2 -bonding and hybridization

1. Theories of chemical bonding 1
Theories of Chemical Bonding
Theories of bonding: explanations for chemical bond, Lewis dot
structures and the following.
Valance-bond (VB) theory
Hybridization of atomic orbitals
Multiple covalent bonds
Molecular orbital (MO) theory
Delocalized electrons
Bonding in metals
Practice mental reasoning and verbal explanation

2. Theories of chemical bonding 2
Energy of Interaction Between Two H Atoms
Potential
energy
distance
–346 kJ mol
–1

H

– H bond
+346 kJ mol
–1

antibonding
Energies of attraction and
repulsion as functions of
distance between two H
atoms are shown here.
The minimum of the
attraction force occur at
H–H bond length of 74 pm,
at which, the antibonding
orbital is +346 kJ mole
–1

above 0, energy when H
atoms are far apart.
How does energy affect the two-atom system?

3. Theories of chemical bonding 3
The Valence-bond Method
Valence bond method considers the covalent bond as a result of
overlap of atomic orbitals. Electrons stay in regions between the two
atoms. Some bond examples
s-s s-p s-d p-p p-d d-d
H-H H-C H-Pd C-C Se-F Fe-Fe (?)
Li-H H-N in Pd P-P
H-F hydride
But overlapping of simple atomic orbitals does not explain all the
features. Thus, we have to take another look, or do something about
atomic orbitals – hybridization.
How does valence-bond approach explain
the formation of chemical bonds?

4. Theories of chemical bonding 4
Hybridization of Atomic Orbitals
The solutions of Schrodinger equation led to these atomic orbitals.
1s, 2s, 2p, 3s, 3p, 3d, 4s, 4p, 4d, 4f, etc.
However, overlap of these orbitals does not give a satisfactory
explanation. In order to explain bonding, these orbitals are combined to
form new set of orbitals – this method is called hybridization.
During the lecture, these hybridized orbitals will be explained:
sp2 sp hybrid orbitals from mixing of a s and a p orbital
sp
2
3 sp
2
hybrid orbitals from mixing of a s and 2 p orbital
sp
3
fill in you explanation please

sp
3
d 5 sp
3
d hybrid orbitals from mixing of a s and 3 p and a d orbital
sp
3
d
2
____________
Provide a description for hybrid orbitals sp, sp
2
, sp
3
, sp
3
d, and sp
3
d
2

5. Theories of chemical bonding 5
The sp Hybrid Orbitals
The sp hybrid orbitals: formation oftwo sp hybrid orbitals
+++ -= + -
+ – + -= - +
hybridization of s and p orbitals = 2 sp hybrid orbitals
­_ ­_ __ __
­¯ __ __ __ Two sp hybrid orbitlas =>
Two states of Be

6. Theories of chemical bonding 6
Bonds with sp Hybrid Orbitals
Formations of bonds in these molecules are discussed during the
lecture. Be prepared to do the same by yourself.
Cl–Be–Cl H–CºC–H H–CºN : O=C=O
Double and triple bonds involve pi p bonding, and the the application
of valence bond method to p bonds will be discussed.
You are expected to be able to draw pictures to show the p bonding.

7. Theories of chemical bonding 7
A p Bond
Overlap of 2 2p orbitals for
the formation of p bond
Sigma (s) bond is symmetric about axis.
Pi (p) electron distribution above and
below axis with a nodal plane, on which
probability of finding electron is zero; p
bond is not as strong as sigma - less
overlap.
Nodal plane
Bonding of C
2
H
4
C
2s 2p 2p 2p
sp
2
sp
2
sp
2
2p
How are pi bonds formed?

8. Theories of chemical bonding 8
Triple Bonds in H-CºC-H
H-C-C-H: three s bonds due to overlapping of 1s
H
– sp
C
; sp
C
– sp
C
;
and sp
C
– 1s
H
.
Two p bonds in HCºCH and HCºN triple bonds are due to
overlapping of p orbitals results.
Draw and describe how atomic orbitals overlap
to form all bonds in acetylene, H–CºC–H
p
y
over lap
p
x
over lap
H H
sp hybrid orbitals
Two nodal planes of p
bonds are perpendicular
to each other.
in p bond
in p bond
C
2s 2p 2p 2p
sp

sp 2p 2p

9. Theories of chemical bonding 9
Two p Bonds in H–CºC–H
A triple bond consists of a sigma and two pi bonds. Overlaps of
two sets of p orbitals form of two p bonds.

