For B.Tech.

MECH Chemistry

Unit-1
MOLECULAR STRUCTURE AND THEORIES OF BONDING
Atomic orbitals:
• An atomic orbital is a mathematical function that describes the wave like behavior of either
one electron or a pair of electrons in an atom.
• This function can be used to calculate the probability of finding any electron of an atom in
any specific region around the nucleus of the atom.
• In atoms, electrons occupy atomic orbitals, but in molecules, they occupy similar molecular
orbitals which surrounding the molecule.
• Each orbital in an atom is characterized by a set of values of four quantum numbers n, l, s
and m. This corresponds to the energy and angular momentum (n, l), spin (s) and angular
momentum vector component (m) respectively.
• Each such orbital can be occupied by a maximum of two electrons, each with its own spin
quantum number (s) i.e. the orbitals s, p, and d and f orbitals.
• Atomic orbitals have fixed shapes
Molecular orbitals:
• Atomic orbitals join together to form molecular orbitals. So, Molecular orbitals can be
obtained from the combination of atomic orbitals which predict the location of an electron in
an atom.
• A molecular orbital can be used to represent the regions in a molecule where an electron
occupying that orbital is likely to be found.
• Molecular orbital depicts the location where the electron can probably be found in a molecule
as a whole.
• Molecular orbitals can change their shapes depending on the hybridization they undergo.

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Molecular Orbital Theory

According to wave mechanics, two theories of chemical bonding exist. One is Valence Bond
Theory (VBT) and the other is molecular orbital theory (MOT). In VBT, the atoms in a molecule
retain their individuality. The bond is formed due to interaction of the valence electrons when the
atoms come closer.
The VBT is modified by Mullikan, Hund and Jones and proposed molecular orbital theory.
The postulates of MOT:
1. Atomic orbitals of atoms overlap to form molecular orbitals.
2. The number of MOs formed is equal to the number of overlapping atomic orbitals.
3. Two atomic orbitals after overlapping yield two MOs. Ex: One bonding molecular orbital
with lower energy and one antibonding molecular orbital with higher energy.
4. The decrease in energy of bonding MO is approximately the same as the increase in energy
of antibonding MO.
5. Each MO can accommodate two electrons with opposite spin just like atomic orbitals.
6. Depending on the type of overlapping, MO are designated as σ, σ*, π, π* and 𝛿, 𝛿*.

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7. Only atomic orbitals which possess similar energies only can combine to form MOs as well
as proper orientations. For example, 1s atomic orbital can overlap with 1s atomic orbital but
not with 2s atomic orbital. 2s orbital can overlap with 2s orbital. 2px overlap with 2px. 2py
overlap with 2py. 2pz overlap with 2p. But 2px cannot overlap with 2py (or) 2pz etc.
8. The filling of electrons in various MOs obeys Aufbou and Hund’s rule and Pauli’s principle.
9. Y1, Y 2 are the wave functions of two overlapping AO’s and the process of their overlapping
is called linear combination of atomic orbitals (LCAO) method.
10. According to LCAO method, linear combination of atomic orbitals can take place either by
addition (constructive) (or) subtraction (destruction) of wave functions of atomic orbitals
involved.
11. MO obtained by addition of wave function of atoms is called bonding molecular orbital (BMO).

The energy of BMOs (bonding molecular orbitals) is less than that of constituent overlapping
atomic orbitals. The energy difference between the combining AOs and the MO formed is called
stabilization energy.

12. Molecular orbitals are obtained by the substraction of wave functions of concerned atoms is
called antibonding molecular orbitals (ABMO).

The energy of ABMO is more than that of constituent atomic orbitals. The energy difference
between ABMO and combining AO’s is called destabilization energy. ABMO destabilizes
the molecule.
Differences between characteristics of BMO and ABMO

BMOs ABMOs
1. It possesses lower energy than that of 1. It possesses higher energy than that of the
combining atomic orbitals. combining atomic orbitals.
2. It possesses high electron density in the 2. It possesses low electron density in the
region between the two nuclei. region between nuclei.
3. It imparts stability to the molecule. 3. It causes instability to the molecule.
4. Every electron in BMO contributes to 4. Every electron in it contributes to repulsion
attraction between the two atoms. of two combing atoms.
5. BMO is formed only when the lobes of 5. It is formed when the lobes of combing
atomic orbitals possess same sign. atomic orbitals possess opposite sign.

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13. The probability of bonding MO formation (Ψ2) is greater than that of (Ψ*2) ABMO
formation. Probability = square of amplitude Ψ2.

