Crystal Field Theory (CFT)

Crystal Field Theory
• This theory was proposed by Hans Brethe and Ven Vleck.
• This theory was originally applied mainly to ionic crystals.
• Therefore it is known as Crystal field Theory.
• It was not until 1952 that Orgel popularized its use for Inorganic
Chemists.
• A second approach to the bonding in complexes of the d-block
metals is crystal field theory.
• This is an electrostatic model and simply uses the ligand electrons
to create an electric field around the metal centre.
• Ligands are considered as point charges and there are no metal–
ligand covalent interactions.
• As we have just seen, the classic valence-bond approach was
unable to explain many of the aspects of transition metal
complexes.
• In particular, VBT did not satisfactorily explain the different
numbers of unpaired electrons that we find among the transition
metal ions.

• For example, the hexaaquairon(II) ion, [Fe(OH2)6]2+, has four
unpaired electrons, whereas the hexacyanoferrate(II) ion,
[Fe(CN)6]4-, has no unpaired electrons.

• Despite its simplistic nature, crystal field theory (CFT)
has proved remarkably useful for explaining the
properties of period 4 (1st row d-block) transition metal
complexes.
• The theory assumes that the transition metal ion is free
and gaseous, that the ligands behave like point charges,
and that there are no interactions between metal d
orbitals and ligand orbitals.
• The theory also depends on the probability model of the
d orbitals, that there are two d orbitals whose lobes are
oriented along the Cartesian axes (axial) dx
2
-y
2 and dz
2
(following figure)
Period 4 (1st row d-block)

and three d orbitals whose lobes are oriented between the
Cartesian axes (interaxial) dxy, dxz, and dyz (following
figure).
Figure: Representations
of the shapes of the 3dx
2
-y
2
and 3dz
2 orbitals.
Figure: Representations of the shapes of the 3dxy, 3dxz, and
3dyz orbitals.

Oriented along the Cartesian axes
• The dz
2 and dx
2
-y
2 orbitals lie on the same axes as
negative charges.
• Therefore, there is a large, unfavorable interaction
between ligand (-) orbitals.
• These orbitals form the degenerate high energy pair of
energy levels.
Oriented between the Cartesian axes
• The dxy, dyx and dxz orbitals bisect (between the axes) the
negative charges.
• Therefore, there is a smaller repulsion between ligand
and metal for these orbitals.
• These orbitals form the degenerate low energy set of
energy levels.

The energy gap is
referred to as Δ0 (10 Dq),
the crystal field splitting
energy.
d-orbitals (dx
2
-y
2 and dz
2) pointing directly
at axis are affected most by electrostatic
interaction
d-orbitals (dxy, dyx and dxz) not pointing
directly at axis are least affected
(stabilized) by electrostatic interaction
Ligands approach metal
Inter-axial, t2g
Axial, eg

Important Features of CFT
• The central metal cation is surrounded by ligands which
contain one or more lone pairs of electrons.
• The ionic ligands (e.g., F
-
, Cl
-
, CN
-
etc.) are regarded as
negative point charges (also called point charges) and the
neutral ligands (e.g., H2O, NH3 etc.) are regarded as
point dipoles or simply dipoles.
– If the ligand is neutral, the negative end of this ligand
dipole is oriented towards metal cation.
• The CFT does not provide for electrons to enter the
metal orbitals.
– Thus the metal ion and the ligands do not mix their
orbitals or share electrons, i.e., it does not consider
any orbital overlap.

• According to CFT, the bonding between metal cation and ligand is
not covalent but it is regarded as purely electrostatic or coulombic
attraction between positively charged (i.e., cations) and negatively
charged (i.e., anions or dipole molecules which act as ligands)
species.
– Complexes are thus presumed to form when centrally situated
cations electrically attract ligands which may be either anions or
dipole molecules.
– The attraction between the cations and the ligands is because
the cations are positively charged and the anions are negatively
charged and the dipole molecules, as well, can offer their
negatively incremented ends for such electrostatic attractions.
" t " → Triply degenerate set of orbitals
" e " → Doubly degenerate of orbitals
Ionic ligands → Negative point charges
Neutral ligands → Point dipoles or simply dipoles

Salient features of crystal field theory
• Focuses on the d-orbitals of the metal.
• The central metal cation is surrounded by ligands which contain
one or more lone pairs of electrons.
• The ionic ligands (e.g., F-, Cl-, CN- etc.) are regarded as:
– Negative point charges (also called point charges)
and the neutral ligands (e.g., H2O, NH3 etc.) are regarded as:
– Point dipoles or simply dipoles, i.e., according to this theory
neutral ligand are dipolar.
• If the ligand is neutral, the negative end of this ligand dipole is
oriented towards the metal cation.
• The interaction between the metal cation and the ligands is
regarded as purely electrostatic, i.e. the metal—ligand bond is
considered to be 100% ionic.
Ionic ligands → Negative point charges
Neutral ligands → Point dipoles or simply dipoles

• Electrostatic interactions in a complex between +ve metal
ion and –ve charges of ligand - treats ligands as point
(negative) charges.
– If the ligand is negatively charged
• Ion-ion interaction
– If the ligand is neutral
• Ion-dipole interaction
• Provides stability and holds complex together.
• Repulsion between the lone pair of electrons on the ligand
and the electrons in the d-orbital of the metal ion.
• This influences the d-orbital energies

Why we consider ligand as a point charge in crystal
field theory?
• CFT assumes that the metal atom and the ligands are
linked by electrostatic forces of attraction.
• Thus ligands are considered as negative charges whereas
for neutral ligands the most electronegative atom points
towards the atom.

Grouping of Five d-Orbitals into t2g and eg sets of Orbitals
• On the basis of orientation of the lobes of the five d-orbitals with
respect to coordinates these have been grouped into following two
sets.
eg sets of orbitals (dz
2 and dx
2
– y
2 orbitals)
• This set consists of two orbitals which have their lobes along the
axes and are called axial orbitals.
• These are dz
2 and dx
2
– y
2 orbitals.
• This theory calls these orbitals eg orbitals in which e refers to
doubly degenerate set.
t2g sets of orbitals (dxy, dyz and dzx orbitals)
• This set include three orbitals whose lobes lie between the axes
and are called non-axial orbitals.
• These are dxy, dyz and dzx orbitals.
• This theory calls these orbitals t2g orbitals in which t refers to
triply degenerate set.

Splitting of d-orbital energies in octahedral fields
Valence bond theory approach
• There are several characteristics of coordination compounds
that are not satisfactorily explained by a simple valence bond
description of the bonding.
• For example, the magnetic moment of [CoF6]3- indicates that
there are four unpaired electrons in the complex, whereas
that of [Co(NH3)6]3- indicates that this complex has no
unpaired electrons, although in each case Co3+ is a d6 ion.
• In these complexes as involving sp3d2 ([CoF6]3-) and d2sp3
([Co(NH3)6]3-) hybrid orbitals, respectively, but that does not
provide an explanation as to why the two cases are different.
• Another area that is inadequately explained by a simple
valence-bond approach is the number of absorption bands
seen in the spectra of complexes.

Crystal field theory approach
(Crystal Field Splitting of d-Orbitals in Octahedral Complexes)
• One of the most successful approaches to explaining these
characteristics is known as crystal or ligand field theory.
• When a metal ion is surrounded by anions in a crystal, there is an
electrostatic field produced by the anions that alters the energies of
the d orbitals of the metal ion.
• The field generated in this way is known as a crystal field and it
explain the spectral characteristics of metal ions in crystals.
• It soon became obvious that anions surrounding a metal in a crystal
gave a situation that is very similar to the ligands (many of which
are also anions) surrounding a metal ion in a coordination
compound.
• In cases where the ligands are not anions, they may be polar molecules,
and the negative ends of the dipoles are directed toward the metal ion
generating an electrostatic field.
• Strictly speaking, the crystal field approach is a purely electrostatic one
based on the interactions between point charges, which is never exactly the
case for complexes of transition metal ions.

• In view of the fact that coordinate bonds result from electron pair
donation and have some covalency, the term ligand field is used to
describe the effects of the field produced by the ligands in a
complex.
• In the 1930s, J. H. Van Vleck developed ligand field theory by
adapting the crystal field approach to include some covalent nature
of the interactions between the metal ion and the ligands.
• Before we can show the effects of the field around a metal ion
produced by the ligands, it is essential to have a clear picture of
the orientation of the d orbitals of the metal ion.
• Following figure shows a set of five d orbitals, and for a gaseous
ion, the five orbitals are degenerate.

Figure. The spatial orientations of the set of five d orbitals for
a transition metal.

Explanation
• In case of free metal ion all the five d-orbitals are degenerate i.e., these
have the same energy.
• Now let us consider an octahedral complex [ML6]
n+
in which central
metal cation, M
n+
is placed at the centre of octahedron and is
surrounded by six ligands which reside at the corners of the
octahedron as shown in the figure.
Figure: Position of
central metal cation,
M
n+
and six ligands in
an octahedral complex
[ML6]n+
• The three axes, viz. x-, y-, and z-axes which
point along the corners have also been shown.
• Now suppose both the ligands on each of the
three axes are allowed to approach towards the
metal cation, M
n+
from both the ends of the
axes.
• In this process the electrons in d-orbitals of the
metal cation are repelled by negative point
charge or by the negative end of the dipole of
the ligands.

