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
Directionalities of atomic orbitals are not compatible with the H-O-H bond angle.
2
Orbital hybridization - sp
Hybrid orbitals – generated by mixing the characters of atomic orbitals
)(2
122_ xpshybridsp
)(2
122_ xpshybridsp
sp hybridized valence state is a formalism and is not a ‘real’ observation
3
Orbital hybridization – sp2
xpshybridsp 22_2 32
31
yx ppshybridsp 222_2 21
61
31
yx ppshybridsp 222_2 21
61
31
Trigonal planar molecule, BH3
Each B-H interaction is formed by the overlap of one B sp2
hybrid orbital with the 1s atomic orbital of an H atom
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
zyx pppshybridsp 2222_3 2
1
zyx pppshybridsp 2222_3 2
1
zyx pppshybridsp 2222_3 2
1
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-
5
Valence bond theory – multiple bonding in polyatomic molecules
Valence bond theory – multiple bonding in polyatomic molecules
6
Valence bond theory – multiple bonding in polyatomic molecules
Molecular orbital theory:
ligand group orbital approach in triatomic molecules
12
Derive the symmetries of the valence orbitals and symmetries for the ligand group orbitals (LGOs) to derive a qualitative MO diagram for BF3. Determine the composition of each LGO in terms of the individual wavefunctions ψ1, ψ2, … and sketch the resulting LGO.
D3h
26 m E 2C3 3C2 h 2S3 3v
1A 1 1 1 1 1 1
2A 1 1 –1 1 1 –1 E 2 –1 0 2 –1 0
1A 1 1 1 –1 –1 –1
2A 1 1 –1 –1 –1 1
E 2 –1 0 –2 1 0
Molecular orbital theory: BF3
13
S3
S3
ψ1
ψ2
ψ3
S3
ψ3
ψ1
ψ2
S3
ψ2
ψ3
ψ1
ψ1
ψ2
ψ3
S3
ψ3
ψ1
ψ2ψ2
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.
16
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.
E C3 C2 C4 C2(C4
2)i S4 S6 h d
6 0 0 2 2 0 0 0 4 2
C2
Use the reduction formula to find the resulting symmetries: a1g, t1u, eg
Could derive the equations for the LGOs for the F6 fragment.
6543211 61)( ga
6111 21)( ut
4221 21)( ut
5331 21)( ut
6543211 22121)( ge
54322 21)( ge
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