Inorganic Chemistry

1
Lectures 1-6 and 7

• Quantum-mechanics basis of the Periodic Table
• Periodic properties of atoms
• Molecular symmetry
• Symmetry elements and operations
• Point group
• Matrix representation of point groups
• Molecular properties
• dipole moment (67-69)
• chirality(102-103)
• IR vibrations (103-110)

2
From Molecular Formula to Properties

• Molecule
• Structure
• Point Group
• Orbital Symmetry
• Bonding Description
• Properties

3
Point Group Assignment

• Does the molecule belong to a special group?
• linear molecules D8h (CO2) or C8v (HCl, CO)
• molecules with multiple high order axes
• Oh octahedral (SF6) or Td tetrahedral (CH4)
• Molecule doesnt have proper or improper rotation
  axes
• C1, no symmetry element except identity, CHClBrF
• Cs, molecule has only a symmetry plane, H2CCBrCl
• Ci, molecule has only an inversion center
• Molecule has only Sn axes, Sn
• Decision tree for C and D groups

4
Dipole Moment and Optical Activity

• Molecule types that may have dipole moment
  (Section 3-3)
• molecules with no inversion center
• molecules with coincident Cn axes
• molecules with one mirror plane and no Cn axis
• molecules with mirror planes that contain the
  coincident Cn axes
• molecules with no symmetry
• Only molecules of symmetry Cn, Cnv, and Cs, may
  have a dipole moment.
• Molecules that may be chiral (Section 4-4-1)
• molecules with no symmetry operation
• molecules that have only proper axes of rotation
• Only molecules of symmetry Cn, Dn , T, O, and I
  may be chiral.

5
Optical Activity(Figure 4-19, page 103)
Electric field of left circularly polarized light
Absorption spectrum
CD spectrum
Electric field of right circularly polarized light
6
IR and Raman Spectroscopy
IR Spectroscopy
Incident Light
Transmitted Light
Sample cell
Scattered Light
Sample cell
Incident Light
Raman Spectroscopy
7
Molecular Vibrations for H2O
Matrix for C2 rotation
z
O
z
H
z
x
H
O
O
x
H
E C2 svxz svyz
H
C2v
H
y
x
y
O
H
H
G 9 -1 3 1
y
H
8
Character Table of Point Groups(See also Table
4-7 of textbook)
h, Order of group symmetry
operations 12122 8
Classes of operations
c, Dimension of irreducible representations
of classes of operations irreducible
representations h sum(cE(j))2, j represents
irreducible representations Formula for reducing
reducible representations
of operations in class R
character of reducible representation for class
R
character of irreducible representation for
class R
9
Molecular Vibrations for H2O
Translations along x, y, and z A1,B1,B2 Rotations
around x, y, and z A2,B1,B2 Vibrations 2A1B1
(A1) (1x9-1x13x11x1)/4 3 (A2)
(1x9-1x1-3x1-1x1)/4 1 (B1)
(1x91x13x1-1x1)/4 3 (B2)
(1x91x1-3x11x1)/4 2 G 3A1 1A2 3B1
2B2
10
Molecular Vibrations for H2OTable 4-11, p. 106
11
Topics for Quiz on February 13

• Apply symmetry operations to (x,y,z) axes
• Reduce a reducible representation to irreducible
  ones in the specific point group
• Identify the irreducible representation for s,
  p,and d orbitals of the central atom of a
  molecule using the Character Table of the Point
  Group
• Calculate the total degrees of freedom for a
  given molecule