1 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 Chapter 5 Bonding in polyatomic molecules
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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
Chapter 5
Bonding in polyatomic molecules
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Orbital hybridization - sp
Hybrid orbitals – generated by mixing the characters of atomic orbitals
)(2
122_ xpshybridsp ψψψ +=
)(2
122_ xpshybridsp ψψψ −=
3
Orbital hybridization – sp2
xpshybridsp 22_2 32
31 ψψψ +=
yx ppshybridsp 222_2 21
61
31 ψψψψ +−=
yx ppshybridsp 222_2 21
61
31 ψψψψ −−=
4
sp3 hybrid orbitals – one s and three p atomic orbitals mix to form a set of four orbitals with different directional properties
( )zyx pppshybridsp 2222_3 2
1 ψψψψψ +++=
( )zyx pppshybridsp 2222_3 2
1 ψψψψψ −−+=
( )zyx pppshybridsp 2222_3 2
1 ψψψψψ −+−=
( )zyx pppshybridsp 2222_3 2
1 ψψψψψ −−−=
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-
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Valence bond theory – multiple bonding in polyatomic molecules
Valence bond theory – multiple bonding in polyatomic molecules
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Valence bond theory – multiple bonding in polyatomic molecules
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Molecular orbital theory:
ligand group orbital approach in triatomic molecules
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Molecular orbital theory: BF3
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S3
S3
ψ1
ψ2
ψ3
S3
ψ3
ψ1
ψ2
S3
ψ2
ψ3
ψ1
ψ1
ψ2
ψ3
S3
ψ3
ψ1
ψ2
ψ2
ψ3
ψ1
Consider the S3 operation (=C3·σh) on the pz orbitals in the F3 fragment.
S3
C32
σhC3
Unique, ‘S3’
Unique, ‘S32’
The resulting wavefunction contributions from the S3 and S32
operations are –ψ3 and –ψ2, respectively.
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BF3 Resonance StructuresBF3 Resonance Structures
The presence of the resonance contributions account for the partial double bond character in BF3
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SF6
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3
1
2
4
6
5 Find number of unchanged radial 2p orbitals that are unchanged under each Ohsymmetry operation.
C2 Note the C2 axis bisect the planes containing 4 p orbitals. The C2 axis contains no 2p orbitals.
0
S6
0
S4
24022006
σdσhiC2(C4
2)C4C2C3E
C2
Use the reduction formula to find the resulting symmetries: a1g, t1u, eg
Could derive the equations for the LGOs for the F6 fragment.
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( )6543211 61)( ψψψψψψψ +++++=ga
( )6111 21)( ψψψ −=ut
( )4221 21)( ψψψ −=ut
( )5331 21)( ψψψ −=ut
( )6543211 22121)( ψψψψψψψ +−−−−=ge
( )54322 21)( ψψψψψ −+−=ge
Three-center two-electron interactions
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