14. AO gives e– probability around nucleus, while MO gives electron probability around group
of nuclei.
15. Shape of MO formed depends on the type of combining atoms. BMO’s are represented by σ,
π, and 𝛿 etc. and ABMOs are represented by σ*, π*, 𝛿* etc.
16. The inner MOs which do not take part in bond formation are called non-bonding MO.
17. MO’s of equal energy are called degenerate MO, are filled as per Hund’s rule.
18. Magnetic properties (Para or dia magnetism) are judged in a molecule, based on the number
of unpaired and paired e–s.
Higher the number of unpaired e–s in a molecular, higher will be its paramagnetic nature. If
there are no unpaired electron in a molecular it will be diamagnetic.
19. Bond order – is the number of bonds between two bonding atoms.
Bond order = 1/2 [number of e–s in bonding MOs – number of e–s in ABMOs]
Bond order may be whole number, or a fraction. It is directly proportional to strength of the
bond (stability) and inversely proportional to bond distance.

Linear Combination of Atomic Orbitals (LCAO)

Linear combination of atomic orbitals (LCAO) gives a qualitative picture of the molecular
orbitals in a molecule.
According to quantum mechanics, exact position and momentum of an electron cannot be
determined accurately (Heisenberg’s uncertainity principle). So, to understand the structure of an
atom or chemical combination, wave mechanics is used. According to wave mechanics, atomic
orbitals can be represented by wave functions ΨA and ΨB.
Consider two atoms A and B which have atomic orbitals, which can be represented by the wave
functions Ψ (A) and Ψ (B).
When these two atoms approach, the electron clouds of these two atoms undergo overlap and
produce molecular orbital Ψ (AB). It can be produced by the linear combination of Ψ A and Ψ B.
Ψ (AB) = N (C1 Ψ (A) + C2 Ψ (B)

where N = Normalising constant which is used to find the probability of finding the electron in
the space is unity
C1 and C2 = constant used to give minimum energy for Ψ (AB).
The probability of finding an electron in a volume of space dv is Ψ2 dv, these force the
probability density for the combination of two atoms is related to wave function squared Ψ2.
Ψ2(AB) = C12 Ψ2(A) + C22 Ψ2(B) + 2C1 C2 Ψ (A) Ψ (B)

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Where C12Ψ2(A) is the probability of finding electron on atom A if is an isolated atom & C22Ψ2(B)
is the probability of finding an electron on atom B if B is an isolated atom.
Then term 2C1C2ΨAΨB is important as the overlap between the two atomic orbitals increases, and
this term 2C1C2ΨAΨB is called overlap integral. This term represents the main difference between
the electron clouds in individual atoms and in the molecule. The larger this term, the stronger is
the bond.

Rules for LCAO

In order to decide, which atomic orbitals may be combined to form molecular orbitals, the
following rules must be considered.
(a) The atomic orbitals must possess roughly the same energy particularly while
considering the overlap of two different types of atoms.
(b) The orbitals must overlap one another as much as possible. They must be close enough
for effective overlap.
(c) In order to produce bonding and anti-bonding LCAO molecular orbitals, the symmetry
of two atomic orbitals must remain uncharged (or) both atomic orbitals charge symmetry
in identical manner when rotated about inter nuclear axis.

Shapes of Molecular Orbitals

Molecular orbital may be of two types s molecular orbital and p-molecular orbital. Σ (sigma)
molecular orbital is formed by the overlap of two atomic orbitals along the inter nuclear axis.
When the two atomic orbitals overlap sideways, then the resulting molecular orbital is called Pi
(π) molecular orbital.

Overlap of 1s with 1s (or) 2s with 2s orbital.

σ (1s) MO orbital is formed by overlap of atomic orbitals along inter nuclear axis. It is formed by
constructive overlapping.

σ* (1s) is formed by destructive overlap of two s-orbitals.

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Overlap of P-s orbitals. It also results in s bonding and σ* antibonding MO.

Axial P-P overlap of atomic orbitals results in s MO and σ* antibonding MO

Side way overlap: when ‘P’ orbitals overlap side ways, it results in p antibonding MO and p*
antibonding MO.
Side to side overlap

π- bonding MO

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Energy level diagram for diatomic MOs - Molecular Orbital of O2, N2, and F2
N2 molecule
N2 molecule has a total of 14 electrons.
Its MO configuration
σ(1s2) σ*(1s2), σ(2s2), σ*(2s2), π(2px2), π(2py2) σ(2pz2)

In N2 molecule these are two non-bonding MO σ (1s) and σ*(1s)

Thus the number of bonding electrons Nb = 2 x 4 = 8
Number of antibonding electrons Na = 2 x 1 = 2
Bond order = ½ (Nb-Na) = ½(8-2) = 3. Hence N2 forms triple bond.
Magnetic property
N2 is diamagnetic since all e–s in bonding and antibonding orbitals are paired.

