COORDIANTION CHEMISTRY

UNIT 1-Structural Aspects and Bonding

Classification of Complexes based on Coordination Numbers and Possible Geometries

The number of atoms bonded to the central metal ion in a coordination complex is known as
coordination number. The most common coordination numbers are 4 and 6. Apart from
these, complexes with coordination numbers 1, 2, 3, 5, 7, 8, 9, 10 and 12 are known. But there
are no reports for the complex with coordination number 11.
Coordination Number 1
Ion pairs such as Na+Cl- in the vapour phase can be considered as example for coordination
number 1. There are a few other examples known. For instance, the aryl radical derived from
the highly sterically hindered 1, 3, 5-triphenylbenzene, forms one-to-one organometallic
compounds of the type CuC6H2 (C6H5)3 and AgC6H2(C6H5)3.

Coordination Number 2
Few complex ions are known with a coordination number of 2. They are generally limited to
the +1 ions of the Group 11 metals and the closely related Hg (II) species (d10). Examples are
[Cu(NH3)2]+,[Ag(NH3)2]+, [Au(CN)2]-,Hg(CN)2 etc. These complexes are less stable and
sometimes react with additional ligands or sometimes undergo polymerisation to form higher
coordination numbers.
For example,

Solid KCu(CN)2 possesses a chain structure (by undergoing polymerisation) in which the
coordination number of the copper(I) is 3.
There are only two possible geometries are possible for compounds with coordination number
2. Liner and Bent. When the central ion utilises the two hybrid orbitals for bonding with the
ligands and does not contain any lone pair of electrons, it forms linear complexes otherwise
bent. Above mentioned Complexes of Cu(I), Au (I), Ag (I) etc. shows linear geometry.
Examples of complexes with bent arrangements are rare.
Coordination Number 3
This coordination number is uncommon, rather rare. Many compounds seem to be three
coordinated were actually four coordinated. K[Cu (CN)3] is a three coordinated complex.
[HgI3]- is another example. The possible geometry is trigonal planar.
 Fig. Trigonal planar arrangement in HgI3-
Coordination Number 4
In this case two principal geometries encountered are (1) tetrahedral and (2) Square planar.
Complexes with coordination number four is the first which for which isomerism to be
expected.
1. Tetrahedral Geometry. This geometry is common amongst complexes of transition as well
as non transition elements. Some of the common examples are [BeF4]2-, [BF4]-, [Cd(CN)4]2-
etc. The geometry of [BeF4]2- is shown below;

Fig. Tetrahedral geometry of [BeF4]2-

Tetrahedral complexes are favoured by steric requirements, either simple electrostatic
repulsion of charged ligands or van der Waals repulsions of large ones. From a valence bond
view point tetrahedral structures are sp3 hybridised. From CF or MO point of view we have
seen in general, the tetrahedral structures are not stabilised by large LFSE. Tetrahedral
complexes are favoured by ligands like Cl-, Br- and I- and small metal ions of three types (a)
those with a noble gas configuration such as Be 2+; (b) those with a pseudo-noble gas
configuration (n-1) d10 ns0 np6, such as Zn2+ and Ga3+ (c) those transition metal ions which do
not strongly favour other structures by virtue of the LFSE, such as Co2+, d7. Tetrahedral
complexes do not exhibit geometrical isomerism. However, they are potentially chiral just as
is tetrahedral carbon.
(2) Square planar complexes: This geometry is common amongst complexes of transition
metals only. The common examples are [PtCl4]2-, [Ni(CN)4]2- etc. Generally square planar
complexes are less sterically favoured than tetrahedral complexes. Non bulky strong field
ligands are usually favoured for S.P complexes. d8 metal species like Ni2+, Pd2+, Pt2+, and Au3+
usually form S.P complexes. Square planar complexes of the type [Ab2c2] may exhibit
geometrical isomerism. But these complexes rarely show optical isomerism. The plane formed
by the four ligating atoms and the metal ion will ordinarily be a mirror plane and prevent the
possibility of chirality.
 Fig. Square planar geometry of [Ni(CN)4]2-
Coordination number 5
Complexes with coordination number 5 like those with coordination number 3 are rather rare.
Several complexes in which metal ion was considered to be having coordination number 5
were later on shown to have the metal ion with different coordination number. Two principal
geometries are possible (1) Trigonal Bipyramidal and (2) Square pyramidal.
(1)Trigonal Bipyramidal: In this case the ligands lie at the vertices of trigonal bipyramid.
Examples are Fe(CO)5, MoCl5, CuCl53- and SnCl5-.
In most of the TBP structure, more electronegative elements prefer the axial position and best
π accepting ligands will prefer the equatorial position. Note the most ligands occur in both axial
and equatorial positions depending upon what other ligands are present.
In contrast to PCl5 molecule (there axial bonds are longer than equatorial bonds), the axial
bonds in Fe(CO)5 is shorter than the equatorial bonds.

Fig. TBP structure of Fe(CO)5

(2)Square Pyramidal: In this case, the ligands lie at the vertices of a square pyramid.
Examples are SbF52-, VO(acac)2 and [Ni{(C6H5)P}2Br3] In square pyramidal geometry the
central atom may be in the plane of the basal ligands or above it to varying degrees.

Fig. Square pyramidal structure of SbF52-

Coordination Number 6
Coordination number 6 is most common and has been extensively studied. The regular
geometric arrangement is octahedral although due to distortions the geometry may changes to
tetragonal. Oh geometry is shown by large number of complexes like [Cu(NH 3)6]2+, FeF63-,
TiF62- etc. An example for tetragonally distorted octahedron is furnished by [CoCl 2(NH3)4]+
ion.

Fig. Oh geometry of FeF63-

Coordination Number 7
There are only a few compounds in which coordination number is 7. Three geometrical forms
known in this case are as follows
1. One of these which is most regular is pentagonal bipyramidal. this geometry us found
in [UO2F5]3-, UF73- and ZrF73-
2. The second arrangement is supposed to result from the addition of a seventh atom at
the centre of one face of a distorted octahedron. An example is furnished by [NbOF6]3-
3. The third arrangement is derived by putting a seventh atom above the centre of one of
the rectangular faces of a trigonal prism. This arrangement occurs in [NbF7]2- and TaF7
2-

Coordination Number 8

This coordination number is the most common after 6and 4. Three types of geometries are
possible for this C.N. these are

1. Cubic 2. Square antiprism 3. Dodecahedral

1. Cubic: The most symmetrical arrangement is simple cubic. This occurs however, only in
the case of a few compounds as for example, in [UF8]3-

2. Square antiprism: This depicts a distortion in the cubic geometry which is adopted to
minimise the repulsion between the anions. The common examples are [TaF8]3-, [ReF8]2-,
[Zr(acac)4].

3. Dodecahedral Geometry: This type of geometry is exhibited by complexes such as

[Mo(CN)8]4- and [Zr(ox)4]4-.

