7/22/2019 Vincent Group theory

1/11

Molecular Symmetry and Group Theory

Alan Vincent(Wiley, 1988)

Chapter 2

7/22/2019 Vincent Group theory

2/11

7/22/2019 Vincent Group theory

3/11

H H H

There is no need to include h or d in the symmetry symbol.If the principal axis is a three-fold axis what is the symmetry

symbol in this case?

7/22/2019 Vincent Group theory

4/11

en

7/22/2019 Vincent Group theory

5/11

Many molecules have no symmetry at all (i.e. their onlysymmetry element is the identity, E. Such molecules belong tothe C1 point group.

The following are examples ofmolecules with only one or twosymmetry elements .What are their point groups?

C

Cl

F

H

H

C

Cl

Br

H

H

A/ B/

7/22/2019 Vincent Group theory

6/11

A simple rule to remember is that any n-fold staggered structure (likeC

2H

6, Mn

2(CO)

10etc) belongs to the point group D

nd, and you may find

it easier to remember this rule.

C2

C2

C2C2

d

d

d

7/22/2019 Vincent Group theory

7/11

Note particularly that it is the symmetry OPERATIONS, not theelements which form a group.Confirm rule c. for the elements C2, , and of the C2v group, i.e. work

out the effect of (C2 ) and of C2 ( ).

7/22/2019 Vincent Group theory

8/11

(call the new position P)

7/22/2019 Vincent Group theory

9/11

P C3 is clockwise

7/22/2019 Vincent Group theory

10/11

C2 v

C2 v

C3 S3

B Cl

Cl

Cl

7/22/2019 Vincent Group theory

11/11

the small letter is omitted |Horizontal plane (h) present Dnh

|n Vertical planes (dihedral planes, d,bisecting angles between C2 axes)present Dnd

|Absent - Dn

|Horizontal plane (h)present Cnh| |n Vertical planes present(d) Cnv

|Absent - Cn