[lanbeiming]

Hi, everyone, here's the question from homework:

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 still feel confused with the concept of reducible and irreducible concepts, from the book, i know the "reduce formula" to get the irreducible from the reducible, but i have no idea what does this reducible representation mean? does it mean a 8*8 matrix, for example?

[CopperSmurf]

first you need to find its point group symmetry. After that, use the character table for that point group and then you can find the "reducible representation".

"reducible representation" are the numbers you get after determining whether the bonds stay (+1) or move (0) for each symmetry operation (found in the character table).

after that, hopefully you can figure it all out.