This PPT explains you the formation of molecular orbitals from atomic orbitals.

1. Series of lecture on
Bonding in Molecules
Lecture-5
Molecular Orbital
Theory: Part- I
D. R. Shinde
Associate Professor in
ChemistryDepartment of Chemistry
P.D.E.A’s.
Prof. Ramkrishna More
Arts, Commerce and Science College
Akurdi, Pune-411044
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2. In this Lecture
we will learn
i. Limitations of VBT
ii. Atomic and Molecular Orbitals [AO’s and MO’s]
iii. Bonding and Antibonding MO’s
iv. Sigma and Pi MO’s and their energies
D. R. Shinde, Asociate Prof., P.D.E.A's. Prof Ramkrishna More College, Akurdi, Pune
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3. a. Orbitals of the atoms overlap with each other to form a bond. Sigma and pi bond
formation take place by axial and side wise overlap respectively
b. With the help of concept of hybridization of atomic orbitals one can explain the
shape of molecules.
c. Lewis structure introduced electronic concept bonding. VSEPR model helps us
to visualize structure of molecule. VBT added the simplicity of Lewis structures
and the relatively straightforward concept of hybridization to explain structure
of the molecules. It also explained nature of force in a bond.
Advantages of VBT
limitations of VBT
It do not explain observed
a) magnetic properties of molecules
b) Spectral properties of molecules.
c) Bond length in polyatomic molecules. D. R. Shinde, Asociate Prof., P.D.E.A's. Prof Ramkrishna More College, Akurdi, Pune 3

4. Molecular Orbital Theory (MOT):
MOT was introduced by the American physicist Robert Mulliken (and others) around
1932. MOT is based on the Quantum Theory of physics applied in chemistry.
The basis of MOT is formation of molecular orbitals (MO’s) from atomic
orbitals and arrangement of MO in an Molecule
How MO is formed in a Molecule?
MO is formed in a molecule by combination of atomic orbitals.
Two or more atomic orbitals of different atoms combine in a molecule to form MO.
1 s orbital
1st atom
1 s orbital
2nd atom
+
MO Obtained from two 1s
orbitals in H2 Molecule
D. R. Shinde, Asociate Prof., P.D.E.A's. Prof Ramkrishna More College, Akurdi, Pune 4

5.  What is AO?
AO represent the area in an atom where there is maximum
probability of finding the electron.
 What is MO?
MO represent the area in a molecule where there is
maximum probability of finding the electron.
1 s orbital
MO formed from
1 s orbital
Thus, MO is different from AO.
i. MO is different in shape from AO.
ii. AO localized over one atom, MO delocalized over
two or more atoms.
iii. AO and MO has different shapes.
iv. AO and MO has different energies.
D. R. Shinde, Asociate Prof., P.D.E.A's. Prof Ramkrishna More College, Akurdi, Pune 5

6. How, AO’s Combine to form MO’s?
MO is based on principles of quantum physics now called as quantum chemistry.
One of the simple method of quantum chemistry to explain formation of MO is
Linear Combination of Atomic Orbitals (LCAO Method).
In brief method can be explained as follows, excluding much mathematical details.
1. The motion of electron in an atom or orbital
can be explained / represented by sin wave.
D. R. Shinde, Asociate Prof., P.D.E.A's. Prof Ramkrishna More College, Akurdi, Pune 6

7. Example: Formation of MO’s in H2 Molecule
 Now, consider two atoms hydrogen atoms HA and HB forming H2 molecule. The 1s orbital of
each atom combine to form MO’s.
 Suppose, wavefunction for the orbital in atom HA = ΨA and for atom HB = ΨB.
 When the two atoms approach towards each other, then at bonding distance, the electron clouds
of these two atoms fuse together to form MO’s. Under this condition, wave function for the
molecule(Ψ) can be obtained by a linear combination of the atomic orbitals.
Two orbital of two atoms
can by two different ways
D. R. Shinde, Asociate Prof., P.D.E.A's. Prof Ramkrishna More College, Akurdi, Pune 7

8. 1. Two wave function of two orbital can interact with each other in phase.
ΨA + ΨB i.e. substation of wave function
These Two types of orbital interactions between two atom can be represented
+
ΨA
-
+
-
ΨB
This is in phase interaction, means what?
+Ve wave function one wave overlap with +ve
wavefunction of second wave.
Likely,
-Ve wave function one wave overlap with -ve
wavefunction of second wave.
+
-
ΨA+ ΨB
+
D. R. Shinde, Asociate Prof., P.D.E.A's. Prof Ramkrishna More College, Akurdi, Pune 8
Resultant is a large wave with
sum of amplitude of two waves

9. -
These Two types of orbital interactions between two atom can be represented
This is out of phase interaction, means what?
+Ve wave function one wave overlap with -ve
wavefunction of second wave.
1. Two wave function of two orbital can interact with each other out of phase.
ΨA - ΨB i.e. summation of wave function
+
ΨA
-
-
+
ΨB
ΨA- ΨB
D. R. Shinde, Asociate Prof., P.D.E.A's. Prof Ramkrishna More College, Akurdi, Pune 9
Resultant is a cancellation of wave