10. Theories of chemical bonding 10
Bonding of CO
2
For CO
2
, the C atom forms a s bond and a p bond with each of two O
atoms. The two nodal planes of the two p bonds are also perpendicular.
During the lecture, I draw diagrams and explain the two s two p bonds
in CO
2
. You are expected to be able to do the same, in a test.
p
y
over lap in p bond
Overlap p–p in s bonds
p
x
over lap in p bond
O=C=O or H
2
C=C=CH
2
Discuss the bonding of allene H
2
C=C=CH
2
See extra problems B17 in the handout
Resonance structures
: O – C º O :
: O º C – O :
. .

11. Theories of chemical bonding 11
09_174
O C O
sigma bond
(1 pair of electrons)pi bond
(1 pair of
electrons)
pi bond
(1 pair of
electrons)
(a)
(b)
O C O
Bonding in CO
2
– another view
Compare with H
2
C=C=CH
2

12. Theories of chemical bonding 12
The sp
2
Hybrid Orbitals
Ground state and excited state
electronic configuration of B
­_ ­_ ­_ __
­¯ ­_ __ __
The hybridization of a s and two
p orbitals led to 3 sp
2
hybrid
orbitals for bonding.
Compounds involving sp2 hybrid
orbitals: BF
3
, CO
3
2–
, H
2
CO,
H
2C=CH
2, NO
3
–
, etc
Nov. 25

13. Theories of chemical bonding 13
An example of using sp
2
hybrid orbitals
__ orbitals for bonding?
Dipole moment = ____?

14. Theories of chemical bonding 14
Bonding of H
2
C=CH
2
molecules
Utilizing the sp
2
hybrid orbitals, each C atom form
two H–C s bonds for a total of 4 s H–C bonds.
The C–C s bond is common to both C atoms.
A C–C p bond is formed due to overlap of p
orbitals from each of the C atoms.
Hybrid orbitals (sp
2
) for
H–C and C–C s bond
Overlap of p orbital
for C–C p bond
C
2s 2p 2p 2p
sp
2
sp
2
sp
2
2p

15. Theories of chemical bonding 15
The sp
3
Hybridized Orbitals
Ground state and excited state
electronic configuration of C
­_ ­_ ­_ ­_
­¯ ­_ ­_ __
The hybridization of a s and three
p orbitals led to 4 sp
3
hybrid
orbitals for bonding.
Compounds involving sp
3
hybrid
orbitals: CF
4
, CH
4
, : NH
3
, H
2
O::,
SiO
4
4–
, SO
4
2–
, ClO
4
–
, etc

16. Theories of chemical bonding 16

C
2s 2p 2p 2p
sp
3
sp
3
sp
3
sp
3

17. Theories of chemical bonding 17
The sp
3
d Hybrid Orbitals
Hybridization of one s, three p, and a d
orbitals results in 5 sp
3
d hybrid
orbitals. The arrangement of these
orbitals is a trigonal pyramid. Some
structures due to these type of orbitals
are PClF
4
, TeCl
4
E, and BrF
3
E
2
.
How many unshared
electron pairs are present
in TeCl
4
and BrF
3
?
What are their shapes?

18. Theories of chemical bonding 18
The sp
3
d
2
Hybrid Orbitals
Hybridization of one s, three p, and
two d orbitals results in 6 sp
3
d
2

hybrid orbitals. The arrangement of
these orbitals is an octahedron.
Compounds using these type of
orbitals are shown here.
AX
6
, AX
5
E, AX
4
E
2
AX
3
E
3
and AX
2
E
4
IOF
5
, IF
5
E, XeF
4
E
2

No known compounds of AX
3
E
3
and AX
2
E
4
are known or recognized,
because they are predicted to have a T shape and linear shape
respectively when the lone pairs of electrons are ignored.

