9. Molecular Symmetry

10. Symmetry Elements and Operations
Using Symmetry in Chemistry
Understand what orbitals are used in bonding
Predict IR spectra or Interpret UV-Vis spectra
Predict optical activity of a molecule
Symmetry Elements and Operations
Definitions
Symmetry Element = geometrical entity such as a line, a plane, or a point, with respect to which one or more symmetry operations can be carried out
Symmetry Operation = a movement of a body such that the appearance after the operation is indistinguishable from the original appearance (if you can tell the difference, it wasn’t a symmetry operation)
The Symmetry Operations
E (Identity Operation) = no change in the object
Needed for mathematical completeness
Every molecule has at least this symmetry operation

11. Cn (Rotation Operation) = rotation of the object 360/n degrees about an axis
The symmetry element is a line
Counterclockwise rotation is taken as positive
Principle axis = axis with the largest possible n value
Examples:
C23 = two C3’s
C33 = E
C17 axis

12. s (Reflection Operation) = exchange of points through a plane to an opposite and equidistant point
Symmetry element is a plane
Human Body has an approximate s operation
Linear objects have infinite s‘s
s h = plane perpendicular to principle axis
s v = plane includes the principle axis
s d = plane includes the principle axis, but not the outer atoms

13. i (Inversion Operation) = each point moves through a common central point to a position opposite and equidistant
Symmetry element is a point
Sometimes difficult to see, sometimes not present when you think you see it
Ethane has i, methane does not
Tetrahedra, triangles, pentagons do not have i
Squares, parallelograms, rectangular solids, octahedra do

14. Sn (Improper Rotation Operation) = rotation about 360/n axis followed by reflection through a plane perpendicular to axis of rotation
Methane has 3 S4 operations (90 degree rotation, then reflection)
2 Sn operations = Cn/2 (S24 = C2)
nSn = E, S2 = i, S1 = s
Snowflake has S2, S3, S6 axes

15. Examples:
H2O: E, C2, 2s
p-dichlorobenzene: E, 3s, 3C2, i
Ethane (staggered): E, 3s, C3, 3C2, i, S6
Try Ex. 4-1, 4-2

18. Point Groups Definitions:
Point Group = the set of symmetry operations for a molecule
Group Theory = mathematical treatment of the properties of the group which can be used to find properties of the molecule
Assigning the Point Group of a Molecule
Determine if the molecule is of high or low symmetry by inspection
a. Low Symmetry Groups

19. b. High Symmetry Groups

20. 2. If not, find the principle axis
3. If there are C2 axes perpendicular
to Cn the molecule is in D
If not, the molecule will be in C or S
a. If sh perpendicular to Cn then Dnh or Cnh
If not, go to the next step
b. If s contains Cn then Cnv or Dnd
If not, Dn or Cn or S2n
c. If S2n along Cn then S2n
If not Cn

21. C∞v
D∞h Td C1 Cs Ci Oh Ih
C. Examples: Assign point groups of molecules in Fig 4.8

22. Rotation axes of “normal” symmetry molecules

23. Perpendicular C2 axes
Horizontal Mirror Planes

24. Vertical or Dihedral Mirror Planes and S2n Axes
Examples: XeF4, SF4, IOF3, Table 4-4, Exercise 4-3

25. D. Properties of Point Groups
Symmetry operation of NH3
Ammonia has E, 2C3
(C3 and C23) and 3sv
b. Point group = C3v
Properties of C3v (any group)
Must contain E
Each operation must
have an inverse; doing both
gives E (right to left)
Any product equals
another group member
Associative property