8/3/2019 Chem 373- Lecture 24: Applications of Valence Bond Theory
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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 Molecules14.3 Polyatomic Molecules
Lecture on-line
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Applications of valence Bond Theory (PDF)
Handout for this lecture
8/3/2019 Chem 373- Lecture 24: Applications of Valence Bond Theory
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H H
Valence Bond Theory Applications
A 1sH; B 1sH
-bond:invarient to rotation
I. Diatomics
A B
(1,2) = [A(1)B(2)+ A(2)B(1)] ×[ (1) (2)− (1) (2)]
In general we write (re,RN)as the product of electron paifunctions i(r2i−1, r2i) as
(re ,RN) 1(r1, r2 ) 2(r3, r4 )
.. i(r2i 1, r2i) j(r2 j 1, r2j ).. n(r2n 1, r2n)
Pair 1
Pair 2
Pair i Pair j
Pair n
A li i
8/3/2019 Chem 373- Lecture 24: Applications of Valence Bond Theory
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H Cl
Applications
(1,2) = [A(1)B(2)+ A(2)B(1)] ×[ (1) (2)− (1) (2)]
+
sp(B):
1
2[3s + 3pz ]
Valence Bond Theory
Atomic orbitals on H(Hydrogen)
1sH
Atomic orbitals on C(Chlorine)
3sCl 3pzCl
3pxCl 3py
Cl
Hybride orbitals on H
(Hydrogen)
1sA
Hybride orbitals on Cl(Chlorine)
−sp(B) :
1
2[3s − 3pz ]
3px
Cl
3py
Cl
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Valence Bond Theory
A = 1sH;B = +sp(Cl)for -bond
Electron pairingand formation of bonds
(1,2) = [A(1)B(2)+ A(2)B(1)] ×[ (1) (2)− (1) (2)]
Electron pairingand formation oflone-pairs
A=
−
sp(Cl)
;B=
−
sp(Cl)
for lone-pair
H Cl
H Cl
3pxCl
A = 3pxCl
;B = 3pxCl
for lone-pair
H Cl
A = 3pyCl;B = 3py
Cl
for lone-pair
3pyCl
H Cl
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Atomic orbitals on Cl # 2
3sCl 3pzCl
3pxCl 3py
Cl
Cl Cl
Valence Bond Theory Applications
(1,2) = [A(1)B(2)+ A(2)B(1)] ×[ (1) (2)− (1) (2)]
Atomic orbitals on Cl # 1
3sCl 3pzCl 3pxCl 3pyCl
Hybride orbitals on Cl # 1
3pxCl 3py
Cl
+sp(Cl −
sp(Cl
Hybride orbitals on Cl # 2
3pxCl 3py
Cl+
sp(Cl−
sp(Cl
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Electron pairingand formation of bonds
Cl Cl
Valence Bond Theory Applications
(1,2) = [A(1)B(2)+ A(2)B(1)] ×[ (1) (2)− (1) (2)]
A = +
sp(Cl1);B = +
sp(Cl2
Cl Cl
−bond
Electron pairingand formation of
lone-pairs
A = −sp(Cl1) ;B = −
sp(Cl1)
for lone-pair
ClCl
3pxCl
A = 3pxCl1
;B= 3pxCl1
for lone-pair
Cl Cl
A = 3pyCl;B = 3py
Cl
for lone-pair
3pyCl
Cl Cl
Same for Cl # 2
8/3/2019 Chem 373- Lecture 24: Applications of Valence Bond Theory
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The orbital overlap
and spin-pairing
between electrons
in two collinear porbitals that result
in the formation
of a ( bond.
Valence Bond Theory Applications
(1,2 ) = [A(1)B(2)+A(2)B(1)] ×[ (1) (2)− (1) (2)]
Valence Bond Theory Applications
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Valence Bond Theory Applications
(1,2 ) = [A(1)B(2)+A(2)B(1)]×[ (1) (2)− (1) (2)]
I. Diatomics
N N C O
A =+
sp(1);B =
+
sp(2)
for -bond
+
sp(1):
1
2[2s + 2pz ]
+
sp(1):
1
2
[2s − 2pz ]
A = −sp(1) ;B = −
sp(1)
for lone-pairs
A = 2px1;B = 2px
1
A = 2py1;B = 2py
1
−
bonds
Orbitals change signon reflexation in plancontaining 1- 2 bond
vector
Valence Bond Theory Applications
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Valence Bond Theory Applications
(1,2 ) = [A(1)B(2)+A(2)B(1)]×[ (1) (2)− (1) (2)]
I. Diatomics
The structure of bonds in a nitrogen molecule,
which consists of one band and two bands.
The electron density has cylindrical symmetry
around the internuclear axis.
