CHM 501

Homework 2

Due February 29, 2016



1. Identify the irreducible representations for all of the vibrations for [PdCl4]2–. Which of these vibrations are allowed by IR absorption spectroscopy?

First, draw the structure and label the important symmetry operations: The point group is D4h.

D4h

E

2C4

C2

2C2'

2C2"

i

2S4

σh

v

d

 

 

a1g

1

1

1

1

1

1

1

1

1

1

 

x2 + y2, z2

a2g

1

1

1

-1

-1

1

1

1

-1

-1

Rz

 

b1g

1

-1

1

1

-1

1

-1

1

1

-1

 

x2–y2

b2g

1

-1

1

-1

1

1

-1

1

-1

1

 

xy

eg

2

0

-2

0

0

2

0

-2

0

0

(Rx, Ry)

(xz, yz)

a1u

1

1

1

1

1

-1

-1

-1

-1

-1

 

 

a2u

1

1

1

-1

-1

-1

-1

-1

1

1

z

 

b1u

1

-1

1

1

-1

-1

1

-1

-1

1

 

 

b2u

1

-1

1

-1

1

-1

1

-1

1

-1

 

 

eu

2

0

-2

0

0

-2

0

2

0

0

(x, y)

 

Γcoordinates

15

1

-1

-3

-1

-3

-1

5

3

1

 

 

All coordinates transform as a1g + a2g + b1g + b2g + eg + 2a2u + b2u + 3eu. The translations transform as a2u + eu, the rotations transform as a2g + eg, which leaves the irreducibile representations for the vibrations as a1g + b1g + b2g + a2u + b2u + 2eu. Only the a2u + 2eu are IR active.

2. Determine the irreducible representations of the CO stretching vibrations in Ni(CO)4. Which of these vibrations are allowed by IR absorption spectroscopy?

First, draw the structure and label the important symmetry operations: The point group is Td.

Td

E

8C3

3C2

6S4

d

 

 

a1

1

1

1

1

1

 

x2 + y2 + z2

a2

1

1

1

-1

-1

 

 

e

2

-1

2

0

0

 

(2z2–x2–y2, x2–y2)

t1

3

0

-1

1

-1

(Rx, Ry, Rz)

 

t2

3

0

-1

-1

1

(x, y, z)

(xz, yz, xy)

ΓCO

4

1

0

0

2

 

 

The CO stretches transform as a1 + t2. Only the t2 vibration is IR active.

3. Find the irreducible representations for the σ orbitals in PF5. What is the hybridization on the P atom? What atomic orbitals are used to create the hybrid orbits? Be specific.

First, draw the structure and label the important symmetry operations: The point group is D3h.

D3h

E

2C3

3C2'

σh

2S3

v

 

 

a1'

1

1

1

1

1

1

 

x2 + y2, z2

a2'

1

1

-1

1

1

-1

Rz

 

e'

2

-1

0

2

-1

0

(x, y)

(x2–y2, xy)

a1"

1

1

1

-1

-1

-1

 

 

a2"

1

1

-1

-1

-1

1

z

 

e"

2

-1

0

-2

1

0

(Rx, Ry)

(xz, yz)

Γσ

5

2

1

3

0

3

 

 

The σ bonds transform as 2a1' + e' + a2".

The hybrid is sp3d with components of 3s (a1') + 3pz (a2") + (3px, 3py) (e') +3dz2 (a1').