (a) [Os6(CO)18]2. (b) H2Os6(CO)18 and (c)
Os6(CO)18Py. They are isoelectronic with a TEC of 86e and 7e pairs,
suggesting an octahedral structure. But actually (a) is only an octahedron.
Whereas, (b) and (c) have different structures -nido and arachno
respectively and both of them may be derived from a monocapped
octahedron (Fig. 9.24). The nido structure is a monocapped square
pyramid and the arachno structure is an edge capped TBP;

remove vertex add vertex

remove vertex

monocapped monocapped edge capped edge capped

octahedron sq. pyramid tetrahadron TBP
98e 86e 74e 74e

Fig. 9.24: Deriving an edge capped trigonal bipyramid from a monocapped

octahedron.

You can find the metal-metal distance and the magnitude of the bridge angle
from the single crystal X-ray studies. The magnetic properties of a
magnetically concentrated complex depend on them.

SAQ 3
Give the total electron count, number of skeletal electron pairs and the number
of vertices of parent polyhedron for Rh6(CO)16, Os5(CO)15 and [Fe4C(CO)12]2 .
Also conclude about their structures.

9.5 SUMMARY
In this unit we have discussed in detail about compounds with metal-metal
multiple bonds. Thereafter, metal atom cluster compounds and metal carbonyl
type clusters were discussed also. Lastly discussion on electron counting in
252 medium size clusters and the Capping Rule have been done.
Unit 9 Metal Clusters II

9.6 TERMINAL QUESTIONS

1. Give an example of tetragonal prismatic structure of metal cluster with
suitable diagram.

2. Give an example each of tetranuclear tungsten cluster and hexanuclear

molybdenum cluster.

3. How can you obtain more reactive derivatives can be obtained from the
Ru3(CO)12 and Os3(CO)12 clusters?

4. Give the predictions for TEC for the closo, nido and arachno cases and
give one suitable example.

9.7 ANSWERS
Self Assessment Questions

1. Because of the weakness of the  bond, the gain or loss of electrons from
 or  orbitals has only a slight effect on the strength of the M–M bond.
But the M–M bond length may change when the electron is removed
from  or  orbital as there is a drastic change in the effective nuclear
charge as a consequence. The change in the M-M bond lengths as given
occurs due to this. The formal bond order changes from 3.0 through 3.5
to 4.0 when the  electrons are removed, but there is only a small change
in the Re–Re distance. This happens as the d orbitals contract making
poorer overlap in the  bonds as there is the simultaneous increase in the
oxidation state of the metal atoms. So even though the antibonding
electrons are lost, the bonds do not become stronger.

2. Two main classes of metal atom cluster compounds:

(i) Those with the metal atoms in very low formal oxidation states, where
the ligands are mostly CO groups. These also tend to occur mostly
with the later transition elements, groups 7-10.

(ii) Those in which the metal atoms are in somewhat higher oxidation
states (+2 to +4) and the ligands are typically halide, sulfide, or oxide
ions and some others of the same ilk as those in mononuclear
Werner complexes. Clusters of this type are most common among the
early transition elements, groups 5-7.

3. Cluster Total electron count No. of skeletal Vertices of parent Structural

(TEC) electron pairs (S) polyhedron conclusion
Rh6(CO)16 (69) + (216) = 86 ½[86(612)] = 7 6 Closo
Os5(CO)15 (58) + (215)+4 = 74 ½[74(512)] = 7 6 Nido
2
[Fe4C(CO)12] (48) + (212)+4+2 = 62 ½[62(412)] = 7 6 Arachno

Terminal Questions
1. Tetragonal Prismatic Structures: These group of compounds have M-M
bonds up to quadruple and have been studied in detail. [Re 2Cl8]2- ions,
idealized structure (Fig. 9.9). 253
Block 2 Organometallic Chemistry

2. Example in Fig. 9.14. W 2(OR)6 dimerizes to form W 4(OR)12, a tetranuclear

cluster. W 4(OR)16, a tetramer has also been prepared similarly.
Hexanuclear clusters of molybdenum is Mo6Cl12 or [Mo6Cl8]Cl4, structure
of Mo 6Cl82  given in Fig. 9.15. Four single bonds of one Mo(II) ion is
shared with four other Mo(II) ions and four dative bonds from four chloride
ions are also received by it.

3. Take reactions from Scheme 9.1. Ru3(CO)12 also behave similarly.

4. The predictions for TEC: (where n is the number of vertices in the parent
polyhedron for the nido and arachno cases – not the actual number of
metal atoms in the cluster itself):

closo 12n + 2(n +1)

nido 12(n  1) + 2(n +1)

arachno 12(n  2) + 2(n +1)

When we want to predict the structure, then we do the reverse, that is,
from the actual TEC we have to subtract 12e for each metal atom and get
the number of skeletal pairs (S). On the basis that (S + 1) pairs are
required for a polyhedron of S vertices, one may select the most likely
structure or structures. Let us understand this better with the following
example:

For Rh6(CO)16 the TEC is (6  9) + (2  16) = 86. The number of skeletal

pairs (S) will be obtained by subtracting 6  12 from 86 and dividing by 2;
the result is 7. Since the number of vertices of the parent polyhedron is
S1, so the structure may be predicted as a six-vertex polyhedron (e.g.,
an octahedron). Since there are six metal atoms, we conclude that a closo
structure, so an octahedron is the correct prediction.

