**1. **Ch 4 Lecture 1 Symmetry and Point Groups Introduction
Symmetry is present in nature and in human culture

**2. **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

**3. **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

**4. **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

**5. **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

**6. **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

**7. **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

**10. **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

**11. **b. High Symmetry Groups

**12. **
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

**13. **C. Examples: Assign point groups of molecules in Fig 4.8 C8v D8h Td C1 Cs Ci Oh Ih

**14. **Rotation axes of ?normal? symmetry molecules

**15. **Perpendicular C2 axes
Horizontal Mirror Planes

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

**17. **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