All Known Molecules Belong to One of 32 Symmetry Groups (Point Groups)

All known molecules belong to one of 32 Symmetry Groups (Point Groups).

Assigning the Point Group of a molecule.

Follow the questions in the Flow Chart to find the Point Group label of the molecule.

The ‘Special Groups’ – Linear (C∞v, D∞h) Tetrahedral (Td), Octahedral (Oh) and Icosahedral (Ih)– are eliminated first.

Then the distinction between Rotation(C, D, S) and non-Rotation groups (Ci, Cs, C1).

Then the distinction between simple rotation (C), dihedral rotation (D) and improper rotation (S) groups.

There are tables in nearly all Inorganic, Physical and Spectroscopy textbooks that give all the symmetry operations (elements) of the Point Groups.

From CM3003 exam 2005

Summer (i) List, and then illustrate, the elements of symmetry in each of the following species. State to which point groups these molecules belong?

a) O=PCl3

b) tetrachloroethene, C2Cl4

c) IF5

2- e) [PtCl4] (8 marks) Autumn (i) List, and then illustrate, the elements of symmetry in each of the following species. State to which point groups these molecules belong?

a) SF4 b) 1, 4 - dichlorobenzene

c) IF5

- d) the cyclopentadienyl anion [C5H5] (8 marks) The elements of a Group are collected into Classes. A Class is a set of symmetry operations that are identical except for their orientation.

(The real definition is much more detailed.)

C2v : E C2 σv(yz) σv(xz) (4 Classes)

C3v : E 2C3 3σv (3 Classes)

D2h: E C2(z) C2 (y) C2 (x) i σv(xy) σv(xz) σv(yz) (8 Classes)

2 3 D5d: E 2C5 2C5 5C2 i 2S10 2S10 5σd (8 Classes)

Td: E 8C3 3C2 6S4 6 σd (5 Classes)

φ 2φ 3φ C∞v: E 2C∞ 2C∞ 2C∞ … ∞σv (∞ Classes)