Unit 1.pdf

Molecular Orbitals & Bonding Unit-1

1. MOLECULAR STRUCTURE
AND THEORIES OF BONDING
UNIT - 1

2. OBJECTIVE
To impart the basic knowledge of atomic, molecular and•
electronic modifications which makes the student to
understand the technology based on them.
OUTCOME
The knowledge of atomic , molecular and electronic•
changes, band theory related to conductivity can be
acquired.

3. CONTENT
Atomic and Molecular Orbitals
Linear Combination of Atomic Orbitals (LCAO)
Molecular orbitals of Diatomic Molecules
Molecular Orbital energy level diagrams of N2, O2 and F2 
Molecules

4. π molecular orbitals of butadiene and benzene
Crystal Field Theory (CFT): Salient features
Crystal Field Splitting of transition metal ion d-
orbitals in Tetrahedral, Octahedral and Square
planar geometries
Band structure of solids and effect of doping on
conductance

5. TERMS AND DEFINITIONS
Orbitals - They represent the probability of finding an
electron in any one place. They correspond to different
energies. So an electron in an orbital has definite energy.
Orbitals are best described with quantum mechanics.
Atomic Orbitals – the region in space just outside the
nucleus of the atom where the probability of finding the
electrons is at the highest (95%).
Molecular Orbitals – formed as a result from the overlap of
two atomic orbitals, wherein a pair of electrons occupying.

6. Electron Density – a measure of the probability of finding an
electron in an orbital.
Wave Function – mathematical description of the volume of
space occupied by an electron having a certain amount of
energy.
A node in an orbital – is the place where a crest and a trough
meet. Probability of finding an electron in a node region is zero
Quantum Mechanics is based on the wave properties of matter.
Quantization of energy is the consequence of these properties

7. ATOMIC ORBITALS
The energy levels about the nucleus contain group of these
atomic orbitals.
Each orbital ( designated as s, p, d, and f) has a unique energy
associated with it, can contain a maximum of two electrons and
varies in shape and spatial orientation.
We are mainly concerned with the s and p orbitals since most of
the elements found in organic molecules have their electrons in
the 1s, 2s, and 2porbitals.
For the shapes of f orbitals, are quite complicated.

8. Higher d and f orbitals are utilized by elements further down
in the periodic table . These are further discussed by
inorganic chemists.
The s orbital is spherical, like a fuzzy hollow ball with its 
center at the nucleus of the atom.
There are three p orbitals of equal energy, designated px, py,
and pz.
Each p orbital is dumbbell shaped. Each consists of two
lobes with atomic nucleus lying between them and each has
a nodal plane at the nucleus, where the probability of the
electron’s location is zero.

9. Shapes of the s orbital
1s
It contains no nodes
because it is closest
to the nucleus. It has
the lowest energy of
all the atomic
orbitals.

10. 2s
The 2s atomic orbital has
a small region of electron
density surrounding the
nucleus, but most of the
electron density is farther
from the nucleus, beyond
a node.

11. 3s
For any atom there is only one 3s
orbital. The intensity of colouration
indicates the positions where the
electron is likely to be found on any
plane cutting through the nucleus.
There are two spherical nodes in the
3s orbital.

12. Shapes of the p orbitals
px
py
pz

13. The three p orbitals in the second shell of electrons are
totally different from the 1s and 2s orbitals. Each p orbital
consists of a “dumb bell” or “tear drop” shape on either
side of the nodal plane that runs through the centre of the
nucleus.
Their orientation is 90 ˚ from each other in the three spatial
direction and have identical energies and shapes.
Chemists call them as degenerate orbitals. 
Electrons in the three 2p orbitals are farther from the
nucleus than those in the 2s orbital and they are at a higher
energy level.

14. Shapes of d orbitals

15. d- orbitals are wave functions with l=2.
They have an even more complex angular distribution
than the p-orbitals.
d – orbitals have “clover-leaf” distribution i.e., double
dumb bell shape in a plane.
These have two angular nodes where the probability of
finding an electron is zero.
The three d – orbitals dxy, dyz and dxz will have lobes in
between the axes and the other two d - orbitals dx
2
-y
2
and dz
2
will have lobes on the axes.