Coordination Number 9

There is only one symmetrical arrangement known for this coordination number. This is
derived from a trigonal prism by placing the three additional atoms outside the centres of the
tree vertical faces. Eg. [Nd(H2O)9]3+

Coordination numbers 10 and 12

There are no complexes with coordination number 10 or more with distinct monodentate
ligands. However a few ten-coordinate chelate structures with bidentate nitrate or carbonate
ligands have been observed. One possible is a ‘double trigonal bipyramid’ with nitrate or
carbonate ions at each the TBP sites. Coordination numbers as high as 12 are also known with
six bidentate nitrate ligands along the edges of a dodecahedron, but these complexes are rare.

Generalisations about Coordination Numbers

Factors favouring low coordination numbers are

• Soft ligands and metals in low oxidation numbers prefers low coordination numbers
because extensive pi bonding compensate the absence of additional sigma bonds.
• If the ligands are large and bulky, it will prevent additional ligands to coordinate with
the metal even though the metal is in coordinatively unsaturated state.
• Counter ions of low basicity also favours low coordination numbers

Factors favouring high coordination numbers

• High oxidation state and hard ligands

• Small steric requirements of the ligands
• Large nonacidic cationic countries will tend to stabilize the crystal lattice in high
coordinated complexes.

Sigma and Pi bonding Ligands (π acceptor or π acid ligands)

The π acceptor ligands are those which possess vacant π orbitals in addition to the lone pair of
electrons. These ligands donate their lone pairs to the metal to form a normal sigma bond. In
addition to it, the vacant orbitals accept electrons form the filled metal orbitals to form a type
of π bond which supplements the sigma bond. These ligands are thus called π acid (since they
accept πelectrons charge to their vacant π orbital) or π acceptor ligands or π bonding ligands.

eg. CO, CNR, PR3, NO etc.

In many of the complexes formed by π acceptor ligands, the metal atom is in low positive or
zero oxidation state. That is these ligands stabilise lower oxidation states. This is because of
the fact that there is higher electron charge density on the metal in its lower oxidation state than
its higher state.

Some of the common π acid ligands are discussed below;

1. Carbon monoxide (CO)

According to VBT, CO molecule is represented by the structure

In this structure, both C and O atoms are in sp hybridized.

The CO sigma bond is formed by the overlap between the singly occupied sp hybrid orbitals
while CO pi bond results by the overlap between singly filled 2py orbitals on C and O atoms.
The ‘O C’ coordinate bond is obtained by the donation of an electron pair residing in 2pz
orbital on oxygen atom to vacant 2pz orbital of carbon atom. The electron pair present in sp
hybrid orbital of both atoms remains as lone pair of electrons on these atoms.

The electronic configurations of C and O atoms are 1s 22s22p2 and 1s22s22p4 respectively. Thus
a total of 10 outer electrons are to be accommodated in the molecular orbitals of CO molecules.
Because of electronegativity of oxygen, it atomic orbitals would be of lower energy than the
corresponding atomic orbitals of C.

The 2s and 2pz atomic orbitals of C atom as well as O atom mix to produce two atomic orbitals
of mixed s-pz character in each case.

Fig .M.O. diagram of CO

Bonding:

M-CO sigma bond is formed by donating a pair of electron from the HOMO of CO (3σ) to the
empty hydrid orbital metal orbital. The metal then donates a filled dπ electron to the low lying
anti bonding molecular orbital (3π or 4π) of CO to form M-CO π bond (dπ-pπ*). This bonding
is known as π back bonding. The sigma and pi back bonding influence each other and
strengthen the M-C bond. Such an effect is known as synergic effect. But due to this effect, the
C-O bond strength decreases.

Different types of bonding modes

There are 4 different modes of ligation for CO;

CO molecule act as a terminal carbonyl group

This mode happens when CO molecule gets attached with the metallic atom in carbonyls
through the lone pair of electrons present in sp hybrid orbitals on carbon atom.

CO molecule act as a bridging (ketonic) carbobyl group when CO is attached with two metallic
atoms through two unpaired electrons present in the two sp hybrid orbitals on carbon atoms.
This may happen in two ways as shown below;

The stretching frequencies of free CO and CO with different ligation are given below;

2. Nitric Oxide (NO)

The electronic configuration if N and O atoms are 1s22s22p3 and 1s2 2s22p4 respectively. A
total of 11 outer electrons are to be accommodated in the M.O. of NO. The bond order of NO
is 2.5

Since NO contains an unpaired electron, it is paramagnetic in nature and is less stable than N 2

The following categories of NO complexes are known

1. Complexes derived from NO+ ion: The odd electron in π* orbital of NO molecule is
quite readily lose to produce stable NO+ ion (B.O = 3). This fact receives conformation
form the IR absorption spectra of free NO (ν =1800cm-1) with those of salts containing
NO+ ion (ν = 2200-2300cm-1). A large number of complexes of nitric oxide are reported
to have NO+ ion (nitrosonium ion) as the ligand which too act as three electron donor.
The ligation of NO+ to the metal in complexes can be observed to taking place in the
following steps;
• Initially, during its complexation with the metal, NO loses one π* electron to
the metal, reducing its valance by one unit and getting itself converted to NO +
 • In the 2nd step, NO+ which is isoelectronic with CO (14 electron) donates a pair
of electron to the metal to get coordinated to the metal. In this way NO in its
nitrosonium complexes act as a 3 electron donor. The M-N bond would,
evidently be highly polar. Hence the electron charge from filled dπ orbitals of
the metal gets transferred to π* M.O of NO+. The IR absorption frequency of
NO+ in nitrozonium complexes between 1600-1900 cm-1 which is much lower
than the absorption frequency of NO+ in its ionic salts (containing NO as free
cation) which falls between 2200-2300 cm-1

2. Complexes derived from NO: If the π* electron NO remains localized on NO itself,

and is not transferred to metal, the ligand would act as a 2 electron sigma donor
thorough its nitrogen atom and the metal complex formed would be paramagnetic.
Several complexes such as [Mn(NO)(CN)5]2- and [Cr(NO)(CN)5]3- are paramagnetic
and at one time these were thought to be derived from NO. But it has now been
established that the unpaired electron in most of such complexes is localized on the
metal rather than on the ligand NO.
3. Complexes derived from NO-: In these complexes, nitric oxide is bound to the metal
in such a manner that it appears to have accepted on electron from M n+ to get converted
into NO-. The NO- then donated two electrons through its N atom to the resulting
M(n+1)+ to forma sigma coordinate bond. In this way nitric oxide in these complexes acts
effectively as one electron donor.
During the conversion of NO to NO- it can be assumed that one electron from dπ orbital
of the metal gets transferred to π* molecular orbital of the ligand. It is therefore
expected that IR absorption frequency and bond order of NO- in the complexes of NO-
should be lower than those in free NO.
eg. [Co(NH3)5(NO)]2+ (1100-1200cm-1)

Modes of Ligation of nitrosyl group

Nitrosyl group ligate to the metal in (i) terminal (ii) bridging fashion

Although nitrosyl ligand appear to be linear consistent with sp hybridisation of the N, a few
cases of distinctive bent species are known. Here the N can be considered to sp2 hybridised and
bears a lone pair. It is this lone pair that causes the nitrosyl group to be bent.