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O2 Molecule
σ(1s2) σ*(1s2), σ(2s2), σ*(2s2), σ(2pz2), π(2px2), π(2py2), π*(2px1), π*(2py1)
In O2 molecule, σ(2pz2) is at lower level than π(2px), π(2py).
In O2 molecule, these are two non-bonding MO. [σ(1s) and σ*(1s)]. 4-bonding MO. [σ(2s)],
π(2px), π(2py) and σ(2pz) containing 2e–s each. It contains one antibonding MO. [σ*2s]
containing 2e–s and two antibonding MO. π*(2px), and π*(2py) containing one electron each.

Bond order = ½ [Nb – Na] = ½ [8 – 4] = 2

i.e. oxygen molecule contains= a double bond.
Magnetic property: O2 molecule is paramagnetic because, it contains two unpaired e–s in π*(2px)

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and π*(2py) MO.

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F2 Molecule
The fluorine molecule F2 has two more electrons than O2 and consequently has the electron
configuration σ(1s2) σ*(1s2), σ(2s2), σ*(2s2), σ(2p z2), π(2p x2), π(2p 2y), π*(2p 2x), π*(2p 2y). The net
of 8 – 6 = 2. The two bonding electrons correspond to a single electron-pair bond. Its
dissociation energy is 155 kg mol–1 which is comparatively small. The reason being that, the 4
electrons in the π* anti-bonding orbitals exerts greater anti-bonding effect than bonding effect of
(4) four electron in the p bonding orbital.
In contrast to MOT approach, the valence bond picture of F2 treats the 2s orbitals and two of the
2p orbitals on each atom as nonbonding or atomic in nature. These nonbonding orbitals
accommodate six electrons on each atom and a single electron pair is formed by overlap of
remaining p orbitals.

AO = Atomic orbital MO = Molecular orbital

Bond order = ½ [Nb – Na] = ½ [8 – 2] = 1 (F2 contains single bond)
Magnetic property

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F2 is diamagnetic since all e–s in bonding and antibonding orbitals are paired.

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Pi-molecular Orbitals of Butadiene and Benzene

Pi-molecular Orbitals of 1, 3-Butadiene
The structure of 1, 3-Butadiene consists of two conjugated double bonds. The structure has four
sp2 hybridized C atoms. Each atom contributes a p atomic orbital consisting of one electron.

The combinations of pi molecular orbitals of two ethene molecules produces π molecular orbitals
for which we need to make an in-phase and an out-of-phase combination for π and π* of ethene.

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The diagram represents the relative energies of pi molecular orbitals of 1, 3-butadiene which
is a derived compound of ethene. The energy of the p orbital of a C atom is denoted by the
horizontal center line. The orbitals lying below the horizontal line are bonding whereas the
orbitals above the line are anti-bonding.
Each p orbital contributes one electron, resulting in the arrangement of four electrons from four
p-orbitals which combine in four different ways and form four molecular orbitals designated by
ψ 1, ψ 2, ψ 3, and ψ 4.
• ψ1 has bonding interactions in between C1- C2, C2 - C3 and C3 - C4. Therefore, there exist 3
bonding interactions.
• ψ2 has bonding interactions between C1-C2 and C3-C4 and anti-bonding interactions between
C2-C3. Therefore, they have single bonding interaction. It is the highest occupied molecular
orbital (HOMO).
• ψ3 has bonding interactions between C2-C3 but anti-bonding interactions between C1-C2 and
C3-C4. Therefore, they have single anti-bonding interaction. It is the lowest unoccupied
molecular orbital (LUMO).
• ψ4 has anti-bonding interactions between C1-C2, C2-C3 and C3-C4. Therefore, they have 3
anti-bonding interactions.
So we get that out of the four orbitals available, the molecular orbitals ψ1 and ψ2 are bonding
molecular orbitals whereas the molecular orbitals ψ3 and ψ4 are anti bonding molecular orbitals.
The p-orbitals from which they are formed are at higher energy than the two bonding MOs,
whereas the two anti-bonding MOs are higher in energy than the p orbitals from which they are
formed. The energy in molecular orbital increases with the rise in the number of nodes.
Pi-molecular Orbitals of Benzene
Each molecular orbital of benzene consist of a combination of the six p orbitals. Bonding
interaction occurs when the orbitals to line up in a way that each lobe overlapping another p
orbital has same signs. An orbital lining up with an opposite sign creates an anti-bonding
interaction and a node between the orbitals. The figure shows the overlapping of p-orbital.
The three π bonds of benzene are formed by the overlapping of six p orbitals on six adjacent
carbon atoms. The six p orbitals form six molecular orbitals by combining in six different ways.
The six MOs are designated by ψ1, ψ2, ψ3, ψ4, ψ5, ψ6. Of these six MOs ψ1, ψ2, ψ3 are
bonding molecular orbitals whereas ψ4, ψ5, ψ6 are antibonding orbitals. Each molecule orbital
can accommodate two electrons having opposite spins. Therefore, addition of six electrons to the
molecule orbitals beginning from the lowest energy molecule orbital results in the filling of all
three bonding molecular orbital. The three higher energy antibonding orbitals remain empty. Due
to the presence of three filled bonding molecular orbitals in benzene, it possesses a closed
bonding shell which makes Benzene stable.

