Chapter 5
Bonding in polyatomic molecules
Polyatomic species: contains three or more atoms
Three approaches to bonding in diatomic molecules
1. Lewis structures
2. Valence bond theory
3. Molecular orbital theory
1
Orbital hybridization - sp
ψ sp _ hybrid =
ψ sp _ hybrid =
Hybrid orbitals – generated by mixing
the characters of atomic orbitals
1
(ψ 2 s + ψ 2 px )
2
1
(ψ 2 s − ψ 2 px )
2
2
Orbital hybridization – sp2
ψ sp 2 _ hybrid =
1
2
ψ 2 s + ψ 2 px
3
3
ψ sp 2 _ hybrid =
1
1
1
ψ 2 s − ψ 2 px + ψ 2 p y
3
6
2
ψ sp 2 _ hybrid =
1
1
1
ψ 2 s − ψ 2 px − ψ 2 p y
3
6
2
3
sp3 hybrid orbitals – one s and three p atomic orbitals mix to
form a set of four orbitals with different directional properties
(
)
(
)
(
)
ψ sp 3 _ hybrid =
1
ψ 2 s −ψ 2 p x + ψ 2 p y −ψ 2 p z
2
(
)
ψ sp 3 _ hybrid =
1
ψ 2 s −ψ 2 p x − ψ 2 p y −ψ 2 p z
2
ψ sp 3 _ hybrid =
1
ψ 2 s +ψ 2 px +ψ 2 p y +ψ 2 p z
2
ψ sp 3 _ hybrid =
1
ψ 2 s + ψ 2 p x −ψ 2 p y −ψ 2 p z
2
sp3d hybrid orbitals – one s, three p, and one d atomic orbitals
mix to form a set of five orbitals with different directional properties
[Ni(CN)5]3-
4
Valence bond theory – multiple bonding in polyatomic molecules
Valence bond theory – multiple bonding in polyatomic molecules
5
Valence bond theory – multiple bonding in polyatomic molecules
6
Molecular orbital theory:
ligand group orbital approach in triatomic molecules
7
8
9
10
11
Molecular orbital theory: BF3
12
Consider the S3 operation (=C3·σh) on the pz orbitals in the F3 fragment.
C3 2
ψ2
ψ1
S3
ψ3
ψ2
ψ1
Unique, ‘S3’
S3
ψ1
ψ3
S3
ψ1
ψ3
ψ2
S3
S3
ψ2
ψ2
ψ2
σh
C3
ψ1
ψ3
S3
ψ3
ψ3
ψ1
Unique, ‘S32’
The resulting wavefunction contributions from the S3 and S32
operations are –ψ3 and –ψ2, respectively.
13
BF33 Resonance Structures
The presence of the
resonance
contributions account
for the partial double
bond character in BF3
14
SF6
15
5
Find number of unchanged radial 2p
orbitals that are unchanged under each Oh
symmetry operation.
2
3
C2 Note the C2 axis bisect the planes
containing 4 p orbitals. The C2 axis
contains no 2p orbitals.
1
4
C2
6
E
C3
C2
C4
6
0
0
2
C2 i S4
(C42)
2
0 0
S6
σh
σd
0
4
2
Use the reduction formula to find the resulting symmetries: a1g, t1u, eg
Could derive the equations for the LGOs for the F6 fragment.
16
1
(ψ 1 +ψ 2 +ψ 3 +ψ 4 +ψ 5 +ψ 6 )
6
1
ψ (t1u )1 =
(ψ 1 −ψ 6 )
2
1
ψ (t1u ) 2 =
(ψ 2 −ψ 4 )
2
1
ψ (t1u )3 =
(ψ 3 −ψ 5 )
12
ψ (eg )1 =
(2ψ 1 −ψ 2 −ψ 3 −ψ 4 −ψ 5 + 2ψ 6 )
12
1
ψ (eg ) 2 = (ψ 2 −ψ 3 + ψ 4 −ψ 5 )
2
ψ (a1g ) =
Three-center twoelectron interactions
17
18
19
20