# Homework Help: Question about reducible presentation

1. Dec 2, 2009

### lanbeiming

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: Dec 2, 2009
2. Dec 2, 2009

### monty37

where's your attempt at solution?