16. MOLECULAR ORBITAL THEORY
INTRODUCTION
Molecular Orbital Theory can
also be written as “MOT”.
This Theory was proposed by
“Hund, Mulliken, John
Lennard-Jones”.
This theory is also known as
“Hund - Mulliken” Theory.

17. MOT is a Method for
determining molecular
structures.
Electrons are not assigned to
individual bond between atoms
.
They are treated as moving
under the influence of nuclei of
the whole molecule.
APPLICATIONS OF MOT

18. MOT deals with “Linear
Combination of Atomic
Orbital's”.
A linear combination of
atomic orbital's or LCAO is a
quantum superposition of
atomic orbital's and a technique
for calculating molecular
orbital's in quantum chemistry.
It represents molecular orbital
resulting from bonds between
atom.
LINEAR COMBINATION OF ATOMIC ORBITALS
1. Valence bond theory
2. Molecular Orbital Theory

19. Molecular Orbitals are of two types.
Bonding Molecular Orbitals.a)
b)Anti-Bonding Molecular Orbitals
TYPES OF MOLECULAR ORBITALS

20. BONDING MOLECULAR ORBITALS
It is with lower energy and contains electron pair.
Waves with the same phase will interfere  
constructively  and increase their amplitude.
Bonding Orbitals concentrates electron density in
the region between the two nuclei of the pair of atoms
.
Bonding molecular orbitals are denoted by σ,
(σ1s,σ2s, 2px,2py,……etc.)

21. ANTI-BONDING MOLECULAR ORBITALS
It is with higher energies and may be vacant.
Waves with opposite phases  interfere
destructively to decrease  their  amplitude.
Anti-Bonding molecular orbitals
concentrates electron density behind each
nucleus i.e., the node develops between the
nuclei.
Anti-Bonding molecular orbitals 
are denoted as σ*, * etc.

22. Molecular orbital diagram of H2

23. Molecular orbitals formed by p - orbitals

24. Relation between Electronic Configuration and Molecular behaviour
1. Stability of Molecules:
Let Nb = No. of electrons present in the bonding orbitals
Na = No. of electrons present in the anti-bonding orbitals
If Nb > Na then molecule is stable because of the more net force of attraction.
If Nb < Na then molecule is unstable because of the more net repulsive forces.
If Nb = Na then also molecule is unstable because the influence of electrons in
anti-bonding orbitals is more than the electrons in the bonding orbitals.
2. Bond Order:
It is defined as the half of the difference between the number of the electrons
present in bonding and anti-bonding orbitals.
Bond order = [ Nb – Na]
2
If Nb > Na then bond order is positive and the molecule is said to be stable.
If Nb < Na then bond order is negative and the molecule is said to be unstable.
Stability is directly proportional to the bond order.
Bond length decreases with increase in bond order
Bond energy is directly proportional to bond order.

25. 3. Magnetic Nature :
If all the electrons in the molecular orbital are paired then it is
said to be Diamagnetic in nature. (Repelled by magnetic field).
If all the electrons in the molecular orbital are unpaired or
single then it is said to be Paramagnetic in nature ( attracted by
magnetic field).

26. Molecular Orbital energy level diagram of Nitrogen
A.O of N
M.O of N2
A.O of N

27. Atomic Number of Nitrogen = 71.
Electronic Configuration of Nitrogen atom = 1s
2
2s
2
2p
3
2.
Total electrons in Nitrogen molecule = 143.
Molecular Configuration = 4.
σ1s
2
< σ*1s
2
< σ2s
2
< σ*2s
2
< π2px
2
= π2py
2
< σ2pz
2
5. Bond Order = No.of bonding electrons – No.of anti-bonding electrons
2
= 6 – 0 = 3
2
Bond Order of Nitrogen molecule is 3 i.e, there will be a triple bond
between two nitrogen atoms to form one nitrogen molecule.
6. Magnetic nature : Nitrogen is a Diamagnetic molecule as the
highest electronic configuration has a paired up electrons.
Important points of Nitrogen

