This document discusses molecular orbital theory, which describes how atomic orbitals combine to form molecular orbitals in chemical bonds. When two atomic orbitals overlap, they form one bonding molecular orbital that is lower in energy, and one antibonding orbital that is higher in energy. The number of electrons in bonding orbitals minus the number in antibonding orbitals gives the bond order, which indicates the bond strength and stability. Molecular orbital diagrams are used to illustrate these bonding and antibonding molecular orbitals.

1. Inorganic Chemistry
Dr. Bhuse V. M
Department of Chemistry, Institute of Science, Nagpur
Molecular Orbital Theory
Books to follow
Inorganic Chemistry by Shriver & Atkins
Physical Chemistry: Atkins

2. Structure of an Atom:
e- movement
route
o
o
o
o
o o
o
o
o
o
o
o
o
o
o
o
o
Nucleus of atom
(Proton + Neutron)
size 10-15
m
Electrons
Revolve round the nucleus
in different path

3. ORBITAL:
 Orbital : The region around the
Nucleus where probability of finding
electron is more (appreciable).
 The probability never become zero
e-
o
o
o
o
o o
o
o
o
o
o
o
o
o
o
o
o
This is not the end of
ORBIT

4. Chemistry:
 The ‘Chemistry’ of any element is
associated with the rearrangement of
electrons of participating atoms.
 This smaller invisible electron although is
particle, mostly behave as wave.
 Light : Behave as wave
 Stone: Behave as partical.

5. If light can behave as particles,why not
particles behave as wave?
Louis de Broglie
The Nobel Prize in Physics 1929
French physicist (1892-1987)

6. Louis de Broglie
 Particles can behave as
wave.
 Wave Particle
Duality

7. Time period = T=Wavelength, Velocity = v,
v = l/T, Frequency, n = 1/T, v = n l,
Concept of wave

8. A = maximum amplitude
Frequency= 1/l = n
l= is wavelength
x
y
l
A
Trough
Crest
l 2l

9. x
y
 If e- is considered as wave, we can
write a wave equation (Ψ) for it.

10. We can write wave equation for electron.
Electron is present in orbitals (s,p,d,f etc), so we can write wave
equation for orbital also
Thus, for every system, we can write a wave function Ψ which
is continuous, single-valued function of the coordinates of all
the particles and of time.
From these functions, all possible predictions about the
physical properties of the system can be obtained.
The Wave Equation (Function)
If we know the wave function we can know everything about the compound.

11. THEORY OF BONDING
b) Molecular Orbital Theory
 The another theory that describe the bonding
in compound
 It considers the wave nature of electrons.

12. MOT: Principles
1. Each electron can be represented by a wave, .
2. An atomic orbital contains an e-, so it can also be
represented by another wave, 
3. When atoms combine, the atomic orbitals mix
completely (called linear combination) to produce
Molecular orbitals (M.O) [SIMILAR TO HYBRID
ORBITAL]
4. However, here, two kind of MO’s are produced.
5. We, therefore can write wave equation for MO also.
6. Each  is associated with a definite shape & energy .
7. Regular rules of filling electrons apply to MO’s (Aufbau
Principle Pauli Exclusion )

13. Rules for linear combination
1. Atomic orbitals must be roughly of the same energy.
2. The orbital must overlap one another as much as
possible-
3. Atoms must be close enough for effective overlap.
4. AO should have the same symmetry
(i.e symmetry of two AO must remain unchanged when
rotated about the internuclear line
or, Both AO must change symmetry in identical manner.
Linear combination of atomic orbitals

14. Rules for linear combination….
4. When two AOs mix, two MOs will be produced (i.e.
combination should be equal in number) If for any atom, no
suitable AO available on adjacent atom, that AO remain as Nonbonding
(NBMO)
Each orbital can have a total of two electrons
(Pauli principle)
Lowest energy orbitals are filled first (Aufbau
principle)
5. Unpaired electrons have parallel spin (Hund’s rule)
6. Bond order = ½ (bonding electrons – antibonding
electrons)

15. 7. For atoms with both s and p orbitals, there are two
types of interactions:
 The s and the p orbitals that overlap axially gives 
type bonding and antibonding molecular orbitals.
 The other two sets of p orbitals that overlap
laterally gives  type bonding and antibonding
molecular orbitals.
 Thus, there are both  and  bonding molecular
orbitals and * and * antibonding molecular
orbitals.