Geometry of linear Vs bent of nitrosyl ligands

Stretching frequencies of nitrosyl complexes in different forms

Free NO -1880 cm-1

NO+ in salts – 2200-2300 cm-1

NO+ in complexes – 1600-1900 cm-1

NO- in complexes – 1100-1200 cm-1

NO as terminal – 1672 cm-1

NO bridged – 1505 cm-1

3. Isocyanide complexes (RNC)

Isocyanide (RNC) group is similar to CO group since N:R is isoelectronic with O atom. Thus
an isocyanide group can enter into similar type of σ-π synergic bonding as is done by CO group
as shown below

Fig. sigma and pi bonding

In contrast with CO, the σ donor lone pair on the C-atom of isocyanides is antibonding in nature
and upon complexation the CN bond is strengthened and ν CN increases. At the same time, π
back bonding lowers the νCN depending on the balance of sigma bonding vs pi back bonding,
the νCN can either be raised [for eg. upon complexation with poor pi donor metal such as pt
(II)] or lowered (for example upon complexation with the strong pi donor metal such as Ni (0)].
Example for isocyanide complexes are Cr(CNR)6, Ni(CNR)4

There are several compounds containing isocyanide group of the type shown below;
4. Triphenyl phosphine (PPh3/PAr3) and trialkyl phosphine (PR3)

In PR3, PAr3 etc. the trivalent P acts as pi acceptor ligands. This is because P has vacant d
orbitals which are of proper symmetry to overlap with the d orbitals of the central metal atom.
The overlap facilitates shifting of the electron charge form the metal to the ligand through pi
back bonding

Phosphorous primarily function as Lewis bases interacting with metals as sigma donor ligands.
they also can accept electron density from metal.

The availability of d orbitals of P atom to the d orbitals of the metal is however influenced by
the electronegativity of the group attached to P atom. For eg. in PF3, F atom being highly
electronegative would polarize sigma electron cloud from P toward F. therefore by reducing
sigma donor character of P atom. But this shifting of the electron charge form P would at the
same time, increases the pi acceptor character of the 3d orbitals of P atom. In the case of
P(C2H5)3, the effect is just the opposite. This implies that PF3 would behave as a better pi
acceptor ligand than P(C2H5)3. Similarly, the ligand P(Ar)3 is thus a poor sigma donor but a
better pi acceptor than PR3 type ligands.

Stability of complexes

Most of the complexes are quite stable. However, they dissociate in aqueous solutions to a
slight extent to establish equilibrium with the central metal ion and the ligands from which they
are derived. Thus for a complex of the type MLn, the following equilibrium exists.

The equilibrium constant K designated as ‘Kdis’and is given by the following expression

Evidently smaller the value of dissociation constant, the greater will be the stability of the
complex. The reciprocal of dissociation constant is therefore called stability constant, of the
complex. The grater the value of the stability constant, the greater will be the stability of the
complex.
For example, consider the complex ion [Ag(NH3)2]2+

Here Kdis = 6x10-8, a very small value which indicates the stability of the complex ion. The
reciprocal of dissociation constant is stability constant. Here the stability constant of the
complex ion [Ag(NH3)2]2+ is the equilibrium constant (Kdis) of the reverse reaction.

Thermodynamic stability

The subject of stability of metal complexes is important in understanding the properties of the
complexes. There are two types of stability viz., the thermodynamic stability and kinetic
stability for a complex when we are interested in stability. From the thermodynamic view, then
we must deal with metal to ligand bond energies, stability constant and the thermodynamic
variables derivable from them. If we are interested in stability from the kinetic point of view,
then we must deal with the rates and mechanisms of reactions and also with the energies
involved in the formation of the activated complex. In the kinetic point of view, it will be more
proper to speak of complexes as being inert or labile. But in thermodynamic point of view, we
consider complexes as stable or unstable.

When a, metal ion in aqueous solutions interact with a neutral and monodentate ligand, the
system at equilibrium may be described by,

Where x is the number water molecules and n is the oxidation no. of metal ion. When L is an
uni-ionic ligand, the ligand equilibrium would be,

We may write the equilibrium reaction in a simplified and generalised form without referring
to the no. of coordinated water molecule as follows;

The equilibrium constant of the reaction is given by

Kf is called the formation constant of the complex. If a large amount of the complex is formed
then the equilibrium concentration [ML] is larger than the product [M][L] then Kf is more than
1.0. Such a situation would arise when a ligand L binds to the metal more tightly than H2O.
Thus a large value of Kf merely indicates that L is a stronger ligand than H2O. Similarly when
Kf is less than 1.0., then L is a weaker ligand than H 2O. The magnitude of the formation
constant is a measure of stability of a coordination complex in a thermodynamic sense. The
formation constants are also called stability constants and are used by coordination chemists as
a measure of thermodynamic stability of the metal complex.

Stepwise formation constant

When more than one coordinated water molecule if [M(H2O)x]n+ is replaced by a ligand L, then
we have to consider several steps. At each steps we need to consider an equilibrium constant
called stepwise formation constant or step wise stability constant. For a general case of the
formation of MLn complexes from aquated metalation M and monodentate ligand L, there
would be n equilibrium reactions and n stepwise stability constants

The overall formation constant or overall stability constant for the formation of the species
MLn form M and L at equilibrium is given by

The product of individual stepwise stability constants is called over all stability constant. It is
given by

With few exceptions, it is generally observed that the stepwise formation constant decreases
steadily as the number of ligands increases.

k1 > K2 >K3>.....>Kn

The above trend is explained in terms of (a) increased steric hindrance as the no. of ligand
increases (b) statistical factors related to the number of opportunities for reaction and (c)
electrostratic factors when charged ligand are involved. However, there are cases where, K n+1
is found to be larger than Kn (eg. K2>K1). Usually a structural change or a change in the spin
state of the metal ion associated with the binding of additional ligands may be responsible for
the reversal of the expected change.

Factors affecting stability

Stability constants vary over a very wide range of values even when we consider the reaction
of a particular metal with a no. of ligands or particular ligands with a variety of metals.

Factors related to metal:

1. Change of the central metal ion: Greater the positive oxidation state of the central metal ion
greater will be its attraction for the ligands; hence greater will be the stability of the complex

2. Size of the central metal ion: Generally, stabilities of the complexes increase with decrease
in size of the metal ion. Keeping the charge constant, as the size of the central metal ion
decreases, the specific charge per unit surface area increases. Hence the metal’s attraction for
the ligand increases.

3. Outer electronic configuration of the central metal ion: Generally, complexes of transition
metal ions are more stable than that of non-transtion metal ions like alkali metal ions. This is
mainly due to the fundamental electronic differences.

It is a well known fact that the transition metal’s electronic configuration is much poorer in
shielding the excess positive charge located on the nucleus than the electronic configuration of
non-transition metals. Hence the effective nuclear charge is greater in transition metal ions that
it is in non-transition metal ions. Thus the transition metal ion has greater attraction for the
electrons offered by ligands. Consequently they form more stable complexes than non
transition metal ions.