10. What is the result of in phase interaction?
Molecular orbital will be formed, where maximum electron density which is constructed in
between two atomic nuclei. This MO is called as Bonding MO. This Gives rise to
bonding interaction in molecule.
Bonding MO Obtained in phase interaction
of two 1s orbitals in H2 Molecule
1 s orbital
1st atom
1 s orbital
2nd atom
++ -
1 s orbital 1-s orbital
1st atom 2nd atom
++ +
Anti-Bonding MO Obtained out of phase
interaction of two 1s orbitals in H2 Molecule
+
++ - -
D. R. Shinde, Asociate Prof. P.D.E.A's. Prof Ramkrishna More
College, Akurdi, Pune
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11. Rules for combining AO’s to MO’s
Two AO’s combine can combine to form MO
i. Their energy is comparable
ii. They same / appropriate symmetry and orientation.
iii.They can combine with same signs of lobe to form bonding MO and opposite signs
of lobe to form antibonding MO.
iv.Overlap of AO’s along internuclear axis form σ bond while overlap of
perpendicular to internuclear axis
Following types of combination of AO’s is possible to form MO’s
i. s orbital can combine with another s orbital to form sigma bond
ii. s orbital can combine with any of the p-orbital (s-px, s-py, s-pz)
iii. pz-pz orbital can combine to form sigma bond.
iv. px-px, py-py orbital combine to form pi bond.
D. R. Shinde, Asociate Prof., P.D.E.A's. Prof Ramkrishna More College, Akurdi, Pune 11

12. s-s orbital can give rise +ve-+ve overlap to form sigma bonding MO
Bonding MO Obtained by in
phase interaction of two s orbitals
s-s orbital in phase i.e. +ve - +ve overlap
++ +
+
s-s orbital can give rise +ve and -ve overlap to form sigma bonding MO
s-s orbital out of phase i.e.
+ve - -ve overlap
++ -
Anti-Bonding MO Obtained by out of
phase interaction of two s orbitals
++ - -
 Note that: +ve and –ve signs are the signs of wave
functions. Orbital shape indicate the shape of orbital
i.e. area enclosing electron density
D. R. Shinde, Asociate Prof., P.D.E.A's. Prof Ramkrishna More College, Akurdi, Pune
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13. s-pz orbital can give rise +ve-+ve overlap to form sigma bonding MO
s-pz orbital can give rise +ve and -ve overlap to form sigma Anti-bonding MO
s-pz orbital in phase i.e. +ve - +ve overlap
++
+
-
Bonding MO Obtained by in phase
interaction of s - pz orbitals
+
-
s-pz orbital in phase i.e. +ve - +ve overlap
to form sigma bond
++
-
+
Anti-bonding MO Obtained by out of phase
interaction of s - pz orbitals
+
+
-
D. R. Shinde, Asociate Prof., P.D.E.A's. Prof Ramkrishna More College, Akurdi, Pune 13

14. pz-pz orbital can give rise +ve-+ve overlap to form sigma bonding MO
pz-pz orbital can give rise +ve and -ve overlap to form sigma anti-bonding MO
Bonding MO formed by in phase
interaction of pz - pz orbitals
+
pz -pz orbital overlap in phase
(+ve - +ve overlap)
+
-
+
-
+
- -
Anti-Bonding MO formed by out of
phase interaction of pz - pz orbitals
+
pz -pz orbital overlap out of phase (+ve -
+ve overlap) to form sigma bond
-
+
+
-
+- -+
D. R. Shinde, Asociate Prof. P.D.E.A's. Prof Ramkrishna More
College, Akurdi, Pune
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15. +
+
+
-
px -px orbital overlap in phase
(+ve - +ve, overlap)
Bonding MO formed by in phase
interaction of px - px orbitals
+
-
+ -
-
+
+
+
-
px -px orbital overlap in phase (+ve - -ve,
overlap)
Anti-Bonding MO formed by out of phase
interaction of px - px orbitals
px-px orbital can give rise +ve-+ve or –ve - -ve overlap to form Pi bonding MO
px-px orbital can give rise +ve--ve overlap to form Pi anti-bonding MO
D. R. Shinde, Asociate Prof. P.D.E.A's. Prof Ramkrishna More
College, Akurdi, Pune
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16. Non-Bonding Interaction: In this interaction +ve wavefunction of one orbital
overlap with +ve as well as –ve wave function of another orbital simultaneously.
In this case +ve - +ve interaction is exactly cancelled by +ve - -ve
overlap. This is called as non-bonding interaction.
Example: s-orbital can overlap with px orbital to give rise non-bonding
interaction.
+
+
+
+
s -px orbital overlap in non-bonding
interaction
+
D. R. Shinde, Asociate Prof., P.D.E.A's. Prof Ramkrishna More College, Akurdi, Pune 16

17. Energies of bonding and anti-bonding MO’s
When orbital combines to form MO, energies of AO’s get distributed among the MO’s.
 When electrons are filled into Bonding Orbitals then it results into force of attraction
among the atoms. Therefore, the energy of these orbital is lower than AO as well as
antibonding MO’s.
 When electrons are filled into Anti-bonding Orbitals then it results into force of
repulsion among the atoms. Therefore, the energy of these orbital is higher than AO as
well as bonding MO’s.
+ +- -
1S AO 1S AO
Energy
Bonding MO
Anti Bonding MO
D. R. Shinde, Asociate Prof., P.D.E.A's. Prof Ramkrishna More College, Akurdi, Pune
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18. Characteristics and differences between bonding and anti-bonding MO’s
Bonding MO
1. Maximum electron density is constructed
between two atomic nuclei.
2. Result into bonding interaction i.e. when
electrons are filled in this orbital there
exists force of attraction between two
atoms.
3. They are lower in energy than AO.
Anti-Bonding MO
1. Maximum electron density is constructed
out of two atomic nuclei.
2. Result into antibonding interaction i.e.
when electrons are filled in this orbital
there exists force of repulsion between
two atoms.
3. They are higher in energy than AO.
D. R. Shinde, Asociate Prof., P.D.E.A's. Prof Ramkrishna More College, Akurdi, Pune
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19. D. R. Shinde, Asociate Prof., P.D.E.A's. Prof Ramkrishna More College, Akurdi, Pune
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