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Band structure of solids

This is the quantum mechanical treatment of the metallic bond and is similar to molecular orbital
approach of covalent bond. Unlike simple covalent molecules during formation of metallic
crystal, a very large number of atoms in the order of 1023 or more are brought together so that
their AOs undergo linear combination to form exactly same number of MOs. The energies of
these MOs are so closely spaced that they appear to be a continuum known as quasi-continuous
energy band. Hence, the name band theory. The MOs formed are delocalized, i.e., belong to the
crystal as a whole.
Formation of crystal of lithium metal:
Imagine the construction of a crystal lithium metal by adding Li-atoms like Li2, Li3, Li4,
Li5,.............. LiN.
The electronic configuration of each Li atom is 1S2, 2S1, 2P0. The 2s-atomic orbitals overlap in
Li2 to form two molecular orbitals.
In Li3 the 3s – atomic orbitals overlap to form 3 molecular orbitals.
Similarly in LiN the Ns – atomic orbitals overlap to form a band f N closely spaced MO as shown
in figure.
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Figure: Band theory of Li solid

Formation of various bands in solids
Formation of various bands can be explained with example of lithium.
1s band:
This is called non conduction band. It is formed by the combination of completely filled
orbitals.

1s band, 2s band and 2p bands in Li crystal

2s band:
This is called valence band as it is half filled. The upper half of this is empty, while the lower
half is completely filled. Since energy difference between these two halves is very small, the
electrons can move from lower half to upper half.

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2p band:
This is called vacant band (or) overlapping band. Since 2s and 2p energy levels are close to
each other, these two orbitals can overlap, so that the electrons from 2s orbitals can move to 2p
orbitals. Thus it is also called conduction band.

Thus, a band that is ether partially filled (or) completely vacant is called conduction band.
When an electric field is applied across a lithium crystal, the electrons start moving in one
direction and so lithium is a good conductor of electricity.
Classification of materials (solids) based on band gap
The materials are classified into the following 3 categories depending the energy gap between
the valence and conduction bands.
1. Insulators:
In insulators (non-metals) there is a large band gap between the fileld valence bands and empty
conduction bands. Therefore electrons cannot be promoted from the V. B. to C.B. where they can
move freely.

Energy band in a) Insulators b) Conductors c) Semi conductors

2. Conductors:
In conductors (metals) the valence bands and conductions bands overlap, so there is no band gap.
Therefore electrons can freely move.
3. Semiconductors:
In semi conductors there is a small band between the filled V.B. and empty C.B. therefore
electrons can be promoted from V.B. to C.B. with rise in temperature (or) by adding dopants.

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Effects of doping on conductance:
The conductivity of semiconductors is very low at room temperature. Therefore, their
conductivity is increased by adding an appropriate amount of suitable impurity. This process is
known as doping.
Doping:
The process by which impurity is introduced in semiconductors to enhance their conductivity is
called doping. It can be done with an impurity which is electrons rich (or) electrons deficient.
Such impurities introduce electronic defects in them.
Types of doping
On the basis of impurities, added for doping, semiconductors are of two types.
1. n-type semiconductors:
Silicon and germanium belong to group 14 and have four valence electrons each. In their crystal,
each atom forms four covalent bonds with its neighbors.