19. Theories of chemical bonding 19
Molecules with more than one central atom
Describe the structure of CH
3
NCO.
Draw the skeleton and add all valence electrons
H
3C – N – C – O
Which Lewis dot structure is the most important (stable)?
N = C = O
H–C
H H
120
o
109
o
180
o
What hybridized orbitals are used for bonding in N and C? Why are the
bond angles as indicated? No of s and p bonds = __, __?
Give formal charges to all atoms in all structures.
Take a new look at slide
22 in Bonding Basics
Which
structure is
more stable,
and why?
NºC–O
H–C
H H
N–CºO
H–C
H H

20. Theories of chemical bonding 20
Why Molecular Orbital (MO) Theory
Lewis dot and valence bond theories do not always give satisfactory
account for various properties of molecules.
For example, the dot and VB theory does not explain the fact that O
2
is
paramagnetic and has a double bond.
Dot and VB structures : O O :• O O •
are unsatisfactory.
MO theory, different from VB in that MO theory considers the orbitals of
the whole molecules. However the approach of linear-combination-of-
atomic-orbitals (LCAO) is usually used.
There are other reasons, but it’s human nature to theorize. The theory
is beautiful, and worth learning or teaching.

21. Theories of chemical bonding 21
The Molecular Orbital (MO) Theory
The two atoms in the H
2
molecule may be
represented by A and B. Their s orbitals 1s
A

and 1s
B
respectively, are used for two MOs:
s* = 1s
A
– 1s
B
s = 1s
A + 1s
B
The energy levels of these AO and MO are
represented by the diagram here, with the math
hidden.
For a molecule, there are certain orbitals each of which accommodates
two electrons of opposite spin.
The MO theory combines atomic orbitals (AO) to form MOs, & this
method is called LCAO
1s
A
1s
B
s
MO
s*
AO AO

22. Theories of chemical bonding 22
MO for H
2
–type molecules: H
2
+
, H
2
, H
2
–
, He
2
+

Generalize the technique of LCAO

23. Theories of chemical bonding 23
Electronic configuration, s
2
, for H
2
molecules
Generalize the technique of LCAO

24. Theories of chemical bonding 24
Electronic Configuration of H
2
-type Molecules
From the previous theory, we can fill the M Os with electrons for the
H
2
-type molecule:
Moleculee-configurationBond orderbondlength
H
2
+
1s (1s
1
) ½ 106 pm
H
2, He
2
2+
1s
2
1 74, ~75
H
2
–
, He
2
+
1s
2
1s* ½ ~106, 108
H
2
2–
, He
2

1s
2
1s*
2
0 not formed
Describe the relationships of bondlength & bondorder
and e-configurations; learn to reason

25. Theories of chemical bonding 25
Sigma MOs Formed Using p AOs
Sigma MOs (s
2p
s
2p
*
) can be formed using p AOs, similar to VB
theory. The gain in bonding orbital s
2p
(lower energy) is at the
expense of the anti-bonding orbital s
2p
*
(higher energy)
Generalize the technique of LCAO

26. Theories of chemical bonding 26
Pi p MOs from p AOs
Generalize the technique of LCAO

27. Theories of chemical bonding 27
MO Diagrams for O
2
and F
2
A full diagram of the energy
level of molecular orbitals of
O
2
and F
2
is shown here.
The relative (approximate)
height of these energies will
be explained verbally during
the lecture, and you are
suppose to be able to do the
same.
Write the electronic
configurations for O
2
,
O
2
–
, F
2, F
2
–
& Ne
2.

