Chapter 5 Bonding in polyatomic molecules

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

Directionalities of atomic orbitals are not compatible with the H-O-H bond angle.

1 Orbital hybridization - sp

1   (  ) sp _ hybrid 2 2s 2 px

1   (  ) sp _ hybrid 2 2s 2 px Hybrid orbitals – generated by mixing the characters of atomic orbitals

sp hybridized valence state is a formalism and is not a ‘real’ observation

2 Orbital hybridization – sp2

1 2      sp2 _ hybrid 3 2s 3 2 p x

1 1 1  sp2_ hybrid   2s   2 p   2 p 3 6 x 2 y

1 1 1        sp2_ hybrid 3 2s 6 2 px 2 2 py

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

3 sp3 hybrid orbitals – one s and three p atomic orbitals mix to form a set of four orbitals with different directional properties

1 1         sp3_ hybrid   2s  2 p  2 p  2 p  sp3_ hybrid 2 2s 2 px 2 py 2 pz 2 x y z 1 1  sp3_ hybrid   2s  2 p  2 p  2 p   sp3_ hybrid   2s  2 p  2 p  2 p  2 x y z 2 x y z

sp3d hybrid orbitals – one s, three p, and one d atomic orbitals mix to form a set of five orbitals with different directional properties

3- [Ni(CN)5]

4 Valence bond theory – multiple bonding in polyatomic molecules

Valence bond theory – multiple bonding in polyatomic molecules

5 Valence bond theory – multiple bonding in polyatomic molecules

Molecular orbital theory: ligand group orbital approach in triatomic molecules

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

7 8 The bonding is described by a consideration of all three bonding MOs

9 NH3

10 CH4

Td

11 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 E 2C3 3C2 h 2S3 3v 6m2

A1 1 1 1 1 1 1

A2 1 1 –1 1 1 –1 E 2 –1 0 2 –1 0

A1 1 1 1 –1 –1 –1

A2 1 1 –1 –1 –1 1 E 2 –1 0 –2 1 0

Molecular orbital theory: BF3

12 Consider the S3 operation (=C3·σh) on the pz orbitals in the F3 fragment. 2 C3

ψ ψ 2 1 ψ3

S3 S3

ψ3 ψ2 ψ ψ ψ 1 1 3 ψ2 Unique, ‘S3’ S3 σh S3 C3

ψ1 ψ3 ψ2

S3 S3

ψ ψ1 2 ψ3 ψ3 ψ2 ψ1

2 Unique, ‘S3 ’

2 The resulting wavefunction contributions from the S3 and S3 operations are –ψ3 and –ψ2, respectively.

13 Partial MO diagram that illustrates the formation of delocalized CO -bonds

14 SF6

15 5 Find number of unchanged radial 2p 2 orbitals that are unchanged under each Oh symmetry operation. 3 C2 Note the C2 axis bisect the planes containing 4 p orbitals. The C axis 1 2 contains no 2p orbitals.

4 C2 6

E C3 C2 C4 C2 i S4 S6 h d 2 (C4 ) 6 0 0 2 2 0 0 0 4 2

Use the reduction formula to find the resulting symmetries: a1g, t1u, eg

Could derive the equations for the LGOs for the F6 fragment.

1  (a )         1g 6 1 2 3 4 5 6 1  (t )     1u 1 2 1 6 1  (t )     1u 2 2 2 4 1  (t1u )3   3  5  12  (e )  2      2  g 1 12 1 2 3 4 5 6 1  (e )       g 2 2 2 3 4 5

16 Three-center two- electron interactions

17 B2H6

18 19