8/3/2019 Chem 373- Lecture 24: Applications of Valence Bond Theory
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Valence Bond Theory Applications
CH C H
2. Linear molecules
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 Applications
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Valence Bond Theory Applications3.Trigonal planar
C
H
H
C
H
HC2H4
C
H
H
O
CH2O
tr1
tr2
x
y
tr3
tr11
3 [s px ]
tr21
3[s
1
2px
3
2py ]
tr31
3 [s1
2 px3
2py ]
C2H4
CH2O
Valence Bond Theory Applications
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Valence Bond Theory Applications
C
H
H
C
H
HC2H4
C2H4
(a) An s orbital and two p orbitals can be
hybridized to form three equivalent orbitals
that point towards the corners of an equilateraltriangle. (b) The remaining, unhybridized p
orbital is perpendicular to the plane.
3.Trigonal planar
Valence Bond Theory Applications
8/3/2019 Chem 373- Lecture 24: Applications of Valence Bond Theory
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CH
H
H
H
X
y
z
t1
t2
t3
t4
Valence Bond Theory Applications
4.Tetrahedral
t11
2[s px py pz ]
along (x,y,z)
t21
2[s px py pz ]
along (-x,-y,z)
t31
2[s px py pz ]
along (-x,y,-z)
t41
2[s px py pz]
along (x,-y,-z)
sp
3
hybrides
Valence Bond Theory Applications
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An sp3 hybrid orbital formed from thesuperposition of s and p orbitals on the same
atom. There are four such hybrids: each one
points towards the corner of a regular
tetrahedron. The overall electron densityremains spherically symmetrical.
CH
H
H
H
Valence Bond Theory Applications
4.Tetrahedral sp3 hybrides
Valence Bond Theory Applications
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A more detailed representation of theformation of an sp
3 hybrid by interference
between wavefunctions centred on the same
atomic nucleus. (To simplify the
representation, we have ignored the radial
node of the 2 s orbital.)
CH
H
H
H
Valence Bond Theory Applications
4.Tetrahedral
sp3 hybrides
= +
V l B d Th Applications
8/3/2019 Chem 373- Lecture 24: Applications of Valence Bond Theory
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OH
H
NH
H
H
(1,2 ) = [A(1)B(2)+A(2)B(1)] ×[ (1) (2)− (1) (2)]
Valence Bond Theory Applications
4.Tetrahedral
sp3 hybrides
X
y
z
t1
t2
t3
t4
CH
H
H
H
X
y
z
t1
t2
t3
t4
X
y
z
t1
t2
t3
t4
Valence Bond Theory Applications
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A first approximation to the valence-bond
description of bonding in an H2O molecule.Each bond arises from the overlap of an H1s
orbital with one of the O2 p orbitals. This
model suggests that the bond angle should be
90°, which is significantly different from the
experimental value.
(1,2 ) = [A(1)B(2)+A(2)B(1)] ×[ (1) (2)− (1) (2)]
Valence Bond Theory Applications
4.Tetrahedral sp3 hybrides
OH
H
X
y
z
t1
t2
t3
t4
use of sp3 hybrides
Use of
p - orbitals
Valence Bond Theory Applications
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Valence Bond Theory Applications
5.Bipyramidal d2sp2 hybrides
PF
F
F
F
F
tr1
1
3[s p
x
]
tr21
3[s
1
2px
3
2py ]
tr3
1
3[s
1
2p
x
3
2p
y
]
tr1
tr2
x
y
tr3
d412
[pz dz2 ]
d51
2[pz d
z2 ]
d4
d5
z
SF
F
F
F
Valence Bond Theory Applications
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Valence Bond Theory Applications
5.Bipyramidal
d2sp2 hybrides
PF
F
F
F
F S
F
F
F
F
(1,2 ) = [A(1)B(2)+A(2)B(1)] ×[ (1) (2)− (1) (2)]
Valence Bond Theory Applications
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y pp
6. Octahedral
d2sp3 hybrides
(1,2 ) = [A(1)B(2)+A(2)B(1)] ×[ (1) (2)− (1) (2)]
1
2
34
56
x
y
z oc116
[s 2dz2 3pz ]
oc2
1
6[s
1
2d
z2
3
2d
x2 y2 3px ]
oc3
1
6[s
1
2d
z2
3
2d
x2 y2 3py ]
oc4
1
6[s
1
2d
z2
3
2d
x2 y2 3px ]
oc5
1
6[s
1
2d
z2
3
2d
x2 y2 3py ]
oc6
1
6[s 2d
z2 3p
z
]
Valence Bond Theory Applications
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y pp
6. Octahedral
d2sp3 hybrides
(1,2 ) = [A(1)B(2)+A(2)B(1)] ×[ (1) (2)− (1) (2)]
x
y
z
SF
F
F
F
F
F
What you should learn from this lecture
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What you should learn from this lecture
1. You are not required to know the mathematicalform of the s and p atomic orbitals as well as
the sp,sp2, sp3, sp2d2, sp3d2 hybrides. However youshould be able to draw their shapes
2. You should be able to convert Lewis structuresbased on bonds and lone- pairs into valencebond 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 centersfor bonds ,and orbitals on the same centerfor lone-pairs