Hybridization and molecular orbital theory

1. MOLECULAR ORBITALS
THEORY Dr. A.
Rajasekhar
Reddy

2. VALENCE BOND THEORY
Explains the structures of covalently bonded
molecules
 ‘how’ bonding occurs
VSEPR is part of VB theory
Principles of VB Theory
 Bonds form from overlapping atomic orbitals and
electron pairs are shared between two atoms
 A new set of hybridized orbitals can form
 Lone pairs of electrons are localized on one atom

3. SIGMA () BONDS
Sigma bonds are characterized by
 Head-to-head overlap.
 Cylindrical symmetry of electron density about the
internuclear axis.

4. PI () BONDS
Pi bonds are
characterized by
 Side-to-side overlap.
 Electron density above and
below the internuclear
axis.

5. SINGLE BONDS
Single bonds are always  bonds, because 
overlap is greater, resulting in a stronger bond
and more energy lowering.

6. MULTIPLE BONDS
In a multiple bond one of the bonds is a 
bond and the rest are  bonds.

7. MULTIPLE BONDS
In a molecule like
formaldehyde (shown
at left) an sp2 orbital on
carbon overlaps in 
fashion with the
corresponding orbital
on the oxygen.
The unhybridized p
orbitals overlap in 
fashion.

8. MULTIPLE BONDS
In triple bonds, as
in acetylene, two
sp orbitals form a 
bond between the
carbons, and two
pairs of p orbitals
overlap in  fashion
to form the two 
bonds.

9. DELOCALIZED ELECTRONS:
RESONANCE
When writing Lewis structures for species like
the nitrate ion, we draw resonance structures
to more accurately reflect the structure of the
molecule or ion.

10. DELOCALIZED ELECTRONS:
RESONANCE
In reality, each of the four
atoms in the nitrate ion has a
p orbital.
The p orbitals on all three
oxygens overlap with the p
orbital on the central
nitrogen.
This means the  electrons
are not localized between the
nitrogen and one of the
oxygens, but rather are

11. RESONANCE
The organic molecule
benzene has six 
bonds and a p orbital
on each carbon atom.

12. RESONANCE
In reality the  electrons in benzene are not
localized, but delocalized.
The even distribution of the electrons in
benzene makes the molecule unusually stable.

13. MOLECULAR ORBITAL(MO)
THEORY
Explains the distributions and energy of electrons
in molecules
Useful for describing properties of compounds
 Bond energies, electron cloud distribution, and magnetic
properties
Basic principles of MO Theory
 Atomic orbitals combine to form molecular orbitals
 Molecular orbitals have different energies depending on
type of overlap
 Bonding orbitals (lower energy than corresponding AO)
 Nonbonding orbitals (same energy as corresponding AO)
 Antibonding orbitals (higher energy than corresponding AO)

14. FORMATION OF MOLECULAR
ORBITALS
 An electron in an atomic orbital can be
described as a wave function utilizing the
Schrödinger equation.
 The ‘waves’ have positive and negative
phases.
 To form molecular orbitals, the wave
functions of the atomic orbitals combine.
 How the phases or signs combine determine
the energy and type of molecular orbital.

15. FORMATION OF MOLECULAR
ORBITALS
Bonding orbital – the wave functions are
in-phase and overlap constructively (they
add).
 Bonding orbitals are lower in energy than AOs
Antibonding orbital – the wave functions
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 formed.

16. OVERLAP OF TWO 1S ATOMIC
ORBITALS
Two MO’s are formed when the two
1s atomic orbitals overlap
 The in-phase combination produces a 1s
molecular bonding orbital.
 Has lower energy than corresponding AO’s
 The out-of-phase contribution produces a
molecular antibonding orbital
 Has higher energy than corresponding AO’s
*
s
1


17. OVERLAP OF TWO 1S ATOMIC
ORBITALS
2 1s orbitals that are far apart
Constructive interference from the 1s orbitals (1s)
Destructive interference 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


18. OVERLAP OF 2PX ORBITALS
Head-on overlap produces a p (actually )
and a (actually ). These are also
termed as sigma orbitals since they are
cylindrically symmetric about the internuclear
axis.
Constructive interference from the 2px orbitals
Destructive interference for the 2px orbitals
x
p
2

*
p

*
p
2 x


19. OVERLAP OF 2PX ORBITALS

20. OVERLAP OF 2PY ORBITALS
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
 The antibonding combination also has a nodal plane
bisecting the internuclear axis
y
p
2

*
p
2 y


21. OVERLAP OF 2PY ORBITALS
Constructive interference from the 2py
orbitals
Destructive interference from the 2py

22. OVERLAP OF 2PZ ORBITALS
The 2pz atomic orbitals can overlap in the same
fashion except that the orientation in space is
different
 The 2pz atomic orbitals overlap ‘side-on’ to produce a
bonding and an antibonding  orbital
Together, the 2pz and the 2py atomic orbitals produce
two bonding orbitals and two antibonding orbitals. MO
theory commonly illustrates these orbitals as the same.

23. MOLECULAR ORBITAL
FILLING-ENERGY DIAGRAM
Order of filling of MO’s obeys same rules as
for atomic orbitals.
Including
 Aufbau principle
 Hund’s Rule
Recall that bonding orbitals have lower energies than the
corresponding atomic orbitals and antibonding orbitals have
higher energies than corresponding atomic orbitals

24. MOLECULAR ORBITAL FILLING-
ENERGY DIAGRAM FOR
HOMONUCLEAR MOLECULES

25. BOND ORDER AND BOND
STABILITY
𝑏𝑜𝑛𝑑 𝑜𝑟𝑑𝑒𝑟 =
# 𝑜𝑓 𝑏𝑜𝑛𝑑𝑖𝑛𝑔 𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑛𝑠 − # 𝑜𝑓 𝑎𝑛𝑡𝑖𝑏𝑜𝑛𝑑𝑖𝑛𝑔 𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑛𝑠
2
Usually, the bond order corresponds to the number of bonds
described by the VB theory
A bond order equal to zero indicates that there are the same
number of electron in bonding and antibonding orbitals
The greater the bond order, the more stable the molecule or ion.
Also, the greater the bond order, the shorter the bond length and
the greater the bond energy.
Bond energy is the amount of energy necessary to break a mole of
bonds.

26. HOMONUCLEAR DIATOMIC
MOLECULES
Draw the energy level diagrams and
write the MO electron configurations
 H2
 He2
 B2
 N2
 O2 and O2
-
Notice the differences in the energy diagrams
(it switches)

27. ENERGY LEVEL DIAGRAM
FOR NO

28. 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.

29. FORMATION OF MO’S IN HF
The bond in HF involves the 1s
electron of H and the 2p orbital of F
 A bonding and antibonding MO are produced
 sp and MO’s
 The remaining 2p orbitals on F have no overlap
with H orbitals. They are termed as ‘nonbonding’
orbitals. These orbitals retain the characteristics
of the F 2p atomic orbitals.
Lack of overlap to produce nonbonding orbitals is
much more pronounced for side-on bonding
*
sp


30. THE ENERGY LEVEL DIAGRAM
FOR HF