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 Molecules 14.3 Polyatomic Molecules Lecture on-line Applications of Valence Bond Theory (PowerPoint) Applications of valence Bond Theory (PDF)
Handout for this lecture
H H
Valence Bond Theory Applications
A =1sH;B =1sHσ-bond: invarient to rotation
I. Diatomics
A B
ξ(1,2) =[A(1)B(2)+A(2)B(1)]×[α(1)β(2)−β(1)α(2)]
In general we write ψ(re,RN)as the product of electron pairfunctions ωi(r2i−1,r2i) as
ψ(re,RN) = ω1(r1,r2 ) × ω2(r3,r4 ) ×..ωi(r2i−1,r2i) × ωj(r2j−1,r2j).. × ωn(r2n−1,r2n)
Pair 1Pair 2
Pair i Pair jPair n
H Cl
Applicationsξ(1,2) =[A(1)B(2)+A(2)B(1)]×[α(1)β(2)−β(1)α(2)]
σ+sp(B) :
12
[3s+3pz]
Valence Bond Theory
Atomic orbitals on H (Hydrogen)
1sH
Atomic orbitals on Cl (Chlorine)
3sCl 3pzCl
3pxCl 3py
Cl
Hybride orbitals on H (Hydrogen)
1sA
Hybride orbitals on Cl (Chlorine)
σ−sp(B) :
12
[3s−3pz]
3pxCl 3py
Cl
Valence Bond Theory
A =1sH;B=σ+sp(Cl)
for σ-bond
Electron pairing and formation of bonds
ξ(1,2) =[A(1)B(2)+A(2)B(1)]×[α(1)β(2)−β(1)α(2)]
Electron pairing and formation oflone-pairs
A =σ−sp(Cl);B=σ−
sp(Cl)
for lone-pair
H Cl
H Cl
3pxCl
A = 3pxCl;B=3px
Cl
for lone-pair
H Cl
A = 3pyCl;B=3py
Cl
for lone-pair
3pyCl
H Cl
Atomic orbitals on Cl # 2
3sCl 3pzCl
3pxCl 3py
Cl
Cl Cl
Valence Bond Theory Applications
ξ(1,2) =[A(1)B(2)+A(2)B(1)]×[α(1)β(2)−β(1)α(2)]
Atomic orbitals on Cl # 1
3sCl 3pzCl
3pxCl 3py
Cl
Hybride orbitals on Cl # 1
3pxCl 3py
Clσ+sp(Cl) σ−
sp(Cl)
Hybride orbitals on Cl # 2
3pxCl 3py
Clσ+sp(Cl) σ−
sp(Cl)
Electron pairing and formation of bonds
Cl Cl
Valence Bond Theory Applicationsξ(1,2) =[A(1)B(2)+A(2)B(1)]×[α(1)β(2)−β(1)α(2)]
A =σ+sp(Cl1) ;B =σ+
sp(Cl2)
Cl Cl
σ−bond
Electron pairing and formation oflone-pairs
A =σ−sp(Cl1);B=σ−
sp(Cl1)
for lone-pair
Cl Cl
3pxCl
A= 3pxCl1;B=3px
Cl1
for lone-pair
Cl Cl
A = 3pyCl;B=3py
Cl
for lone-pair
3pyCl
Cl Cl
Same for Cl # 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
ξ(1,2) =[A(1)B(2)+A(2)B(1)]×[α(1)β(2)−β(1)α(2)]
Valence Bond Theory Applications
ξ(1,2) =[A(1)B(2)+A(2)B(1)]×[α(1)β(2)−β(1)α(2)]
I. Diatomics
N N C O
A =σ+sp(1);B=σ+
sp(2)
for σ-bondσ+sp(1) :
12
[2s+2pz]
σ+sp(1) :
12
[2s−2pz]
A =σ−sp(1);B=σ−
sp(1)
for lone-pairs
A =2px1;B=2px
1
A =2py1;B=2py
1
π−bonds
Orbitals change signon reflexation in planecontaining 1-2 bond vector
Valence Bond Theory Applications
ξ(1,2) =[A(1)B(2)+A(2)B(1)]×[α(1)β(2)−β(1)α(2)]
I. Diatomics
The structure of bonds in a nitrogen molecule,which consists of one σ banda ndt woπ bands.
Theelect ron densi ty h ascylindrica l symmetryar ound th e internucle araxi .s
Valence Bond Theory Applications
CH C H
2. Linear molecules
A representation of the structure of a triple bond in ethyne; only the π bonds are shown explicitly. The overall electron density has cylindrical symmetry around the axis of the molecule.