16. A B
A B
Linear Combination of Atomic Orbitals (LCAO)
MO formation can be considered as constructive and
distructive interference of the two waves A and B
•If waves interact constructively, the resulting orbital is lower
in energy: called bonding molecular orbital.
If waves interact destructively, the resulting orbital is higher in
energy: an antibonding molecular orbital.

17. +. +. . .
+
-bonding
b
Amplitudes are added
Molecular Orbital:
1. Bonding MO: Constructive interference
 = A+B
Constructive interference

18. The electron remains between the two nuclei Nuclei are
shielded from each other
The electrons spend much time in this MO.
It interacts strongly with both nuclei therefore attract two
nuclei togather, so MO is called Bonding MO.
The energy of the molecule is lower
Bonding MO
. .
+

19. Amplitudes of
wave functions
subtracted.
Molecular Orbitals:
2. Antibonding MO: Destructive interference
+. -. .
.
node
antibonding
+ -
 = A-B Destructive Interference

20. The electrons are excluded from internuclear region.
The electrons remain outside of the area between
two nuclei.
Both nuclei repels to each other
No shielding of Nuclear charge.
Therefore this MO is destabilizing the bond so
called Antibonding MO.
The energy of the molecule is higher
.
.
+ -
Antibonding MO

21. 2AO =2MO

22. Comparison of AO & MO
AO MO
Monocentric Bi/polycentric
Under influence of one
nuclei
Under influence of more
than one nuclei
e.g. are S,
Px,Py,Pz,dxy,dyx,dxz,
dx2-y2,dz2
Bonding MO, antobonding
MO, nonbonding MO,
sigma MO, pi MO.

23. BMO ABMO
Addition overlap Substraction overlap
viewed as constructive
interference of waves
 = A+B
viewed as distructive
interference of waves
 = A-B
Lower in energy Higher in energy
Electron in bMO shield
nuclear charge between
two nuclei i.e. binds two
nuclei, so called bonding
MO.
Electron in abMO cannot
shield nuclear charge
between two nuclei (i.e
cannot bind), so called
bonding MO.
Nuclear density
concentrated between
internuclear line joining
two nuclei.
Nuclear density
concentrated outside of
nuclear line.
Electron in BMO increases
bond order
Electron in ABMO
decreases bond order

24. Points to remember in MOT
 Two atomic orbitals combine => two molecular orbitals
result.
 Of each pair of molecular orbitals, one is a bonding
molecular orbital.
 The bonding orbital is at a lower energy than the
separate atomic orbitals.
 Electrons in a bonding orbital increase the stability
of the molecule.
 The second orbital is an antibonding orbital.
 The antibonding orbital is at a higher energy than
the AOs.
 Electrons in an anti bonding orbital decrease the
stability of the molecule.

25. Molecular Orbitals
Two AOs in
hydrogen atoms
combine to form …
… a bonding
molecular orbital,
lower in energy than
the AOs, and …
… an antibonding
molecular orbital,
higher in energy
than the AOs.
Electron density
between the nuclei
is increased.
Electron density
between the nuclei
is decreased.

26. Types of Overlap:
1.s-s
Constructive interference from the 1s orbitals (1s)
Destructive inteference form the 1s orbitals ( )
The molecular orbital has a nodal plane bisecting the
internuclear axis. A node or nodal plan is a region in
which the probability of finding an electron is zero.
*
s
1

*
s
1


27. 2. px-px
 Head-on overalp produces sigma molecular
orbitals .
 Constructive interference from the 2px orbitals
 Destructive interference for the 2px orbitals

28. 3. py-py/pz-pz
 These atomic orbitals overlap ‘side-on’
forming  molecular orbitals
 The bonding combination is
 The antibonding combination is
 Termed as  molecular orbitals because they
have a nodal plane along the internuclear axis
y
p
2

*
p
2 y


29. Constructive interference from the 2py/2pz orbitals
Destructive interference from the 2py/2pz orbitals

30. Types of overlap (sigma and pi)
The two px orbitals
combine to form
sigma bonding and
antibonding MOs.
The two py orbitals
and the two pz
orbitals give pi
bonding and
antibonding MOs.

