Symmetry and the point groups

1
Symmetry and the point groups
2
(No Transcript)
3
Symmetry Elements and Symmetry Operations

• Identity
• Proper axis of rotation
• Mirror planes
• Center of symmetry
• Improper axis of rotation

4
Symmetry Elements and Symmetry Operations

• Identity gt E

5
Symmetry Elements and Symmetry Operations

• Proper axis of rotation gt Cn
• where n 2, 180o rotation
• n 3, 120o rotation
• n 4, 90o rotation
• n 6, 60o rotation
• n , (1/ )o rotation
• principal axis of rotation, Cn

6
2-Fold Axis of Rotation
7
3-Fold Axis of Rotation
8
Rotations for a Trigonal Planar Molecule
9
Symmetry Elements and Symmetry Operations
Mirror planes
sh gt mirror plane perpendicular to a
principal axis of rotation
sv gt mirror plane containing principal axis of
rotation
sd gt mirror plane bisects dihedral angle made
by the principal axis of rotation and two
adjacent C2 axes perpendicular to principal
rotation axis
10
Mirrors
sv
sv Cl Cl sh I
sd sd Cl Cl
11
Rotations and Mirrors in a Bent Molecule
12
Benzene Ring
13
Symmetry Elements and Symmetry Operations

• Center of symmetry gt i

14
Center of Inversion
15
Inversion vs. C2
16
Symmetry Elements and Symmetry Operations

• Improper axis of rotation gt Sn
• rotation about n axis (360 /n) followed by
  reflection through a plane perpendicular to the
  axis

17
Improper Rotation in a Tetrahedral Molecule
18
S1 and S2 Improper Rotations
19
Successive C3 Rotations onTrigonal Pyramidal
Molecule
20
Linear Molecules
21
Selection ofPoint Group from Shape

• first determine shape using Lewis Structure and
  VSEPR Theory
• next use models to determine which symmetry
  operations are present
• then use the flow chart to determine the point
  group

22
(No Transcript)
23
Decision Tree
24
(No Transcript)
25
(No Transcript)
26
(No Transcript)
27
Selection ofPoint Group from Shape
1. determine the highest axis of
rotation 2. check for other non-coincident axis
of rotation 3. check for mirror planes
28
H2O and NH3
29
(No Transcript)
30
(No Transcript)
31
Geometric Shapes
32
E, S4, C2

Point Groups with improper axes S2n (n 2)
1,3,5,7-tetrafluorocycloocta-1,3,5,7-tetraene
(S4)
33
2) Point Groups of high symmetry (cubic groups)

• In contrast to groups C, D, and S, cubic symmetry
  groups are characterized by the presence of
  several rotational axes of high order ( 3).
• Cases of regular polyhedra
• Td (tetrahedral) BF4- , CH4
• Symmetry elements E, 4C3, 3C2, 3S4, 6sd
• Symmetry operations E, 8C3, 3C2, 6S4, 6sd
• If all planes of symmetry and i are missing, the
  point group is T (pure rotational group, very
  rare)

34
3) Point Groups of high symmetry

• Oh (octahedral) TiF62-, cubane C8H8
• Symmetry elements E, i, 4S6, 4C3, 3S4, 3C4,
  6C2, 3 C2, 3sh, 6sd
• Symmetry operations E, i, 8S6, 8C3, 6S4, 6C4,
  6C2, 3 C2, 3sh, 6sd
• Pure rotational analogue is the point group O (no
  mirror planes and no Sn very rare)

35
4) Point Groups of high symmetry
Th group (symmetry elements E, i, 4S6, 4C3, 3C2,
3sh) can also be considered as a result of
reducing Oh group symmetry (E, i, 4S6, 4C3, 3S4,
3C4, 6C2, 3 C2, 3sh, 6sd ) by eliminating C4,
S4 and some C2 axes and sd planes
36
Point Groups of high symmetry

• Ih (icosahedral) B12H122-, C20
• Symmetry elements E, i, 6S10, 6C5, 10S6, 10C3,
  15C2, 15s
• Pure rotation analogue is the point group I (no
  mirror planes and thus no Sn, very rare)

37
Enantiomer Pairs
38
Enantiomer Pairs
39
Polarimeter
40
(b) Chirality A chiral molecule not
superimposed on its mirror image. optically
active (rotate the plane of polarized)
A molecule may be chiral only if it does not
posses an axis of improper rotation Sn. All
molecules with center of inversion are achiral ?
optically inactive. S1s any molecule with a
mirror plane is achiral.
41
(No Transcript)