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Lecture 24: Applications of Valence Bond
Theory
The material in this lecture covers the following in Atkins.
14 Molecular structure
Valence-bond theory
14.2 Homonuclear Diatomic Molecules
14.3 Polyatomic Molecules
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Handout for this lecture
Valence Bond Theory
Applications
I. Diatomics
(1,2) = [A(1)B(2)  A(2)B(1)] 
[(1)(2)  (1)(2)]
A  1sH;B  1sH
 - bond :
invarient to rotation
H
H
A
B
In general we write (re ,RN )
as the product of electron pair
functions i (r2i1, r2i ) as
(re ,RN )  1(r1,r2 )   2 (r3 ,r4 ) 
..i (r2i1,r2i )   j (r2j1,r2j )..  n (r2n1,r2n )
Pair i
Pair j
Pair n
Pair 1
Pair 2
Valence Bond Theory
H
Cl
Atomic orbitals on H
(Hydrogen)
1sH
Applications
(1,2) = [A(1)B(2)  A(2)B(1)] 
[(1)(2)  (1)(2)]
Hybride orbitals on H
(Hydrogen)
1sA
Hybride orbitals on Cl
(Chlorine)
Atomic orbitals on Cl
(Chlorine)
sp(B) 1

:
[3s  3pz ]
2
3s
Cl
Cl
Cl
Cl
3p
3pz 3px
y
sp(B) 1

:
[3s  3pz ]
2
Cl
3pCl
3p
x
y
Valence Bond Theory
Electron pairing
and formation of bonds
sp(Cl)
A  1sH;B   
H
for  - bond
Cl
(1,2) = [A(1)B(2)  A(2)B(1)] 
[(1)(2)  (1)(2)]
Cl
A  3pCl
;B

3p
x
x
for lone - pair
H
Electron pairing
and formation of
lone - pairs
sp(Cl)
A  sp(Cl)
;B




for lone - pair
3pCl
x
Cl
A  3pCl
;B

3p
y
y
for lone - pair
H
H
Cl
Cl
3pCl
y
Cl
Valence Bond Theory Applications
Cl
Cl
Atomic orbitals on Cl # 1
3s Cl
Cl
Cl
Cl
3p
3pz 3px
y
Atomic orbitals on Cl # 2
3s
Cl
Cl
Cl
Cl
3p
3pz 3px
y
(1,2) = [A(1)B(2)  A(2)B(1)] 
[(1)(2)  (1)(2)]
Hybride orbitals on Cl # 1
sp(Cl)

Cl
sp(Cl)
Cl
3p

y
3px
Hybride orbitals on Cl # 2
sp(Cl)

Cl
sp(Cl)
Cl
3p

y
3px
Valence Bond Theory Applications
(1,2) = [A(1)B(2)  A(2)B(1)] 
Cl
Cl
[(1)(2)  (1)(2)]
Electron pairing
and formation of bonds
Cl1
A  3pCl1
;B

3p
x
x
for lone - pair
sp(Cl1)
sp(Cl2)
A  
;B =  
Cl
Cl
3pCl
x
  bond
Electron pairing
and formation of
lone - pairs
sp(Cl1)
A  sp(Cl1)
;B




for lone - pair
Cl
Cl
Cl
Cl
Cl
A  3pCl
;B

3p
y
y
for lone - pair
3pCl
y
Cl
Cl
Same for Cl # 2
Valence Bond Theory
Applications
(1, 2) = [A(1)B(2)  A(2)B(1)] 
[(1)(2)  (1)(2)]
The orbital overlap
and spin-pairing
between electrons
in two collinear p
orbitals that result
in the formation
of a ( bond.
Valence Bond Theory
Applications
I. Diatomics
(1, 2) = [A(1)B(2)  A(2)B(1)] 
[(1)(2)  (1)(2)]
N
N
sp(1)
C
O
sp(2)
A  
; B  
for  - bond
sp(1) 1