Figure: Perfect germanium crystal

When silicon (or) germanium crystal is doped with a group 15 element like P or As which
contains five valence electrons, they occupy some of the lattice sites in silicone (or) germanium
crystals (figure). Four out of five electrons are used in the formation of four covalent bonds with
the four neighboring silicon atoms. The fifth electron is not used in bonding thus, it is considered
as extra hence doped germanium with electron rich impurity is called n-type semiconductor.

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2. p-type semi conductor:
When silicon (or) germanium is doped with a group 13 element like B (or) Al, which is contains
only 3 valence electrons. In place of fourth electron, a hole is created. This is called electron
hole (or) electron vacancy. (Figure)
An electron from a neighboring atom can come and fill the electron hole, but in doing so it
would leave an electron hole at its original position.
In this way, this hole move through the crystal like positive charge giving rise to electrical
conductivity.

When an electric field is applied, the electrons move towards positively charged plate and
electron holes move towards negatively charged plate. Hence silicon and germanium doped with
electron deficit impurities are called p-type semiconductors.

Coordination Complexes
A coordination complex consists of a central atom or ion which is usually metallic and is called
coordination center and a surrounding array of bound molecules or ions that are in turn, known
as ligands or complexing agents. Ligands are Lewis bases containing at least one pair of
electrons to donate to a metal atom or ion.
Nature of complex
Depending on the charge, a complex may be cationic, anionic or neutral.
[Fe (H2O)6]2+ cationic complex
[Fe (CN)6]4- anionic complex
[Ni (CO)4] neutral complex
Coordination Number (Ligancy)
Number of atoms, ions or molecules holds with a central atom or ion as its nearest neighbors in a
complex or coordination compound or in a crystal is known as coordination number. In the
above complexes, it is 6, 6 and 4 respectively.

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Classification of ligands
Ligands are classified in various ways-
1. On the basis of charge, ligand may be neutral anionic and cationic
Anionic- halide ion, CN –
Cationic- NO+, [N2H5] +
Neutral – NH3, H2O
2. On the basis of ligand field strength
I-, Br-, Cl-, F-, H2O - weak field ligands
CN-, CO, o-dipyridyl, 1,10 phenanthroline, ethylene diamine, ammonia, pyridine - strong field
ligands

3. On the basis of number of coordinating sites

Mono dentate- NH3, H2O
Ambidentate- monodentate ligands with different sites of bonding -SCN- -NCS
Bidentate - o-dipyridyl, 1,10 phenanthroline, ethylene diamine
Multi dentate-
Terpyridine - tridentate
Ethylene diamine tetra acetic acid -hexa dentate
Bidentate and multidentate ligands are also known as chelating ligands and form more stable
complexes than monodentate ligands
4. On the basis of nature of bonding-
π donor – C2H4, first donation occurs from π electrons of ethylene to vacant orbital of metal ion
and second back donation from metal filled d orbitals to vacant antibonding orbitals of ethylene.
σ donor- NH3, H2O, lone pair of electrons are donated to vacant orbital of the metal ion.
5. Hard and Soft ligands
Hard ligands- F, O, N donors- H2O, NH3, OH-, F-, Cl-, (CH3COO)-, (CO3)2-. These are
highly electronegative, have low polarizability and associated with vacant orbitals of high energy
which are inaccessible. Hard bases have highest occupied molecular orbitals (HOMO) of low
energy.
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Soft ligands- I, S, P donors - I-, R3P, R2S, CO, C2H4, C6H6, H-, SCN-. These are less
electronegative, have high polarizability and have easily accessible vacant low lying orbitals.
Soft bases have HOMO of higher energy than hard bases.
The affinity of soft acids and bases is mainly covalent in nature while that of hard acid and hard
bases for each other is mainly ionic in nature.

Crystal Field Theory (CFT):