• This repulsion will raise the energy of all the five d-orbitals.
• If all the ligands approaching the central cation are at an equal
distance from each of the d-orbitals (i.e., the ligand field is
spherically symmetrical), the energy of each of five d-orbital will
raise by the same amount, i.e., all the d-orbitals will still remain
degenerate, although they will have now higher energy than before.
• This is only a hypothetical situation.
• Since the lobes of the two eg orbitals lie directly in the path of the
approaching ligands, the electrons in these orbitals experience greater
force of repulsion than those in three t2g orbitals whose lobes are
directed in space between the path of the approaching ligands.
• So, energy of eg orbitals is increased while that of t2g is decreased.
• Remember: Greater the repulsion, greater is the increase in energy.
• Thus we find that under the influence of approaching ligands, the
five d-orbitals which were originally degenerate in the free metallic
cation are now split (or resolved) into two levels viz., t2g level which
is triply degenerate and is of lower energy and eg level which is
doubly degenerate and is of higher energy.

Figure. Splitting of the d orbitals in a crystal field of
octahedral symmetry.
Five degenerate d-orbitals
on the central metal cation
which are free from any
ligand field
Hypothetical
degenerate d-orbitals at
a higher energy level
Splitting of d-orbitals
under the influence of
six ligands in octahedral
complex
----------------------
No splitting state
+0.6Δo = +6Dq = (3/5) Δo
-0.4Δo = -4Dq = (2/5) Δo

• In other words the degeneracy of the five d-orbitals is removed
under the influence of the ligands.
• The separation of five d-orbitals of the metal ion into two sets
having different energies is called crystal field splitting or energy
level splitting.
• This concept of crystal field splitting makes the basis of CFT.

• As shown in following figure, an octahedral complex
can be considered as a metal ion surrounded by six
ligands that are located on the axes.
Figure. An octahedral complex with the six ligands lying
on the x, y, and z axes.

• When six ligands surround the metal ion, the degeneracy
of the d orbitals is removed because three of the orbitals,
the dxy, dyz, and dxz orbitals, are directed between the
axes while the others, the dx
2
-y
2 and the dz
2, are directed
along the axes pointing at the ligands.
• Therefore, there is greater repulsion between the
electrons in orbitals on the ligands and the dx
2
-y
2 and dz
2
orbitals than there is toward the dxy, dyz, and dxz orbitals.
• Because of the electrostatic field generated by the
ligands, all of the d orbitals are raised in energy, but two
of them are raised more than the other three.
• As a result, the d orbitals have energies that can be
represented as shown in following figure.

• The two orbitals of higher energy are designated as the eg orbitals,
and the three orbitals of lower energy make up the t2g orbitals.
• These designations will be described in greater detail later, but the
“ g ” subscript refers to being symmetrical with respect to a center
of symmetry that is present in a structure that has Oh symmetry.
• The " t " refers to a triply degenerate set of orbitals, whereas " e "
refers to a set that is doubly degenerate.
• The energy separating the two groups of orbitals is called the
crystal or ligand field splitting, Δo.
• Splitting of the energies of the d orbitals as indicated in above
figure occurs in such a way that the overall energy remains
unchanged and the “ center of energy (Barycentre) ” is maintained.
" t " → Triply degenerate set of orbitals
" e " → Doubly degenerate of orbitals

• The eg orbitals are raised 1.5 times as much as the t2g orbitals are
lowered from the center of energy.
• Although the splitting of the d orbitals in an octahedral field is
represented as Δo, it is also sometimes designated as 10 Dq, where Dq
is an energy unit for a particular complex. (1Δo = 10Dq)
• The two orbitals making up the eg pair are raised by 3/5 Δo (+0.6Δo or
+6Dq) while the t2g orbitals are lowered by 2/5 Δo (-0.4Δo or -4Dq)
relative to the center of energy.
• In terms of Dq units, the eg
orbitals are raised by 6Dq
while the three t2g orbitals are
4Dq lower than the center of
energy.
Crystal field splitting of d-orbitals
in octahedral complex.
3/5 Δo
2/5 Δo

Hypothetical steps for complex formation
We can consider complex formation as a series of events:
Step 1
• The initial approach of the ligand electrons forms a spherical shell
around the metal ion.
• Repulsion between the ligand electrons and the metal ion electrons
will cause an increase in energy of the metal ion d orbitals.
Step 2
• The ligand electrons rearrange so that they are distributed in pairs
along the actual bonding directions (such as octahedral or
tetrahedral).
• The mean metal d orbital energies will stay the same, but the
orbitals oriented along the bonding directions will increase in
energy, and those between the bonding directions will decrease in
energy.
• This loss in d orbital degeneracy will be the focus of the crystal
field theory discussion (that is crucial for the explanation of the
color and magnetic properties of transition metal complexes).

Step 3
• Up to this point, complex formation would not be
favored, because there has been a net increase in energy
as a result of the ligand electron–metal electron repulsion
(step 1).
• Furthermore, the decrease in the number of free species
means that complex formation will generally result in a
decrease in entropy.
• However, there will be an attraction between the ligand
electrons and the positively charged metal ion that will
result in a net decrease in energy. It is this third step that
provides the driving force for complex formation.
• These three hypothetical steps are summarized in
following figure.

Figure. The hypothetical steps in complex ion formation according
to crystal field theory.

High- and Low-Spin States
• The paramagnetism is a characteristic of some d-block
metal compounds.
• Let us simply state that magnetic data allow us to
determine the number of unpaired electrons.
• In an isolated first row d-block metal ion, the 3d orbitals
are degenerate (of the same energy) and the electrons
occupy them according to Hund’s rules:
– e.g., following diagram shows the arrangement of six
electrons.

• However, magnetic data for a range of octahedral d6
complexes show that they fall into two categories:
– Paramagnetic
– Diamagnetic
• The former (paramagnetic) are called high-spin
complexes and correspond to those in which, despite the
d orbitals being split, there are still four unpaired
electrons.
• The diamagnetic d6 complexes are termed low-spin and
correspond to those in which electrons are doubly
occupying three orbitals, leaving two unoccupied.
Diamagnetic = Low-spin = Covalent complex (3d) = Inner orbital
complex
Paramagnetic = High-spin = Ionic complex (4d) = Outer orbital
complex

Crystal field theory (CFT) splitting diagram
Example of influence of ligand electronic properties on d orbital
splitting. This shows the comparison of low-spin versus high-
spin electrons.
First-row transition metals = 3d or 4d
d2sp3 = Diamagnetic = Low-spin = Covalent complex (3d) = Inner
orbital complex
sp3d2 = Paramagnetic = High-spin = Ionic complex (4d) = Outer orbital
complex

Explanation
• The cobalt atom in the ground state has the outer electron
configuration:
• The 2+ and 3+ ions have the following outer electron
configuration:
and

Weak ligand → F-
• With weak ligands, such as F-, both ions (Co2+ and
Co3+) form octahedral complexes in which the ligand
electrons are accommodated in sp3d2 hybrid orbitals.
• In other words, the partially filled inner d-orbitals
are not used.
• This type of complex is known as an outer d-orbital
complex.

Strong ligand → -CN
• With strong ligands, such as -CN ions, spin-pairing of
the inner d-electrons, occurs and both ions (Co2+ and
Co3+) form octahedral complexes in which the ligand
electrons are accommodated in d2sp3 hybrids.
• In other words the partially filled d-orbitals are used,
and this type of complex is known as an inner d-orbital
complex.

Energetics
Electrostatic between metal ion and donor atom (ligand)
• Step i: Separate metal and ligand high energy
• Step ii: Coordinated metal - ligand stabilized
• Step iii: Destabilization due to ligand - d electron
repulsion
• Step iv: Splitting
due to octahedral
field.

What happens to the energies of electrons in the d-
orbitals as six ligands approach the bare metal ion?
• When six ligands approach the bare metal ion:
• If we compare the dxy and the dx
2
-y
2, we can see that there
is a significant difference in the repulsion energy as ligand
lone pairs approach d-orbitals containing electrons.
Electrons in the dxy
orbital are
concentrated in the
space between the
incoming ligands.
Electrons in the dx
2
-y
2
orbital point straight at
the incoming ligands.

• Now, dxz and dyz behave the same as dxy in an octahedral field, and
dz
2 behaves the same as dx
2
-y
2.
• This means that the d-orbitals divide into two groups, one lower
energy than the other, as shown in the following diagram.
• The dxy, dxz, and dyz orbitals are collectively called the t2g orbitals,
whereas the dz
2 and dx
2
-y
2 orbitals are called the eg orbitals.
• The octahedral splitting energy is the energy difference between the
t2g and eg orbitals.
• In an octahedral field, the t2g orbitals are stabilized by 2/5 Δo, and
the eg orbitals are destabilized by 3/5 Δo.

Absorption spectrum of [Ti(H2O)6]3+
• The effect of crystal field splitting is easily seen by studying the
absorption spectrum of [Ti(H2O)6]3+ because the Ti3+ ion has a single
electron in the 3d orbitals.
• In the octahedral field produced by the six water molecules, the 3d
orbitals are split in energy as shown in the following figure.
• The only transition possible is promotion of the electron from an orbital
in the t2g set to one in the eg set.
Crystal field splitting of d-orbitals in
octahedral complex.
3/5 Δo
2/5 Δo
• This transition gives rise to a single
absorption band, the maximum of
which corresponds directly to the
energy represented as Δo.
• As expected, the spectrum shows a
single, broad band that is centered at
20,300 cm-1, which corresponds
directly to Δo (following figure).