Factors related to ligands:

1. Nature of the ligand atom: The atoms which are bound directly to metal ion in complexes
are those of the more electronegative elements on the right hand side of the periodic table (such
as halogens, oxygen, sulphur, arsenic, phosphorus, nitrogen etc.). For most metals, the order of
stabilities of halides follow the sequence F- >Cl- >Br-> I-. But this order is reversed for a few
metals like Pt2+, Cu+, Ag+, Hg2+ and Tl+, where back donation occurs.

2. Basicity of the ligands; Greater the basicity of the ligand, greater will be the tendency to
donate electron pairs. This means that the more basic ligands will form more stable complexes.

3. Chelating ability of the ligand: Chelate effect:

When a bidentate or polydentate ligand is attached through two or more donor atoms to the
same central metal ion forming a ring structure, the ligand is called chelating ligand. The
resulting complex with ring structures is called a chelate. The process of chelate formation is
known as chelation. Due to chelation the stability of the complex is enhanced. This extra
stability conferred on a complex due to chelation is called the chelate effect.

Ligands like en, dien, trien, DMG, EDTA, acac etc. are few examples for chelating ligands.
Some complexes of metal chelates are [Cu(en)2]2+, [Ni(dien)2]2+, Ni(DMG)2, [Ca-EDTA]2-.
Thermodynamically, the chelate effect can be related to entropy change of the reaction. When
a solvated metal ion in solution reacts with a chelating agent, the solvent molecules in the
coordination sphere of the metal ion are replaced by the chelating agent. For example,

During this chelate formation, the number of particles increases, that means the degree of
randomness or entropy of the reaction increases. This causes greater complex stability.

Conditions for Chelation

• The chelating agents must possess at least two donor groups per molecule. i.e, the
ligands should be polydentate.
• These donor groups must be so situated in the molecule in such a way that they permit
the formation of a ring with the metal atom without any strain. The donor atoms should
be sterically capable of coordinating to the same metal to form chelate. Hydrazine
(NH2-NH2), even though a polydentate ligand, does not form a stable chelate, because
it does not satisfy the last condition pertaining to steric condition.

Factors affecting stability of chelates

1. A factor of great importance in chelation is the size of the chelate ring produced. If
there is no double bond in the chelate ring, then a 5-membered ring is the most stable.
Chelate rings having more or less than 5-membered are generally less stable.

2. Another factor which determines chelate stability is the influence of the number of
chelate rings in a chelate molecule. Greater the number of chelate rings grater will be
the stability of the complex.
3. One more factor of significance in chelation is the steric factor. This arises due to the
presence of a bulky group either attached to or near to a donor atom to cause mutual
repulsion between the ligands and thereby weakening the metal-ligand bond. This leads
to lesser stability.

Resonance and chelation: Some chelating ligands are capable of experiencing resonance
stabilisation if their molecules. This stabilisation is extended to the metal chelates formed by
them. For example, acetylacetone can form a chelate with an M(III) ion , [M(acac) 3]. Where
M = Al, Cr or Co. One ring of the structure if the complex is represented as two resonance
forms;
 Resonance stabilisation of chelate

Thermodynamic aspects of complex formation-Irving William Order of stability

Metal ions are empirically classified into three classes based on the stabilities of complexes
formed by them with ligands having donor atoms from group VA, VIA or VIIA

Class a metal ions are those ions which form complexes of the greatest stability with the lightest
element of each of these groups as the donor atom. Examples of class metal ions are

Li+ Na+ K+

Be2+ Mg2+ Ca2+ Sr2+

Al3+ Ga3+ Cr3+ Fe3+ Co3+ etc.

Class b metal ions are those which form least stable complexes with the lightest element of
each group as donor atom.

Examples of class b metal ions are

Cu+ Ag+ Au+ Tl+

Hg2+ Pd2+ Pt2+ Tl3+

Some metal ions form complexes whose stabilities cannot be predicted on the basis of the order
which was observed for class a and class b metal ions. Those ions are classified as border line
class. Examples of border line class are Mn2+, Fe2+ Co2+ Ni2+ Cu2+ Zn2+ etc.

For these metal ions, the stability of complexes with a given ligand is almost in the order

Mn2+ < Fe2+< Co2+ < Ni2+ < Cu2+ > Zn2+

This order is known as the Irving-William series, this is illustrated for some ligands the
following figure. Although the figure shows the trend in K1 vales, the Irving-William, series
generally holds good for K2 and K3 also.
 COORDIANTION CHEMISTRY
UNIT 1-Structural Aspects and Bonding

Crystal Field theory (CFT)

This theory was first proposed and modified later by H. Bethe and J.H. Van Vleck
respectively. This theory involves an electrostatic approach to the bonding in complexes. It
was first applied to ionic-type crystalline substances. Therefore, it is very often called the
Crystal field theory (CFT). This theory considers the metal ion as being placed in an
electrostatic field created by the surrounding ligands. This electric field changes the energies
of the d electrons and as a result the degenerate d orbitals split.

Important assumptions of CFT

• This theory considers a complex as a combination of a central ion surrounded by other

ions or molecules with electric diploes called ligands
• The anionic ligands are regarded as point charges while neural ligands are
considered as point dipoles
• The bonding between the metal cation and ligands arises due to the electrostatic
attraction between the nucleus of the metal and the partial negative charge invariably
present on the ligands. Thus the bond between the metal and the ligand is purely
ionic.
• The interaction between the electrons of the cation and those of the ligands is entirely
repulsive. These repulsive forces are responsible for the splitting of the d orbitals of
the metal cation. That means the d orbitals which are degenerate in a free metal ion
have their degeneracy destroyed by the approach of the ligands during the formation
of a complex.

Crystal Field Splitting of d Orbitals in Different Geometries;

Splitting of d Orbitals in Octahedral Field

• The five d orbitals in a free metal ion are degenerate. When a spherically symmetric
field due to six ligands is placed around the central metal ion, all the five orbitals will
be raised in energy as a result of the repulsion between the negative filed and the
electrons of the metal ion. Although they still remain in degenerate, they will have
higher energy than before.
• But when these six ligands approaches the metal ion along the axes, the electrons in
the orbitals lying along the axes (dz2, dx2-y2; eg) experience greater repulsion than
electrons in the orbitals lying in between the axis (dxy, dxz and dyz; t2g).
• As a result the five degenerate d orbitals of metal ion split in to two sets t 2g (triply
degenerate set) and eg (doubly degenerate set). This splitting of degenerate metal d
orbitals under the influence of ligands during complex formation is called crystal filed
splitting.
 • During splitting, the energy of t2g gets decreased by 0.4Δo or 4Dq where as the energy
of eg orbital get increased by 0.6Δo or 6Dq in an octahedral field. The energy
difference between the t2g and eg is thus Δo or 10Dq.