28. MOLECULAR ORBITAL ENERGY LEVEL DIAGRAM OF OXYGEN
A.O of O
M.O of O2
A.O of O

29. Atomic Number of Oxygen = 81.
Electronic Configuration of Oxygen atom = 1s
2
2s
2
2p
4
2.
Total electrons in Oxygen molecule = 163.
Molecular Configuration = 4.
σ1s
2
< σ*1s
2
< σ2s
2
< σ*2s
2
< π2px
2
= π2py
2
< σ2pz
2
< π*2px
1
= π*2py
1
5. Bond Order = No.of bonding electrons – No.of anti-bonding electrons
2
= 6 – 2 = 2
2
Bond Order of Oxygen molecule is 2 i.e, there will be a double bond
between two oxygen atoms to form one oxygen molecule.
6. Magnetic nature : Oxygen is a Paramagnetic molecule as the highest
electronic configuration has a unpaired electrons.
Important points of Oxygen

30. MOLECULAR ORBITAL ENERGY LEVEL DIAGRAM OF FLUORINE

31. Important points of Fluorine
Atomic Number of Fluorine = 91.
Electronic Configuration of Fluorine atom = 1s
2
2s
2
2p
5
2.
Total electrons in Oxygen molecule = 183.
Molecular Configuration = 4.
σ1s
2
< σ*1s
2
< σ2s
2
< σ*2s
2
< π2px
2
= π2py
2
< σ2pz
2
< π*2px
1
= π*2py
1
5. Bond Order = No.of bonding electrons – No.of anti-bonding electrons
2
= 6 – 4 = 1
2
Bond Order of Fluorine molecule is 1 i.e, there will be a single bond
between two fluorine atoms to form one fluorine molecule.
6. Magnetic nature : Fluorine is a Diamagnetic molecule as the highest
electronic configuration has paired up electrons.

32. Π MOLECULAR ORBITAL OF BUTADIENE
Butadiene contains two double bonds and they are conjugated.
Every carbon atom undergoes SP2 hybridisation and forms strong 
σ – bonding with hydrogens and adjacent carbon atom.
The unhybridized fourth Pz orbital containing one electron of each
carbon atom undergo molecular bonding by overlapping, forming
molecular orbital above and below the carbon atom.
An alternative way to build the π molecular orbitals is by
combining the π molecular orbitals of ethane.

33. Π Molecular orbitals of Ethene
ψ1ψ2
Ψ1 – ψ2
Ψ1 + ψ2

34. The in-phase and out-phase combinations for both the π and π* of Ethene will give
molecular orbitals of Butadiene.
Combinations are:
Π + Π + ψ11.
Π – Π - ψ22.
Π* + Π* + ψ33.
4. Π* - Π* - ψ4



ψ


ψ


ψ
The number of nodes increases as the energy level increases. By arranging in the
increasing order of number of nodes, we get Molecular orbitals of 1, 3- butadiene

35. ψ4
ψ3
ψ2
ψ1

36. As there are 4π electrons in 1,3 – butadiene, these are all paired in the two
stabilised π bonding molecular orbitals with wave functions ψ1 and ψ2.
The Highest Occupied Molecular Orbital (HOMO) is ψ2 in the 1,3 –
butadiene.
In contrast, the π* anti-bonding orbitals contain no electrons.
So, the Lowest Unoccupied Molecular Orbital (LUMO) will be ψ3 in 1,3-
butadiene.
The wave equation for butadiene may therefore be written as 
ψ = C1 ψ1 + C2 ψ2 + C3 ψ3 + C4 ψ4
Where ψ1 to ψ4 are wave functions of four Pz orbitals and C1 to C4 are
their respective coefficients of each molecular orbital.

37. Π MOLECULAR ORBITAL OF BENZENE
Molecular Formula Benzene is C6H6 and it is a
planar cyclic compound.
It has a combination of six Pz orbitals and all the
six Pz orbitals are atomic orbitals containing a
valence electrons.
We can take the help of Propene Molecular
Orbitals to explain the molecular orbitals of
benzene.

38. Molecular Orbitals of Propene
Molecular structure of Propene
Bonding Molecular
Orbital
Non-Bonding
Molecular Orbital
Anti-Bonding Molecular
Orbital

39. Different combinations of Propene to get Molecular Orbitals of Benzene are:
Bonding + Bonding :- No node1.
Bonding – Bonding :- 2 nodes, 1 nodal plane2.
Non-bonding + Non-bonding:- 2nodes, 1 nodal plane3.
Non-Bonding –Non-bonding :- 4 nodes, 2 nodal planes4.
Anti-bonding + Anti-bonding:- 4 nodes, 2 nodal planes5.
Anti-bonding –Anti-bonding:- 6 nodes, 3 nodal planes6.
Now, by arranging these combinations according to increasing order of number
of nodes on the energy axis, we get Molecular orbital diagram of Benzene.