Crystal field theory is one of the most important theories for explaining nature of bonding in
coordination compounds. This is expounded by H. Bethe and Vleck to explain the color and
magnetic properties of crystalline solids hence called crystal field theory.
It deals with electrostatic interactions between metal ion and the ligands forming complexes with
varying geometries like octahedral, tetrahedral, square planar etc.
The salient features of Crystal field theory:
1. According to this theory, the ligands are treated as negative point charges, and metal ions are
treated positive point charges.
2. The donor electrons of the incoming ligands due to their negative charges attract the positively
charged metal ion. Besides this, there is repulsive interaction between d electrons present on the
metal ion and the ligands.
3. According to CFT the interactions between metal ion and ligand are treated as purely
electrostatic, no covalent interactions are considered. This again is not true; some of the
observations cannot be explained without involving covalent interactions.
4. The ligand can donate an electron pair to the metal ion; produce a field approximately
equivalent to that of a set of negative point charges. Thus it is the interaction of the d-orbitals of
a transition metal with ligands surrounding the metal that produces crystal field effects.
Crystal Field Splitting of‘d’ Orbitals
5. Of the five d orbitals, three namely dxy, dyz, dxz have maximum electron density directed
between the X, Y, Z axes. The set of these three orbitals called as t2g or dε orbitals. The dz2
orbitals have maximum electron density along Z axis, while dx2-y2 orbital has maximum electro
density. These two orbitals together called eg or dγ orbitals.
6. In every free metal ion the five d orbitals have same energy, i.e. they are de generate. However
on the approach of ligands, d-electrons will be repelled by the lone pair of ligands which lead to
increase in energy level d orbitals.
7. Now suppose all the approaching ligands are at equal distance from each of the d-orbitals
(spherically), then in such case energy of each d-orbital will increase by same amount and thus
the five d-orbitals will still remain degenerate, although they now have higher energy than
before.
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8. However above mentioned situation is imaginary because the d-orbitals are not spherically
symmetrical and differ in their orientation.

Figure: Shapes of d-orbitals

• dxy: lobes lie in-between the x and the y axes.
• dxz: lobes lie in-between the x and the z axes.
• dyz: lobes lie in-between the y and the z axes.
• dx2-y2: lobes lie on the x and y axes.
• dz2: there are two lobes on the z axes and there is a donut shape ring that lies on the xy plane
around the other two lobes.
9. Actually the energy of orbitals lying in the directions of the ligand is raised to a larger extent
as they will be more repelled by the ligands (due to larger interaction) than the orbitals lying in
between the ligands.
10. Thus under the influence of the ligands, the five degenerate d-orbitals of the metal ion will
split in to two groups of orbitals of different energy, this effect is known as crystal field splitting
or energy level splitting. This concept forms the basis of the crystal field theory.
Usually the complexes formed by transition metal ions are octahedral, tetrahedral or square
planar, the field provided by the ligands is not at all spherically symmetrical therefore d-orbitals
are unequally affected by the ligands.

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Crystal field splitting of‘d’ orbitals in Octahedral Complexes
In octahedral complexes, the coordination number is 6. In these complexes the ligand approach is
along the axes. As a result, the d-orbitals where electron density is oriented along the axes, dx2-
y2 and dz2 are repelled much more by the ligands while the orbitals dxy, dxz, dyz having electron
density oriented in between the axes are repelled lesser by the ligands. Thus two sets of orbitals
eg and t2g, doubly and triply degenerate respectively, are formed.
Energy of t2g set of orbitals < Energy of eg set of orbitals.

Figure: The octahedral complex showing the placement of six ligands along the three axes
(L-represent ligand)

Figure: Crystal Field splitting of energy levels in an octahedral field of ligands

State I: It represent the degeneracy of all the five d-orbitals of the free metal ion in the absence of
ligands.
Step II: It represents hypothetical degeneracy of all the five d-orbitals at a higher energy level when all
the ligands approaching the central ion are at an equal distance from eac of the d-orbital.

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Step III: It represent splitting of d-orbitals in the octahedral crystal field.

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Actually, the approach of the ligands is considered as a two step process. In the first step, it is
assumed that the ligand approach the metal ion spherically, i.e. at and equal distance from each
of the d-orbitals. At this stage all the d-orbitals are raised in energy by the same amount, that is
the five d-orbitals remain degenerate (state II figure) in the second step the spherical field
changes to the octahydral filed leading to splitting of orbitals (state III figure).
The energy difference between t2g and eg orbitals is commonly known as crystal field splitting
and it is denoted by the symbol Δ or Δo (the subscript ‘o’ indicating octahedral complex),
sometimes Δo is replaced by 10 Dg.
Crystal Field Stabilization Energy (CFSE) and Pairing (P) Energy
The CFSE is defined as net gain in energy achieved by preferential filling of electrons in lower
lying d orbitals over the energy of complete random occupancy of electrons in all five d orbitals.
It is 2 to10% of actual bond energy. The energy required to pair the electrons in the same orbital
is known as Mean Pairing energy and it is constant for the same metal ion.
Noticeable features
1. When magnitude of Δ0 is higher than P, electrons tend to pair in the lower lying orbital thus
spin paired or low spin complexes are formed. On the other hand, if Δ0 is less than P, high spin
or spin free complexes are formed. If Δ0 is approximately equal to P, single temperature changes
may affect spin changes. Sum of CFSE and P gives Total Stabilization Energy (TSE).
2. For d4 and d7 low spin systems only one P is added in CFSE to get TSE because only one
electron is to be paired in the same orbital, rest are paired in natural configuration while for d5
and d6 low spin systems twice of pairing energy is required to be added to get TSE.
3. The 3d metals form high and low spin complexes, on the other hand 4d and 5d metals having
very high CFSE form low spin complexes.