Fig. Splitting of d orbitals in Oh field

Calculation of crystal field stabilisation energy

Consider a metal ion with d1 configuration in an oh filed. Its electronic configuration can be
written as t2g1 eg0. Then crystal field stabilisation energy is calculated by using the following
formula

n =no. of electrons

Thus for d1, CFSE = (1 x -0.4 Δo) +(0 x 0.6 Δo) = -0.4 Δo or 4 Dq (in some text books the
negative sign is avoided)

The complex can thus said to be stabilised by 0.4 Δo. This quantity of decrease in energy
during complex formation is called crystal field stabilisation energy. Similarly for d 2 and d3
the CFSE is calculated to be -0.8 Δo and -1.2 Δo respectively. But in the case of d4 case two
electronic configurations are possible;

t2g4 eg0 (low spin or strong field where Δo >P; P = pairing energy).

t2g3 eg1 (high spin or weak field where Δo < P).

Following table shows the CFSE’s in weak and strong fields

Weak field or High spin case;

dn Configuration Unpaired CFSE

electrons
d1 t2g1 eg0 1 -0.4Δo
d2 t2g2 eg0 2 -0.8 Δo
d3 t2g3 eg0 3 -1.2 Δo
d4 t2g3 eg1 4 0.6 Δo
d5 t2g3 eg2 5 0 Δo
 d6 t2g4 eg2 4 -0.4 Δo
d7 t2g5 eg2 3 -0.8 Δo
d8 t2g6 eg2 2 -1.2 Δo
d9 t2g6 eg3 1 -0.6 Δo
d10 t2g6 eg4 0 0 Δo

Strong field or Low spin case;

dn Configuration Unpaired CFSE

electrons
d1 t2g1 eg0 1 -0.4Δo
d2 t2g2 eg0 2 -0.8 Δo
d3 t2g3 eg0 3 -1.2 Δo
d4 t2g4 eg0 2 -1.6 Δo+P
d5 t2g5 eg0 1 -2.0 Δo+ 2P
d6 t2g6 eg0 0 -2.4 Δo+3P
d7 t2g6 eg1 1 -1.8 Δo
d8 t2g6 eg2 2 -1.2 Δo
d9 t2g6 eg3 1 -0.6 Δo
d10 t2g6 eg4 0 0 Δo

Note: If negative sign is ignored then the P has to be subtracted [e.g. (1.6Δo-P), (2.0Δo-
2P) etc.]

Splitting of d orbitals in tetrahedral Field

• In the formation of tetrahedral complexes the ligands do not directly approach any
metal d orbitals. But they come closer to those orbitals lying in between the axes. As a
result the electrons in those orbitals will face for repulsion from the ligands compared
to two other orbitals lying along the axes. This cause the splitting of d orbitals in to
two sets as e (dz2, dx2-y2)and t2 (dxy, dxz and dyz)
• The energy of e set of orbitals gets lowered while that of t2 gets increased. The energy
gap between the e and t2 level is represented as Δt. It is noted that Δt is less than Δo.
This because of two reasons; (1) in td complexes only four ligands are approaching
the metal and whereas in oh complexes six ligands are approaching the metal. When
number ligands increases the extent of splitting also increases due to greater repulsive
interaction (2) During oh complex formation ligands approaches directly to two metal
orbitals which results in greater splitting. But in td complexes formation no ligands
are directly approaching the orbitals
• It has been found that Δt ≈ 4/9Δo.
• Tetrahedral complexes usually forms high spin complexes due the smaller energy gap
between e and t2 compared to oh complexes where they form both low and high spin
complexes.
 Fig. Splitting in td field

Splitting of d orbitals in Square Planar Field: Lowering of symmetry through

Tetragonal to Square Planar

• If two trans ligands in an Oh ML6 complex are moved either towards or away from
the metal ion (along z axis), the resulting geometry is said to be tetragonally distorted.
This tetragonally distorted Oh geometry is called tetragonal geometry.
• If we elongate along the z axis, the orbitals lying along the z direction will feel less
repulsion from the ligands. As a result the t2g and eg levels split again as shown below;
• If we remove these two ligands lying along z direction (the limiting case of tetragonal
elongation), we will end up with a complex having square planar geometry. Since
there are no ligands along the z direction the energy of orbitals with z component will
be lowered drastically as shown below;

Fig. Splitting in Tetragonal and square planar fields

• Δsp is always greater then Δo (Δsp = 1/3 Δo)

Splitting of d orbitals in square pyramidal Field

Splitting of d orbitals in trigonal bipyramidal Field

Factors affecting magnitude of Crystal field splitting, Δ

• Oxidation state of the metal ion: The magnitude of Δ increases with increasing ionic
charge on the central metal ion.
• Nature of the metal ion: Significant differences in Δ also occur for analogous
complexes within a given group, the trend being 3d <4d <5d. In progressing from Cr
to Mo or Co to Rh the value of Δ increases by as much as 50%
• Number and geometry of the ligands: If the charge and groups are same and differ
only by geometry, then it is seen that tetrahedral splitting is only about 50% as
compared to that in Oh complex splitting. The order of magnitude of splitting for
different geometries is Δsp > ΔOh > Δtd
• Nature of the ligand: There are two types of ligands namely strong filed ligands and
weak field ligands. Strong field ligands cause greater splitting and hence will cause
for high Δ value. Strong field complexes usually result low spin complexes (spin
paired). Whereas weak field ligands show lesser splitting and hence cause low Δ
value. Weak field ligands form high spin complexes (unpaired spin). The ability of a
ligand to split the d orbitals can be understood from spectrochemical seires. In this
series the ligands are arranged in the increasing order of their ability to split d orbitals.
The arrangement is based on the evidences obtained from the electronic spectral
studies of complexes containing particular ligands.

I- <Br- < S22- < SCN- < Cl- < N3- < F- < urea < OH- < ox < O2- < H2O <
NCS- < py < NH3 en < bpy < phen < NO2- < CH3- < C6H5- < CN- < CO

Jahn Teller (JT) effect

Consequences of Crystal field splitting

• Ionic radii of transition metal ions: The ionic radii of first transition metal ion in
complexes are expected to decrease smoothly due to increase in nuclear charge. But
this is not true in the actual case where only the metal ions with d0, d5 and d10 (CFSE
=0 cases) only show the expected variation. All others do not show a smooth
decreasing but abnormally decreased values due to splitting.

• Heats of Hydration of bivalent ions of first transition series: With decrease in size,
the heat of hydration increases. Since the decrease in size along the metal ion of first
transition series decreases irregularly, the heat of hydration ingresses in the same
way.