Figure. The electronic spectrum of
[Ti(H2O)6]3+ in aqueous solution.
e- jumps to
higher level
Absorbed λ
Transmitted λIncoming
λ
t2g
t2g
eg eg
Light of
510nm
λmax = 20,300 cm-1
↓
When the ion absorbs light,
electrons can move from the
lower t2g, energy level to the
higher eg level.
The difference in energy
between the levels (Δ)
determines the wavelengths
of light absorbed.
The visible color is given by
the combination of the
wavelengths transmitted.
Ground state
Excited state

• The energy associated with this band is calculated as
follows:
• We can convert this energy per molecule into kJ mol-1 by
the following conversion.
• This energy (243 kJmol-1) is large enough to give rise to
other effects when a metal ion is surrounded by six
ligands.
• However, only for a d1 ion is the interpretation of the
spectrum this simple.
• When more than one electron is present in the d orbitals,
the electrons interact by spin-orbit coupling.

• Any transition of an electron from the t2g to the eg orbitals is
accompanied ( ‫ہمراه‬‫ہونا‬ ) by changes in the coupling scheme
when more than one electron is present.
• The interpretation of spectra to determine the ligand field
splitting in such cases is considerably more complicated that
in the d1 case.
• The ordering of the energy levels for a metal ion in an
octahedral field makes it easy to visualize how high- and
low-spin complexes arise when different ligands are present.
• If there are three or fewer electrons in the 3d orbitals of the
metal ion, they can occupy the t2g orbitals with one electron
in each orbital.
• If the metal ion has a d4 configuration (e.g., Mn3+), the
electrons can occupy the t2g orbitals only if pairing occurs,
which requires that Δo be larger in magnitude than the energy
necessary to force electron pairing, P.

• The result is a low-spin complex in which there are two
unpaired electrons.
• If Δo is smaller than the pairing energy, the fourth electron
will be in one of the eg orbitals, which results in a high-
spin complex having four unpaired electrons.
• These cases are illustrated in following figure.
Figure. Crystal field
splitting energy compared
to the electron pairing
energy.
> = Greater than
< = Less than

Mean pairing energy (P)
“Mean pairing energy (P) is the energy which is
required to pair two electrons against electron-electron
repulsion in the same orbital.”
Representation and unit
• P is generally expressed in cm-1.
Characteristics
• P is the pairing energy for one electron pair.
• Pairing energy depends on the principal energy level (n)
of d-electrons.
Calculation of total pairing energy of dx ion
• If m is the total number of paired electrons in t2g and eg
orbitals in dx ion and P is the pairing energy for one
electron, then
• Total pairing energy for m electron pairs = mP cm-1.

Example
• Calculate the total pairing energy of d7 ion in high spin
as well as in low spin octahedral complexes.
Solution
• We know that the configuration of d ion in high spin
state is t2g
5eg
2 which shows that m = 2 + 0 = 2.
• Total pairing energy for 2 paired electrons = 2 x P = 2P
• The configuration of d7 ion in low spin state is t2g
6 eg
1
which gives m = 3 + 0 = 3.
• Total pairing energy for 3 paired electrons = 3 x P = 3P

Example
• Calculate the total pairing energy for [Cr(H2O)6]2+ ion in
high spin and low spin state. Given that mean pairing
energy = 23,500 cm-1.
Solution
• In [Cr(H2O)6]2+ ion, Cr is present as Cr2+ which is a d4
ion.
• Thus the configuration of d4 ion in high spin state is t2g
3
eg
1 which gives m = 0 and hence:
• Total pairing energy of [Cr(H2O)6]2+ ion in high spin
state = 0 x P = 0
• The configuration of d4 ion in low spin state is t2g
4eg
0
which gives m = 1 and hence
• Total pairing energy of [Cr(H2O)6]2+ ion in low spin
state = 1 x P = 1 x 23,500 cm-1 = 23,500 cm-1

The effect of ligands and splitting energy on orbital
occupancy
• s-electrons are lost first.
– Ti3+ is a d1
– V3+ is d2
– Cr3+ is d3
Hund s rule
• First three electrons are in separate d-orbitals with their spins
parallel.
• Fourth e- has choice
Electron will go to:
– Higher orbital → if Δ0 is small: High spin
– Lower orbital → if Δ0 is large: Low spin
• Weak field ligands
– Small Δ0, high spin complex → lead to a smaller splitting
energy
• Strong field ligands
– Large Δ0, low spin complex → lead to a larger splitting energy
Assignment
Q: What is the effect of ligands and
splitting energy on orbital occupancy?

No field
Maximum number
of unpaired electrons
Free Mn2+ ion
t2g
t2g
eg
eg
[Mn(H2O)6]2+
[Mn(CN)6]4-
Weak-field ligand
High-spin complex
P > Δ0
Strong-field ligand
Low-spin complex
P < Δ0
small large
large
[Cr(H2O)6]2+
[Cr(CN)6]4-
t2g
t2g
eg
eg
small
P > Δ0
P < Δ0
> = Greater than
< = Less than
[Δ0 < P]
[Δ0 < P]
[Δ0 > P]
[Δ0 > P]

Weak-field ligand
Strong-field ligand
• The possible electronic configurations for octahedral dn (d1
to d10, n = 1–10) transition-metal complexes [M(H2O)6]n+
.
• Only the d4 through d7 cases have both high-spin and low-
spin configurations.
P > Δ0
[Δ0 < P]
P < Δ0
[Δ0 > P]

The various electronic configurations for low spin
octahedral complexes

The various electronic configurations for high spin
octahedral complexes

Factors for the magnitude of the ligand field
splitting
• Of course, we have not yet fully addressed the factors that
are responsible for the magnitude of the ligand field
splitting.
• The splitting of the d orbitals by the ligands depends on:
– The nature of the metal ion and the ligands
– The extent of back donation
– π bonding to the ligands
Assignment
Q: Write note on:
a) The effect of ligands and splitting
energy on orbital occupancy?

Covalency
• Covalency is the number of electron pairs an atom can
share with other atoms.
• The total number of orbitals available in the valence
shell is known as covalency, whether the orbitals are
completely filled or empty .

Chemical and theoretical background
A reminder about symmetry labels
• The two sets of d orbitals in an octahedral field are
labelled eg and t2g (following figure).
Figure. Splitting of the d orbitals in an octahedral crystal field, with
the energy changes measured with respect to the barycentre.

• In a tetrahedral field (following figure), the labels become e
and t2.
• The symbols t and e refer to the degeneracy of the level:
– a triply degenerate level is labelled → t
– a doubly degenerate level is labelled → e
• The subscript g means gerade and the subscript u means
ungerade.
• The German words gerade (even) and ungerade (odd)
designate the behaviour of the wave function under the
operation of inversion, and denote the parity ‫ساوات‬ُ‫م‬‫بادلہ‬ُ‫م‬‫۔‬
‫برابری‬-‫ساوات‬ُ‫م‬‫۔‬‫جيسے‬‫قدار‬ِ‫م‬،‫تبہ‬ُ‫ر‬‫ميں‬ (even or odd) of an
orbital.
• The u and g labels are applicable only if the system possesses
a centre of symmetry (centre of inversion) and thus are used
for the octahedral field, but not for the tetrahedral one.

Figure. Crystal field splitting diagrams for octahedral (left-hand side)
and tetrahedral (right-hand side) fields. The splittings are referred to a
common barycentre.

Figure. The changes in the energies of the electrons occupying the
d orbitals of an Mn+ ion when the latter is in an octahedral crystal
field. The energy changes are shown in terms of the orbital energies.

Energy difference between the two sets of d-orbitals
• The energy difference between the two sets of d orbitals
in the octahedral field is given the symbol ∆oct.
• The sum of the orbital energies equals the degenerate
energy (sometimes called the barycenter).
• Thus, the energy of the two higher-energy orbitals (dx
2
-
y
2 and dz
2) is +3/5∆oct (+0.6∆oct), and the energy of the
three lower-energy orbitals (dxy, dxz, and dyz) is -2/5∆oct
(-0.4∆oct) below the mean.
(+0.6∆oct)
(-0.4∆oct)
(1∆oct)

Barycenter
• The barycenter (or barycentre) is the center of mass of two or more
bodies that are orbiting each other, or the point around which they
both orbit.
• It is an important concept in fields such as astronomy and
astrophysics.
• The point at the centre of a system; an average point, weighted
according to mass or other attribute.
• I can't figure out what that barycentre part of the diagram means.
• The first section of the diagram represents the energy of the d
orbitals before the ligands come into the picture and the 3rd section
represents the energy of the d orbitals after the 6 ligands have
arranged in an octahedral structure.
• What does the 2nd section of the graph represent?
• On one explanation of CFSE they say this:
– If you put an electron into the t2g, like that for Ti3+, then you stabilize
the barycenter of the d orbitals by 0.4 Δo. but I have no idea what this
means.
• What is the barycentre?

• Barycenter literally means center of mass.
• In this case, it is just representing the idea that, since energy must
be conserved, and you split two states up (doubly degenerate eg
level) and three states down (triply degenerate t2g level), the
barycenter is just the place where the five-fold degenerate energy
level would have been in the absence of the splitting, but including
the average effect of the crystal field interaction, distributed over 5
orbitals.

• The only explanation of barycentre I could find were ones
relating to astronomy.
• As for this concept, I've settled for the idea that the middle part
of the graph represents the situation in which the ligands form a
theoretical spherical charge around the atom as opposed to their
charges arranged in an octahedral (or tetrahedral, square planar
etc.) structure.
• In this imaginary spherical distribution of charge each d orbital
feels the same amount of repulsion so they remain degenerate.

