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The Character Table for C 2 v The Character Table for C 3 v
Outline
1 Introduction to Character Tables
2 The Character Table for C 2 v
3 The Character Table for C 3 v
The Character Table for C 2 v The Character Table for C 3 v
Quote from Eugene Paul Wigner
See also: Current Science, vol. 69, no. 4, 25 August 1995, p. 375
From the preface to his book on group theory:
Wigner relates a conversation with von Laue on the use of group
theory as the natural tool with which to tackle problems in
quantum mechanics. “I like to recall his question as to which
results... I considered most important. My answer was that the
explanation of Laporte’s rule (the concept of parity) and the
quantum theory of the vector addition model appeared to me most
significant. Since that time, I have come to agree with his answer
that the recognition that almost all rules of spectroscopy follow
from the symmetry of the problem is the most remarkable result.”
The Character Table for C 2 v The Character Table for C 3 v
What Makes Up a Character Table
Character tables contain information about how functions transform in response to the
operations of the group
Five parts of a character table
1 At the upper left is the symbol for the point group
2 The top row shows the operations of the point group,
organized into classes
3 The left column gives the Mulliken symbols for each of the
irreducible representations
4 The rows at the center of the table give the characters of the
irreducible representations
5 Listed at right are certain functions, showing the irreducible
representation for which the function can serve as a basis
The Character Table for C 2 v The Character Table for C 3 v
What Makes Up a Character Table
Character tables contain information about how functions transform in response to the
operations of the group
Five parts of a character table
1 At the upper left is the symbol for the point group
2 The top row shows the operations of the point group,
organized into classes
3 The left column gives the Mulliken symbols for each of the
irreducible representations
4 The rows at the center of the table give the characters of the
irreducible representations
5 Listed at right are certain functions, showing the irreducible
representation for which the function can serve as a basis
The Character Table for C 2 v The Character Table for C 3 v
What Makes Up a Character Table
Character tables contain information about how functions transform in response to the
operations of the group
Five parts of a character table
1 At the upper left is the symbol for the point group
2 The top row shows the operations of the point group,
organized into classes
3 The left column gives the Mulliken symbols for each of the
irreducible representations
4 The rows at the center of the table give the characters of the
irreducible representations
5 Listed at right are certain functions, showing the irreducible
representation for which the function can serve as a basis
The Character Table for C 2 v The Character Table for C 3 v
The C 2 v Character Table
The Character Table for C 2 v The Character Table for C 3 v
Transformation Properties of an s Orbital in C 2 v
What happens when the E operation is applied?
The E operation is a rotation by 360
about an arbitrary axis
The Character Table for C 2 v The Character Table for C 3 v
Transformation Properties of an s Orbital in C 2 v
The E operation returns the original configuration of the s orbital
The result of this corresponds to a character of 1
The Character Table for C 2 v The Character Table for C 3 v
Transformation Properties of an s Orbital in C 2 v
What happens when the C 2 operation is applied?
The C 2 operation is a rotation by 180
about the z axis
The Character Table for C 2 v The Character Table for C 3 v
Transformation Properties of an s Orbital in C 2 v
What happens when the C 2 operation is applied?
The C 2 operation is a rotation by 180
about the z axis
The Character Table for C 2 v The Character Table for C 3 v
Transformation Properties of an s Orbital in C 2 v
The C 2 operation returns the original configuration of the s orbital
The result of this corresponds to a character of 1
The Character Table for C 2 v The Character Table for C 3 v
Transformation Properties of an s Orbital in C 2 v
What happens when the σv (xz) operation is applied?
The σv (xz) operation is a reflection through the xz plane
The Character Table for C 2 v The Character Table for C 3 v
Transformation Properties of an s Orbital in C 2 v
The σv (xz) operation returns the original configuration of the s orbital
The result of this corresponds to a character of 1
The Character Table for C 2 v The Character Table for C 3 v
Transformation Properties of an s Orbital in C 2 v
The σv (xz) operation returns the original configuration of the s orbital
The result of this corresponds to a character of 1