• Lattice energy and CFSE’s: Shows the same pattern as in the case of heat of
hydration.
Merits of CFT

• This theory can be used to predict the most favourable geometry of a complex
• It accounts for the fact that certain four-coordinated complexes are square planar
whereas others are tetrahedral
• It also explains the fact that certain ligands form outer orbital octahedral complexes
whereas other form inner orbital octahedral complexes. They in turn correspond to
low spin and high spin complexes
• This theory is successful in explaining the magnetic properties taking into
consideration the orbital contribution also
• The colours of transition metal complexes can be readily interpreted using this theory
• Electronic spectral properties of many transition metal complexes can be easily
explained by this theory
• This theory helps predict site selection in spinel and antispinel structures: Normally
the ion, which is crystal field stabilised tends to occupy octahedral sites in the
structure (because of its higher stabilisation energy that is Δo> Δt). In Mn3O4 both
Mn2+ (d5, CFSE =0) and Mn3+ (d4, with net CFSE). Here Mn3+ is crystal field
stabilised and hence occupies the Oh sites and other in the tetrahedral sites. Thus it
adopts normal spinel

Theoretical failures/limitations of crystal field theory

• CFT considers only the metal ion d orbitals and gives no consideration at all to other
metal orbitals s and p orbitals and ligand π orbitals. Therefore to explain all the
properties of the complexes dependent on the π-ligand orbital will be outside the
scope of CFT
• The point charge model assumed by this theory does not exactly represent the actual
situation of a metal ion in the field of the surrounding ligands.
• CFT unable to account satisfactorily for the relative strengths of ligands. e.g. it gives
no explanation as to why H2O appears in the spectrochemical series as a stronger
ligand than OH- .
• According to CFT, the bond between the metal and ligand is purely ionic. It gives no
account of the partly covalent nature of the metal-ligand bonds
• In several complexes, the bonding strength and chemical properties cannot be
explained solely on the basis of electrostatic attraction as emphasised by this theory

Modified Crystal Field Theory: The Ligand Field Theory

As we all know, the crystal field theory assumes that the source of metal-ligand bond is the
pure electrostatic interaction between the metal ion and the ligand. The theory predicts the
splitting of d orbitals as being due to the electrostatic potential of the ligands to which the d
electrons of the metal ions get exposed. The crystal field theory can explain the spectra of the
metal ions and of the complexes on the assumption that these arise from the transition of
electrons form lower energy d orbitals to higher energy d orbitals. However, the positions and
intensities of spectral band calculated on the basis of crystal field theory do not coincide with
those determined experimentally. There are frequent deviations. Apart from this, a pure
electrostatic interaction between the metal ion and the ligands fails to explain the relative
positions of ligands in the spectrochemical series.

In addition to the above, there is clear evidence that covalent bonding too makes a significant
contribution towards the metal ligand bonding. This aspect is discussed below in some
details.

Evidence of covalency in the metal-ligand bond

1. Lande’s splitting factor, g: The Lande’s splitting factor g which is employed to predict
the magnetic behaviour of transition metal complexes can also determine the extent of
delocalisation (or penetration) of d electrons of the metal into the orbitals of the ligand. The
value of g determined experimentally shows that the metal d electrons are almost always
delocalised to some extent into the ligand orbitals. This can happen only due to the
overlapping of the metal d orbitals with the ligand orbitals through covalent bonding. It has
been deduced from the value of g that even in the bonds of F- ions with metals in fluoro
compounds, which are conventionally taken as ionic, there is around 5% covalent character.

2. Electron Spin Resonance (ESR): The ESR spectral studies conducted on the complexes
of paramagnetic metal ions reveal the presence of unpaired electrons in the molecular orbitals
formed due to the overlapping of orbitals of the ligand and the metal ion

3. Nuclear magnetic resonance (NMR): The NMR spectral studies clearly indicate that the
spin of an unpaired electron of a metal ion interacts with the nuclear spin of 19F in the fluoro
complex of a paramagnetic metal ion. This electron spin-nuclear spin interaction is possible
only if the unpaired electron spends more than negligible time on the 19F nucleus. This is
possible through the overlapping of orbitals of the ligand and the metal ion that is through
covalent bonding

4. Interelectronic repulsion; The Nephelauxetic Effect: Electrons in the partly filled d

orbitals of a metal ion repel one another and give rise to a number of energy levels
depending upon the arrangement of these electrons in the d orbitals. The energy of each of
these levels can be expressed in terms of some interelectronic repulsion parameters called
Racah parameters B and C. The energy gap between two such energy levels which have the
same spin multiplicity cab be expressed in terms of Dq and B and the energy gap between
two energy levels having different multiplicities is expressed in terms of Dq, B and C. It is
observed experimentally that the magnitude of these interelectronic repulsion parameters
always decreases on the complexation of the metal ion. This is possible only if interelectronic
repulsion between the d electrons of the metal ion decreases on complexation.

The magnitude of the interelectronic repulsion is inversely proportional to the distance r

between the regions of maximum charge density if the d orbitals which are occupied by the
electrons. This repulsion would decrease only if the distance r increases or if the lobes of the
d orbitals (containing the electrons) extend in space.
The extension of the lobes of the d orbitals which means the expansion of the d electron
charge cloud, is known as nephlelauxetic effect (from Greek, meaning ‘cloud expanding’).

The extension of d orbitals of the complexed metal ion in space occurs obviously to
maximise the overlap of these orbitals with the orbitals of the ligand. This is an essential
condition for covalent bonding. In other words, it is covalent bonding in metal-ligand bond
which decreases the interelectronic repulsion parameters when a free metal ion gets
complexed. The larger the decrease in the interelectronic repulsion parameters, the greater is
the extent of covalent bonding in metal-ligand bond of the complex

5. Nuclear Quadrupole Resonance (NQR) Studies: The NQR data on the complexes
containing halide ion as the ligands clearly show that the metal-halogen bond is partially
ionic and partly covalent in character.

It is amply clear from the above discussion that the metal-ligand bond has definitely a partial
covalent character. The crystal field theory, according to which the interaction between the
metal ion and the ligands are purely electrostatic in character, thus needs modification so as
to include the contribution of covalent bonding as well in the metal –ligand bond. The crystal
field theory modified to include covalent character in metal-ligand bond is known as the
Ligand Field theory

Jahn-Tellar (JT) Effect

It was stated by Jahn and Teller that any non-linear molecular system in orbitally degenerate
electronic state (i.e., a sate which represents more than one electronic arrangements of the
same energy) would be unstable and that it would get stabilised by undergoing distortion in
its geometry and thus by causing a split in its orbitally degenerate electronic state. The above
statement is known as Jahn-Tellar effect. The distortion in the geometry of the non-linear
molecular system thus produced is known as Jahn-Tellar distortion. The lowering of
symmetry of the non-linear system due to Jahn-Tellar effect always occurs in a manner which
results in decrease in the energy of the system. Jahn-Tellar distortion is thus automatic for the
non-linear molecular systems of the above mentioned type

Consider a d9 octahedral complex [CuL6]2+ where L = unidentate ligands. The Cu2+ in a

perfect octahedral environment has the ground state electronic configuration t2g6 eg3 which
represent two electronic arrangements t2g6 d2z2 d1x2-y2 and t2g6 d1z2 d2x2-y2 of equal energy.