Crystal Field Splitting Energy (∆0)
• The energy gap between t2g and eg sets is donated by ∆0 or 10Dq
where 0 in ∆0 indicates an octahedral arrangement of the ligands
round the central metal cation.
• This energy difference arises because of the difference in the
electrostatic field exerted by the ligands on t2g and eg sets of orbitals
of the central metal cation.
• ∆0 or 10Dq is called crystal field splitting energy.
• With the help of simple geometry it can be shown that the energy of
t2g orbitals is 0.4 ∆0 (=1Dq) less than that of hypothetical degenerate
d-orbitals and hence that of eg orbitals is 0.6 ∆0 (= 6Dq) above that
of the hypothetical degenerate d-orbitals.
• Thus, we find that t2g set loses an energy equal to 0.4 ∆0 (= 4Dq)
while eg set gains an energy equal to 0.6 ∆0 (= 6Dq).
• The loss and gain of energies of t2g and eg orbitals is expressed by
negative (-) and positive (+) signs respectively (Following figure).

Assignment
Q: Use crystal field theory to draw the most probably structure
of hexafluorocobaltate(III) [CoF6]3− (F- is a weak field ligand).
– Co:1s2, 2s2, 2p6, 3s2, 3p6, 3d7, 4s2
– Co3+: 1s2, 2s2, 2p6, 3s2, 3p6, 3d6, 4s0
• According to CFT, when six F- approaches the Co3+, the d-orbitals
split in the following manner:
Conclusion
• Δo → smaller
• Complex → high spin
• Geometry → octahedral
• Magnetic nature → paramagnetic
← Electronic configuration

Crystal field stabilization energy:
high- and low-spin octahedral complexes
• We now consider the effects of different numbers of electrons
occupying the d orbitals in an octahedral crystal field, the
electrons will all fit into the lower-energy set.
• This net energy decrease is known as the crystal field
stabilization energy (CFSE).
• For a d1 system, the ground state corresponds to the
configuration t2g
1.
Figure. The d-orbital filling for the d1, d2, and d3 configurations.

• With respect to the barycentre, there is a stabilization
energy of -0.4∆oct; this is the so-called crystal field
stabilization energy, CFSE.
Figure. Splitting of the d orbitals in an octahedral crystal field,
with the energy changes measured with respect to the barycentre.

• For a d2 ion, the ground state configuration is t2g
2 and the
CFSE = -0.8∆oct;
a d3 ion (t2g
3) has a CFSE = -1.2∆oct.
• For a d4 ion, two arrangements are available:
– The four electrons may occupy the t2g set with the
configuration t2g
4, or
– May singly occupy four d orbitals, t2g
3eg
1
, depending on
which situation is more energetically favorable.
• If the octahedral crystal field splitting, ∆oct, is smaller than
the pairing energy, then the fourth electron will occupy the
higher orbital.
• If the pairing energy is less than the crystal field splitting,
then it is energetically preferred for the fourth electron to
occupy the lower orbital.

• The two situations are shown in following figure.
• The result having the greater number of unpaired
electrons is called the high-spin (or weak field) situation,
and that having the lesser number of unpaired electrons
is called the low-spin (or strong field) situation.
• Configuration t2g
4 corresponds to a low-spin
arrangement, and t2g
3eg
1 to a high-spin case.
Low-spin
High-spin
Figure. The two possible spin situations for the d4
configuration.
d4

• The preferred configuration is that with the lower energy
and depends on whether it is energetically preferable to
pair the fourth electron or promote it to the eg level.
• Two terms contribute to the electron-pairing energy, P,
which is the energy required to transform two electrons
with parallel spin in different degenerate orbitals into
spin-paired electrons in the same orbital:
– The loss in the exchange energy which occurs upon
pairing the electrons
– The coulombic repulsion between the spin-paired
electrons
• For a given dn configuration, the CFSE is the difference
in energy between the d electrons in an octahedral crystal
field and the d electrons in a spherical crystal field
(following figure).

• To exemplify this, consider a d4 configuration.
• In a spherical crystal field, the d orbitals are degenerate
and each of four orbitals is singly occupied.
• In an octahedral crystal field, following equation shows
how the CFSE is determined for a high-spin d4
configuration.
• For a low-spin d4 configuration, the CFSE consists of
two terms: the four electrons in the t2g orbitals give rise
to a -1.6∆oct term (4 x -0.4 = -1.6 ∆oct), and a pairing
energy, P, must be included to account for the spin-
pairing of two electrons (-1.6 + P).
• Now consider a d6 ion.
• In a spherical crystal field, one d orbital contains spin-
paired electrons, and each of four orbitals is singly
occupied.

• On going to the high-spin d6 configuration in the
octahedral field (t2g
4eg
2), no change occurs to the number
of spin-paired electrons and the CFSE is given by
following equation.
• For a low-spin d6 configuration (t2g
6eg
0) the six electrons
in the t2g orbitals give rise to a -2.4 ∆oct term (6 x -0.4 = -
2.4 ∆oct ).
• Added to this is a pairing energy term of 2P which
accounts for the spin pairing associated with the two
pairs of electrons in excess of the one in the high-spin
configuration.
• Following table lists values of the CFSE for all dn
configurations in an octahedral crystal field.
Important
↓↓

Table. Octahedral crystal field stabilization energies (CFSE) for dn configurations;
pairing energy, P, terms are included where appropriate. High- and low-spin
octahedral complexes are shown only where the distinction is appropriate.

• Two possible spin conditions exist for each of the d4,
d5, d6, and d7 electron configurations in an octahedral
environment.
• The number of possible unpaired electrons
corresponding to each d electron configuration is
shown in following table, where h.s. and l.s. indicate
high spin and low spin, respectively.

Table. The d electron configurations and corresponding
number of unpaired electrons for an octahedral
stereochemistry

• Following inequalities show the requirements for high-
or low-spin configurations.
• First inequality holds when the crystal field is weak,
whereas second expression is true for a strong crystal
field.
• Following figure summarizes the preferences for low-
and high-spin d5 octahedral complexes.
Assignment
Q: What is the value of CFSE for high- and low-spin
octahedral complexes in case of d4 to d7 system. Also
calculate the number of unpaired electrons in d9 system by
considering Cu2+ ion.
> = Greater than
< = Less than

Figure. The occupation of the 3d orbitals in weak and strong field Fe3+
(d5) complexes. Splitting of five d-orbitals in presence of strong(er) and
weak(er) ligands in an octahecral complex. (a) Five d orbitals in the free
metal ion (b) Splitting of d-orbitals in presence of weak(er) ligands (c)
Splitting of d-orbitals in presence of strong(er) ligands.
xy yz zx x2 x2-y2
x2 x2-y2
xy yz zx
xy yz zx
x2 x2-y2
Small
↓
Large
↓
(a)
(b) (c)
High spin
Low spin

• We can now relate types of ligand with a preference for
high- or low-spin complexes.
• Strong field ligands such as [CN]- favour the formation
of low-spin complexes, while weak field ligands such as
halides tend to favour high-spin complexes.
• However, we cannot predict whether high- or low-spin
complexes will be formed unless we have accurate
values of ∆oct and P.
• On the other hand, with some experimental knowledge in
hand, we can make some comparative predictions:
– If we know from magnetic data that [Co(H2O)6]3+ is
low-spin, then from the spectrochemical series we can
say that [Co(ox)3]3- and [Co(CN)6]3- will be low-spin.
• The only common high-spin cobalt(III) complex is
[CoF6]3-.

Figure. Distribution of d6 electrons of Co3+ ion in the
weak-field complex, [CoF6]3- and strong field
complex, [Co(NH3)6]3+.

Coulomb’s Law
• Energy of interaction between two charges q1 q2 is
proportional to the product of charges divided by the
distance between there centres.

Assignment
Justify the following statement:
• However, we cannot predict whether high- or low-spin complexes
will be formed unless we have accurate values of ∆oct and P.
Ans:
• Suppose d5 system.
• If we have the data of μ = 5.9 BM
• Its mean there are 5 unpaired electrons which is only possible if Δ0
will be small.
• So we can say that the given system is high-spin.
• If we have the data of μ = 1.8 BM
• Its mean there is only 1 unpaired electron which is only possible if
Δ0 will be large.
• So we can say that the given system is low-spin.

How to predict the spin state of a given octahedral
complex ion?
• By comparing the values of Δ0 and P of a given metallic
ion, the spin state of the octahedral complex ion formed
by that metallic ion can be predicted.
• Δ0 tends to force as many electrons to occupy t2g orbitals
while P tends to prevent the electrons to pair in t2g
orbitals.
• This discussion show that:
– When Δ0 < P, the electrons tend to remain unpaired
and hence high spin (weak-field or spin free)
octahedral complex ions are obtained.
– When Δ0 > P, the electrons tend to pair and hence low
spin (strong-field or spin paired) octahedral complex
ions are obtained.

• Examples of some HS- and LS-octahedral complexes are given in
following table.
• In this table the value of P (in cm-1) of the central metal ion of the
corresponding complex determined from spectroscopic data and
that of Δ0 (in cm-1) for the complexes are also listed.
• From this table it may be seen that the spin-state of the complexes
predicted by CFT is the same as that observed experimentally.
Conclusion
• In every case where Δ0 < P:
– HS-complex is formed
• In every case where Δ0 > P:
– LS-complex is formed
> = Greater than
< = Less than

Table. Examples of some LS-and HS-octahedral
complexes.

