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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

2

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-

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

7

Molecular orbital theory:

ligand group orbital approach in triatomic molecules

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9

10

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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

15

SF6

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.

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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