By George Davidson (auth.)
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Extra info for Group theory for chemists
B) Draw an R. rotation vector for XeF4 and use it to generate a representation of the point group. 13. 5). 3 Obtain a representation of the C 4v point group using as bases: (a) a dxLy2 orbital, and (b) the Px and Py orbitals situated on the Br atom of BrF5 . 13 The translation vectors, Tx and Ty, for the molecule BrF5 (C4v) 5 Reducible and irreducible representations We need to know the relationship between any arbitrary reducible representation and the irreducible representations of that point group.
How can this be done? 1 Reducing representations Consider any matrix, of dimension n x n (all transformation matrices are square, since the number of vectors or functions is not changed by any symmetry operation): all a21 52 a12 azz aln azn Reducible and irreducible representations 53 In this matrix, the zero elements (if any) will be distributed randomly about the matrix. If, however, the matrix belongs to a reducible representation, it will be possible to rearrange the matrix so that zero elements are distributed symmetrically about the diagonal.
2 Highest order axis is C3 . 3 No C2 axes perpendicular to this, but three point group is C3v· 1