FURTHER READING
1. F. Albert Cotton, Geoffrey Wilkinson, Carlos A. Murillo and Manfred
Bochmann, Advanced Inorganic Chemistry, 6th Edition, Wiley-India
Edition.

2. James E Huheey, Ellen A Keiter, Richard L Keiter & Okhil K Medhi,

Inorganic Chemistry (4th Edition), PEARSON.
3. R.C. Mehrotra and A. Singh, Organometallic Chemistry, Second edition,
New Age International (p) Limited Publishers.

4. Mark Weller, Fraser Armstrong, Jonathan Rourke & Tina Overton

(Formerly D. F. Shriver, P. W. Atkins and C. H. Langford, Inorganic
chemistry, 6th edition, Oxford University Press, India.

5. CHE_P11_M29 (epgpathshala module)

6. Keith F. Purcell, John, C. Kotz, Inorganic Chemistry, Indian Reprint 2010,

Cengage Learning India Private Limited.

254
 INDEX

 Elimination, 95 cyclopentadiene, 89
 antibonding, 136 cyclopentadienyl complexes, 189
 hydrogen, 96 cyclopentadienyls, 93
4 –cyclobutadiene, 192 cyclophosphazenes, 77
-bonded organometallics, 88 d-p bond, 54
-bonded organometallics, 89 dative bond, 233
18-electron Rule, 123 dialkyl-, diarylphosphido ligands, 178
actinoids, 11, 87 dichlorophosphazene, 75
Agostic Alkyls, 98 dinitrogen and dioxygen complexes, 163
alkaline earth, 16 dodecaborane, 211
alkene complexes, 184 EAN rule, 123
alkylidenes, alkylidynes, and carbides, 105 edge-sharing bioctahedra, 234
alkyls and aryls, 93 effective nuclear charge, 17
alkyne complexes, 186 electrode potential, 33
Allred and Rochow, 31 electronegativity,14
allyl complexes, 188 equatorial position, 50
Anionic and Hydrido Clusters, 244 fluxional organometallic compounds, 113
antibonding orbitals, 54 geometric and optical isomers, 43
arachno clusters, 249 gerade symmetry, 70
arachno-Carboranes, 219 Halide Elimination, 99
atomic radii, 14,18 halogen substitution, 115
Bent’s rule, 43 hapticity, 90
beryllium sandwich compounds, 92 Hemocyanin, 169
B-H bond, 214 hemoglobin, 169
bonding in Carbonyl Compounds, 135 heteroboranes, 228
Borane Anions, 211 heterocyclic phosphorus ligands, 178
borazine, 201 homoleptic nitrosyl, 162
boron trihalides, 210 homoleptic/heteroleptic, 94
bridging alkyls, 105 hydrogen atom, 11
bromotriborohydride anion, 211 icosahedral carboranes, 221
Capping rule, 248 interatomic forces, 25
carboranes, 216 ionic radius, 16
closo boranes, 248 ionisation energies, 25
closo polyhedral cluster, 249 lanthanoid contraction, 21
closo-carboranes, 217 lanthanoids,11, 87
covalent radius,14 Latimer Diagrams, 38
cyclo and linear phosphonitrilic Limitations and Exception, 251
compounds, 69 linear polyphosphazenes, 73
cyclobutadiene, 204 low-spin complexes,22
cyclometallated phosphine complexes, 178 macrocyclic phosphines, 177
cyclopentadiene, 190 Metal Atom cluster Compounds, 240
Metal Carbonyl Type Clusters, 241 Reductive Elimination, 99
metal carbonyls, 121 semiconductors, 87
metal nitrosyl, 158 s-p hybrids, 57
metalacycles, 106 spider’s web, 215
metallate acylation reaction, 102 stereoisomerism, 60
metallate alkylation reaction, 102 structural elucidation of carbonyls, 141
metallic radius, 16 Superlarge clusters, 247
metalloboranes and metallocarboranes, Synthesis of Metal Clusters, 246
223 tetragonal prismatic structures, 235
metallocenes, 197 tetrameric phosphazenes, 71
metal-metal bonding in metal clusters, 232 tetrasulfur compounds, 78
molybdenocene, 193 thermochemical parameters, 33
Mulliken's scale, 31 transition metal alkyls and aryls, 101
multidecker metal sandwich, 228 transition series, 13
myoglobin, 169 trigonal antiprismatic structure, 236
N2 complexes, 165 trigonal bipyramidal, 56
nickelocene, 197 Valence Shell Electron Pair Repulsion, 43
nido clusters, 249 van der Waals radii,15
nido-Carboranes, 219 Vaska’s Complex, 169
nitrosonium salts, 162 vibrational coupling, 148
non classical, multicentre bonding and vibrational spectra of metal carbonyls, 140
 complexes, 88 Wade’s Rules, 214
organocopper compounds,114 Zeise’s salt, 86
organometallic compounds,86
oxidation states, 33
oxidative addition, 102
Pauling, 30
pentaborane, 215
pentahalophenyl ligands, 106
periodicity in electronegativity, 32
Periodicity in Ionisation, 26,29
phosphazene polymers, 71
phosphines, 173
phosphinidine ligands, 179
phosphite ligand, 177
phosphorus-nitrogen compounds, 69
photoelectric effect, 27
polydentate phosphines, 176
Polyhedral clusters, 214
principal quantum number, 17
pyramidal shape, 45
quadruple bonds, 236
radial distribution, 12