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

7

MO diagram is constructed by allowing interactions between orbitals of the same symmetry.

8

9

The bonding is described by a consideration of all three bonding MOs

10

NH3

11

CH4

Td

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.

14

Partial MO diagram that illustrates the formation of delocalized CO -bonds

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.

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

17

Three-center two-electron interactions

18

B2H6

19