In first case (t2g6 d2z2 d1x2-y2), the d electron charge density will obviously become higher in Z
direction than in X or Y direction. The screening of the positive charge on Cu2+ nucleus by d
electrons will, therefore, be more in Z direction than in X or Y direction. The negative charge
on the Ligand along the Z direction will thus be less attracted by the nuclear charge on Cu 2+
than the negative charge on the ligand along X and Y directions. Consequently the Cu2+-
ligand attraction will be less than Cu2+-ligand attraction along the X and Y directions. As a
result, the ligands along Z direction will move away from the metal ion whereas the ligands
along X and Y directions will draw nearer to the metal ion. In other words the octahedral
geometry of the complex will get distorted to tetragonal geometry which is elongated along Z
direction (Z out) and compressed X and Y directions. As a result the dz2 orbital becomes
lower in energy and dx2-y2 orbital become higher in energy. In this way the degeneracy of the
two orbitals gets lifted.

Similarly in the second case (t2g6 d1z2 d2x2-y2), the J-T distortion take place and the octahedral
geometry lowers to tetragonal geometry by elongation along the X and Y directions and
compression along the Z direction (Z in).

Fig. Zout and Zin

 Fig. J-D in Octahedral complexes (General)

To sum up:

1. J-T distortions occur in octahedral complexes in which the metal ions have the ground
sate configuration , t2g3 eg1 t2g4 eg1 t2g2 eg2 t2g5 eg2t2g6 eg1 and t2g6 eg3, t2g1 t2g2 t2g4 and t2g5

2. J-T distortions are automatic and are not imposed in the system

3. J-T effect is operative not only in complexes with anionic ligands but also in
complexes with neutral dipolar ligands

4. J-T effect shown by t2g orbitals (δ2) is much weaker than that shown by eg orbitals
(δ1), ie, δ2<< δ1

Consequences of J-T distortions and its illustrations

1. Due to JTeffect some Oh complexes found to possess distorted octahedral geometry

(tetragonal geometry). Tetragonal structure of Cu(II) complexes: The Cu(II) ion is a
d9 system and expected to show Jahn-Teller distortion and depart considerably from
octahedral geometry. The Cu(II) ion in the aqueous medium is surrounded by six
water molecules in tetragonal geometry i.e., four of which are at the corners of square
plane and are at shorter distances with stronger interactions, whereas, the remaining
two are weakly interacting with the metal ion at distant axial positions.
2. JT effect cause strain in chelate rings and make them unstable due to the elongation of
bonds of the rings. For example [Cu (en)3]3+ with three chelate ring is unexpectedly
less stable than [Cu(en)2(H2O)2]2+ with just two chelate rings. In the former case two
of the chelate rings make use of two elongated bonds along the z axis. But in the
second molecule, the chelate rings are not along z axis.

3. The splitting of absorption bands in the UV-VIS spectra of complexes due to

Jahn-Teller distortion: E.g. The absorption band in the electronic spectrum of
aqueous Ti(III), a d1 octahedral system, is not symmetric but rather shows a distinct
broad shoulder. It is because of Jahn-Teller distortion. The Jahn-Teller distortion is
negligible in case of degenerate t2g orbitals in the ground state. Hence no distortion in
the ground state. But when the electron gets excited, the configuration now becomes
t2g0 eg1, which is again degenerate. Hence in the excited state, the Jahn Teller
distortion is possible. Now the promotion of electron may occur to either of the two
non degenerate eg orbitals, the dz2 and dx2-y2. Thus, two transitions are possible. But a
shoulder appears since the energy difference between two transitions is small.

4. Distortion also affects the reactivity of complexes. For example, [Cu(H2O)6]2+ (d9
system) exchanges two of its H2O molecule on the elongated z axis more rapidly than
its four H2O molecules in the xy plane.
 5. Coordinatively labile nature of [Cr(H2O)6]2+ & [Co(NH3)6]2+: The
[Cr(H2O)6]2+ undergoes substitution easily since the Cr(II) ion is a high spin d4 system
with one electron in the eg orbital. Hence it is electronically degenerate and shows
Jahn-Teller distortion. Hence the hydrated Cr(II) ion is coordinatively labile. On the
same lines, the easy substitution of [Co(NH3)6]2+ by water molecules can be
explained. In this case the Co(II) ion is coordinatively labile since it is a low spin
octahedral d7 ion which is degenerate in eg set. Hence it undergoes J-T distortion and
is labile.

6. Disproportionation of Au(II)salts: Au(II) ion is less stable and undergoes

disproportionation to Au(I) and Au(III) even though the Cu(II) and Ag(II) ions are
comparatively more stable. One may expect same stability since all are d9 systems and
undergo the Jahn-Teller distortion. However, the Δ value increase down the group.
Hence, in Au(II) ion, it reaches a maximum, which causes high destabilization of the
last electron, which is now occupying the dx2-y2. This makes Au(II) reactive, which
may undergo either oxidation to Au(III), a d8 system or reduction to Au(I), a
d10 system. The d8 system, Au(III) is stable as the electron from the dx2-y2 is removed.
Mostly it prefers square planar geometry and more stable than both Au(II) and Au(I).
The d10 system, Au(I) favors mostly linear geometry with coordination number = 2.

Note:

Static Jahn-Teller distortion: Some molecules show tetragonal shape under all conditions
i.e., in solid state and in solution state; at lower and relatively higher temperatures. This is
referred to as static Jahn-Teller distortion. It is observed when the degeneracy occurs in
eg orbitals. Hence the distortion is strong and permanent.

Dynamic Jahn-Teller distortion: In some molecules, the distortion is not seen either due to
random movements of bonds which does not allow the measurement within a time frame or
else the distortion is so weak as to be negligible. However the distortion can be seen by
freezing the molecule at lower temperatures. This condition is referred to as dynamic Jahn-
Teller distortion.

E.g. 1) The complexes of the type M2PbCu(NO2)6 show dynamic Jahn-Teller distortion.

Here, M= K, Rb, Cs, Tl;

They show tetragonal symmetry at lower temperatures due to static Jahn-Teller distortion.
But at higher temperatures, these molecules appear octahedral due to the dynamic Jahn-Teller
effect.

2) The complex [Fe(H2O)6]2+ shows dynamic Jahn-Teller distortion and appears octahedral.
In this case, the distortion is small since the degeneracy occurs in t2g orbitals. Remember
Fe2+ in above complex is a high spin d6 system with t2g4 eg2 configuration.

Molecular Orbital Theory (MOT)

The covalent character of M-L bond in complexes may be explained in terms of the
Molecular orbital theory (MOT). This theory begins with the idea that overlap of atomic
orbitals of the metal ion and the ligand occurs to some extent whenever the conditions of
energy, overlap and symmetry permit.

• The symmetry of the combining atomic orbitals must be same so that the additive
combination of atomic orbitals permits the maximum overlap of orbitals.
• The difference in the energies of the combining orbitals should not be large.
• If the two atomic orbitals are of unequal energies, then the bonding MO would have
more characteristics of the lower energy atomic orbitals and the anti bonding MO
would have more characteristics of the higher energy atomic orbital.
• The fundamental assumption of MOT is that the metal and ligand orbitals will overlap
and combine to give MO’s by the linear combination of atomic orbitals (LCAO)
method.
• Only the valence orbitals are considered here and combinations of metal and ligand
orbitals of widely deferring energies are neglected.