40. ψ2 ψ3
ψ4 ψ5
ψ6
Bonding Molecular Orbital
Anti-Bonding Molecular
Orbital
Non-Bonding
Molecular Orbital
ψ1
ψ3ψ2
Ψ4* Ψ5*
Ψ6*

41. CRYSTAL FIELD THEORY (CFT)
Crystal Field Theory (CFT) was proposed by Bethe and Van
Vleck in 1930 to explain the colour, magnetic properties and
some other properties of crystalline substances.
Even though this theory was known even at the time when
the valence bond theory was proposed, it took 20 years for
chemists to identify this theory.
So, In 1951, since different theoretical chemists used crystal
field theory to explain the spectra of the complexes formed
by the transition elements, the development and application
of the theory to complex compounds increased extensively.

42. Salient Features of Crystal Field Theory
As per this theory the bond between the central metal atom and the ligand in the complex will have
ionic character. This will be present as ion-ion attractions between the positive metal ion and the
negative ligand ions and as ion –dipole attraction between neutral ligand and the positive metal ion
.
Ligands behave as point charges.
This theory is based on the basis of the d- orbitals of the metal and the electrons present in it. This
means that the effect of ligands only on the d- orbitals of the metal is taken into consideration . The
properties of the metal therefore depend on the distribution of electrons in the d- orbitals
influenced by the ligands.
The d – orbitals of free metal ion are degenerate. They all possess same energy. The d- orbitals are
split as per energy by the influence of ligand field effect and they lose their degeneracy. This is
known as Crystal Field Splitting.
The Crystal Field Splitting d-orbitals is the main basis of the crystal field theory.

43. CRYSTAL FIELD STABILISATION ENERGY (CFSE)
Under the influence of crystal field, the d-orbitals of the
metal get split. Therefore the electrons enter selectively in
d-orbitals of lower energy and the complex attains stability.
The stabilisation energy thus attained by the complex is
called crystal field stabilisation energy CFSE.
d- orbitals splits into two different levels i.e., t2g (dxy, dyz
and dxz) and eg (dx
2
-y
2
and dz
2
) orbitals on approach of
ligands.

44. Crystal field splitting of Transition Metal ion d-orbitals in Tetrahedral Complexes
In tetrahedral complex, four ligands are attached to the central metal ion.
In this geometry, ligands approach the central metal ion in between the axes
.
Therefore the orbitals dxy, dyz and dxz experience more repulsion and attain
higher energy (0.4dq) while dx
2
-y
2
and dz
2
orbitals experience lower energy
(0.6dq).
The energy difference between eg and t2g sets is denoted by ∆td, where td
indicates tetrahedral arrangement of ligands around the transition metal ion.
∆td is called CFSE. 

45. Structure and splitting of d-orbitals in Tetrahedral Geometry
Tetrahedral splitting ∆td is found experimentally to be
4/9 of the Octahedral ∆o
∆td = 4/9 ∆o

46. Crystal field splitting of Transition Metal ion d-orbitals in
Octahedral Complexes
In the Octahedron geometry, central metal ion is at the centre
and six ligands occupy six corners of the octahedron.
Ligand approaches the metal ion along the axis.
The reason for the splitting of d-orbitals is due to the
electrostatic interactions between electrons of the ligand and
the lobes of d- orbitals.
As ligand approach along the axes, the d- orbitals i.e., dx
2
-y
2

and dz
2
will have interactions with the ligand and repel.

47. Thereby, the energy of these eg orbitals increases by 0.6dq
and the energy of t2g orbitals will decrease by 0.4dq
because of the absence of interactions in between the axes.
The distance between the eg and t2g orbitals is given by ∆o
i.e., Crystal Field Stabilisation Energy of Octahedral
Complex

48. t2g orbitals
eg orbitals
∆o
Structure and splitting of d- orbitals in Octahedral
structure.