Valence Bond Theory Applications3.Trigonal planar
C
H
H
C
H
HC2H4
C
H
H
O
CH2O
tr1
tr2
x
y
tr3
tr1 =13[s +px ]
tr2 =13[s −
12px +
32py ]
tr3 =13[s −
12px −
32py ]
C2H4
CH2O
Valence Bond Theory Applications
C
H
H
C
H
HC2H4
C2H4
(a) An s orbital and two p orbitals can behybridized to form three equivalent orbitalsthat point towards the corners of an equilateraltriangle. (b) The remaining, unhybridized porbital is perpendicular to the plane.
3.Trigonal planar
CH
H
H
H
X
y
z
t1
t2
t3
t4
Valence Bond Theory Applications
4.Tetrahedralt1 =
12[s +px +py +pz ]
( ,along x ,y )z
t2 =12[s −px −py +pz ]
(- ,along x- ,y )z
t3 =12[s −px +py −pz ]
(- ,along x ,y - )z
t4 =12[s +px −py −pz]
( ,along x- ,y - )z
sp3 −hybrides
An sp3 hybrid orbital formed from thesuperposition of s and p orbitals on the sameatom. There are four such hybrids: each onepoints towards the corner of a regulartetrahedron. The overall electron densityremains spherically symmetrical.
CH
H
H
H
Valence Bond Theory Applications
4.Tetrahedral sp3 −hybrides
A more detailed representation of theformation of an sp3 hybrid by interferencebetween wavefunctions centred on the sameatomic nucleus. (To simplify therepresentation, we have ignored the radialnode of the 2s orbital.)
CH
H
H
H
Valence Bond Theory Applications
4.Tetrahedral
sp3 −hybrides
= +
OH
H
NH
H
H
ξ(1,2) =[A(1)B(2)+A(2)B(1)]×[α(1)β(2)−β(1)α(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
A first approximation to the valence-bonddescription of bonding in an H2O molecule.Each σ bond ari sesfro m t he overl ap ofa 1n Hsorbita l wit h one o f th e 2O p orbitals. Thismode l sugge sts tha t t he bond ang leshoul d be90°, whi ch is significantl y differen t fro mtheexperimenta l value.
ξ(1,2) =[A(1)B(2)+A(2)B(1)]×[α(1)β(2)−β(1)α(2)]
Valence Bond Theory Applications
4.Tetrahedral sp3 −hybrides
OH
HX
y
z
t1
t2
t3
t4
use of sp3 −hybrides
Use of p - orbitals
Valence Bond Theory Applications
5.Bipyramidal d2sp2 −hybrides
PF
F
F
F
F
tr1 =13[s +px ]
tr2 =13[s −
12px +
32py ]
tr3 =13[s −
12px −
32py ]
tr1
tr2
x
y
tr3
d4 =12[pz +dz2 ]
d5 =12[pz −dz2 ]
d4
d5
z
SF
F
F
F
Valence Bond Theory Applications
5.Bipyramidald2sp2 −hybrides
PF
F
F
F
F S
F
F
F
F
ξ(1,2) =[A(1)B(2)+A(2)B(1)]×[α(1)β(2)−β(1)α(2)]
Valence Bond Theory Applications
6. Octahedral
d2sp3 −hybridesξ(1,2) =[A(1)B(2)+A(2)B(1)]×[α(1)β(2)−β(1)α(2)]
1
2
34
5
6 x
y
zoc1 =
16[s + 2d
z2+ 3pz ]
oc2 =16[s−
12dz2
+32dx2−y2
+ 3px ]
oc3 =16[s−
12dz2
−32dx2−y2
+ 3py ]
oc4 =16[s −
12dz2
+32dx2−y2
− 3px ]
oc5 =16[s −
12dz2
−32dx2−y2
− 3py ]
oc6 =16[s + 2d
z2− 3pz ]
Valence Bond Theory Applications
6. Octahedral
d2sp3 −hybridesξ(1,2) =[A(1)B(2)+A(2)B(1)]×[α(1)β(2)−β(1)α(2)]
x
y
z
SF
F
FF
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,sp2,sp3,sp2d2,sp3d2 hybrides. However youshould be able to draw their shapes
2. You should be able to convert Lewis structures based on bonds and lone-pairs into valencebond pair functions ξ(1,2) =[A(1)B(2)+A(2)B(1)]×[α(1)β(2)−β(1)α(2)]where A and B are atomic orbitals (or hybrides)on different centersfor bonds ,and orbitals on the same center for lone-pairs
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