Assignment
Q: In the following configuration:
– d5
– d6
• For [Mn(H2O)6]2+ and [Co(NH3)6]3+ predicts the value of P (cm-1)
and Δ0 (cm-1).
• Determine their spin-state, either the value of spin-state observed
experimentally match with predicted by CFT.
Ans:
d5
• [Mn(H2O)6]2+ → P (cm-1) = 25500
→ Δ0 (cm-1) = 7800
• Spin-state → Observed experimentally = HS
→ Predicted by CFT = HS
d6
• [Co(NH3)6]3+ → P (cm-1) = 21000
→ Δ0 (cm-1) = 23000
• Spin-state → Observed experimentally = LS
→ Predicted by CFT = LS
Δ0 > P
Δ0 < P

Splitting of d orbital energies in fields of other
symmetry
The tetrahedral crystal field
• Although the effect on the d-orbitals produced by a field
of octahedral symmetry has been described, we must
remember that not all complexes are octahedral or even
have six ligands bonded to the metal ion.
• For example, many complexes have tetrahedral
symmetry, so we need to determine the effect of a
tetrahedral field on the d-orbitals.
• Following figure shows a tetrahedral complex that is
circumscribed ( ‫محدود‬‫کرنا‬ ) in a cube where alternative
corners are vacant.
• Also shown are lobes of the dz
2 orbital and two lobes
(those lying along the x-axis) of the dx
2
-y
2 orbital.

Figure. A tetrahedral complex
shown with the coordinate
system. Two lobes of the dz
2
orbital are shown along the z-axis
and two lobes of the dx
2
-y
2 orbital
are shown along the y-axis.
Figure. Tetrahedral
arrangement of four ligands
(L) around the metal ion
(Mn+) in tetrahedral complex
ion, [ML4]n+.

• Note that in this case none of the d-orbitals will point directly at the
ligands.
• However, the orbitals that have lobes lying along the axes (dx
2
-y
2 and
dz
2) are directed toward a point that is midway along a diagonal of a
face of the cube.
• That point lies at (2½ /2)l from each of the ligands.
• The orbitals that have lobes projecting between the axes (dxy, dyz,
and dxz) are directed toward the midpoint of an edge that is only l/2
from sites occupied by ligands.
• The result is that the dxy, dyz, and dxz orbitals are higher in energy
than are the dx
2
-y
2 and dz
2 orbitals because of the difference in how
close they are to the ligands.
• In other words, the splitting pattern produced by an octahedral field
is inverted in a tetrahedral field.
• The magnitude of the splitting in a tetrahedral field is designated as
Δt, and the energy relationships for the orbitals are shown in
following figure.

Summary
• The distance of dx
2
-y
2and dz
2 from ligands = (2.5/2)l
• The distance of dxy, dyz, and dxz from ligands = (l/2)
• Its mean the lobes dx
2
-y
2 and dz
2 are away from ligands so have less
energy while the lobes dxy, dyz, and dxz are comparatively close to
ligands so have greater energy.
• Due to this fact the orbitals are inverted as compared to octahedral
geometry.
dx
2
-y
2 and dz
2 orbitals → less in energy
dxy, dyz and dxz orbitals → higher in energy

Differences between the splitting in octahedral and tetrahedral
fields
• There are several differences between the splitting in octahedral and
tetrahedral fields.
1. Not only are the two sets of orbitals inverted in energy, but also the
splitting in the tetrahedral field is much smaller than that produced
by an octahedral field.
Figure. The orbital splitting pattern in a tetrahedral field that is
produced by four ligands.

2. First, there are only four ligands producing the field rather
than the six ligands present in the octahedral complex.
3. Second, none of the d-orbitals point directly at the ligands
in the tetrahedral field.
• In an octahedral complex, two of the orbitals point directly
toward the ligands and three point between them.
• As a result, there is a maximum energy splitting effect on
the d-orbitals in an octahedral field.
• In fact, it can be shown that if identical ligands are present
in the complexes and the metal-to-ligand distances are
identical, Δt = (4/9)Δo [Δt = 0.45Δo].
• The result is that there are no low-spin tetrahedral
complexes because the splitting of the d-orbitals is not
large enough to force electron pairing.

4. Third, because there are only four ligands surrounding the
metal ion in a tetrahedral field, the energy of all of the d
orbitals is raised less than they are in an octahedral complex.
• The subscripts " g " do not appear on the subsets of orbitals
because there is no center of symmetry in a tetrahedral
structure.
Formation of tetragonal field
• Elongation: Suppose we start with an octahedral complex
and place the ligands lying on the z-axis farther away from
the metal ion.
• As a result, the dz
2 orbital will experience less repulsion, and
its energy will decrease.
• However, not only do the five d-orbitals obey a “center of
energy" rule for the set, but also each subset has a center of
energy that would correspond to spherical symmetry for that
subset.
g is used in Oh symmetry
mean in octahedral structure

• Conservation of energy: Therefore, if the dz
2 orbital is
reduced in energy, the dx
2
-y
2 orbital must increase in
energy to correspond to an overall energy change of zero
for the eg subset.
• The dxz and dyz orbitals have a z-component to their
direction.
• They project between the axes in such a way that moving
ligands on the z-axis farther from the metal ion reduces
repulsion of these orbitals.
• As a result, the dxz and dyz orbitals have lower energy,
which means that the dxy orbital has higher energy in order
to preserve the center of energy (2) for the t2g orbitals.
• The result is a set of d-orbitals that are arranged as shown
in following figure.

• With the metal-to-ligand bond lengths being greater in the z-
direction, the field is now known as a tetragonal field with
z-elongation.
• Compression: If the ligands on the z-axis are forced closer
to the metal ion to produce a tetragonal field with z-
compression, the two sets of orbitals shown above are
inverted.
• Following figure shows the d-orbitals in this type of field.
Figure. The arrangement of the d
orbitals according to energy in a
field with elongation by moving the
ligands on the z-axis farther from
the metal ion in an octahedral
complex.

Figure. The arrangement of d
orbitals in a field with
compression of the ligands
along the z-axis.

Figure. Crystal field splitting diagrams for octahedral (left-hand
side) and tetrahedral (right-hand side) fields. The splittings are
referred to a common barycentre.
• Following figure compares crystal field splitting for octahedral
and tetrahedral fields; remember, the subscript g in the symmetry
labels is not needed in the tetrahedral case.

• Since ∆tet is significantly smaller than ∆oct, tetrahedral
complexes are high-spin.
• Also, since smaller amounts of energy are needed for an t2 ←
e transition (tetrahedral) than for an eg ← t2g transition
(octahedral), corresponding octahedral and tetrahedral
complexes often have different colours.
Chemical and theoretical background
Notation for electronic transitions
• For electronic transitions caused by the absorption and
emission of energy, the following notation is used:
– Emission: (high energy level) → (low energy level)
– Absorption: (high energy level) ← (low energy level)
• For example, to denote an electronic transition from the e to t2
level in a tetrahedral complex, the notation should be t2 ← e.
Tetrahedral complexes → only high-spin

Explain Δt = (4/9)Δo
• In case of a cubic symmetry, the ligands do not approach
any of the d-orbitals along the orbital axis (following
figure).
• They just interact more with the t2 orbitals lying midway
between coordinate axes, directed along the edges of the
cube than with e orbitals pointing towards the face of the
cube.
• Hence the t2 levels are raised (by 4Dq) whereas the e
levels are lowered (by 6Dq) to maintain the barycentre.
• It can be shown that the eight ligands in a cubic
symmetry will produce a field nearly 8/9 times as strong
as the corresponding octahedral field, so that:
(10Dq)cubic ≈ 8/9(10Dq)octahedral

• If four ligands are now removed from the alternative
corners of the cube, the remaining four ligands form a
tetrahedral arrangement around the central atom.
• Though the energy levels remain similar, the crystal field
splitting is reduced to half, so that
(10Dq)tet = 1/2 (10Dq)cubic ≈ 4/9(10Dq)oct
Figure. A cubic and
tetrahedral arrangement of
four ligands (L) around the
metal ion (Mn+) in tetrahedral
complex ion, [ML4]n+.
Assignment
Q: Explain Δt = (4/9)Δo

Formation of square planar complex from octahedral
complex
• A square planar arrangement of ligands can be formally derived
from an octahedral array by removal of two trans-ligands
(following figure).
Figure. A square planar complex can be derived from an
octahedral complex by the removal of two ligands, e.g. those on
the z-axis; the intermediate stage is a Jahn–Teller distorted
(elongated) octahedral complex.

• If we remove the ligands lying along the z-axis, then the
dz
2 orbital is greatly stabilized; the energies of the dyz and
dxz orbitals are also lowered, although to a smaller
extent.
• The resultant ordering of the metal d-orbitals is shown at
the left-hand side of following figure.
Assignment
Q: What will be the splitting of d-orbitals about the barycentre in
trigonal bipyramidal?

Figure. Crystal field splitting diagrams for some common fields referred
to a common barycentre; splittings are given with respect to ∆oct.
Barycentre

The square planar crystal field
[Crystal field splitting of d-orbitals in tetragonal
(elongated distorted octahedral) and square planar
complexes]
• Before considering the splitting of d-orbitals of the central
metal cation in these complexes, we should understand how
tetragonally distorted octahedral and square planar
geometries are obtained from regular octahedral geometry.
a) Regular octahedral geometry
• Consider a regular (symmetrical) octahedral complex,
[M(Lb)4 (La)2] in which M is the central metallic cation, La
are two trans-ligands (i.e., La are the ligands lying along
the z-axis) and Lb are the basal equotorial ligands lying in
xy plane.
• In this complex all the six bond distances (four M-Lb and
two M-La distances) are equal [following figure (a)].

