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- Why is it unnecessary to consider whether an irreducible representation from C4h is orthogonal to an irreducible representation of D6h?- Determine the irreducible representations with reasons in the following character table. C I R R, R xy.Explain what is meant by irreducible representations, non-degenerate representations and degenerate representations. Which point groups will have degenerate directional properties?
- Molecule: [W(CN)8] 2- . Point Groupd D4h. Use the CN bond vectors as your basis to determine a irreducible representations and total representation.The molecule of NO2 belongs to the C, point group, with the C, axis bisecting the ONo angle. Taking as a basis the N(2s), N(2p) and O(2p) orbitals, identify the irreducible representations generated by these basis and construct the SALC's.Neopentane, C(CH3)4, has Tď symmetry, with character table provided below. Suppose the characters of a reducible representation of this point group are x(E) = 17, x(C3) = 2, x(C₂) = 5, x(S4) = -3, and x(od) = -5 (this is shown explicitly in the last row of the character table). (a) Use the T₁ irreducible representation to determine the order of the point group using the Little Orthogonality Theorem (Vallance Eq. 1.15.13, see Problem 3). (b) Determine how many times each irreducible representation in Ta is contained in this reducible representation. Td A₁ A₂ E Τ1 T₂ r E 1 1 2 3 3 17 8C3 1 1 -1 1 0 0 2 3C₂ 1 1 2 -1 6S4 1 -1 1 101 1.5 7 0 1 713 7. 1.5 -1 -1 60d -3 -1 -1 -5
- Show that the sums of the products of the irreducible representations for C3v are orthonormal.A symmetry group of order h = 8 is known to have five (5) classes. Three of its irreducible representations have a dimensionality of 1. Based on this, what are the dimensions of its remaining irreducible representation(s)? 1, 1, 1 1, 2 1, 1, 1, 1, 1 2,2 1, 2, 2 OOOD3h Г E 6 Reduce the following representation into its irreducible components 2C3 2S3 30v 3 1 4 3C₂ Oh 2 4