28. Theories of chemical bonding 28
The O
2
+
, O
2, O
2
–
, & F
2
+
, F
2, F
2
–
Molecules
·O=O·
Paramagnetic ,
bond length
indicates double
bond, electronic
configuration
agrees
F–F
Electronic
configuration agree
with single bond.
For ·O=O·
­_ ­_
See p. 457 for two MO
energy-level diagrams

29. Theories of chemical bonding 29
MO Energy Level Diagram for Be
2 – N
2

Due to close energy levels of 2s and 2p, the MO energy level diagram
for Be
2
to N
2
differs from those of O
2
to F
2
. Reasons and explanation
are given during the lecture. Hope you can do the same.
Give electronic
configurations
for Be
2
+
,
Be
2
–
, B
2
+
,
B
2
,
B
2
–
, C
2
+
,
C
2
,
C
2
–
, N
2
+
,
N
2
,
N
2
–
.
See p. 457 for two MO
energy-level diagrams

30. Theories of chemical bonding 30
A more realistic energy level diagram for
Be
2
– N
2
involving sp mixing, not in text
_ _ _
2p
_
2s
Atomic
orbital
__ s*
2p
__ __ p*
2p
__ s
2p
__ __p
2p
__ s*
2s
__ s
2s
Molecular orbitals
_ _ _
2p
_
2s
Atomic
orbital
This diagram from my CaCt
website accounts for the sp
mixing of the AO for the bonding
consideration. This sp mixing
effect is more detailed than that
required for freshman chemistry
(not to be tested).
The sp mixing of AO gives
stronger s
2s
bond and a weaker
s*
2s
bond. Thus, the split from 2s
is not even. Effects on other bonds
are also shown, but qualitatively.

31. Theories of chemical bonding 31
Benzene
The benzene structure has fascinated scientists for centuries. It’s bonding is
particularly interesting. The C atom utilizes sp2 hybrid AO in the sigma
bonds, and the remaining p AO overlap forming a ring of p bonds.
Sigma s bonds are
represented by lines,
and the p orbitals for
the p bonds are shown
by balloon-shape blobs.
Note the + and – signs
of the p orbitals. Thus,
we represent it by
+
–
+ +
+
– –
–
+
+

32. Theories of chemical bonding 32
More About Benzene
Chem120 students may ignore
this slide.
The p and p* of C
6
H
6
are shown
here; the symmetry is also
interesting.

33. Theories of chemical bonding 33
Delocalized electrons in Benzene and Ozone
When p bonds are adjacent to each other or separated by on single C-C
bonds, the p bonding electrons are delocalized. The delocalized electron
path for benzene and ozone are shown here. These pictures represent p
electron of the the structures formula contribute most to their structures.
O
O O
CO
3
2–
& have delocalized electrons

34. Theories of chemical bonding 34
Joy on structure of benzene – a story
Kathleen Londsdale (1903-1971) came from a very poor family in
Kildare who moved to Essex when she was five. She studied physics,
math and chemistry at school and went to college in London when she
was 16, where she did extremely well. She was offered a place in the
research team of William Bragg, so starting her life's work on X-ray
crystallography.
In 1929 she showed, by her analysis of hexamethyl benzene, that the
benzene ring was flat. Benzene has fascinated scientists, and its precise
structure was a matter of controversy till then.
In 1945 she was elected the first ever woman Fellow of the Royal Society.
She was also created a Dame Commander of the Order of the Brittish
Empire in 1956.

35. Theories of chemical bonding 35
MO for Heteronuclear Diatomic Molecules

For heteronuclear
diatomic molecules,
the atomic orbitals
are at different
energy levels. Thus,
the MO shifts are
different from those
of homonuclear
diatomic molecules.
The interactions of
AO for MO for HF,
LiF are similar, and
explained in lectures.
Chem120 students may ignore this slide.

36. Theories of chemical bonding 36
Review
Explain the bonding and anti-bonding orbitals, with a picture if possible
Describe a s and a p bond, picture may be used.
Give the electronic configurations and bond orders for N
2
, N
2
+
, N
2
2+
, N
2
–
,
N
2
2–
, O
2,
Draw the Lewis dot structure for ozone. Describe the molecular shape
and justify for it. Explain the delocalized electrons of ozone.
Use the MO theory to explain the fact that O
2
is paramagnetic, and has
a double bond. A diagram of the MO energy levels will help. Give a few
compounds that have the same number of electrons as O
3
.