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Ch 4 Lecture 1 Symmetry and Point GroupsPowerPoint Presentation

Ch 4 Lecture 1 Symmetry and Point Groups

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Ch 4 Lecture 1 Symmetry and Point Groups

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- Introduction
- Symmetry is present in nature and in human culture

- 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

- 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

- E (Identity Operation) = no change in the object

- 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

- 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
- sh = plane perpendicular to principle axis
- sv = plane includes the principle axis
- sd = plane includes the principle axis, but not the outer atoms

- 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

- 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

- 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

- 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

- Determine if the molecule is of high or low symmetry by inspection

- Definitions:

b.High Symmetry Groups

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

C∞v

D∞h

Td

C1

Cs

Ci

Oh

Ih

C.Examples: Assign point groups of molecules in Fig 4.8

Rotation axes of “normal” symmetry molecules

Perpendicular C2 axes

Horizontal Mirror Planes

Vertical or Dihedral Mirror Planes and S2n Axes

Examples: XeF4, SF4, IOF3, Table 4-4, Exercise 4-3

D.Properties of Point Groups

- Symmetry operation of NH3
- Ammonia has E, 2C3
(C3 and C23) and 3sv

b.Point group = C3v

- Ammonia has E, 2C3
- 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