Understanding Character Tables - PowerPoint PPT Presentation

1 / 19
About This Presentation
Title:

Understanding Character Tables

Description:

A fundamental will be Raman active if the normal mode involved belongs to the ... no Raman-active vibration is also infrared active, and no infrared-active ... – PowerPoint PPT presentation

Number of Views:417
Avg rating:3.0/5.0
Slides: 20
Provided by: IITB8
Category:

less

Transcript and Presenter's Notes

Title: Understanding Character Tables


1
(No Transcript)
2
Understanding Character Tables !
  • The top row consists of the symmetry operations.
  • The first column consists of irreducible
    representations for the group.
  • The table elements are the characters.
  • The final two columns show the first and second
    order combinations of Cartesian coordinates.
  • Infinitesimal rotations are listed as Rx, Ry, and
    Rz in the second to last column.


3
Reducing By Decomposition Formula
ai the number of contributions for the
irreducible representation (i.e.
the number of A1 in the total representation) ,
R refers to one particular operation (e.g. C2)
h the order of the group (the number of
symmetry operations in the point group,
i.e. E, C2,C3, etcbe sure to 3sv's as three)
g is the number of elements in the class (e.g.
how many sv or C2 axes we have) Xi (R) is the
character of the irreducible representation
(that operations value in the character
table) and XG (R) is the character for the
analogous operation R in the total
representation. (?r value for that
operation),
4
 ?r 9 -1 1 3
aA1 1/4 g XA1 (E) Xt (E) g XA1 (C2) Xt
(C2) g XA1 (sv) Xt (sv) g XA1 (sv') Xt
(sv') 1/4 1 19 11 (-1) 1 1
1 113 1/4 9 1 -1 3
12/4 3A1 aA2 1/4 g XA2 (E) Xt (E) g
XA2 (C2) Xt (C2) g XA2 (sv) Xt (sv) g XA2
(sv') Xt (sv') 1/4 1 19 11
(-1) 1 1 (-1) 1(1-)3 1/4
9 - 1 -1 - 3 A2 aB1 1/4 1 19
1 (-1) (-1) 1 1 1 1(-1)3
1/4 9 1 1 - 3 2B1 aB2 1/4 1
19 1 (-1) (-1) 1(-1)1 113
1/4 9 1 -1 3 3B2  
The total representation consists of the sum of
the irreducible representations 3A1, 1A2, 2B1 and
3 B2 which describes all the degrees of freedom
of the molecule.
5
  • Selection Rules for Fundamental Vibrations
  • A fundamental will be infra-red active if the
    normal mode which is excited belongs to the same
    representation as any one or several of the
    Cartesian coordinates
  • A fundamental will be Raman active if the normal
    mode involved belongs to the same representation
    as any one or more components of the
    polarizability tensor of the molecule
  • Mutual Exclusion Principle
  • In a centrosymmetric molecule,
  • no Raman-active vibration is also infrared
    active, and no infrared-active vibration is also
    Raman active

6

7

8

9
(No Transcript)
10

11

12
Raman vs IR

13

14
(No Transcript)
15
(No Transcript)
16
(No Transcript)
17
(No Transcript)
18
(No Transcript)
19
(No Transcript)
Write a Comment
User Comments (0)
About PowerShow.com