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lanbeiming

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**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.

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**

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