31. H2 Molecule:
(2 nuclei and 2 electron)
 Let the two Hydrogen in H2 be labeled as HA and HB.
Therefore e-s in their AO’s can be described by
wave functions as A & B.
 The overlap of AO can be visualized as overlap of
two waves, A and B .
 The overlap is given by algebric addition of two
waves (i.e. addition followed by subtraction)
  = CAA ± CBB
 Where C is extent of overlap

32.  A and B are same atomic orbitals (except for their
different origin)
  = A± B
 This is LCAO.
 It has two terms
  = A+ B (Addition) &
  = A- B (Substraction)
 The addition gives Bonding Orbital (BMO).
 The substraction gives Antibonding Orbital (AbMO).
 Order of filling e- is same as that AO.
 BMO have low energy than individual energy of AO.
 AbMO have high energy than that of individual AO.

33. How to draw MO Diagram?
High energy Antibinding MO, (AbMO)
Energy
a
Low energy bonding MO, (BMO)
b
1S1
H
1S1
H
AO of one
H atom
AO of other
H atom
MO of H2
Molecule

34. Bond Order and Bond Stability
2
electrons
g
antibondin
of
#
electrons
bonding
of
#
order
bond


*BO gives the number of bonds formed between atoms.
*BO=0 means no bonding (as there are same number of
electron in bonding and antibonding orbitals)
*More the bond order, more the stability of molecule.
*More the bond order, shorter the bond length & greater the
bond energy.
*Bond energy is the amount of energy necessary to break a
mole of bonds.

35. Molecular Orbital Diagrams:
a) Homonuclear Diatomic Molecules
b) Homonuclear Diatomic Molecules
 Draw the energy level diagrams / Molecular
Orbital Diagram (MOD) and write the MO
electron configurations
 H2
 He2
 Be2
 N2
 O2 and O2
-

36. In H2 the two electrons go
into the bonding molecular
orbital and none in the
antibonding MO.
The bond order is =
1
2
(2 - 0) = 1
a) Homonuclear Diatomic Molecules
1. H2 molecule

37.  Electronic
Configuration:
 He(2): 1s2
 In the case of He2,
the bond order would
be
1
2
(2 - 2) = 0
• Bond order is zero.
• That is no bond between
two He atom.
• Therefore, He2 does not
exist.
a) Homonuclear Diatomic Molecules
2. He2 Molecule

38. 1. Principle energy level n =2

39. a) Homonuclear Diatomic Molecules
3. Li2 molecules
1s2, *1s2, 2s2
Bond order: 1
Li
Energy
Li
Li2
1s 1s
1g
1u*
2s 2s
2g
2u*

40. 1s2, *1s2, 2s2, *2s2
Bond order: 0
Be
Energy
Be
Be2
1s 1s
1g
1u*
2s 2s
2g
2u*
a) Homonuclear Diatomic Molecules
4. Be2 Molecules

41. Energy Diagram for Homonuclear Molecules

42. Simplified
a) Homonuclear Diatomic Molecules
5. O2 Molecule

43. Homonuclear Diatomics
• Energy level sequence:
• 1s 1s* 2s 2s* 2p y(2p) = z(2p)
y*(2p) z*(2p)2p*.

44. b) Heteronuclear Diatomic Molecules
 Molecular orbital diagrams for heteronuclear
molecules is different than homonuclear ones
 The more electronegative elements are lower
in energy than those of the less
electronegative element.
 A few diatomics have unpaired electrons in the
MO’s. These diatomics would be classified as
being paramagnetic.
 Diamagnetic species have no unpaired
electrons.

45. Heteronuclear Diatomic Molecules
 The energy differences between bonding
orbitals depend on the electronegativity
differences between the two atoms
 The larger the difference the more polar the
bond that is formed (ionic character increases)
 The difference reflects the amount of overlap
between the bonding orbitals. If the difference
is too great the orbitals cannot overlap
effectively and nonbonding orbitals will be
formed.

46. Energy Level Diagram for NO

48. Summary
 Explains the distributions and energy of
electrons in molecules
 Useful for describing properties of
compounds Bond energies, electron
cloud distribution, and magnetic
properties etc
 The electron in an atomic orbital is
described as a wave function utilizing
the Schröndinger equation.
 The ‘waves’ have positive and negative
phases.
 To form molecular orbitals, the wave
functions of the atomic orbitals must

49. Summary
 How the phases or signs combine
determine the energy and type of
molecular orbital.
 Bonding orbital – the wavefuntions are in-
phase and overlap constructively (they
add).
 Bonding orbitals are lower in energy than
AOs
 Antibonding orbital – the wavefunctions
are out-of-phase and overlap destructively
(they subtract)
 Antibonding orbitals are higher in energy
than the AO’s
When two atomic orbitals combine, one
bonding and one antibonding MO is