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Problems
1. Calculate CFSE for the complex [Cr (H2O)6]2+
Chromium in ground state is [Ar]3d54s1, in +2 state, will be a d4 system with t 2g3 eg1
configuration of electrons because H2O is a weak field ligand. CFSE will be therefore
-0.4 Δ0X 3+ 0.6 Δ0 = -0.6 Δ0
2. Calculate TSE for [Fe(CN)6]4-
6 0
Iron in ground state is [Ar]3d64s2, in +2 state it will be a d6 system with t 2g eg configuration of
electrons because CN- is a strong field ligand. Therefore, TSE will be
-0.4 Δ0X 6+ 2P = - 2.4 Δ0+ 2P
Since it is t2g4eg2 by the configuration itself, only 2 electrons have to be paired.

Crystal field splitting ‘d’ orbitals in Tetrahedral Complexes

In tetrahedral complexes, the coordination number is 4. In tetrahedral geometry, the ligand
approach is in between the axes (Figure). Thus it clear that the ligands interact (repulsion) more
with t2g (dxy, dxz, dyz) orbitals located close to the direction of the approaching ligand than the
eg (d x2-y2 and dz 2) orbitals lying between the ligands. Thus three t2g orbitals have higher energy
than eg (figure).
Energy of t2g set of orbitals > Energy of eg set of orbitals.

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Figure: Splitting of d orbitals in a tetrahedral field of ligands

Noticeable features
1. The t2g orbitals are closer than eg orbitals and therefore get repelled more than eg orbitals.
2. It can simply be stated that the d orbital splitting diagram in tetrahedral complexes is just
inverse of octahedral complexes.
3. Here the crystal field splitting energy is denoted by Δt.
4. In tetrahedral field, since d-orbitals are not interacting directly with ligand field, splitting of d-
orbitals is less than that in the octahedral complexes. The crystal Field Splitting parameter Δt is
4/9 of Δ0.
5. Tetrahedral complexes are high spin (Para magnetic) complexes as the energy gap between
two sets of orbitals is roughly half of octahedral complexes.
6. In tetrahedral complexes, an electron going into eg orbital is stabilized by 0.6Δt by that going
into t2g orbital is destabilized by 0.4Δt. Thus here, the first two d electrons will go to two eg
orbitals as per as the third and onwards electrons is concerned, their entry to eg or t2g depends on
the nature of the ligand field (strong and weak) as explained in case of octahedral complexes.

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7. As evident from the above data CFSE in tetrahedral complexes is much smaller than
octahedral complexes, these should not be energetically favored. Since tetrahedral complexes are
very much known to exist, their formation can be possible under the conditions when loss in
CFSE is meager.
A. Metal is in low oxidation state like in Ni(CO)4, Ni is in zero oxidation state.
B. Ligand is weak field, for example Cl- in [MnCl4]2-.
C. Metal ion with d0, d5 (weak field) or d10 configurations [ MnO4]-, [ MnCl4]2- and [ZnCl4]2-
respectively where CFSE is zero in octahedral field.
D. In tetrahedral complexes the bond angle being 109028’ is larger than that in octahedral
complexes, 900. Therefore, bulky ligands may form tetrahedral complexes as have lesser steric
hindrance.
E. The configurations of metal ions where symmetrical filling of electrons in degenerate orbitals
is present may form tetrahedral complexes. For example,
e0t20, e2t20, e2t23, e4t 23, e4t 26.

Crystal field splitting ‘d’ orbitals in Square Planar Complexes

The crystal field theory of square planar complexes derived from the octahedral field by
removing the two trans ligands located along the Z axis, that mean here the four ligands are
placed along the X and Y axes. Withdrawing of two trans ligands situated along the Z axis of the
complex leads to following two situations.
i. If the ligands lying on the z-axis are moved away (not removed completely), the remaining
ligands in the XY plane tend to approach the central metal ion more closely. Due to this the
d-orbital in the XY plane are repelled to a greater extent from the ligands than in case of
octahedral structure. This will naturally increase the energy of the d-orbitals in XY plane,

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i.e. dx2-y2 and dxy orbitals.