:
[2s  2pz ]
2
sp(1)
A  sp(1)
;
B




for lone - pairs
sp(1) 1

:
[2s  2p z ]
2
A  2p1x;B  2p1x
A  2p1y;B  2p1y
  bonds
Orbitals change sign
on reflexation in plane
containing 1- 2 bond
vector
Valence Bond Theory
Applications
I. Diatomics
(1, 2) = [A(1)B(2)  A(2)B(1)] 
[(1)(2)  (1)(2)]
The structure of bonds in a nitrogen molecule,
which consists of one  band and two  bands.
The electron density has cylindrical symmetry
around th e internuclear axis.
Valence Bond Theory
Applications
2. Linear molecules
H C
C H
A representation of the structure of a triple bond
in ethyne; only the  bonds are shown explicitly.
The overall electron density has cylindrical symmetry
around the axis of the molecule.
Valence Bond Theory
3.Trigonal planar
Applications
H H
H
C
C
C
HH
H
C2H4
O
CH2O
tr3
C2H4
x
tr1
tr2
y
1
tr1 
[s  px ]
3
1
1
3
tr2 
[s 
px  p y ]
3
2
2
1
1
3
tr3 
[s 
px  p y ]
3
2
2
CH2O
Valence Bond Theory
3.Trigonal planar
H
H
C
C
H
H
C2H4
C2H4
Applications
(a) An s orbital and two p orbitals can be
hybridized to form three equivalent orbitals
that point towards the corners of an equilateral
triangle. (b) The remaining, unhybr idized p
orbital is perpendicular to the plane.
Valence Bond Theory
Applications
H
4.Tetrahedral
H
sp3  hybrides
C
1
t1  [s  p x  p y  pz ]
2
along (x,y, z)
H
H
z
1
[s  p x  p y  pz ]
2
along (-x,-y, z)
t2 
t2
1
[s  p x  py  pz ]
2
along (-x,y, -z)
t3 
t1
y
X
t4
t3
1
t 4  [s  p x  py  p z ]
2
along (x,-y, -z)
Valence Bond Theory
Applications
4.Tetrahedral sp3  hybrides
H
H
C
H
H
An sp3 hybrid orbital formed from the
superposition of s and p orbitals on the same
atom. There are four such hybr ids: each one
points towards the corner of a regular
tetrahedron. Th e overall electron density
remains spherically symmetrical.
Valence Bond Theory
Applications
H
H
4.Tetrahedral
C
H
H
sp3  hybrides
=
+
A more detailed representation of the
formation of an sp3 hybrid by interference
between wavefunctions centred on the same
atomic nucleus. (To simplify the
representation, we have ignored the radial
node of the 2s orbital.)
Applications
Valence Bond Theory
4.Tetrahedral
(1, 2) = [A(1)B(2)  A(2)B(1)] 
[(1)(2)  (1)(2)]
sp3  hybrides
z
z
z
t2
t2
t2
t1
t1
t1
y
y
X
X
t3
t3
t4
t4
H
H
C
H
X
t3
t4
H
H
y
N
H
H
H
O
H
Valence Bond Theory
Applications
4.Tetrahedral sp3  hybrides (1, 2) = [A(1)B(2)  A(2)B(1)] 
[(1)(2)  (1)(2)]
z
t2
t1
y
X
t3
H
O
H
t4
use of sp3  hybrides
Use of
p - orbitals
A first approximation to the valence-bond
description of bonding in an H 2O molecule.
Each  bond arises from the overlap of an H1s
orbital with one o f the O2p orbitals. This
model sugge sts that the bond ang le shou ld be
90, which is significantly different from the
experimental value.
Valence Bond Theory
5.Bipyramidal
F
F
S
F
d2sp2  hybrides
tr3
F
F
P
F
F
Applications
F
z
d4
x
F
tr1
tr2
d5
y
1
tr1 
[s  px ]
3
1
1
3
tr2 
[s 
px  p y ]
3
2
2
1
1
3
tr3 
[s 
px  p y ]
3
2
2
1
d4 
[pz  d 2 ]
z
2
1
d5 
[p z  d 2 ]
z
2
Valence Bond Theory
5.Bipyramidal
d2sp2  hybrides
F
Applications
(1, 2) = [A(1)B(2)  A(2)B(1)] 
[(1)(2)  (1)(2)]
F
F
F
P
F
F
S
F
F
F
Valence Bond Theory
6. Octahedral
d2sp3  hybrides
z
4
y
1
3
5
2
6
x
Applications
(1, 2) = [A(1)B(2)  A(2)B(1)] 
[(1)(2)  (1)(2)]
1
oc1 
[s  2d 2  3pz ]
z
6
1
1
3
oc2 
[s 
d 2  d 2 2  3p x ]
6
2 z
2 x y
1
1
3
oc3 
[s 
d 2  d 2 2  3p y ]
6
2 z
2 x y
1
1
3
oc4 
[s 
d2
d 2 2  3px ]
z
6
2
2 x y
1
1
3
oc5 
[s 
d 2  d 2 2  3p y ]
6
2 z
2 x y
1
oc6 
[s  2d 2  3pz ]
z
6
Valence Bond Theory
Applications
(1, 2) = [A(1)B(2)  A(2)B(1)] 
[(1)(2)  (1)(2)]
6. Octahedral
d2sp3  hybrides
z
F
y
F
F
x
S
F
F
F
What you should learn from this lecture
1. You are not required to know the mathematical
form of the s and p atomic orbitals as well as
the sp, sp 2, sp3 , sp 2d2 , sp 3d2 hybrides. However you
should be able to draw their shapes
2. You should be able to convert Lewis structures
based on bonds and lone - pairs into valence
bond pair functions
(1, 2) = [A(1)B(2)  A(2)B(1)]  [(1)(2)  (1)(2)]
where A and B are atomic orbitals (or hybrides)
on different centers
for bonds , and orbitals on the same center
for lone - pairs