Physical Chemistry , 1st ed.

elements. One can either determine all of the symmetry elements of a given

molecule and compare it to the (relatively short) list of point groups, or one

can use a flowchart like the one reproduced in Figure 13.14.

Example 13.3

Determine the point groups that define the symmetry of the following com-

pounds, whose structures are illustrated in Figure 13.15.

a.Hydrogen sulfide, H 2 S

b.Sulfur hexafluoride, SF 6

c.Acetylene, C 2 H 2

d.Benzene, C 6 H 6

e.The nitrate ion, NO 3 (assume resonance averages the structure into a flat,

triangular species).

Solution

Using Figure 13.14, satisfy yourself that the following point groups are indeed

correct by identifying the individual symmetry elements, if any exist other

than E.

428 CHAPTER 13 Introduction to Symmetry in Quantum Mechanics

h? Ye s Cnh

Cv No i? Ye s Dh

Cs Ye s

Are there n C 2

axes perpendicular to

the principal axis Cn?

One or more

highest-n-fold

Cn axis, n > 1?

h? Ye s Dnh

No Ye s

n v? Ye s Cnv n d? Ye s Dnd

No

i? Ci

C 1

? No Ye s

No

2 or more Cn’s,

n > 2?

No

No

I (^) h Ye s
Ye s N o
i? Td
Oh
C No
5?
Ye s
Ye s
A linear structure?
Does the molecule have:
No
No
S 2 n? Ye s S 2 n Dn
No
Cn
No
No
Yes – Note value of n.
This axis is the principal
axis. If there are more than 1
highest-n-fold axes, choose
one to be principal axis.
Figure 13.14 Flowchart for determining the point group of a molecule. It does not include
O,T,or Rh(3).Rh(3)is the point group of any single atom or ion.Source:Adapted from P. W.
Atkins,Physical Chemistry,5th ed., Freeman, New York, 1994.