Question about reducible presentation

  • Thread starter Thread starter lanbeiming
  • Start date Start date
  • Tags Tags
    Presentation
Click For Summary
SUMMARY

The discussion centers on determining the reducible representation for the planar four-atomic molecule BF3, specifically focusing on its vibrational modes in the xy-plane. The user seeks to find the reducible representation using an 8x8 matrix corresponding to the x and y coordinates of the four atoms, acknowledging the D3h symmetry of BF3. The challenge lies in transitioning from the reducible representation to the irreducible representations, which is essential for calculating vibrational modes. The discussion highlights the need for clarity on constructing the reducible representation before proceeding to irreducible representations.

PREREQUISITES
  • Understanding of molecular symmetry and point groups, specifically D3h symmetry.
  • Familiarity with group theory concepts related to reducible and irreducible representations.
  • Knowledge of vibrational modes in molecular systems.
  • Experience with matrix representation in the context of molecular vibrations.
NEXT STEPS
  • Study the construction of reducible representations in molecular symmetry.
  • Learn about the decomposition of reducible representations into irreducible representations using character tables.
  • Explore vibrational analysis techniques for planar molecules like BF3.
  • Investigate software tools for symmetry analysis in molecular systems, such as Gaussian or ChemSym.
USEFUL FOR

This discussion is beneficial for chemists, molecular physicists, and students studying molecular symmetry and vibrational analysis, particularly those working with planar molecules and group theory applications.

lanbeiming
Messages
7
Reaction score
0
1.hi, everyone. here's the question :BF3 is a planar four-atomic molecule. For simplicity, we ignore the degrees of
freedom in the z-axis (principal axis).
a) Find the reducible representation for a base consisting of the 8 unit vectors with origin
at each atom, being parallel to the x and y directions.
b) Decompose it into a sum of irreducible representations. How many vibrational modes
in the xy-plane exist? i know how to get the irreducible linear representation from the reducible representation, but i hardly gain any idea about how to determine the reducible representation which help me for the later calculation to the irreducible representation.

i guess wether the reducible representation is a 8*8 matrix corresponding to the each (x.y) coordinates for the four atoms. then there should have 6 such matrix since BF3 symmetry is D3h. But i don't know then how to gain the irreducible representation from such matrix
 
Last edited:
Physics news on Phys.org
where's your attempt at solution?
 

Similar threads

Undergrad Calculating group representation matrices from basis vector/function
  • · Replies 6 ·
Replies
6
Views
2K
Understanding solution to equations of motion of n coupled oscillators
  • · Replies 4 ·
Replies
4
Views
2K
Deriving info from reducible representations
  • · Replies 1 ·
Replies
1
Views
5K
Graduate 3 questions about matrix lie groups
  • · Replies 2 ·
Replies
2
Views
3K
High School I can't understand more than 3 spatial dimensions
  • · Replies 6 ·
Replies
6
Views
4K
Graduate Question about energy transfer between Rare-Earth ions
  • · Replies 5 ·
Replies
5
Views
2K
Graduate About the strategy of reducing the total suffering in a queue
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Trying To Conceptualize Two Dimensions Of Time
  • · Replies 2 ·
Replies
2
Views
5K
Undergrad Time Dilation: Layperson Question About Gravity's Effect on Time
  • · Replies 4 ·
Replies
4
Views
2K
Question about the register plus immediate addressing mode
  • · Replies 23 ·
Replies
23
Views
6K