Figure. To get tetragonal and square planar geometries from octahedral
geometry.

b) Elongated distorted octahedral (tetragonal) shape
• Now if two La ligands are moved slightly longer from the
central metal cation, M so that each of the two M-La
distances becomes slightly longer than each of the four co-
planar M-Lb distances, the symmetrical shape of
octahedral complex gets distorted and becomes distorted
octahedral shape [above figure (b)].
• In this shape, since the two trans-ligand have elongated,
the distorted octahedral shape is also called elongated
distorted octahedral shape.
• Obviously the elongation of two trans-ligands takes place
along +z and -z axes.
• Elangated distorted octahedral gemoetry is also called
tetragonally distorted octahedral shape or simply
tetragonal shape.

c) Square planar geometry
• Now if the two La ligands are completely removed away
from the z-axis, the tetragonally distorted octahedral shape
becomes square planar which is a four-coordinated
complex [above figure (c)].
Splitting of d-orbitals from regular octahedral geometry
to square planar geometry
• Now in order to consider the splitting of d-orbitals in
elongated distorted octahedral and square planar
complexes, we start with the splitting of d-orbitals in
octahedral complexes.
• We have already seen that in octahedral complexes, the
energy of dxy, dyz, and dzx orbitals (t2g orbitals) is decreased
while that of dz
2 and dx
2
-y
2 orbitals (eg orbitals) is increased
[following figure (b)].

• Now in elongated distorted octahedral complex, since the
distance of the trans-ligands (La ligands) is increased from
the central metal ion by removing them away along the z-
axis, d-orbitals along the z-axis (i.e., dz
2 orbital), d-orbital
in yz plane (i.e. dyz orbital) and d-orbital in zx plane (i.e.
dzx orbital) experience less repulsion from the ligands than
they do in the octahedral complex while the d-orbitals in
xy plane (i.e., dxy and dx
2
-y
2 orbitals) experience more
repulsion than they do in the octahedral complex.
• Consequently the energy of dz
2, dyz and dzx orbitals
decrease while that of dx
2
-y
2 and dxy orbitals increase
[above figure (c)].
• Note that dyz, and dzx orbitals still remain degenerate as
they are in the octahedral complex.

• In square planar geometry the energies of dz
2, dyz and dzx
orbitals again fall down while those of dx
2
-y
2 and dxy
orbitals rise up [above figure (d)].
• Thus the splitting of d-orbitals into various orbitals in
square planar complexes takes place as shown at (d) of
above figure.
• The relative energy order between the various splitted d-
orbitals in square planar complexes is uncertain but the
order shown in above figure (d) has been established for
5d8 configuration from spectroscopic data.
• The extent of splitting of d-orbitals in square planar
complexes depends on the nature of the central metal atom
and ligands.
• Semi-quantitative calculations for square planar complexes of Co2+
(3d7), Ni2+ (3d8) and Cu2+ (3d9) have shown that ∆1 = ∆0, ∆2 = 2/3∆0
(or 0.66 ∆0) and ∆3 = 1/12∆0 (or 0.08 ∆0)

and hence
Figure. The orbital splitting
parameters for a square-planar
complex.
For the square planar complexes of Pd2+ (4d8) and Pt2+(5d8)
spectroscopic results have shown that:
for complexes of the same metal and ligands with the same M-L
bond lengths.

Diamagnetic property of d8 ions having square planar geometry
• The energy level diagram for the d-orbitals in a square planar field is
shown in following figure.
• It can be shown that the energy separating the dxy and dx
2
-y
2 orbitals is
exactly Δo, the splitting between the t2g and eg orbitals in an octahedral
field.
• d8 ions such as Ni2+, Pd2+, and Pt2+ form square planar complexes that are
diamagnetic.
• From the orbital energy diagram shown in above figure, it is easy to see
why (following figure).
Figure. Energies of d orbitals
in a square planar field
produced by four ligands.

Figure. The d8-orbital energy diagram for the square planar
environment, as derived from the octahedral diagram.

• Eight electrons can pair in the four orbitals of lowest
energy leaving the dx
2
-y
2 available to form a set of dsp2
hybrid orbitals.
• If the difference in energy between the dxy and the dx
2
-y
2 is
not sufficient to force electron pairing, all of the d-orbitals
are occupied, and a complex having four bonds would be
expected to utilize sp3 hybrid orbitals, which would result
in a tetrahedral structure.
• The fact that square planar d8 complexes such as
[Ni(CN)4]2- are diamagnetic is a consequence of the
relatively large energy difference between the dxy and dx
2
-y
2
orbitals.
• The following example shows an experimental means
(other than single-crystal X-ray diffraction) by which
square planar and tetrahedral d8 complexes can be
distinguished.

Assignment
Q: The d8 complexes [Ni(CN)4]2- and [NiCl4]2- are square planar
and tetrahedral respectively. Will these complexes be
paramagnetic or diamagnetic?
• Consider the splitting diagrams shown in following figures.
Figure. Crystal field splitting diagrams for octahedral (left-hand
side) and tetrahedral (right-hand side) fields. The splittings are
referred to a common barycentre.

Figure. Crystal field splitting diagrams for some common fields
referred to a common barycentre; splittings are given with respect
to ∆oct.

• For [Ni(CN)4]2- and [NiCl4]2-, the eight electrons occupy
the d orbitals as follows:
Thus, [NiCl4]2- is
paramagnetic while
[Ni(CN)4]2- is
diamagnetic.
Although [NiCl4]2-
is tetrahedral and
paramagnetic,
[PdCl4]2- and
[PtCl4]2- are square
planar and
diamagnetic.
This difference is a consequence of the larger crystal field splitting
observed for second and third row metal ions compared with their
first row congener; Pd(II) and Pt(II) complexes are invariably square
planar.

Factors affecting the crystal field splitting (Δ)
• The energy-level splitting depends on four factors:
1. Charge on the metal ion (Nature of metal cation)
• Increasing the charge on a metal ion has two effects:
– The radius of the metal ion decreases
– Negatively charged ligands are more strongly attracted to it
(metal)
• Both factors decrease the metal–ligand distance, which in turn
causes the negatively charged ligands to interact more strongly
with the d-orbitals.
• Consequently, the magnitude of Δo increases as the charge on
the metal ion increases.
• Typically, Δo for a tripositive ion is about 50% greater than for
the dipositive ion of the same metal; for example, for
[V(H2O)6]2+, Δo = 11,800 cm−1; for [V(H2O)6]3+, Δo = 17,850
cm−1.
Radius → decreases
Ligand (-ve) → strongly attracted

• The influence of this factor can also be studied under the
following four heading:
Different charges on the cation of the same metal
• The cation from the atoms of the same transition series and
having the same oxidation state have almost the same value of ∆0
but the cation with a higher oxidation state has a large value of ∆0
than with the lower oxidation state, e.g.,
(a) ∆0 for [Fe+2(H2O)6]+2 = 10,400 cm-1 ……… 3d6
∆0 for [Fe+3(H2O)6]+3 = 13,700 cm-1 ……… 3d5
(b) ∆0 for [Co+2(H2O)6]+2 = 9,300 cm-1 ……… 3d7
∆0 for [Co+3(H2O)6]+3 = 18,200 cm-1 ……… 3d6
• This effect is probably due to the fact that the central ion with
higher oxidation state will polarize the ligands more effectively
and thus the ligands would approach such a cation more closely
than they can do the cation of lower oxidation state, resulting in
larger splitting.

Different charges on the cation of different metals
• Two different cations having the same number of d-electrons and
the same geometry of the complex but with different charge can
also be compared.
• The cation with a higher oxidation state has a large value of ∆0 than
with a lower oxidation state.
• For example, the behavior towards the same ligand of V(II) and
Cr(III), which are both d3 ion can be compared.
• It is observed that the value of ∆0 in [V+2(H2O)6]+2 is less than that
in [Cr+3(H2O)6]+3 as is shown below:
∆0 For [V+2(H2O)6]+2 = 12,400 cm-1 …… 3d3
∆0 For [Cr+3(H2O)6]+3 = 17,400 cm-1 …… 3d3
• This fact can be expressed in terms of the charge on the cation.
• The Cr+3 ion, which has positive charge than V+2 ion, exerts a
greater attraction for water molecules than does the V+2.
• Hence the water molecules approach the V+2 ion so exert a stronger
crystal field effect on the d- electrons of Cr+3 ion.

Same charges on the cation but the number of d-electrons is
different
• In case of the complexes having the cation with same charges but
with different number of d-electrons in the central metal cation the
magnitude of ∆0 decreases with the increase of the number of d-
electrons, e.g.,
∆0 for [Co+2(H2O)6]+2 = 9,300 cm-1 ……. 3d7
∆0 for [Ni+2(H2O)6]+2 = 8,500 cm-1 ……. 3d8
• From the combination of mentioned above facts, it can be
concluded that:
– For the complexes having the same geometry and the same
ligands but different number of d-electrons, the magnitude of ∆0
decreases with the increase of the number of d-electrons in the
central metal cation (No. of d-electrons is directly proportional to
1/ ∆0)
– In case of complexes having the same number of d-electrons the
magnitude of ∆0 increases with the increase of the charges (i.e.,
oxidation state) on the central metal cation (oxidation state is
directly proportional to ∆0).

