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

Bonding in polyatomic molecules

A comparison of the shape of the H2O molecule (the framework of which is taken as lying in the yz plane) with the spatial properties of the 2s, 2py and 2pz atomic orbitals of oxygen.

2

Orbital hybridization - sp

Hybrid orbitals – generated by mixing the characters of atomic orbitals

)(2

122_ xpshybridsp ψψψ +=

)(2

122_ xpshybridsp ψψψ −=

sp hybridized valence state of a beryllium atom from its ground state

3

Orbital hybridization – sp2

xpshybridsp 22_2 3

2

3

1 ψψψ +=

yx ppshybridsp 222_22

1

6

1

3

1 ψψψψ +−=

yx ppshybridsp 222_22

1

6

1

3

1 ψψψψ −−=

The formation of three sp2 hybrid orbitals from one 2s atomic orbital and two 2p atomic orbitals. The choice of px and py is arbitrary.

The bonding in trigonal planar BH3 can be conveniently described in terms of the interactions between a set of sp2 hybrid orbitals centred on the B atom and three H 1s atomic orbitals. Three pairs of electrons are available (three electrons from B and one from each H) to give three 2c-2e σ-bonds.

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

8

9

10

11

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 σh 2S3 3σv

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

13

Molecular orbital theory: BF3

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.

14

BF3 Resonance StructuresBF3 Resonance Structures

The presence of the resonance contributions account for the partial double bond character in BF3

15

16

SF6

17

3

1

2

4

6

5 Find number of unchanged radial 2p orbitals that are unchanged under each Oh

symmetry 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 σh σd

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.

( )65432116

1)( ψψψψψψψ +++++=ga

( )61112

1)( ψψψ −=ut

( )42212

1)( ψψψ −=ut

( )53312

1)( ψψψ −=ut

( )6543211 2212

1)( ψψψψψψψ +−−−−=ge

( )54322 2

1)( ψψψψψ −+−=ge

18

Three-center two-electron interactions

19

20