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Simultaneously, the d-orbitals lying along the Z axis as well as in the XY and YZ planes
experience relatively smaller repulsion from the ligands with result energy of dZ2 orbital as
well as dzx and dyz orbitals falls appreciably.

ii. If the trans ligands lying along the Z axis are removed completely, a square planar complex
is formed. As the trans ligands lying along Z axis are removed completely, a square planar
compex is formed. This will lead to a further rise in the energies of dx2-y2 and dxy orbitals
and further fall in energies of dz2, dzx, dyz orbitals (figure). The crystal field splitting in the
case of square planar compex is indicated by Δsp.

Octahedral Square planar

Figure: Splitting of d orbitals in a square planar field of ligands

Factors affecting the magnitude of CF splitting:

The following are some of the factors which affect the magnitude of crystal field splitting (D).
(i) Geometry of the complex: The crystal field splitting for octahedral complex is nearly
doubles that of tetrahedral complex.
Dt = 4/9 DO. This is due to the fact that number of ligands in tetrahedral complex is 4 and that of
octahedral complex is 6.
In octahedral complex, the ligands approach along the axis influencing the axial d-orbitals
directly, where as in tetrahedral complexes those‘d’ orbitals are not directly under the influence

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of the ligand.

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(ii) Nature of ligands: The ligands arranged in order of increasing ligand field strength
constitute spectrochemical series.
I- < Br- < S2- < SCN - < Cl- < F- < OH- < C2O4 2- < H2O < NCS- < EDTA-4 < pyridine < NH3҃ <
ethylene diamine < o-dipyridyl < 1,10-phenanthroline < NO2- < CN- < CO
The Ligand with higher field, like CO or CN- would produce more splitting or larger energy gap
while I- being weakest would produce minimum energy gap.
Variation of ligands changes the value of DO.
Example: DO for [CrCl6]3-, [Cr (H2O)6]3+ [Cr(NH3)6]3+ and [Cr (CN)6]3+ is 163, 213, 259 and
314 J/mol respectively. In all these complexes metal ion is Cr +3.
(iii) Charge on the central metal ion: According to CFT the attraction between metal ion and
ligand is purely electrostatic in nature, metal with higher charge produces more splitting than an
ion with lower charge.
Example: [Cr (H2O)6]+2 is 165.9 kJ/mole and for [Cr (H2O)6]+3 is 213 kJ/mole.
(iv) Position of metal in transition series: It has been observed that the value of D0 increases
on descending down the group. The crystal field splitting in the same group is
5d > 4d > 3d
Example: D for [Co (NH3)6]3+ = 296 kJ/mol
[Rh (NH3)6]3+ = 406 kJ/mol
[Ir (NH3)6]3+ = 490 kJ/mol
In these complexes CO+3 is in 3d transition series
Rh is in 4 d transition series
Ir is in 5 d transition series
Descending in a group, for example 3d to 4d series, ΔO increases by approximately 30%.

Applications of crystal field theory:

1. Colour of transition metal complexes: Most of the transition metal complexes are coloured.
The colour of these complexes is attributed to d-d transitions between t2g and eg orbitals. The
difference in energy between these two orbitals is so small that the absorption of even small
amount of light brings about excitation from lower to higher energy d level.
The colour of the complex is complementary to the colour absorbed.
Example: In the complex [Ti(H2O)6]3+, Ti+3 has one d election in the t2g orbital. On absorption
of radiation, this‘d’ electron is promoted to eg orbital (t2g1eg0 → t2g0eg1). It absorbs green and
yellow light and transmits the complementary colour red and blue; hence, it appears violet in

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colour. Similarly CuSO4.5H2O is blue but anhydrous copper sulfate is colour less or white in
colour.
2. Magnetic properties of complexes: Spin only formula μs = √𝑛(𝑛 + 2)+ B.M. is used to find
the spin only magnetic moment of high spin and low spin octahedral complexes.
Magnetic moment values helps in predicting the valence state of the metal ion in octahedral
complex and nature of bonding in the complex.

Limitations of CFT
1. CFT is mainly concerned with metal orbitals and ignores ligand orbitals. In metal orbitals also
it considers only metal d orbitals.
It does not take into account of orbitals like s, px, py, pz orbitals. It does not consider p orbitals of
the ligand. It does not consider p-bonding in complexes.
2. CFT is unable to explain the relative strengths of ligands. It does not explain why H2O is a
strong field ligand than –OH.
3. CFT considers the metal and ligand interaction is purely ionic. It does not take into account
the covalent character of metal ligand bonds.
4. CFT is unable to explain p-bonding in complexes despite its frequent occurrence.

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