2. The identity of the metal
• The crystal field splitting, ∆, is about 50 percent greater for the
second transition series compared to the first, whereas the third
series is about 25 percent greater than the second.
• There is a small increase in the crystal field splitting along each
series.
[Δo (3d) < Δo (4d) < Δo (5d)]
Note: The largest Δos are found in complexes of metal ions from the
third row of the transition metals with charges of at least +3 and
ligands with localized lone pairs of electrons.
3. The oxidation state of the metal
• Generally, the higher the oxidation state of the metal, the greater the
crystal field splitting.
Δo for 2nd → 50% greater then for first transition series
Δo for 3rd → 25% greater then for second transition series

• Thus, most cobalt(II) complexes are high spin as a result of the
small crystal field splitting, whereas almost all cobalt(III)
complexes are low spin as a result of the much larger splitting by
the 3+ ion.
4. Principal quantum number of the metal
• ∆0 increases about 30% to 50% from 3dn to 4dn and by the same
amount again from 4dn to 5dn complexes.
• For a series of complexes of metals from the same group in the
periodic table with the same charge and the same ligands, the
magnitude of Δo increases with increasing principal quantum
number:
Δo (3d) < Δo (4d) < Δo (5d)
• The data for hexaammine complexes of the trivalent group 9 metals
illustrate this point:
Co(II) → H.S
Co(III) → L.S
(3d6)
(4d6)
(5d6)

• The increase in Δo with increasing principal quantum
number is due to the larger radius of valence orbitals down a
column.
• In addition, repulsive ligand–ligand interactions are most
important for smaller metal ions.
• Relatively speaking, this results in shorter M–L distances
and stronger d orbital–ligand interactions.
5. The number of the ligands
• The crystal field splitting is greater for a larger number of
ligands.
• For example, ∆oct, the splitting for six ligands in an
octahedral environment, is much greater than ∆tet, the
splitting for four ligands in a tetrahedral environment.
If ∆ → greater → large number of ligands
Six ligands → ∆ should be large
Four ligands → ∆ should be small

6. The nature of the ligands
• Experimentally, it is found that the Δo observed for a
series of complexes of the same metal ion depends
strongly on the nature of the ligands.
• For a series of chemically similar ligands, the magnitude
of Δo decreases as the size of the donor atom increases.
• For example, Δo values for halide complexes generally
decrease in the order F− > Cl− > Br− > I− because smaller,
more localized charges, such as we see for F−, interact
more strongly with the d-orbitals of the metal ion.
• In addition, a small neutral ligand with a highly localized
lone pair, such as NH3, results in significantly larger Δo
values than might be expected.
• Because the lone pair points directly at the metal ion, the
electron density along the M–L axis is greater than for a
spherical anion such as F−.

• The experimentally observed order of the crystal field
splitting energies produced by different ligands is called
the spectrochemical series.
• The common ligands can be ordered on the basis of the
effect that they have on the crystal field splitting.
• Among the common ligands, the splitting is largest with
carbonyl and cyanide and smallest with iodide.
• The ordering for most metals is:
General guidelines for ordering the ligands
• The general guidelines for ordering the ligands is:
– Halides < oxygen donors < nitrogen donors < carbon donors
• Thus, for a particular metal ion, it is the ligand that
determines the value of the crystal field splitting.

• Consider the d6 iron(II) ion.
• According to crystal field theory, there are the two spin
possibilities: high spin (weak field) with four unpaired
electrons and low spin (strong field) with all electrons paired.
• We find that the hexaaquairon(II) ion, [Fe(OH2)6]2+, possesses
four unpaired electrons.
• The water ligands, being low in the spectrochemical series,
produce a small ∆oct; hence, the electrons adopt a high-spin
configuration.
• Conversely, the hexacyanoferrate(II) ion, [Fe(CN)6]4-, is found
to be diamagnetic (zero unpaired electrons).
• Cyanide is high in the spectrochemical series and produces a
large ∆oct; hence, the electrons adopt a low-spin configuration.
• The values of Δo listed in following table (Δ illustrate the
effects of the charge on the metal ion, the principal quantum
number of the metal, and the nature of the ligand.

Table. Crystal field splitting energies for some octahedral (Δo)* and
tetrahedral (Δt) transition-metal complexes.

7. Colors of transition-metal complexes
• The striking colors exhibited by
transition-metal complexes are caused
by excitation of an electron from a
lower-energy d orbital to a higher-energy
d orbital, which is called a d–d transition
(following figure).
• For a photon to effect such a transition,
its energy must be equal to the difference
in energy between the two d orbitals,
which depends on the magnitude of Δo.
Figure. A d–d Transition. In a d–d transition, an electron in one
of the t2g orbitals of an octahedral complex such as the
[Cr(H2O)6]3+ ion absorbs a photon of light with energy equal to
Δo, which causes the electron to move to an empty or singly
occupied eg orbital.

• The color we observe when we look at an object or a
compound is due to light that is transmitted or reflected,
not light that is absorbed, and that reflected or
transmitted light is complementary in color to the light
that is absorbed.
• Thus a green compound absorbs light in the red portion
of the visible spectrum and vice versa, as indicated by
the color wheel.

• Because the energy of a photon of light is inversely
proportional to its wavelength, the color of a complex
depends on the magnitude of Δo, which depends on the
structure of the complex.
• For example, the complex [Cr(NH3)6]3+ has strong-field
ligands and a relatively large Δo.
• Consequently, it absorbs relatively high-energy photons,
corresponding to blue-violet light, which gives it a yellow
color.
• A related complex with weak-field ligands, the
[Cr(H2O)6]3+ ion, absorbs lower-energy photons
corresponding to the yellow-green portion of the visible
spectrum, giving it a deep violet color.
• We can now understand why emeralds and rubies have
such different colors, even though both contain Cr3+ in an
octahedral environment provided by six oxide ions.

• Although the chemical identity of the six ligands is the same in
both cases, the Cr–O distances are different because the
compositions of the host lattices are different (Al2O3 in rubies
and Be3Al2Si6O18 in emeralds).
• In ruby, the Cr–O distances are relatively short because of the
constraints of the host lattice, which increases the d orbital–
ligand interactions and makes Δo relatively large.
• Consequently, rubies absorb green light and the transmitted or
reflected light is red, which gives the gem its characteristic color.
In emerald, the Cr–O distances are longer due to relatively large
[Si6O18]12− silicate rings; this results in decreased d orbital–
ligand interactions and a smaller Δo.
• Consequently, emeralds absorb light of a longer wavelength
(red), which gives the gem its characteristic green color.
• It is clear that the environment of the transition-metal ion, which
is determined by the host lattice, dramatically affects the
spectroscopic properties of a metal ion.

Gem-quality crystals of ruby and emerald.
The colors of both minerals are due to the presence of small amounts of Cr3+
impurities in octahedral sites in an otherwise colorless metal oxide lattice.
Emerald (‫)زمرد‬Ruby (‫)ياقوت‬

Limitations of crystal field theory
• Crystal field theory is surprisingly useful when one considers its
simplicity.
• However, it has limitations.
• CFT considers only the metal ion d-orbitals and gives no
consideration at all to other metal orbitals such as s, px, py and pz
orbitals and ligand π-orbitals.
• Therefore, to explain all the properties of the complexes
dependent on the π-ligand orbitals will be outside the scope of
CFT.
• CFT does not consider the formation of π-bonding in complexes.
• Although we can interpret the contrasting magnetic properties of
high- and low-spin octahedral complexes on the basis of the
positions of weak- and strong-field ligands in the spectrochemical
series, crystal field theory provides no explanation as to why
particular ligands are placed where they are in the series.

• CFT is 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.
• Thus the effects directly dependent on covalency cannot be
explained by CFT.

Applications of crystal field theory
• The following properties of transition metal complexes can will be
explained on the basis of CFT.
• Uses of CFSE values
• With the help of CFT, we have calculated the CFSE values for dx
configuration of the central metal ion in octahedral and in high spin
tetrahedral complexes.
• With the help of CFSE values we can explain the following:
1. Crystal structure of spinels
• Mixed oxides of the general formula, A2+B2
3+O4 are called spinals
after the name of the mineral spinel, MgAl2O4 ions may be of
different metals or of the same metal.
• In spinals oxygen atom are arranged in a cubic close-packed
lattice.
• In such lattices each oxygen atom has 12 other oxygen atoms
equidistant from it and the holes between oxygen atoms are of two
types:

• Octahedral holes which are so called because these are
surrounded by six oxygen atoms. There is one of such holes for
each oxygen atom.
• Tetrahedral holes which are so called since these are
surrounding by four oxygen atoms. These are two such holes
for each oxygen atoms. These are smaller then the octahedral
holes. There are twice as many tetrahedral holes as there are
octahedral holes. The cations occupy the octahedral and
tetrahedral holes, since these are large enough to be filled by
cations.
• Spinals of A2+B2
3+ O4 type are classified as normal or simple and
inverse spinals.
• In normal spinels all the A2+ cations occupy one of the eight
available tetrahedral holes and all B3+ cations occupy half of the
available octahedral holes.
• Normal spinels are represented as A2+[B2
3+]O4.
• This representation shows that the cations outside the bracket occupy the
tetrahedral holes and cations inside the bracket occupy the octahedral holes.

• Example for normal spinels are Mg2+[Cr2
3+]O4, Ni2+[Cr2
3+]O4,
Mn3O4 or Mn2+[Mn2
3+]O4 etc.
• In inverse spinels all the A2+ and half of the B2
3+ cations are in
octahedral and the other half of the B3+ cations are in tetrahedral
holes.
• Inverse spinels are represented as B3+[A2+B3+]O4.
• This formulation shows that the tetrahedral holes are occupied by
half of the ions B3+ and the octahedral holes are occupied by A2+
Ions and the remaining half B3+ ions.
• Examples of inverse spinals are CuFe2O4 or Fe3+[Cu2+Fe3+]O4 etc.
• Now let us see how CFT helps in predicting the structure of
spinels.
• For example with the help of CFT it can be shown why the oxide
Mn3O4 or Mn2+[Mn2
3+]O4 is a normal spinel while the oxide Fe3O4
or Fe2+[Fe2
+3]O4 is an inverse spinel.
• CFSE values in octahedral and tetrahedral fields have been used
for interpretation.