49. Crystal field splitting of Transition Metal ion d-orbitals in
Square Planar Complexes
By removing two vertically oriented ligands from the
Octahedral complex, we get the Square Planar Complexes.
By removing away the two ligands present on z-axis, the dz
2

orbitals oriented along z-axis is completely free from the
repulsion by the ligand orbitals.
In the similar way, dxz and dyz orbitals having ‘z’ axis
orientation reduce their repulsion by the ligands to some
extent because these orbitals are present in between the axes
xz and yz.

50. Therefore the decrease in the energy of these orbitals is much
less than the decrease in dz
2
orbitals.
The energy of dx
2
-y
2
oriented on x,y axes is very high since
the orbitals are under high repulsion by the orbitals of the
ligands present on the x, y axes.
The crystal field stabilisation energy of Square planar
complexes is given by ∆sp.
The crystal field splitting energy (∆sp) is more than the ∆o.
∆sp = 1.3 ∆o

51. ∆sp
Structure and splitting of d- orbitals in Octahedral
structure.

52. Octahedral
complexes
splitting
Square Planar
complexes
splitting
Splitting of Square Planar complexes geometry from
Octahedral complex geometry

53. BAND STRUCTURE OF SOLIDS
The Molecular orbital is commonly known as the Band Model.
Let us consider the idealised one dimensional lattice of Lithium (Li-Li-
Li……Li-Li-Li)
Lithium molecule is formed by the combination of 2 atomic orbitals 2s and
giving two molecular orbitals. One with lower energy and the other with higher
energy.
Energy
AO
of Li
MO of Li2
AO
of Li
Ef

54. Now Li –atom attaches to Li2 molecule to give Li3 molecule
Energy
AO of Li
atoms
MO of Li3
molecule
AO of Li
atom
Ef
As the length of the chain increases by increasing the number of Li –atoms we get a large
number of molecular orbitals closely spaced together. The energy levels get closer and
closer and becomes continuous. Such group of continuous energy levels are known as
bands.
Lower energy band is called as Valence band which contains MO’s with electrons and the
higher energy band is called conducting band which contains vacant MO’s.

55. The energy gap between valence band and the conducting band is called Fermi energy
gap (Ef).
Nature of the material is decided by Fermi energy gap.
If the Fermi energy gap is more than the material is INSULATOR.1.
If the energy gap is less then the material is CONDUCTOR.2.
If the fermi energy gap is in between the conductor and insulator then the material is3.
said to be SEMI-CONDUCTOR.

56. EFFECT OF DOPING ON CONDUCTANCE
Types of Semi-Conductors
Intrinsic Semi-Conductors1.
In this, the conductivity is due to the jumping of electrons from valence band to
the conduction band due to the less fermi energy gap (Ef) between the bands.
Conductivity of the semi-conductor increases with increase in the temperature
due to the shifting of more number of electrons.

57. 2. Extrinsic Semi-Conductor
In this , Conductivity is due to the doping .
Doping is required due to the more fermi energy gap (Ef) between the valence band and the
conducting band. The addition of impurity into the semiconducting material is called
Doping. Doping reduces the Fermi energy gap (Ef).
Reduced fermi
energy gap
Impurity band /
Donor band
Ef
Ef
’

58. Based on the Doping, extrinsic Semi-
Conductors are of two types:
n-type Semi-Conductors1.
These are produced by doping Si or Ge
with pentavalent impurity atoms like P,
As (i.e., electron rich atoms) .
A minute amount of Si or Ge are
replaced by Phosphorous having 5
electrons in its outer shell.
Only 4 electrons of Phosphorous atom
are in the formation of Covalent bonds
with Si or Ge and the 5
th
electron helps
for conductivity .
The negative charge is due to this
excess electron and it is called n-type.

59. 2. p- type Semi –Conductor
These are produced by doping Si or Ge
with Trivalent impurity atoms like Al,
B, Ga (i.e., electron deficient atoms).
Because of the replacement of the
tetravalent atoms Si or Ge with trivalent
atom like Al, B, Ga we can find the
formation of the positive hole.
Electron migrates from adjacent Si or
Ge atom to this positive hole and a new
positive hole is created and it happens
continuously leading to conductivity.