M.O energy level diagrams for sigma bonding in octahedral Complexes

Let’s explain the sigma bonding in an Oh complex represented as ML6 where L is a

unidentate ligand and M is a transition metal ion.

• At first the six suitable atomic orbitals from six ligands combine linearly to form six
molecular orbitals called Ligand group orbitals (LGO’s). The symmetry of those six
orbitals are a1g, t1u and eg. These are exclusively used for the sigma bond formation.
• The metal orbitals involved are ns, np and (n-1)d orbitals. Here the s orbital has a1g
symmetry, p orbitals have t1u symmetry. The d orbitals have eg and t2g set of
symmetries due to splitting.
• a1g of ligand group orbital linearly combine with the a1g of s orbital of metal ion to
form one bonding and anti bonding MO’s (a1g and a1g*).
• Then the t1u of both metal ion and ligand combine to form again a bonding and
antibonding MO;s (t1u and t1u*)
• Finally the eg sets of metal and ligand combine to form bonding eg and antbonding
eg* MO’s.
• The t1u and a1g of the metal interact well with the LGO’s of the symmetry and thus
split to larger extent compared to eg interactions. In eg, the interaction is poorer and
hence split only to smaller extent as shown in the fig.
• The metal orbital with symmetry t2g don’t have a right partner from the side of ligand
to form MO and hence remain as a nonbonding orbital.
• The energy difference between the t2g and eg* gives the Δo values as proposed by
CFT. If the energy difference between t2g and eg* is small, the complex formed will be
a high spin one and vice versa.
 Fig. MO diagram for Oh complexes without pi bonding

M.O energy level diagrams for sigma bonding in Tetrahedral Complexes

Consider a tetrahedral complex ML4.

• The four atomic orbitals of four ligands linearly combine to for four ligand group
orbitals (LGO’s) with symmetry t1 and a1.
• The nine metal ion orbitals are e, t2 (of five d-orbitals), a1 (one-s orbital) and t2 (three-
p orbitals)
• The two t2 of metal ion and one t2 of ligand combine linearly with a maximum extent
to form one bonding, one slightly anti bonding and one anti bonding MO’s
represented as t2, t2* and t2* .
• The a1of metal and of ligand combine to form bonding and anti bonding MO’s
represented as a1 and a1*
• Since there is no matching orbital for e, it remains as nonbonding MO in the complex.
• The Tetrahedral splitting energy (Δt)is the difference between the energy levels e and
t2 *
 Fig. MO diagram for Td complexes without pi bonding

Pi bonding and MOT in complexes

In addition to sigma bonds many ligands are capable of a pi bonding interaction with a metal.
There are no disputes over which ligand orbitals have the correct symmetry to participate in
pi bonding, energy or size mismatch may lead to insignificant interaction.

Totally there can be five types of pi interactions in metal complexes as given in the
following table.

Sl.No. Type Description Ligand example

1. pπ-dπ Donation of the electron from the filled p RO-, RS-, O2-, F-, Cl-,
orbitals of ligands to empty d orbitals of metal Br-, I-, R2N-
2. dπ-dπ Donation of electrons from filled d orbitals of R3P, R3As, R2S
the metal to the empty d orbital of the ligand
3. dπ-π* Donation of electrons from the filled d orbitals CO, RNC, pyridine,
of the metal to the π anti bonding orbital of the CN-, N2, NO2-
ligand
4. dπ-σ* Donation of electrons from filled d orbital of H2,R3P, alkanes
the metal to empty σ* orbitals of ligand
The extent of π overlapping vary in the order; pπ-dπ >dπ-dπ >dπ-π* >dπ-σ*. It is shown in
the following figure.

Fig. Different types of pi bonding possibilities (a) dπ-pπ (b)dπ-dπ (c) dπ-π* (d) dπ-σ*

MO diagram for Oh complexes with π bonding

• The ligand group orbitals capable of π interactions in an octahedral complex fall into
four symmetry categories; t2g, t1u, t2u and t1g. These are formed form the 12 atomic
orbitals of six ligands
• But in Oh complexes, the metal eg orbitals are participated in strong sigma bonding.
The orbitals which are now available for π interaction is nonbonding t2g and the
ligand group t2g orbitals.
• Due to π bonding, the magnitude of Δo value changes. Ligands like F-, decreases the
Δo whereas the ligands like CO,PR3,SR2 etc. cause to increase the Δo values. The two
cases are shown in the following diagrams

Fig. Weak field ligands like F- decreases the Δo by pi bonding

Fig. Strong field ligands like CO increases the Δo

Fig.MO diagram for Oh complexes with pi bond

MO diagram for Td complexes with π bonding

Two p orbitals from each ligand combine linearly to form eight ligand group orbitals
represented as t1, t2 and e. In order to have a pi bond interaction, the only free orbital is the
one with e symmetry. Thus the e of metal and e of ligand interact to form e bonding and e*
anti bonding MO’s. The energy separation e-t2* and e*-t2* in the event of pi bonding is
generally less than pairing energy (P).Therefore, tetrahedral complexes are almost always
high spin complexes.

Experimental evidences for pi-bonding

Two important evidences for pi bonding in complexes are from the crystallographic studies
and Infrared spectroscopic studies

1. Evidences form Crystallography: An unusual shortening of Metal-ligand bond than that

expected for single sigma bond gives a clear idea about the presence of an additional pi bond
between them. For example, the experimentally determined Re-CO bond distance (M-L) for
Re(CH3)(CO)5 complex is 200.4 ± 0.4 pm, about 24 pm shorter than that predicted for sigma
bond, substantiating the view that the M-CO bond has considerable double bond character.

Further crystallographic evidence for metal-carbonyl pi bonding is found in phosphine and

phosphite derivatives of hexacarbonylchromium. In Cr(CO)6, the bond length of Cr-CO(eq)
and Cr-CO is 188.0 pm and 191.5 pm respectively. But when one CO is substituted by R3P,
the length of Cr-CO (eq) trans to R3P shortens to 184.4 pm due to greater extent of pi bonding
responsibility. This is because CO is a better pi acceptor than phosphine ligands. When the
CO is replaced by phosphite ligand, the length of Cr-CO (eq) also decreases but in lesser
extent that compared to the phosphine derivative. This is due to the fact that the pi acidity of
phosphite is greater than phosphine ligand, which indirectly decreases the pi bonding
responsibility of CO ligand.
2. Evidences from Infrared Spectroscopy: The most widely used experimental method for
analysing metal carbonyl complexes is infrared spectroscopy. In carbonyl compounds when
M-C bond strength increases, the C-O bond strength decreases, then the IR stretching
vibration frequency of C- O also decreases accordingly. We know the C-O stretching
vibrational frequency in free CO is 2143 cm-1. When this ligate with metal, the vibrational
frequency decreases. But this decrease is in great extent in some cases than expected. This
unusual decrease in vibrational frequency is due to additional pi bond between the metal and
CO. The value drops from 2143 to 1489 cm-1.This drastic shift is due to the fact that the
central metal ion gives electron to the π* of the CO ligand to form pi bond.