• For this it is assumed that the oxide ions, O2-, like water molecules,
produce weak field.
• CFSE values (in terms of ∆0) in octahedral and tetrahedral weak
ligand field are given below:
• It is obvious that for Mn3+ (d4) and Fe2+ (d6) ions the CFSE values
are greater for octahedral than for tetrahedral sites.
• Thus Mn3+ and Fe2+ ions will preferentially occupy the octahedral
sites, maximizing the CFSE values of the system.
• Hence in Mn3O4 all the Mn3+ ions occupy octahedral sates and all
Mn2+ ions are in the tetrahedral sites, i.e., it is a normal spinel and
its structure is, therefore, represented as Mn2+[Mn2
3+]O4.
• In Fe3O4 all the Fe2+ ions and half of the Fe3+ ions are in the
octahedral sites, while the remaining half of Fe3+ ions occupy
tetrahedral sites thus it is an inverse spinel and is, therefore
represented as Fe3+[Fe2+Fe3+]O4.

2. Stabilization of oxidation states
• CFSE values also explain why certain oxidation states are
preferentially stabilized by coordinating with certain ligands.
• The following two examples illustrate this use:
• Although H2O molecule which is a weak ligand should be
expected to coordinate with Co2+ and Co3+ ions to form the high-
spin octahedral complexes viz. [Co(H2O)6]2+ respectively,
experiments show that H2O stabilises Co2+ ion and not Co3+, i.e.,
[Co(H2O)6]2+ is more stable than [Co(H2O)6]3+.
• This is because of the fact that Co2+ has a much higher value of
CFSE in weak octahedral configuration (CFSE = 0.8 ∆0) than Co3+
in the same configuration (CFSE = 0.4 ∆0).
• If we consider the coordination of NH3 molecules with Co2+ and
Co3+ ions, it my be seen that NH3 which is a strong ligand
stabilises Co2+ ion by forming [Co(NH3)6]3+ rather than Co2+ ions.
• This is because of the fact that Co3+ ion has much higher values of
CFSE in strong octahedral configuration (CFSE = 2.4 ∆0) than
Co3+ in the same configuration (CFSE = 1.8 ∆0).

3. Stereochemistry of complexes
• (a) CFSE values also predict why Cu2+ ion forms square planar
complexes rather than tetrahedral or octahedral complexes in both
the field.
• This is because of the reason that Cu2+ has a much higher CFSE
value in a square planar configuration (CFSE = 1.22 ∆0) than in
octahedral or tetrahedral configuration (CFSE = 0.18 ∆0).
• (b) Most of the four coordinated complexes of Ni2+ are square
planar rather than tetrahedral [(NiX4)2- is an exception, X = Cl-,
Br-, I-]. This is because CFSE values of d8 ion are higher in square
planar configuration (= 1.45 ∆0) than those of the same ion in
tetrahedral configuration (= 0.36 ∆0).
4. Other application
• With the help of CFT, we can find out.
• The number of unpaired electrons (n) in the central metal ion of a
given complex ion and hence the value of magnetic moment (μ) of
the ion. μ is given by:
• Thus, for n = 0, μ = 0.0 (diamagnetic)

n = 1, µ = 1.73 B.M
n = 2, µ = 2.83 B.M
n = 3, µ = 3.87 B.M
n = 4, µ = 4.90 B.M
n = 5, µ = 5.92 B.M
• (Where B.M. = Bohr Magneton, it is unit of magnetic moment)
• Whether the given complex ion is LS.
• Whether the given complex ion is paramagnetic or diamagnetic.

Experimental evidence for metal-ligand covalent bonding
in complexes
• The following evidences have been presented to show the
metal-ligand covalent bonding in complexes.
Electron spin resonance spectra
• Most direct evidence is obtained from ESR spectrum of
complexes, e.g,. ESR spectrum of [IrIVCl6]2- ion shows that
it has a complex pattern of sub-bands which is called the
hyperfine structure.
• The hyperfine structure has been explained by assuming that
certain of the iridium orbitals and certain orbitals of the
surrounding Cl- ions overlap to such as extent that the single
unpaired d-electron is not localized entirely on the metal ion
but instead is about 5% localized on each Cl- ion.
• Such study of other complexes also gives similar results.

Nuclear magnetic resonance (NMR)
• NMR studies of complexes like KMnF3 and KNiF3 show
that the metal t2g and eg electrons pass a fraction of time
around the Flourine nuclei.
Nuclear quadrupole resonance (NQR)
• The NQR spectrum of some of the square planar complexes
of Pt (II) Pd (II) such as (Pt2X4)2- and (Pd2X4)2- suggest that
there is considerable amount of covalency in the metal-
ligand bond (i.e., Pt-X or Pd-X bonds).
• The unusually large absorption band intensities observed
for tetrahedral complexes like [CoIICl4]2- have been
explained by saying that the metal-ligand bonds have
appreciable covalent character.

Comparison Between VBT and CFT
• The points showing the comparison between the two theories are
given below:
• The inner orbital octahedral complexes of VBT are the same as
the spin-paired or low-spin octahedral complexes of CFT.
• Similarly outer-orbital complexes of VBT are the same as the
spin-free or high-spin octahedral complexes of CFT.
• In the formation of some inner-orbital octahedral complexes of
VBT, the promotion of an electron from d-orbital to s-orbital is
required, while in the formation of spin-paired octahedral
complexes of CFT no such promotion is required.
• According to VBT, the metal-ligand bonding in complexes is
only covalent, since VBT assumes that ligand electrons are
donated to the vacant d-orbitals on the central cation.
• On the other hand, CFT considers the bonding to be entirely
electrostatic. Thus, CFT does not allow the ligand electrons to
enter the metal d-electrons.

Assignments
Assignment-1
• For the complex ion [Fe(Cl)6]3- determine the number of d
electrons for Fe, sketch the d-orbital energy levels and the
distribution of d electrons among them, list the number of
lone electrons, and label whether the complex is
paramagnetic or diamagnetic.
Solution
Step 1
• Determine the oxidation state of Fe.
• Here it is Fe3+.
• Based on its electron configuration, Fe3+ has 5 d-electrons.
Step 2
• Determine the geometry of the ion.
• Here it is an octahedral which means the energy splitting
should look like:
Fe3+: 1s2 2s2 2p6 3s2 3p6 3d5

Step 3
• Determine whether the ligand induces is a strong or weak
field spin by looking at the spectrochemical series.
• Cl- is a weak field ligand (i.e., it induces high spin
complexes).
• Therefore, electrons fill all orbitals before being paired.

Step 4
• Count the number of lone electrons.
• Here, there are 5 electrons.
Step 5
• The five unpaired electrons means this complex ion
is paramagnetic (and strongly so).

Assignment-2
• For each complex, predict its structure, whether it is high spin or
low spin, and the number of unpaired electrons present.
– [CoF6]3−
– [Rh(CO)2Cl2]−
• Given: Complexes
• Asked for: Structure, high spin versus low spin, and the number of
unpaired electrons
• Strategy:
• A: From the number of ligands, determine the coordination number
of the compound.
• B: Classify the ligands as either strong field or weak field and
determine the electron configuration of the metal ion.
• C: Predict the relative magnitude of Δo and decide whether the
compound is high spin or low spin.
• D: Place the appropriate number of electrons in the d orbitals and
determine the number of unpaired electrons.

Solution:
1. A: With six ligands, we expect this complex to be
octahedral.
• B: The fluoride ion is a small anion with a concentrated
negative charge, but compared with ligands with localized
lone pairs of electrons, it is weak field. The charge on the
metal ion is +3, giving a d6 electron configuration.
• C: Because of the weak-field ligands, we expect a
relatively small Δo, making the compound high spin.
• D: In a high-spin octahedral d6 complex, the first five
electrons are placed individually in each of the d orbitals
with their spins parallel, and the sixth electron is paired in
one of the t2g orbitals, giving four unpaired electrons.

2. A: This complex has four ligands, so it is either square
planar or tetrahedral.
• B and C: Because rhodium is a second-row transition
metal ion with a d8 electron configuration and CO is a
strong-field ligand, the complex is likely to be square
planar with a large Δo, making it low spin. Because the
strongest d-orbital interactions are along the x and y axes,
the orbital energies increase in the order dz
2, dyz, and dxz
(these are degenerate); dxy; and dx
2
−y
2.
• D: The eight electrons occupy the first four of these
orbitals, leaving the dx
2
−y
2 orbital empty. Thus there are no
unpaired electrons.

Assignment-3
• For each complex, predict its structure, whether it is
high spin or low spin, and the number of unpaired
electrons present.
– [Mn(H2O)6]2+
– [PtCl4]2−
Answer
[Mn(H2O)6]2+
– Octahedral
– High spin
– Five unpaired electrons
[PtCl4]2−
• Square planar
• Low spin
• No unpaired electrons
Mn2+ = 1s2 2s2 2p6 3s2 3p6 3d5
Pt = [Xe] 6s1 4f14 5d9
Pt2+ = [Xe] 4f14 5d8

Crystal Field Theory (CFT)

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